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Essay Abstract

General relativity and the standard model of particle physics remain the most fundamental physical theories enjoying robust experimental confirmation. The foundational assumptions of physics changed rapidly during the early development of these theories, but the challenges of their refinement and the exploitation of their explanatory power turned attention away from foundational issues. Deep problems and anomalous observations remain unaddressed. New theories such as string theory attempt to resolve these issues, but are presently untested. In this essay, I evaluate the foundational assumptions of modern physics and propose new physical principles. I reject the manifold structure of spacetime, the existence of an independent time parameter and static background structure, the symmetry interpretation of covariance, the commutativity of spacetime, and a number of related assumptions. The central new principle I propose is called the causal metric hypothesis. The classical version of this hypothesis states that the metric properties of spacetime, up to overall scale, arise from the binary relation generating the causal order. The quantum version states that the phases associated with congruence classes of directed paths in causal configuration space are determined by the causal relations of their constituent universes.

Author Bio

Ben Dribus is a Ph.D. student in mathematics at Louisiana State University, studying algebraic geometry and algebraic K-theory. He has a background in physics and is interested in applying modern algebra, order theory, and graph theory to foundational questions.

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Great! Your math is too heavy for me, but you may find my partner's recent submission of today, "TO SEEK UNKNOWN SHORES" interesting to treat more rigorously. 12 pages were insufficient to explain the details of his approach.

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Author Benjamin F. Dribus replied on Aug. 20, 2012 @ 17:28 GMT

Diane,

Thanks. I don't see the submission you referenced, but I imagine it will be posted soon. Mine took about a week to go up on the site.

Benjamin,

Your paper suggests that many assumptions are patched together in an effort to make them fit a preconceived model, even though many of the assumptions are widely doubted. It is comparable to the elephant problem, each observer description comes from someone that is standing too close to the object under investigation and each observer has a limited range of observation. Then the observers get together and try to put the observations together to fit a preconceived model. A problem arises when the observers do not recognize their preconceived model may be completely in error, and as a result they are filling in the unknown spaces with assumptions that they do not all agree on, but they tolerate the assumptions because they do not want any empty spaces.

Quote from your essay: "The first few assumptions I reject are that spacetime is a manifold, that systems evolves with respect to an independent time parameter, and that the universe has a static background structure."

I can agree with rejecting the first assumption. The IEEE paper I cite in my topic, 1294, titled, "A methodology to define physical constants using mathematical constants" contains a mathematical relationship where time is a dependent function. Basically, TIME, as an event duration, is a function of the existence of energy. Sounds radical, but it is completely logical mathematically, without the presence of the parameters that define energy there is no need for TIME.

I notice you do not reject the contemporary assumption on the theory of gravity. If that assumption is wrong then all the assumptions built around it are suspect. I have a paper that I am subjecting to open peer review at the moment that describes the EM field structure that creates an attractant only force. I didn't feel it has had sufficient outside review for this contest, but it is coming together. I added two references in response to one of my reviewers comments, [6] "Electrifying Gravity", and [7] "Newton's Gravitation Constant G as a Quantum Coupling Constant".

Helical EM Gravity

I was unaware of the existence of the two papers I just cited when I originally prepared my paper, I have been working on it for several years. I found the references during a search for the term "quantum coupling". Those two papers should be required reading for those that are attempting to build a model of the universe.

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Author Benjamin F. Dribus replied on Aug. 20, 2012 @ 23:25 GMT

Frank,

Thanks for the feedback! You made several points, so it might be clearest if I itemize my reply.

1. Regarding the continued use of widely doubted assumptions, the reason I mentioned this is because I wanted to make clear that I wasn't offering anything new by rejecting these particular assumptions; of course people have known for years that there are issues with manifold structure, background-dependence, etc., and plenty of people are working on these problems. I don't think that well-educated physicists continue to use these assumptions because they are trying to make them "fit a preconceived model," but rather because they don't yet know what to use in their place. The causal metric hypothesis is new, although Rafael Sorkin and the causal set people have made analogous proposals.

2. I will have to read the IEEE paper you cite. Time and energy are conjugate variables in ordinary quantum theory, so it doesn't seem a priori radical to connect the two, but don't know what paradigm you are using, particularly regarding spacetime structure. I prefer to view time as merely a way of talking about causality, via the causal metric hypothesis, but this is in a much more general paradigm in which spacetime and matter-energy emerge together.

3. I am not sure what you mean by the "contemporary assumption on the theory of gravity." If you mean the general relativistic assumption that gravity is a manifestation of spacetime geometry, then my point of view replaces this assumption entirely, since the geometry itself is emergent.

4. Kaluza and Klein, Einstein, and hundreds of others have attempted to couple gravitation and electromagnetism, and there are various ways to try to do this. I have a lot of sympathy with the early classical attempts to describe electromagnetism in geometric terms, like relativistic gravity, even though these approaches did not work. From looking over some of your papers, it seems that perhaps you take the opposite approach, and try to describe gravity as an interaction, like classical electromagnetism (please correct me if I'm wrong). Obviously it would require more time for me to develop an educated opinion on the details of what you wrote, however.

Frank Makinson replied on Aug. 21, 2012 @ 03:34 GMT

Benjamin,

Item 2: In my opinion space has three dimensions. It seems time has no purpose in these three dimensions unless it is associated with energy. I will provide a link to my postprint, as IEEE no longer allows authors to post the published version anywhere.

Methodology

Item 4: Yes, I consider gravity an electromagnetic (EM) phenomenon. My viXra paper is my attempt to make the EM concept easy to understand using basic classical physics principles. The McPherson and Gilson references provide a mathematical justification why Newton's gravitation constant G should be considered a gravitation quantum coupling constant. The helical EM model, with its separated plus and minus field vectors, with their angular phase position (APP), adds a few complications to what is considered just a "pull" force. My helical gravity model provides a very logical reason for Newtonian gravity's instantaneous influence at a distance. Nothing "spooky" and no new physics involved, classical physics provides the answer.

A helical form for the influence of gravity meshes well with the presence of all the helices, spirals and spin within the universe.

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Alan Lowey replied on Aug. 21, 2012 @ 13:49 GMT

Aren't gravitons as an Archimedes screw model of a force carrying particle a viable alternative to helical EM gravity waves? Otherwise I agree with a lot of what you say Frank.

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Benjamin,

Point #4 of your last post notes that hundreds of scientists have attempted (unsuccessfully) to couple gravitation and electromagnetism. My essay is about this subject. I show what I believe to be the first indication that there is a coupling between these two forces. This essay presents a previously unknown relationship between the gravitational force and the electromagnetic force exerted between particles. The key to finding such a connection is to utilize the wave properties of the particles to express distance and express force on the absolute scale where the largest possible force (Planck force) is equated to 1.

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Author Benjamin F. Dribus replied on Aug. 21, 2012 @ 02:05 GMT

John,

Yes, I read your essay with great interest. While it's obvious that any suitable pair of proportional central forces will exhibit any desired power relationship at an appropriate distance, it does seem interesting, at least to me, that the distance at which Newtonian gravity and the classical electrostatic force exhibit a square relationship in Planck units should be the reduced Compton wavelength. I certainly didn't know that, so I'm thankful to you for pointing it out.

You hint at a much more developed theory presented in an online book, which I have not yet had a chance to look at. The conclusions you draw in your essay seem to go quite a bit further than I would feel comfortable with on the basis of the evidence you present, but it may be that you address various possible objections elsewhere. For example, you freely admit that the example you focus on in the essay is a semiclassical approximation, so I wouldn't feel justified in criticizing the details. You can only explain so much in eight pages!

However, there are a lot of obvious questions that could be asked. You might be justified in claiming a quantum-theoretic relationship between electromagnetism and gravity, but how does this imply gravity is a "true force" rather than implying that electromagnetism is not a true force; e.g. geometric in nature like gravity in general relativity? Also, the concept of "messenger particles" is a way of talking about quantum field theory, but how do the relationships you pointed out say anything about quantum field theory one way or the other? How do you deal with special relativity? And so on and so forth.

In any case, congratulations on a very interesting essay.

John A. Macken replied on Aug. 21, 2012 @ 07:07 GMT

Benjamin,

You say, "It's obvious that any suitable pair of proportional central forces will exhibit any desired power relationship at an appropriate distance..." This statement only addresses equation 4 and ignores equations 6 and 7. Equations 6 and 7 show the square relationship between gravity and the electromagnetic force at ALL distances.

You also dispute that I have shown that gravity is a "true force" rather than perhaps implying that electromagnetism is not a true force. It is correct that the text in the essay assumes that the reader would consider the electromagnetic force the ultimate example of a "true force". However, the book goes much further. In this short post I cannot explain the steps of how I derived gravity and the electromagnetic force from the properties of spacetime. However, I can say that in both cases the properties of spacetime are distorted in a way that produces a net force on the spacetime-based particle model. The magnitudes of the two forces are very different, but the basic mechanism is the same - they both are true forces. One last point, in my model matter does not cause curved spacetime; instead dynamically curved spacetime causes matter.

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Author Benjamin F. Dribus replied on Aug. 21, 2012 @ 12:01 GMT

John,

Thanks for the clarification. I'll have to take a look at your book. Like I said before, it may be that you address all these issues there, so any remarks I made weren't intended as serious criticism. I would have to understand the basis of your ideas much better before I would be qualified to make any definitive remarks of that nature. I am sure part of my confusion arises from differences in terminology; you will recall from my bio that I have a mostly mathematical background, and it sometimes takes me a few tries before I understand what scientists with different backgrounds are talking about. By "true force," I assumed you meant an "interaction" rather than an effect arising from geometry, which is usually how gravitation is distinguished from the other "forces" in my experience. If you are taking electromagnetism as the prototype of a "true force" and simply arguing that gravity is analogous, I have no quarrel with that. In any case, I had better look over your ideas more carefully before making any other remarks, or risk making a fool of myself.

Dear Benjamin F. Dribus,

Your essay is impressive and your overview of principles of physics magnificent! As you point out there are a number of unexplained phenomena in addition to the unresolved conflicts between relativity and quantum theories that motivate attempts to mine new math. Your rejection of a number of assumptions paves the way to apply the new mathematical tools you list on page 7. I do not have sufficient expertise in these areas to provide a useful critique, but you do so yourself to some extent. You note that "local properties are generally more reasonable to impose than non-local properties due to our ignorance of the global structure of the universe", which agrees with my own analysis. You note that a Lorentzian manifold must be recovered from the new tools.

You have transitions replace the notion of time evolution. It may be over simplifying to say this but that seems like shades of automata. Having developed "The Automatic Theory of Physics" I am not averse to automata, but more as a model of physics than as a model of fundamental reality. I find it more likely that the universe arises from a [ONE] continuous field through self-interaction and I suspect discrete or fractal pictures are ultimately inappropriate. I find it feasible to recover the standard particles from one field, while I agree with you that it could be difficult to recover these from causal relations on universes, which, as you note, has not been achieved.

You note that it's impossible to disprove time evolution of manifold structure and impossible to prove your causal metric hypothesis [but potentially disprovable]. Your conclude with a page of interesting discussions.

Thanks for a stimulating essay and good luck in the contest.

Edwin Eugene Klingman

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Anonymous replied on Aug. 21, 2012 @ 18:04 GMT

Edwin,

Thanks for the kind remarks. I will reply in an itemized fashion for clarity.

1. Automata, and particularly the homological/homotopical techniques used to study them, are certainly relevant to the approach I outlined. However, there are too many differences (and too much contextual baggage) to describe it in those terms. Automata tend to be discrete, rely on some type of initialization, involve multiple or weighted edges, simplices, or cubes, and so on.

2. I certainly don't rule out continuum models, though I don't think we should take them for granted. Riemann certainly didn't. In order-theoretic terms, the continuum has properties (like the least upper bound property) that seem to have no direct relationship to physics. As far as measurement is concerned, you could never tell the difference between reals, rationals, dyadic rationals, etc. (dense subsets). The symmetry properties of flat real manifolds seem impressive in light the fact that fundamental particles do appear to correspond to representations of the Poincare group, but only until you realize that the same thing can be described much more generally in order-theoretic terms. There are also plenty of direct physical reasons to doubt the continuum such as black hole entropy and the holographic principle. A lot of the "paradoxes" of quantum theory arise from imagining little point-like particles moving around in a manifold over the continuum.

3. I take it you don't favor the sum-over-histories approach in quantum theory? Do you prefer Hilbert spaces? To me, they appear (like the continuum) to be a too-good-to-be-true idealization that likely arises from something more primitive.

4. By the way, where you get the vector "C-field" you use in your essay? I know people have experimented with hypothetical scalar fields called C-fields in general relativity in the past, and have derived tensor fields from these by differentiation, but I'm not sure where this Ampere-type equation fits into the picture.

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Author Benjamin F. Dribus replied on Aug. 21, 2012 @ 18:06 GMT

Evidently I forgot to login there!

Anonymous replied on Aug. 21, 2012 @ 20:33 GMT

Dear Benjamin,

Thanks for the extensive reply to my comment, and thanks for looking at my essay.

Your response concerning automata agrees roughly with what I had in mind.

I'm glad you don't rule out continuum models. I have my own doubts about reasons to doubt the continuum, ie, black hole entropy and holographic principle. And I do agree that many quantum problems derive from imagining point like particles (with emphasis on 'point'). My particle model is an extended particle plus induced wave.

Nor do I favor sum-over-histories (as physical reality -- mathematically they're fine). For bound (discrete energy) states I am happy with Hilbert spaces. I found your description of the continuum as "too-good-to-be-true" fascinating, and also your opinion that it probably arises from "something more primitive".

The C-field is my own term (with historical conflicts) for the gravito-magnetic field (with gravito-electric G-field). It is treated in the weak field approximation in most general relativity texts, although it doesn't seem to make an impression on most physicists. I did not recall learning about it until I "independently" stumbled over it. Good references to the equation and to experimental measurements of the field are given in my essay.

I'm always impressed by competent mathematicians who work in physics and I always find that we think quite differently about both math and physics. Viva la difference!

Best,

Edwin Eugene Klingman

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Hi Ben,

I just finished reading your paper. I enjoyed your writing style, you express yourself very well. You mentioned many mathematical frameworks in your essay of which I know little, so it is possible that the answers to the questions I am going to ask may already be obvious to someone who knows about these, but it may be still of benefit to those of us who don't know.

So, to return the favor of asking serious questions:

1. You idea seems to me a lot like a (very mathematically oriented) variant of relationism. I would have appreciated some comments that would have differentiated it. How is it different from relationism (or is it)?

2. How does your theory account for the fact that we seem to be able to assign metric relations to even causally unrelated events?

3. How does your framework address the fact that the order of spacelike separated events is frame-dependent?

4. Is there such a thing as a "correspondence principle" between the quantum and classical version of your principle and what is it? I ask because it almost seems like it is inverted according to your idea, the quantum version is determined by the causal relations of "constituent universes" but the universe is defined by the classical version. While it is true that also in standard QM a quantum state is a superposition of classical states, I would have expected as a feature of a more fundamental theory that quantum states can be defined without recourse to classical states unless it offers a "deeper" explanation for that.

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Author Benjamin F. Dribus replied on Aug. 26, 2012 @ 06:22 GMT

Armin,

Thanks for the remarks and questions. Since most of my formal education and my "official" academic work is mathematical, I wrote this essay in an effort to help me begin a dialogue with competent physicists on topics I have thought about a great deal. I knew I would not get the style and focus precisely right at first, but I was hoping that some people could point out obvious flaws...

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Armin,

Thanks for the remarks and questions. Since most of my formal education and my "official" academic work is mathematical, I wrote this essay in an effort to help me begin a dialogue with competent physicists on topics I have thought about a great deal. I knew I would not get the style and focus precisely right at first, but I was hoping that some people could point out obvious flaws and things that required more or different explanations. Let me itemize my reply to correspond to your questions.

1. Binary relations on sets obviously play a central role in my approach, but there are a lot of "relational" theories, and I am not sure if you are referring to a particular one of these (or group of these) when you reference "relationism." For instance, prominent physicists like Rovelli, Thiemann, Baez, Smolin, Markopoulou, Loll, Ambjorn, Sorkin, Rideout, Bombelli, etc. all emphasize binary relations, but they all include assumptions in their work that I disagree with. These physicists work primarily on loop quantum gravity, causal set theory, causal dynamical triangulations, and a number of lesser known variants. Of these ideas, mine are most similar to causal set theory (Sorkin, Rideout, Bombelli, etc.) but there are multiple crucial distinctions that make the overall picture quite different.

2. There are "metric recovery theorems" (for instance, by Malament) that allow recovery of the entire metric structure of Lorentzian spacetime (including spacelike separation, etc.) from the causal structure and appropriate volume information. These play a prominent role in causal set theory; they imply that an appropriate causal set "looks like" a Lorentzian spacetime on sufficiently large scales. At the fundamental scale, you would define spacelike distance by counting relations; for instance, two unrelated elements with a common direct descendant are one unit of distance apart. Only at larger scales does this begin to resemble an ordinary distance function. My framework is more general because I don't assume a constant discrete measure, but the simplest versions still involve counting.

3. Frame-dependent order (relativity of simultaneity) is one of the most important points to understand because it highlights the new meaning of covariance (order rather than symmetry). In my approach (and also in some versions of the above theories), a frame of reference is a refinement of the causal order; i.e., an assignment of order to certain events which are not related in the causal order, just like a frame of reference in relativity assigns order to certain spacelike-separated events. The whole point is that the causal order carries the canonical information; the refined orders carry additional contextual information.

4. I think you point out a good way of comparing the Hilbert space version of quantum theory, in which classical states arise as an appropriate limit (correspondence principle), with Feynman's sum-over-histories version, in which the quantum picture is built up from classical alternatives via superposition. It is an interesting objection to the sum-over-histories version that the "building blocks" are classical; my view is to be grateful to Feynman for making the presence of a Hilbert space physically comprehensible; they're beautiful mathematically, but I prefer to see them arise from something primitive like superposition, just as I prefer to see manifolds arise from something primitive like binary relations.

Great questions; I hope that explanation at least somewhat answers them. Take care,

Ben

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Renate Quehenberger replied on Sep. 29, 2012 @ 01:54 GMT

Hello Ben,

congratulations, your essay is even more a charming tour the force through all concepts of the last 100 years then mine !

I like the Dribus Razor rejecting anything for a universal Schrödinger equation combined with Emmy Noether's conservation law in causal configuration space.

But be careful with rejecting the manifold structures the flaws may enter and you'll get lost without Plato's order of the heavens, means the dimensionality fo space.

Best wishes,

Renate

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Evidently I got cut off there, but anyway, I had only one more question:

5. Can your principles help resolve some of the notorious difficulties that arise when one tries to describe causal relationships?

Overall very well written, although it may be too specialized for many readers on this forum. I would have especially liked an expanded discussion of the short paragraph on how causality connects with our established theories.

All the best,

Armin

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Author Benjamin F. Dribus replied on Aug. 26, 2012 @ 06:41 GMT

Oh, I just missed your last question.

5. There are many philosophical issues related to causality, and I am not sure which you are primarily referring to. However, a lot of these issues result from assuming the existence of other types of structure besides the causal structure, for instance, independent metric structure, or independent matter, energy, etc. I believe most such difficulties (at least, most that I can think of) can be explained in terms of the causal metric hypothesis, but the question is whether or not the explanation is satisfying. For example, the causal metric hypothesis includes the assumption that what we call time is just a way of talking about causality, and what we call causality is just a way of talking about binary relations on sets. If it is right, then it simplifies and solves many things, but it may not be right. And if it is wrong, it ignores some very important philosophical questions.

Dear Benjamin,

I read your essay with great interest. It contains a lot of deep thoughts including a deep analysis of the current situation.

We agree in many points except the importance of the concept 'manifold'. I agree with you about the importance of background-independence. General relativity reach us to consider a diffeomorphism-invariant theory. This property is very restrictive in dimension 3 (and lower). If one fixes the topology (or the binary relation between the subsets) then everything is determined (by using the Geometrization conjecture, you will also obtain a canonicaly metric). That is the reason why one considers the special graph (the spine) of a 3-manifold containing all information. But this fails in dimension 4. But one think remains: one needs countable many subsets to obtain the 4-manifold (or the triangulation and the smoothness structure agree). Among this technical thinks, one important fact troubles me more. You wrote about a substitute of a manifold (a poset etc) and about a configuration space (which you use for the sum-over histories). I would expect in a unified theory that there is only one entity not two. So, if you believe (like I do) in the full geometrization then you need only the spacetime, nothing more.

Furthermore, your concept of causality is interesting but I do not fully understand it: there is a unique path in the past (back to the cause) but different paths in the future (the openess of the future). Does your binary relation reflect this fact?

Good luck for the contest

Torsten

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Author Benjamin F. Dribus replied on Aug. 28, 2012 @ 20:34 GMT

Torsten,

Thanks for the insightful comments. I will try to clarify a couple of the points you raise.

1. I’m not sure if you regard matter-energy to be auxiliary to spacetime, or if you regard the two to be part of a single fundamental structure. I far prefer to regard them as part of a single structure, which I describe at the classical level by a binary relation. Hence, I do...

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Torsten,

Thanks for the insightful comments. I will try to clarify a couple of the points you raise.

1. I’m not sure if you regard matter-energy to be auxiliary to spacetime, or if you regard the two to be part of a single fundamental structure. I far prefer to regard them as part of a single structure, which I describe at the classical level by a binary relation. Hence, I do not expect this structure to be manifold-like at sufficiently small scales. This forces the theory (if it ever becomes sufficiently developed to be called a theory) to predict 4-dimensionality (and many other things) at large scales, probably by means of action principles and entropy.

2. The causal set theorists have done a lot of experimenting over the years with “sprinkling” points in 4-manifolds; as you point out, the binary relation doesn’t determine the geometry, but the argument Rafael Sorkin makes with his “order plus number equals geometry” phrase is that you can recover 4-D geometry from a suitable order if you supply appropriate measure-theoretic information as well. I think this is true. If it is not, then my ideas probably don’t contain enough information. Note that the causal set theorists make a lot of other assumptions I find dubious, however.

3. Regarding fundamental theories and single entities: the desire to describe spacetime and matter-energy as part of the same structure is a lot of the motivation for my ideas. I call the classical “posets” (not really posets in general, of course) “universes” to emphasize background independence: in Feynman’s sum over histories, one thinks of particle “trajectories” but generally ignores the obvious fact that the “underlying spacetime” actually ought to respond in different ways to different trajectories, so one is summing over entire “universes” in this sense, not over trajectories in a single “universe.” However, the “Universe,” which is quantum mechanical, is the entire family of posets with their induced order. After all, similar remarks could be made about manifolds; the etymology even reflects this. A manifold is a set with an atlas, but no one argues that the presence of multiple charts means that the manifold is not a single entity. This analogy is imperfect in multiple obvious ways, but the main point is just that different models partition information in different ways and it is not necessarily easy to uniquely define what “unified” means.

4. Regarding your final point about the open future, a single classical universe contains its entire history, but such a universe may be regarded as the source of any number of different transitions. In this sense the future is open and the past is fixed. However, I suspect this may not entirely answer your question.

Thanks again for the feedback,

Ben

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Yuri Danoyan replied on Sep. 10, 2012 @ 08:35 GMT

I suggest that 3:1 ( examples #1,#2,#3) is enclosed in a total interaction of Bose and Fermi particles or fields, and it is a bootstrapping relationship between mentioned evidences.

Surprisingly, the container(space-time), content(fermions-bosons), content (energy-matter) obey the same law 3:1.

http://www.fqxi.org/community/forum/topic/946

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Dear Benjamin,

When reading at the beginning of your essay

"In this essay [...] I reject the manifold structure of spacetime, the existence of an independent time parameter and static background structure, the symmetry interpretation of covariance, the commutativity of spacetime, and a number of related assumptions."

one may wonder "what remains then?". How far can you go with your causal metric hypothesis? From your essay, it seems that you can do a lot starting from this, although it seems also to remain a lot to do.

Congratulations, and good luck with the contest and your research,

Cristi Stoica

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Author Benjamin F. Dribus replied on Sep. 2, 2012 @ 05:34 GMT

Cristi,

"What remains then" is indeed a legitimate question about my setup, which is quite minimalistic in its most general form. It is also worth asking if the causal metric hypothesis trivializes deep and subtle issues. My view is that one of the principle reasons manifold models have dominated physics is because they are so convenient mathematically; once you know about the continuum and the complex numbers their lure is almost irresistible. Hence, more primitive and messy approaches may have been neglected.

Coming from a math background and working mostly with algebraic schemes and complex manifolds, it is hard for me to believe that the physical world behaves in such a convenient way. Conceptual simplicity and mathematical convenience are very different! This essay and all the unpublished work associated with it represent my attempt to "think physically" rather than just mathematically; my focus here is the basic physical principles, and the associated math is not nearly as convenient as the math encountered in mainstream physics. In any case, I think approaches like this deserve more attention.

You seem to have some of the same philosophical motivations, refusing to reject singularities just because they are "mathematically ugly."

Take care,

Ben

Hi Ben,

I'm a great fan of Causal Sets, and think this is a very timely essay. I like that the assumptions are so minimalistic. It's a possibility that hasn't really been paid enough attention to. Good luck,

B.

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Author Benjamin F. Dribus replied on Sep. 2, 2012 @ 05:48 GMT

Bee,

Thanks for the kind remarks! When I started thinking about this a couple of years ago I didn't yet know about causal sets, and I was amazed when I found Rafael Sorkin's papers. I think he does an excellent job of explaining a lot of the motivating ideas. His students and coworkers have gone on to develop various aspects of the theory, but I still tend to prefer his qualitative considerations and careful explanations.

The causal set community is still relatively small from what I understand, and I come completely from the outside. There are certain assumptions most of them make that I can't seem to convince myself of, but I haven't had much chance to discuss these things with any of them in depth. In any case, I have the utmost respect for their work. I am hoping an expert causal set theorist will come along and say "that won't work because..." and help me sharpen these ideas further.

Take care,

Ben

hello Mr.Dribus,

I d like learn more about this K theory, it seems very relevant considering the geometrical conjecture.

The entropical arrow of times and its causality is proportional at all 3D scales in its pure fractalization.

In all case the maxwell's equations are important considering the heat and thermodynamics.if we consioder a pure cooling, it becomes relevant...

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hello Mr.Dribus,

I d like learn more about this K theory, it seems very relevant considering the geometrical conjecture.

The entropical arrow of times and its causality is proportional at all 3D scales in its pure fractalization.

In all case the maxwell's equations are important considering the heat and thermodynamics.if we consioder a pure cooling, it becomes relevant considering the two main gauges in 3D and its walls separating this infinite light and its universal sphetre in evolution spherization.The internal Energy U is relavant woth the enthalpy with the finite groups. H=U+PV.tHE SUBSTITUTIONS CONSIDERING THEI UNIVETRSAL NUMBER becomes very relevant. The Helmholtz function F=U-TS and the gibbs function G=H-TS. We can insert the finite groups and my equations. The volumes of the entanglement and its number are essential. It is relevant considering the maximum volume of the universal sphere and so the correlated rotating spheres inside this physicality. The quantization of mass so permits to see better. The rotations around the universal central sphere also is relevant.Like is relevant thje volume of this central BH.The measurables quantities are seen with determinsim and rationalism and the unknown can be seen when the finite groups are inserted. See that this quantum number is the same at the cosmological scale that for the quantum uniqueness. So the universal sphere does not turn so it is the maximum mass at the present.

On the other side, the quantum spheres them turn very quickly. It is relevant to see these correlations.The entropy principle is so spiritual in fact. The aim is to fractalize correctly the steps of disponible energies.See that the rotations and the volumes are very relevant. My equation mcosV=constant with this finite number, is relevant because this constant is for all physical spheres in 3D , so the quantum spheres, the cosmological spheres and the universal sphere and its central sphere !There is an interesting link when I extrapolate the maximum volume in 250 billions of years considering my calmculations.At this momment a contraction is correlated , so the volume decreases. But in logic the central sphere, it increases in density and volume logically speaking.So it is a kind of oscillation like a oscilaltion of heart. So the volumes are very complex in fact at all 3D scales.

The differentials appear with a real universality when the roups are finite at all 3D scales. The Universal sphere and its cosmological spheres is like a foto of our quantum uniqueness.

ps Good Physicists Have Studied Under Very Fine Teachers.

ps 2 The entropy is maximum in all, paradoxal but so evident.The steps are fascinating before this planck scale !

ps3 eureka :)

Regards

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Author Benjamin F. Dribus replied on Sep. 2, 2012 @ 06:09 GMT

Hi Steve,

Algebraic K-theory is something I didn't originally plan to specialize in, but it kept coming up in seemingly "purely geometric" situations; particularly involving groups of algebraic cycles and their equivalence relations, the Hodge conjecture, and so on. It also applies to physics via string theory, cyclic homology, noncommutative geometry, the theory of motives, and number-theoretic topics like the Langlands program.

Entropy is something I've studied a great deal over the last few years and still don't adequately understand. Just in the field of quantum information theory, there are a lot of different notions of entropy, and there seem to be added complications in incorporating this into a primitive causal theory like I describe in my essay.

You use some terminology that I don't quite understand, such as "evolution spherization." Also, I am not sure when you are referring to spheres as physical spaces and when you are referring to them as parameter spaces like the Bloch sphere etc. Do you have all this written down somewhere?

Take care,

Ben

Steve Dufourny replied on Sep. 2, 2012 @ 14:37 GMT

Hello Mr. Dribus,

I am understanding. no I have no publications. I am isolated at home without job, without nothing, just my personal probelms. I have not published.I have understood Mr Tegmark, ok. You can make what you want afterr all.I have made my works me, I have shown my theory to the world.If people copies or wants the prizes, you can have them Mr Tegmark and Mr Aguire.I thought that Fqxi was there to help the real innovators.I see simply a strategy. I am sad simply. You can with your friends, have a good life, and travel in private airplanes and buy opulences.Make what you want, me I sleep quiely and serenity. Of course I have neurological probelms and also I have a kind of depression due to my difficult life.But I have faith in God me, I have faith in this universal kindness and universal love. I have faith in this universal sphere. I am going to continue to read and discuss on fqxi. I forgive you all after all, you are simply persons loving monney and vanity.Perhaps you can evolve in a pure universality.

It is the life, it exists a little of all on this planet, good people, bad people, universal people,envious,vanitious,.....the real importance for me is my faith in God.

ps Mr Dribus, the entropy , it is god ! It is simple you know the truth !

Regards

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Steve Dufourny replied on Oct. 13, 2012 @ 10:54 GMT

Hello Mr Dribus,

At my humble opinion, It is not the disorder the entropy. It is simply the infinite light and its physical distribution.

A good occham razzor permits to sort the false extrapolations. It permits to see what are really these spheres of light in evolution of mass.

A sphere for me is a planet, a star, an elementary particules, a water drop, the spheroids are so numerous. Fruits, glands, brains,cells,flowers,....the universe also is a sphere with all its intrinsic spheres, quantic and cosmological. The gauge is a pure 3D, 3 vectors !!!!!

The spheres are everywhere, in us, around us , above us......The spherization, my theory of spherization, shows us how these spheres of light build the spheres of mass !!! inside a pure 3D sphere and its central sphere, the most important BH. The uniqueness serie is essential for a real understanding of quantizations and universal 3D proportions.

The informations are inside the main central spheres, quant.and cosmol.The building is a pure spherization of the universal sphere by quantum spheres and cosmological spheres.The codes are inside these singularities. The number is so important for the serie of uniqueness.See that this number is the same for the two 3d gauges,quantum scale and cosmological scale. The 3D is essential.The road, for a real undertanding of this pure light without motion, time and dimension above our physical walls, is rational and dterministic.We have not pseudo convergences.The real interest is to analyze this universal physical sphere in evolution optimization SPHERIZATION.

The noncommutative geometries must be well extrapolated, like the superimposings, or this or that. If not, we have pseudo sciences.The 3D is essential.The strings can converge with a correct axiomatization of deterministic tools. The rest seems vain.

Best Regards

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Anonymous replied on Oct. 13, 2012 @ 21:14 GMT

The scalars for example cannot be utilized without a kind of universal 3D axiomatization. Let's take the equations of Friedmann Lemaître and the correlated metric. The 3D sphere and its intrinsic quantum spheres and cosmological spheres are all in 3D. We cannot insert extradimensions. The 3D is essential.The Universal sphere is in evolution spherization in a pure 3D. The scalars at my humble...

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The scalars for example cannot be utilized without a kind of universal 3D axiomatization. Let's take the equations of Friedmann Lemaître and the correlated metric. The 3D sphere and its intrinsic quantum spheres and cosmological spheres are all in 3D. We cannot insert extradimensions. The 3D is essential.The Universal sphere is in evolution spherization in a pure 3D. The scalars at my humble opinion are not vectors. the spherical coordonnates inside a closed system is essential. That's why the number of the universal uniqueness(see the fractal of spheres of light from the main spherical volume).It permits to quantize the mass polarizing the light in a pure 3D general point of vue.The quantum scale is in meter, the cosmological scale also.That's why a closed evolutive sphere is essential for the universal sphere. We arrive at an optimization of the model, isotropic and homogene. Like for Einstein. The spherization can bee seen with the help of equations of friedmann Lemaître. The space is curved by this mass and more this mass increases due to evolution, more the spherization acts, the spherization is general due to the increasing of mass due to the polarization mass/light.If we have not the number of uniqueness, it becomes more difficult for the quantization and the understanding of the spherization. The fact that this light is infinite in this Aether without motion, dimension,and times, shows us that this physicality is light in motion,so spheres in rotation. G c and h can be seen in a pure 3D spherization. the series of uniqueness of quantum spheres imply an interesting road for the quantization of evolution correlated with informations. The curves of spacetime are in fact coded by the singularities. The expansion is just a step, a maximum volume is an evidence. a contraction appears so when the density is ok for this contraction, the spherization in 3d is an evidence. The energy is correlated .The bosons and fermions can be seen like turning in opposite sense. The variables and parameters are relevant....sorry I must go,until soon

Regards

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Author Benjamin F. Dribus replied on Oct. 14, 2012 @ 11:12 GMT

Dear Steve,

It took me a long time to realize you had posted here because it is so high up in my thread!

I agree that "disorder" is not a very good description of entropy. In some important cases entropy is actually a measure of symmetry.

By the way, another place in which the sphere arises is in quantum information theory; the space of states of a single qubit is a sphere called the Bloch sphere in this context. It can be identified with the Riemann sphere which is obtained by adding the point at infinity to the complex numbers.

My feeling about dimension is that it is still rather mysterious why dimension 3 is so important. There are a lot of mathematical arguments for this, but I haven't yet seen a convincing explanation. Take care,

Ben

Steve Dufourny replied on Oct. 14, 2012 @ 13:13 GMT

Mr Dribus,

The entropy principle is a concept so difficult to encircle in its pure generality but so simple also. This entropy is like an infinite energy. The steps of fractalization are so numerous inside the pure physical 3D sphere. If this infinite light has created a physical 3D sphere in spherization of mass-gravitation. So we have disponible steps of energy correlated with our...

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Mr Dribus,

The entropy principle is a concept so difficult to encircle in its pure generality but so simple also. This entropy is like an infinite energy. The steps of fractalization are so numerous inside the pure physical 3D sphere. If this infinite light has created a physical 3D sphere in spherization of mass-gravitation. So we have disponible steps of energy correlated with our principle of equivalence. The mass, it is the energy. It is so a pure mesure of symmetries between the gravitation and the polarized light(due to evolution spherization)and its steps. I beleive that the spheres of light in their pure serie of unqueness so are quantas of pure energy correlated with the infinite singularity without motion ,time and dimension. That said, and it is paradoxal, the physicality is a finite system in increasing of mass, so the entropy, physical increases.See that this entropy inside the physicality is so under the physical laws. The infinite entropy so is a reality for both of systems. But the real interest is to utilize the disponible energies.A kind of taxonomy becomes an essential. The volumes of entangled spheres are so essential.The gravitation polarizes the light. The correlated synchonizations seem porportional with energies ,the spherical volumes of stability so are relevant considering the main central sphere as the most important volume of the serie of uniqueness. The cosmological number of spheres inside the universal sphere is the same than an ultim entanglement of spheres.The finite groups are essential. My 2 equations become very relevant considering a closed isotropical and homogeneous Universal Sphere.

You say "By the way, another place in which the sphere arises is in quantum information theory; the space of states of a single qubit is a sphere called the Bloch sphere in this context. It can be identified with the Riemann sphere which is obtained by adding the point at infinity to the complex numbers."

The spheres are everywhere ,I beleive that the simulations of quantum informations can be optimized. The Bloch sphere seems relevant considering the qubit informations. It can be optimized in a pure 3D convergence with the spherical volumes furthermore of the serie of uniqueness and its pure finite universal number. The complexs at infinity seems relevant also.They are tools. T

about the dimensions.I beleive that it is very very important to consider an universal axiom for our 3 vectors implying a pure 3D sphere.The metric is a pure 3D. The proportions need to have these 3 vectors. If not we cannot have the pure thermodynamical correlations, universal between all rotating 3D spheres. A closed evolutive system in 3D is essential for our proprotions.

Furthermore, the fact that we have the special relativity implying c and its limits for bosons, show us the road of the perception of 3D creations. c is essential for our contemplations if I can say. The general relativity tell us that the mass curves the space.It is so still an essential this 3D. More the mass increases, more the physical entropy increases, more the spherization of the universal sphere increases. The SR and GR are ok if and only if we have these finite groups inside a closed evolutive sphere. The dimension 3 is at all scale, it is the reason why we have our planck scale in meter and our universal sphere and its bounded limit also in meter.It is essential for all our universal proportions. The fractal of scales is always in 3D.

I wish you all the best in this contest.

Regards

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Ben,

I want to pull out a couple of things that I think are good points

"For example, Einstein's equations in general relativity predict the

curvature of spacetime, but not the dimension; a theory whose dynamical laws also predicted the dimension would be superior in an obvious way."

"Our present understanding of antimatter comes almost entirely from quantum eld theory,"

I think these are good points, my question then would be how do causal metric hypothesis account for these and also, how does it account for the relativity when two observers can assign different ordering of two observed events?

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Author Benjamin F. Dribus replied on Sep. 2, 2012 @ 06:49 GMT

Hi Harlan,

Thanks for the feedback! Those are good questions, and I can only partially answer them. Let me itemize.

1. Regarding the prediction of the dimension, the first question is how you even define the dimension of a causal relation. It will be emergent, only making sense at large enough scales, and it won't be an integer in general, although it must be very close to 4 at...

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Hi Harlan,

Thanks for the feedback! Those are good questions, and I can only partially answer them. Let me itemize.

1. Regarding the prediction of the dimension, the first question is how you even define the dimension of a causal relation. It will be emergent, only making sense at large enough scales, and it won't be an integer in general, although it must be very close to 4 at appropriate scales. Fractal dimension is relevant here. There is actually a fair bit of literature on the dimensions of causal sets, but these papers tend to use hypotheses that seem to obscure part of the structure. I have made some progress on this for structures I consider relevant, but it is not yet developed to my satisfaction.

Then, of course, you have to predict it. One of the greatest difficulties with causal theories like causal set theory and some versions of my own ideas is that there are a lot more "obviously nonphysical" universes than physical ones. This is usually described as an "entropy problem," in the sense that nonphysical solutions tend to dominate just like "disordered" solutions dominate in classical statistical thermodynamics. One way around this is to use a Lagrangian approach which (potentially, hopefully!) selects for "physical" behavior by means of an action principle and interference effects. The million-dollar question is then, "what is the 'correct' Lagrangian/action?" Again, I have some ideas about this, but I don't yet know the answer.

2. Regarding antimatter, I can understand it in the context of causal theory only in a very indirect way. In quantum field theory, the necessity for antiparticles "falls out" of the elementary representation theory of the Poincare group, which is the symmetry group of Minkowski space. In causal theory, the Poincare group is replaced with families of refinements of binary relations, and an analogous "representation theory" must be developed. If anyone has done this, I haven't been able to find it, so I am in the beginning stages of doing it myself. There are some aspects of causal theory that make me confident matter-antimatter asymmetry should ultimately be inevitable from this point of view, but I can't explain that at the moment.

3. Regarding the relativity of simultaneity, this is one of the most natural aspects of causal theory. Different frames of reference, rather than merely involving different orderings of spacelike-separated events, ARE different orderings of spacelike-separated events. This prunes away "imaginary geometry" governing what happens, and leaves behind only what actually does happen.

Take care,

Ben

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Ben -- congrats with your essay. It places IMHO a healthy focus on the key question "How to get an emergent metric from a local causal relationship?"

Two more opportunities I would like to stress: Firstly, seeking recovery of a Lorentzian manifold is indeed a key challenge, but an emergent De Sitter manifold might be the true target that would allow you to get 'dark energy' to be emergent. Secondly, you don't mention unitarity as a key assumption. You might get some further mileage from entertaining the inevitable question "Is unitarity really required?"

Good luck at the contest, I would be disappointed if your contribution doesn't score well!

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Author Benjamin F. Dribus replied on Sep. 4, 2012 @ 18:33 GMT

Johannes,

Thanks for those suggestions... both of them are right on target. Take care,

Ben

Hi Ben,

I want to understand the meaning of "causal metric" hypothesis better. I found on another web page "The causal-metric hypothesis, if correct, greatly simplifies and clarifies theoretical physics. In particular, it is the purest possible version of background independence. A theory is background independent if its entire structure is dynamical, rather than relying on a static embedding space in which the dynamical entities of the theory reside."

I am trying to understand this in contrast to GR now (without Lambda). What is the background that the structure isn't independent from, spacetime?

Regards,

Jeff

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Author Benjamin F. Dribus replied on Sep. 3, 2012 @ 23:54 GMT

Jeff,

Thanks for the feedback! Yes, that's my website... I don't know how you found it because its not ready for primetime yet and I've done nothing to try to promote it (no time; dissertation year!), but anyway...

GR is usually taken as the prototype for background independence (in contrast to QFT and most versions of string theory) because spacetime interacts dynamically with matter-energy in GR. However, the whole point of background-independence is not taking things for granted, particularly things that by their very nature can't be observed, and GR does retain some traces of this. For instance, spacetime is still viewed as "containing" matter-energy even though the two interact; it's not that there is no background, just a dynamical background. This is better than a static background, but it's still something you can't observe; you can only ascribe properties to it by the behavior of matter-energy inside it. The causal metric hypothesis says that there is no background at all; spacetime and matter energy (at the classical level) are two aspects of a single structure.

The potential for paradoxes in GR (time-travel etc.) comes from clashes between two a priori different structures: a metric structure and a causal structure. The causal metric hypothesis says that there is only one structure. In particular, causal cycles are still possible, but they're not paradoxical. Take care,

Ben

Jeff Baugher replied on Sep. 4, 2012 @ 02:10 GMT

Ben,

I can see now why you would like to do away with the manifold structure. It would seem that our essays run counter to each other, which is great for me to develop an understanding of your intended meaning. To me, the constant multiple of the metric represents a static potential for curvature (a potential for energy) whereas the tensor (i.e. Einstein tensor) represents the dynamic portion which gives rise to what we perceive as matter and energy moving in spacetime.

As an analogy, for me it is the derivatives within the fabric and not the fabric itself that is important, but the fabric does exist, whereas you would like to propose that the fabric itself doesn't exist even if the derivatives do?

BTW, I hope you rate my essay as highly as I have yours.

Regards,

Jeff

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Author Benjamin F. Dribus replied on Sep. 4, 2012 @ 18:29 GMT

Jeff,

Well, I don't absolutely object to differentiable manifolds, though I find anything so uniform rather hard to believe in at the fundamental scale. However, one had better recover a Lorentzian structure at large scales and low energies, or the idea won't work. That's part of the task for my approach, but there is good reason to believe that it can be done. What worries me more (but also interests me more) is recovering the representation theory that describes the particles in the standard model. This requires some mathematics that appears to be very little developed and should be a lot of fun to get a handle on. In any case, tensor fields would be emergent, just like the geometry they refer to.

I find the whole rating thing a bit embarrassing, because I'd prefer to just learn about other people's ideas rather than presume to judge the quality of their work. However, I feel justified in giving high ratings to essays that lead me to think about things in new ways, and your essay certainly did. Take care,

Ben

Benjamin, you wrote:

"The first few assumptions I reject are that spacetime is a manifold, that systems evolve with respect to an independent time parameter, and that the universe has a static background structure."

I reject too.

See my essay

http://fqxi.org/community/forum/topic/1413

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Author Benjamin F. Dribus replied on Sep. 7, 2012 @ 06:33 GMT

Yuri,

Thanks for the feedback. I just read your essay, which I found interesting in several regards. I note that you mention the idea that space can be described in terms of angles. Julian Barbour suggests something similar with his "shape dynamics," but doesn't suggest quantization.

You point out that the strong, weak, and electromagnetic interactions are of similar strengths and that gravity is much weaker. This is true, of course, but it's also interesting to think about the size scales on which these interactions dominate. The strong and weak interactions have very short range, while electromagnetism dominates up to about the everyday scale, where gravity takes over.

You also point out some interesting numerical relationships. There is much speculation about the dimensionality of space and the number of particle generations, but the 18-degree thing is something I have not heard of before. Take care,

Ben

Yuri Danoyan replied on Sep. 13, 2012 @ 13:24 GMT

You wrote: "The strong and weak interactions have very short range, while electromagnetism dominates up to about the everyday scale, where gravity takes over".

I think because c and G speed variation the same. See my essay part.3

h is eternal constant and Planck unite of mass also eternal.

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Author Benjamin F. Dribus replied on Sep. 13, 2012 @ 19:31 GMT

Yuri,

Let me make sure I understand. So you think that the ratio c/G is constant, but neither G nor c are independently constant? Do you mean constant in "space" or constant in "time?" Take care,

Ben

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Dear Ben, I liked your idea of casual metric very much. You said in my thread that "you and I have perhaps different ideas on the nature of time" but I don't think so. In my mind, time is the expression of changes in energy state, and what can be more causative than that?

Our major difference lies in you regarding matter and space as a single structure --like a true mathematician!-- and on a certain scale and at certain energies this is right. But there is also an intermediate scale, at low everyday energies, where this approach is not well suited, imo.

Here are the quotes from your essay that especially resonated with me:

Re : "These phenomena suggest the promise of physical models that naturally incorporate scale-dependence,.."

Agree with you: scale is everything.

Re : "The first few assumptions I reject are that spacetime is a manifold, that systems evolve with respect to an independent time parameter, and that the universe has a static background structure."

Agree again: time as an independent parameter is suitable only on macro scales, while on the quantum scale, I believe, the micro-processes themselves (not 'particles'!) define spacetime volumes they trace, which can be mapped into time and distances at different scales. As for the universe having a static structure -- who actually thinks so? I can't even fathom it.

Re : "Dimension becomes an emergent property, and is no longer assumed to be constant, nondynamical, or an integer."

I see it exactly the same way.

Re : "If spacetime has a sufficiently simple structure, "...

Yeah, what is spacetime?

Re : "Finally, the dimension of space as well as its curvature might vary with energy density, "...

Just my thoughts. See, we have more in common than it seemed at first.

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Author Benjamin F. Dribus replied on Sep. 7, 2012 @ 06:11 GMT

Thanks for the thoughtful feedback! I re-read your section on time, and it does seem that we are in closer agreement than I thought at first. In particular, your concept of time seems to arise from local properties of the "fundamental energy units," while the overall order emerges from a tendency toward uniformity, which seems like a description of some sort of potential energy or entropic condition. I tried to suggest something similar in my essay, but only very briefly, since I don't know how to describe this condition precisely yet. You also describe "things in space" as a way of talking about alterations or defects of the structure, which I completely agree with.

Also, when I said "if spacetime has a sufficiently simple structure," I guess I was being lazy... what I meant was "if the underlying structure, from which what is commonly called spacetime emerges, is sufficiently simple..."

Take care,

Ben

Yuri Danoyan replied on Sep. 10, 2012 @ 08:40 GMT

See also http://www.fqxi.org/community/forum/topic/946

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Benjamin,

Wonderful dose of sense and lack of maths for a mathematician. Sound approach to the issues and nicely presented. I also agree most assumptions are reasonable, but I think you fall short of the path to the holy grail. First some favourite bits;

"...complete unification of relativity and quantum theory was gradually understood to be a particularly intractable problem..." and;

"...a variety of unexplained phenomena have been recognized." also;

"Recovery of a Lorentzian manifold from a physically relevant causal relation is necessary at some level of approximation."

Lastly on Dark matter; "However, this phenomenon does behave like ordinary matter in many respects, as observed in the collision of galaxies and in certain examples of gravitational lensing." I think this last point has started to be forgotten.

Certainly worth a good score. But I'd also like to invite you to study the mechanisms embodied in my own essay, which I think finds the R postulates direct from a long known QM. I hope you are well versed in logic. I referred to PDL but had to omitt Truth propositional Logic, the exact hierarchical structure of which I've found applies to my emergent model on (non manifold) dynamic space-time frames.

Please do study and see if you can assimilate the ontological structure from the components discussed. I throw in a bit of theatre just to help visualisation.

Best of luck in the scoring. I hope mine will help.

Peter

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Author Benjamin F. Dribus replied on Sep. 11, 2012 @ 20:51 GMT

Peter,

Thanks for the feedback! I'll be sure to have a careful look at your essay when I get back from my trip. I won't be too discouraged if my approach "falls short of the path to the holy grail," as you put it; I believe it's fine to think, speculate, and theorize about the biggest questions, but I'm not quite that ambitious about my ideas; at best they're part of the story.

Your ideas sound interesting as you describe them here, though I haven't yet had a chance to read your submission. Of course I have studied the common aspects of mathematical logic and some of the particular ideas applied to quantum settings, but I'm by no means an expert on this. Hopefully I can at least understand what you propose. Take care,

Ben

Dear Ben

I enjoyed reading our manuscript very much! You made the point about the current situation very clear and synthetic, and I agree on many of your points. As you will see in my answer to your post on my essay http://fqxi.org/community/forum/topic/1506, even though there are some strong common points between our two manuscripts, there are also some relevant differences, about which...

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Anonymous replied on Sep. 14, 2012 @ 22:21 GMT

Hello Mr.D'Ariano,Mr Dribus,

I didn't know this Deutsch turing machine. It is relevant. I say me that it is possible to insert the organic semiconductors with my equations and spheres.The informations can be classed with the sortings and synvhros.of evolution. The fermionic spheres and the bosonic spheres can be seen in a pure 3D sphere and spherization evolution. The synmmetry seems essential. I ask me if the system is fusioned or binar for the serie of uniqueness ?

In the reality, I prefer a fusion fermions/bosons.For the simulations and the convergences in 3D, it is seems interesting to insert the symmetry between the 2 systems for a better understanding of these synchros and sortings of evolution. mcosV=constanst is very relevant when the serie of uniqueness is insereted.

I beleive that for a real understanding of the system of uniqeness. This number ! It is essential to understand the decreasing of volumes from the main central sphere, the number 1. We see that the lattices disappear in the perfect contact between spheres.Just due to this decerasing of spherical volumes. A little if I said that all the cosmological spheres are attracted towards the universal central sphere.The finite serie is so essential for the two systems, quant.and cosm.It is relevant also when we consider the volumes diffrenciating the bosons and fermions.Always with this serie of uniqueness and its precise number. It seems not possible to calculte correctly this number, that said it is possible to appraoch it. In logic, the cosmological number is the same, so ....between 1 ....and x :)

The algorythms .......can converge !

Regards

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Dear Mauro,

I appreciate the excellent analysis. I will have to break my response into a couple of segments, so I will post them as new posts rather than replies. To the points on which we seem to agree, I have little more to add, though I am interested in the “Planck-scale experiment” you referenced. One point is that the generalization of covariance I have in mind is much more...

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Dear Mauro,

I appreciate the excellent analysis. I will have to break my response into a couple of segments, so I will post them as new posts rather than replies. To the points on which we seem to agree, I have little more to add, though I am interested in the “Planck-scale experiment” you referenced. One point is that the generalization of covariance I have in mind is much more general than semigroup representations. For the points on which we may disagree, I will itemize.

1. Regarding transitivity, I must insist on distinguishing between the “causal order” (of a classical universe) and the “binary relation generating the causal order.” On large scales, the intransitivity I am talking about is as simple as the fact that the statement “Jane talked to Bill, then Bill talked to Susan,” is not the same as the statement “Jane talked to Bill, then Jane and Bill talked to Susan.” In either case, Susan received information from Jane, so the two statements are indistinguishable in their causal orders. However, in the first instance, the information is transmitted only through Bill, whereas in the second case it is transmitted both through Bill and directly. Thus, there are two different binary relations that generate the same causal order: the intransitive one in which information passes only through Bill, and the transitive one in which information also reaches Susan directly from Jane. These two are a priori different. At an ordinary scale, this is obvious to everyone.

For fundamental physics, the reasoning is as follows. Many scientists (by no means all!) agree that “causality,” however you define it, is one of the most fundamental concepts in physics. The question then becomes: how do you define/describe causality? Well, a cause and effect certainly seem to define a direction; you can imagine an arrow pointing from the cause to the effect. This is completely local. Include lots of causes and effects (vertices), and arrows (directed edges) without yet imposing any other conditions, and you get a directed graph, which is equivalent to a binary relation on the set of vertices. At this stage, there is nothing to rule out cycles, and certainly nothing to impose transitivity, which are both generally nonlocal phenomena. There is a “causal order” generated by this directed graph, which is the relation defined by closing the graph relation under transitivity. I put “order” in quotes because this is still more general at this stage than the usual definition of a partial order; it may still have cycles, for instance.

This is all purely classical. To obtain a quantum theory, you need the superposition principle. The appropriate version of this in this case is a path sum over a configuration space of classical causal universes; i.e., directed graphs. I will explain why this is the appropriate version below. The question then becomes, “which graphs should be included in the configuration space?” This is the first real choice in the entire procedure, and involves a judgment about what types of graphs correspond to physical reality. My personal guess would be “acyclic locally finite directed graphs,” but I want to make it clear that these are second-level assumptions that come further along in the development. I prefer acyclicity because we don’t seem to observe causal cycles, and I choose local finiteness because I suspect that volume has something to do with counting (not necessarily as simple as Sorkin’s “order plus number equals geometry”, but in the same spirit).

I particular, it makes an a priori difference if you include only transitive graphs (graphs in which there is an edge between two vertices whenever there is a path between them). It’s conceivable that this difference would fall out of the path sum, but I see no justification for assuming this at the outset.

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2. You make the very helpful analogy that “the causal links are the "wires" in the quantum circuit.” If so, I don’t see any disagreement on this point, because the directed graphs representing quantum circuits are not transitive graphs. Also, the classical causal networks in your arXiv paper seem not only intransitive, but almost “maximally so” in this sense.

3. Regarding my reasoning for not absolutely ruling out cycles, I actually think GR is very discouraging to fans of time travel, and I’m certainly not trying to rescue GR here. It’s true that GR gives a sliver of hope to believers in causal cycles, but I don’t take these solutions very seriously. My reasoning is partly caution and partly based on some potentially interesting or suggestive properties of graphs containing cycles. The models I have thought the most about are acyclic, however.

4. Of course you’re correct that a binary relation doesn’t determine a metric in general. Sorkin discusses this at length. His “order plus number equals geometry” motto is based on metric recovery theorems that take as input an appropriate binary relation together with some volume data. His choice of how to provide volume data is the simplest (counting), but there are other ways, defined by taking advantage of local data in the graphs. For a homogeneous graph, simple counting is probably the only option, but I don’t prefer the assumption of homogeneity.

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5. I clearly did not explain my use of the sum over histories method adequately enough, and it is no wonder given the length constraints. First, in his 1948 paper Feynman discussed summing over particle trajectories in Euclidean spacetime and thereby recovered “standard” quantum theory, with its Hilbert spaces, operator algebras, Schrodinger equation,...

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5. I clearly did not explain my use of the sum over histories method adequately enough, and it is no wonder given the length constraints. First, in his 1948 paper Feynman discussed summing over particle trajectories in Euclidean spacetime and thereby recovered “standard” quantum theory, with its Hilbert spaces, operator algebras, Schrodinger equation, etc. Feynman was able to take all the trajectories to be in the same space because he was working with a background-dependent model; the ambient Euclidean space is unaffected by the particle moving in it. Now, if GR has taught us anything, it is that “spacetime” and “matter-energy” interact, so different particle trajectories mean different spacetimes. Hence, in a background-independent treatment, Feynman’s sum over histories becomes a sum over “universes,” with a different classical spacetime corresponding to each particle trajectory. His original version is a limiting case in which the effect of the particle on the spacetime is negligible.

What are the “classical spacetimes” in my approach? Well, they are directed graphs. However, it is not quite right to just sum over graphs. The reason why can be understood by looking at Feynman’s method more carefully. He considered a region R of spacetime, and interpreted his path sum as the amplitude associated with measuring the particle somewhere on the upper (i.e., future) boundary given an initial measurement on the lower boundary. Hence, the path sum measures not the amplitude of a particular universe, but the amplitude of “transition” from one family of universes to another. A discrete approximation of this represents each particle trajectory as a sequence of directed segments in the corresponding configuration space, which inherits a partial order from the time-orders of the individual spacetimes. It is now clear how to generalize to the nonmanifold case: the appropriate sums are sums over paths in causal configuration space.

Take care,

Ben

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Your essay does a excellent job of summarizing the problems with current physics models as well as pointing out some of the assumptions that need to be questioned.

The scope of the essay far exceeds what one would expect to find in so little space. Lots of food for thought requires lots time to digest. In the case of your essay, we're easily talking months.

As I read the essay, a number of questions immediately came to mind.

First, I would like to understand better how you determined which of the fundamental assumptions needed to be questioned and why. What was your starting point(s)?

Also, you mention the necessity for a new theory to recover established physics that has proven to be successful. Wouldn't this condition constrain the development of an entire class of new theories, particularly those from which established physics cannot be recovered and which, in some case, may come in direct opposition to them?

Wouldn't you think that all that should required of a theory, besides internal consistency, is that it be in agreement with observational and experimental data, and not necessarily with any theoretical interpretation of it? For instance, a theory may account perfectly for the bending of light near a massive structure yet be based on a axiom set that excludes general.

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Author Benjamin F. Dribus replied on Sep. 16, 2012 @ 19:19 GMT

Daniel,

I appreciate the feedback. I will itemize my reply:

1. The length requirement did limit my ability to explain my background thoughts. My emphasis on causality is principally motivated by two factors:

First, most of science, and particularly the experimental method, consists of establishing "causal" relationships between things ("whenever we do so-and-so, we observe...

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Daniel,

I appreciate the feedback. I will itemize my reply:

1. The length requirement did limit my ability to explain my background thoughts. My emphasis on causality is principally motivated by two factors:

First, most of science, and particularly the experimental method, consists of establishing "causal" relationships between things ("whenever we do so-and-so, we observe such-and-such"). The success of this approach is obvious, and I feel that its full potential should be exploited. Remarkably, much of modern theoretical physics has relegated causality to a secondary and sometimes obscure role, and many recent theories reject its fundamental importance altogether. Instead, they are based on objects like continuum manifolds, which have undeniable mathematical advantages, but which are disturbingly idealistic and exhibit properties that are obviously physically irrelevant (like the least upper bound property, nonmeasurable subsets, etc.)

Second, it is startling how much of the structure of even such idealized theories can be recovered from causal relations, and how almost every "spacetime-related concept" you can think of has an analogous "causal interpretation" that is more natural and more general. For instance, a "light cone" in relativity is an abstract geometric locus of events in spacetime, and the rule that "information cannot escape its light cone" is viewed as secondary. In causal theory, the light cone is simply the scope of information flow, and the idealized view of a geometric locus is secondary. As another example, "frames of reference" in relativity are associated with abstract local coordinate systems on a manifold, and the relativity of simultaneity is viewed as secondary. In causal theory, frames of reference are different orderings of events compatible with the causal order, so the physical idea of relativity of simultaneity is direct, and the idealized view of a coordinate system is secondary. In both examples, I think it's obvious which is the more natural and physical point of view.

2. Regarding the recovery of established physics, I don't mean that every prediction of currently accepted models, including those that haven't been experimentally verified, must be reproduced; that would be pointless. What I mean is that a new theory must do at least as well as current theories in explaining and predicting what we actually see. For instance, general relativity modifies Newton's laws only very slightly for solar system dynamics; if general relativity had predicted an inverse cube force for the gravity between the earth and the moon, it would have been thrown out. Similarly, a new theory must look like general relativity and quantum theory in any situation where those theories have been proven to work.

3. Regarding the general requirements for a theory, yes, I agree completely. Experimental evidence is the final judge.

Take care,

Ben

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Daniel L Burnstein replied on Sep. 17, 2012 @ 18:32 GMT

Thanks for the clarifications, Ben. I understand your essay much better now.

Daniel

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Inger Stjernqvist replied on Oct. 2, 2012 @ 15:07 GMT

Dear Ben and Daniel,

So do I, thanks to your conversation above.

Best regards,

Inger

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Ben,

Will you be able to recover Minkowski spacetime and relativity in general from your new principles without additionally assuming the constancy of the speed of light (Einstein's 1905 light postulate)? Einsteinians sometimes claim that "the constant speed of light is unnecessary for the construction of the theories of relativity" but this is a fraud of course:

Jean-Marc...

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Author Benjamin F. Dribus replied on Sep. 17, 2012 @ 12:45 GMT

Dear Pentcho,

Thanks for the feedback! By "recovering" relativity, I don't mean that I believe relativity in Einstein's original form is absolutely valid (otherwise, why would it need to be replaced or superseded?) What I mean is that in any case in which relativity makes good predictions, any theory that supersedes it must do at at least as well. Hence, a new theory must be able to describe/predict anything that relativity can describe/predict.

Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales. "Speed" requires a notion of distance, and my view is that spatial distance (separation) is ultimately just a way of talking about the extent to which events are "unrelated." It begins to look like a traditional distance only at large enough scales.

Regarding photon mass, it was thought for a long time that neutrinos had no mass, but it was eventually discovered that they do have mass after all. Hence, I would be inclined to keep an open mind even about something as "sacred" as that. However, mass itself is again an emergent concept in my view, so the questions of what a "photon" really is and what "mass" really is are things that cannot be taken for granted.

You'll have to remember that my background is mostly mathematical, and therefore I'm inclined to consider the possibility of things that most physicists "know" are wrong. This might be useful in some cases; in others it only reflects my own ignorance. Take care,

Ben

Pentcho Valev replied on Sep. 21, 2012 @ 05:41 GMT

"Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales."

No it makes sense locally. See this:

"vO is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. Hence, the velocity of waves relative to the observer is c + vO. (...) The motion of an observer does not alter the wavelength. The increase in frequency is a result of the observer encountering more wavelengths in a given time."

This author teaches that the speed of light is VARIABLE (varies with the speed of the observer). If he thought it was constant, he would have written:

"vO is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. The velocity of waves relative to the observer is constant,c, because the motion of the observer alters the wavelength. The increase in frequency is a result of the motion of the observer altering the wavelength."

Pentcho Valev

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Pentcho Valev replied on Sep. 24, 2012 @ 04:07 GMT

Ben,

You wrote: "Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales. (...) You'll have to remember that my background is mostly mathematical, and therefore I'm inclined to consider the possibility of things that most physicists "know" are wrong. This might be useful in some cases; in others it only reflects my own ignorance."

Insofar as "the constancy of the speed of light" is concerned, I am afraid your last statement is relevant, Ben.

Pentcho Valev

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Dear Benjamin

You wrote: "Predictions based on quantum field theory and the Planck scale yield a value for the cosmological constant roughly 120 orders of magnitude greater than observation implies."

If you read my posts to my essay attentively you can read next:

Yuri Danoyan wrote on Sep. 4, 2012 @ 00:25 GMT

Appendix 4 Solution of cosmological constant problem

Theory: Cosmological constant is 10^94 g/sm^3

Practice: Cosmological constant is 10^-28 g/sm^3

Planck constant h=10^-28 g x sm^2/sec in 2D space embedding in 3D space

Only right value is experimental value.

Theory based in wrong assumptions noted in my essay.

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Author Benjamin F. Dribus replied on Sep. 17, 2012 @ 18:01 GMT

Dear Yuri,

I did look through the comments on your thread, but I am afraid I don't quite understand. It seems you are suggesting there is a simple dimensional relationship that explains the observed value of the cosmological constant. This would be great, but it's not obvious to me. Do you mind explaining a little more? Take care,

Ben

Yuri Danoyan replied on Sep. 17, 2012 @ 18:19 GMT

I argue that the Planck unit of length at short distances is not applicable, and the space has dimension 2, not 3.

Hence density of space coincides with сonтstant h.

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Planck unit of length not applicable,because no Gn,no Newton gravity law.

See part 3 my essay.No linear link between G and c,as in Planck unit of mass.

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Dear Benjamin

For better clarification my approach

I sending to you Frank 3 keen articles

http://ctpweb.lns.mit.edu/physics_today/phystoday/Ab
s_limits393.pdf

http://ctpweb.lns.mit.edu/physics_today/physt
oday/Abs_limits393.pdf

http://ctpweb.lns.mit.edu/physics_toda
y/phystoday/Abs_limits400.pdf

All the best

Yuri

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I send first all this links to address

'bdribus@math.lsu.edu

but get answer

'bdribus@math.lsu.edu.' on 9/17/2012 12:54 PM

Invalid recipient

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Dear Yuri,

I got two out of the three articles, and I'm sure I can find the other one. I'm not sure why the first didn't come through. I don't know why you got that error message... that is the correct address. In any case, thanks for the articles; fortunately, they were easy to read, but included some information I did not know. I think I understand what you are suggesting about the relationship between the cosmological constant and Planck's constant, but don't you think that perhaps the cosmological constant is a little too small? Take care,

Ben

Yuri Danoyan replied on Sep. 18, 2012 @ 02:01 GMT

http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits
388.pdf

http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs
_limits393.pdf

http://ctpweb.lns.mit.edu/physics_today/physto
day/Abs_limits400.pdf

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Dear Ben,

I enjoyed your comments on Brian's and my essay pages. As promised I have read and will comment on your learned fqxi contribution:

I agree with you that causality (I suppose you mean local causality, but you also refer to universes in the plural so I am left wondering) is the substrate on which to build a rational theory unifying quantum mechanics, relativity and the standard model.

Beyond this understanding, your essay is far too technical for me to follow. You couch your arguments in terms like " acyclicity, morphisms, multicategory theory, transitivity, complex Hilbert spaces" which leave be baffled. Well at least as far as Hilbert spaces are concerned Brian Swingle has thankfully dispensed with those as far as physics is concerned. As a mathematician it is wonderful that you approach physics with this background, as you just might find a new math to explain a whole range of physics - just as quaternions are now found to be useful to explain quantum interactions.

If you will forgive this image - the good wolf mathematicians huff and puff with their theories, circling around the various houses built by the little piggy physicists, and it is an excellent way to test those houses for good solid construction!

I was reminded that we should peer-rate essays as only the top 35 rated essays get read by fqxi's expert panel of judges.

With best wishes for your degree work,

Vladimir

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Author Benjamin F. Dribus replied on Sep. 18, 2012 @ 03:29 GMT

Dear Vladimir,

I appreciate the feedback! And I was quite amused by your metaphor of the three little pigs... although I think the physicists have given mathematicians at least as much of a headache over the years with ideas like path integrals and delta functions!

As a matter of fact, as I wrote on your thread, the math I use here is simply whatever seems necessary to get the job done... the basic physical idea of cause and effect is the motivation. The length limitation for the contest makes it a bit difficult to explain things adequately and still fit in everything you want to say.

I was going to wait to rate the essays until I had read them all, but I will rate yours now just so I don't forget. Take care,

Ben

Dear Benjamin,

I am extremely sorry for the delay in replying to your query. I am glad to know that you have your original way of looking at the fundamental problems of physics and surprised to learn that you suspect too many basic assumptions of physics where as I consider as wrong only one basic assumption. On the basis of your 'causal metric hypothesis', you have tried to explain, in a novel way, the origin of the classical concepts of space-time and also the role of space and time in the quantum world. On the basis of 'causal metric hypothesis' you have attempted to unify both GR and QM leading to the theory of QG. I am also interested in knowing how you account for the appearence of continuous manifolds on the basis of 'discrete reference frames'.

Anyway, you have put too much thought in to the problems facing physics and wish you succeed in solving them in one stroke on the basis of 'causal metric hypothesis'. I rate your essay high because of its originality and want to know how you feel about mine.

Good luck and best regards,

Sreenath.

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Author Benjamin F. Dribus replied on Sep. 19, 2012 @ 03:21 GMT

Dear Sreenath,

I appreciate the feedback! It's true that I doubt a lot of the modern assumptions, but this arises mostly from my doubt about the ultimate physical relevance of manifolds. In my mathematical work, I have come to appreciate how very idealized and mathematically convenient objects like continuum manifolds and algebraic varieties are, and it seems to me that many of the properties that make them mathematically convenient do not arise in any natural or necessary way in physics. Many people think that convenient properties such as the least upper bound property in the order theory of the continuum can be assumed without worrying about their ultimate physical reality, based on the belief that any sufficiently fine approximation will suffice for measurement purposes. However, these properties determine the symmetry groups whose representation theory governs the properties of particle states, so the difference is an important qualitative one, not simply a small quantitative one that vanishes in the limit. My approach is to begin with the concept I view as most central to scientific process, namely cause and effect, and explain as much as possible in these terms. Ultimately, it may not be enough, but it is an approach with obvious motivations and clear and simple principles, and one that has not been adequately explored.

Regarding your essay, I view it positively even though your approach is much different than mine. I don't know if your equations will turn out to be correct, but the advantage of your approach is that you go into very specific details, and it should be possible to evaluate it one way or the other in a reasonable time frame. Like mine, I think your approach is worth trying, which is really all one can ask for. Take care,

Ben

Ben,

As you said my essay was filled with ideas I can reciprocate the comment about yours. The statement you make:

“A number of existing proposals about spacetime microstructure lead naturally

to noncommutative spaces in the sense of Connes [3] via the deformation theory of Hopf algebras, 10 but noncommutative geometry is relevant more generally, and even classical spaces...

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Author Benjamin F. Dribus replied on Sep. 19, 2012 @ 03:38 GMT

Dear Lawrence,

Thanks for the comments. I particularly appreciate your remarks about the FERMI/INTEGRAL experiments; I knew about these but don't feel very confident in interpreting the results. You're right of course that experiment is the final arbiter, but with the caveat that one must be sure what the experiment means.

Torsten's approach is fascinating and is worth understanding at a deeper level. I'll also point out that Jerzy Krol's essay is worth looking at in this regard; the two of them have been collaborating and their submissions are complementary. Jerzy discusses nonstandard models of number systems and their role in defining exotic smoothness structures.

You have the advantage of being well versed in the string/M-theoretic technology, which I am rather a novice at. Superficially, the 4d-to-7d duality of exotic structures you suggest sounds intriguing and perhaps gives another glimpse of why dimension 11 is special, although I'm not qualified to remark further on this. I do note that string/M-theory has been recently assimilating aspects of other approaches (noncommutative geometry, entropic gravity, twistor theory, etc.) in a way that suggests that the serious approaches to QG and unification may prove more amicable than previously thought. The causal theories (causal dynamical triangulations, causal set theory) seem perhaps left out of this picture to a degree, which gives me pause considering that causal theory is my own favorite approach. Take care,

Ben

Lawrence B. Crowell replied on Sep. 19, 2012 @ 19:10 GMT

The Fermi X-ray, gamma ray test of relativity can be found in this review This measurement was followed up by the ESA Integral spacecraft.

There is a lot of confusion over Verlinde’s entropic gravity. Gravity as a dynamic force is conservative. The force in the Newtonian limit is given by F = -∇Φ(r), which is conservative. This means the force evaluated around a closed...

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Author Benjamin F. Dribus replied on Sep. 20, 2012 @ 04:19 GMT

Dear Lawrence,

I appreciate the insight. This is the sort of thing that would require me a lot of time and effort to piece together myself. If there is any connection between Verlinde's entropic description of gravity and my speculative application of entropy to determine transition amplitudes, it's a coincidence, since I didn't even know about Verlinde at the time. I suppose that the hypothesis "gravity is entropic" can mean a lot of different things. My idea came from results in graph dynamics, and entropy in this case is determined by the cardinality of a particular automorphism group. If this works at all, it requires some finiteness assumptions. (I assume you transposed "closed" and "exact" above, unless you were referring to something different than the usual definition of de Rham cohomology.) Take care,

Ben

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Ben,

"The central new principle I propose is the causal metric hypothesis, which states that the metric properties of classical spacetime, up to overall scale, arise from a binary relation, which I will call a causal relation, on a set, which I will call a universe, and that the phase associated with a congruence class of directed paths in the conguration space of such universes is determined by the causal relations of its constituent universes"

How can you imagine let alone model causal relationships of a multiverse? Are the attributes of gravity shared between universes? I struggle with your esoteric essay.

Jim

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Author Benjamin F. Dribus replied on Sep. 19, 2012 @ 12:30 GMT

Dear Jim,

Well, I would rather not call it a multiverse because that is often understood these days to refer to the string-theory multiverse, which means something entirely different. My "causal configuration space" is a "way of talking about the superposition principle of quantum theory in a background independent setting." For some context, in 1948 Richard Feynman showed that you could explain quantum theory by thinking of all the possible paths a particle could follow between two points in space and time. Since general relativity says that the structure of spacetime responds to matter and energy moving through it (background independence), different particle paths correspond to different spacetime structures; i.e., different "universes." So you see that in this context, "universe" doesn't mean "all that exists," it just means a particular classical causal structure.

The fact that the causal configuration space itself has a similar structure to the individual "universes" is a nice thing, in my opinion, but the relationships among the "universes" aren't "causal" in the usual sense. The point of the causal metric hypothesis is that you can describe a lot of different things (causality, spacetime "geometry," the superposition principle, etc.) by means of a single type of structure. I

I hope this helps! Take care,

Ben

Author Benjamin F. Dribus replied on Sep. 19, 2012 @ 12:34 GMT

Jim,

By the way, I agree with Verlinde and others that gravity is likely an entropic phenomenon. But I think it's quite possible that all the "forces" are entropic. Take care,

Ben

Thanks Ben,

The supreme example of the mathematician-physicist is Newton - and of course you are right about the 3 piggies metaphor being inexact - perhaps at the most basic level physics and mathematics are equally artificial, but in conjunction try to describe Nature the best they can. As an artist and inventor I built my physics model using geometry and physically realistic interactions. I suppose topology, knot and graph theory can all be used to describe such models, but I am satisfied with understanding how it works as a sort of mechanical linkage. (I was inspired by Kenneth Snelson's concept of tensegrity - I urged him to present his ideas about the atom in this contest and am glad he did - at age 85!)

I hope that my model can be tested by computer simulation but I had better update my research and present it more succinctly.

Following your remark about gravity and entropy: In one of the discussions of this contest I suddenly realized (and wrote) that my Beautiful Universe model explains why entropy occurs - it is the same causal local mechanism of diffusion of energy as a wave pattern in the lattice, which simultaneously explains probabilistic behavior and uncertainty! But what about solitons? how would entropy be manifested in their behavior?

Thank you for rating my essay, (as I did yours). Last year I also participated in the fqxi contest, and one participant used to sign his messages: Have fun!

Vladimir

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Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Dear Benjamin,

Studying the question of connection of entropy and gravitation, I found Lorentz-invariant formula for entropy in the book: Fizika i filosofiia podobiia ot preonov do metagalaktik. Perm, 1999, 544 pages. ISBN 5-8131-0012-1. In short the question is described in the book: The physical theories and infinite nesting of matter. Perm, 2009-2012, 858 pages. ISBN 978-5-9901951-1-0 in such way: Using the stress-energy tensors for the substance and the gravitational and electromagnetic fields allows us to write the equations of thermodynamics explicitly in the Lorentz-invariant form. As a result the entropy, the amount of heat, the chemical potential, the work and thermodynamic potentials can be represented as tensor functions of microscopic quantities, including the electric and gravitational field strengths, the pressure and the compression function. This allows us in § 21 to find out the meaning of the entropy as the function of the system state - it is proportional to the ratio, taken with the negative sign, of the absolute value of the ordered energy in the system to the heat energy, which is chaotic by nature. The ordered energy means the energy of directed motion of the substance, the compression energy from pressure and the potential energy of the substance in the gravitational and electromagnetic fields. When the system achieves equilibrium, part of the orderly energy inevitably is converted into thermal form and the entropy obtains a positive increment. I hope it may be interesting also for Vladimir F. Tamari and others authors in the contest.

Sergey Fedosin

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Author Benjamin F. Dribus replied on Sep. 19, 2012 @ 17:49 GMT

Dear Sergey,

That's quite a book... 544 pages. Is any of this material posted online? If not, I understand... I have hundreds of pages of unpublished stuff myself. Also, I regret that the only languages I can read are English and a little French and Spanish. Take care,

Ben

Vladimir F. Tamari replied on Sep. 25, 2012 @ 02:43 GMT

Dear Sergey and Benjamin

A lot of fascinating ideas seem to have emerged and are emerging in Russia - but unfortunately I do not have the language either! I have newly discovered that entropy emerges naturally in the same mechanism - diffusion - explaining uncertainty and probability) in my Beautiful Universe model, where also e/m and gravity are realized in local causal building blocks of a universal lattice.

Vladimir

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Author Benjamin F. Dribus replied on Sep. 25, 2012 @ 03:00 GMT

Dear Vladimir,

You mentioned this before, and I will have to think about this idea further. The correct definition and use of entropic principles is one of the things I am a bit hung up on in my own approach. Take care,

Ben

Dear Ben,

I am in general agreement with your critique in regard to the foundational problems. My view is that the problems you have highlighted are secondary, tertiary derivatives that have emerged due to the original foundational problems that Newton (and others) introduced when he intentionally developed Mechanics on a makeshift basis as a stepping stone for what he called the “Truer...

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Dear Ben,

I am in general agreement with your critique in regard to the foundational problems. My view is that the problems you have highlighted are secondary, tertiary derivatives that have emerged due to the original foundational problems that Newton (and others) introduced when he intentionally developed Mechanics on a makeshift basis as a stepping stone for what he called the “Truer Method of Philosophy”.

You have quite rightly pointed out that although certain foundational problems are realized by eminent physicists, they do not know how to rectify them.

For instance you wrote in reply to Frank: “Regarding the continued use of widely doubted assumptions, the reason I mentioned this is because I wanted to make clear that I wasn't offering anything new by rejecting these particular assumptions; of course people have known for years that there are issues with manifold structure, background-dependence, etc., and plenty of people are working on these problems. I don't think that well-educated physicists continue to use these assumptions because they are trying to make them "fit a preconceived model," but rather because they don't yet know what to use in their place. …..”.

This is because there is no single foundation presently. When the problems arose on the original foundation, without analyzing and rectifying them, other foundational concepts (even contradictory ones) were overlaid, while retaining some of the problematic ones (like the point mass) and this process has continued. My view is that the solution to the present crisis must begin with going back to the original foundation of Newton and rectifying its mistakes.

I have done this to a certain extent. I have not only pointed out what the foundational problems are, but I have offered solutions.

I request you to have a look at my essay and comment: http://fqxi.org/community/forum/topic/1549

Since the diagrams have not come out properly in the above pdf version, I am attaching the MS Word version also.

I will continue on this with another post making some introductory comments about my essay.

Best regards,

Viraj

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attachments: 9_A_TREATISE_ON_FOUNDATIONAL_PROBLEMS_OF_PHYSICS2.doc

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Viraj Fernando replied on Sep. 19, 2012 @ 16:56 GMT

Continuing:

Hi Ben,

The following are some matters I wish to bring to your attention about the contents of my essay: http://fqxi.org/community/forum/topic/1549

1. I have listed out a number of assumptions that Newton made that have turned out to be foundational errors.

2. I have not only listed the errors, I have found a new approach to overcome these errors (guided by...

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Author Benjamin F. Dribus replied on Sep. 19, 2012 @ 17:42 GMT

Dear Viraj,

It appears that the first few assumptions you reject ("the primacy of the concepts of space and time," etc.) are the same as mine, although we use different words (I would say "the manifold structure of spacetime," or "an independent time parameter.")

Some of the other assumptions you reject (for instance, those regarding centrifugal force and some of the statements about energy) I would expect to disappear automatically once the usual assumptions about space and time are rejected.

I had better not make any more specific remarks until I have read your essay, however. One thing I will say is that it appears as if you made an honest effort to answer the question posed by the essay contest rather than just writing down your favorite ideas about physics. You will notice that I made a similar effort. Take care,

Ben

Viraj Fernando replied on Sep. 19, 2012 @ 23:54 GMT

Ben,

Thanks for acknowledging that my essay is strictly in context of the topic of the contest. Actually, you may note that I have gone a bit further by, finding alternative solutions, which would confirm my contentions about the identified wrong assumptions.

I am awaiting your comments about my essay. I hope being a young person with an open mind free of dogmatic views on exisitng theories, you would find it easier to understand the point of view I am presenting.

BTW, LSU in which city are you in. I was in Shreveport recently for some time.

Best regards,

Viraj

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Hi Ben,

I report my reply to your questions about my essay Elementary Time Cycles. I have justpresente the theory in DICE2012, Castiglioncello, Italy where I have received entusistinc feedback. I will read asap your assay and let you know my opinion.

-—————

Thank you for your comments on my essay. I present a new idea and it is not immediate to figure it out,...

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Author Benjamin F. Dribus replied on Sep. 20, 2012 @ 04:25 GMT

Dear Donatello,

Thanks, I appreciate it. I'll put subsequent discussion about your program on your thread rather than mine... but I think I'll read your arXiv article first. Take care,

Ben

Dear Ben,

I found your essay very inspiring especially it deals with excellent mathematical arguments. Generally, your presentation is convienced and very good, this more that you touch so many important things on so limited number of pages. Let me comment on some important for me point.

It is certainly something that should be rejected in manifold's model for the space-time valid on every physical scales. But my personal view is that we do not understand or even know at present whole net of mathematical structures related with manifolds. Let it be two things: 4-d smoothness and logico-categorical perspective. Both indicate on discrete and noncommutative structure of smooth 4-manifolds. This discretness does not change or replace the manifolds, it is rather an ever-present leyer of smooth manifolds. Besides, the dimension 4 is crucial here. Fundamental gravity can be, thus, related with the curvature of exotic R4 (standard R4 can be flat exotic can not) where discretness appears naturally. I think that again mathematics shows us the way which is not, however, quite clear yet.

These commentaries expresses rather my personal point of view but I was inspired by your great essay. Congratulations and good luck.

Jerzy

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Author Benjamin F. Dribus replied on Sep. 20, 2012 @ 16:49 GMT

Dear Jerzy,

I really appreciate the kind remarks! As a matter of fact, you and Torsten have convinced me to reconsider a lot of my tentative beliefs about fundamental physics, as have some of the shape dynamics folks and a few others.

The last time I really thought carefully about low-dimensional manifolds was a few years ago, and that was before I was properly aware of noncommutative geometry. I never took nonstandard models seriously until I read Connes, and as you have seen, I still have only the vaguest ideas about them.

I feel fortunate to have perhaps half a dozen serious new directions to think about once the exchange of ideas slows down a bit. Take care,

Ben

Dear Ben,

Thanks for your impartial comments on my essay, on my thread and rating it.

http://fqxi.org/community/forum/topic/1549

However I am responding to it on your thread because I think it has come out incomplete. Can you please check and do the needful if neccesary.

You wrote: "My belief is that its standing will improve as more serious authors read it". I do not think even 10% of the authors will give an unbiased rating. Firstly,because they will not understand what my essay is about with their own pet ideas in their minds, and secondly they will be interested to up their position by rating others low. (As for me I still have not rated even my own essay. I am reading through them and will rate all of them on their merit at a later date).

This points to the facct that all those who have got high Community ratings for their essays seems to have achieved them not by the ratings of authors but from the FQXi 'Community'.

But the big question is how do I get the attention of the "Community". The FQXi, highlights "Top Essays" some authors to the Community, but when I posted some highlights about my essay in that blog to draw their attention, it was removed by the administrator saying that Competitor ads are not allowed. So all competitors are not playing on a level playing field.

Best regards,

Viraj

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Author Benjamin F. Dribus replied on Sep. 20, 2012 @ 17:34 GMT

Dear Viraj,

You're absolutely right... the form evidently won't accept a "less than" sign without putting it in a latex environment, and it deleted everything below, which was 80 percent of my post. I finally got it right, but there was another abortive post in between. I apologize for cluttering your thread, but all the comments are there now at least!

Regarding your remarks about the contest and the rating, there are many more than 35 good essays among the 270 or so in the contest, so no one should be too disappointed if his or her own submission isn't a finalist. For a complete outsider and first-time contributor like myself, the whole point of participating in this contest is to have the opportunity to discuss many interesting ideas with serious and original thinkers, and to make contacts with other scientists of similar interests.

In my opinion, the final community ratings are unlikely to look anything like what they do now; probably most people have not yet voted and it wouldn't be surprising if submissions in the top 10 now finish out of the top 100. The FQXi membership includes many of the most distinguished physicists in the world, and I imagine most of them are very busy. I seriously doubt if they are paying very close attention to this contest on a daily basis or have read or rated most of the essays.

In my view, the ratings are not worth worrying about too much, since doing so only distracts from the science. A high rating would be nice, but I would prefer to try to understand other people's ideas, circulate my own, and let the chips fall where they may. Take care,

Ben

Viraj Fernando replied on Sep. 20, 2012 @ 18:40 GMT

Hi Ben,

Thanks for re-posting your message in my thread.

About your other comments:

It is not that I am dead keen to get a good rating. I too am in the 'contest' more to use it as a forum to get to know people and ideas, and to circulate my own. You know the long forgotten motto of the Olympics - "Not to win but to take part".

But an important aspect of taking part amounts getting the attention of independent parties (eminent scientists who are FQXi members) to my essay for whatever it is worth, as much my reading other participants' essays. But the avenue to reach FQXi members is blocked, while 'Top Essays' are freely advertised in the Main blog. It is also a fact that the content of some of these "Top Essays", do not conform to the context of the topic of the contest.

This is a genuine concern I have about the way the "Contest" is run.

However, I am not worried about the 'contest'. If things are left for chance without manipulations, I know the chips would have fallen in a cetain way, but the way things are it appears they won't. It is just the instinct in me not to take things sitting down that bugs me.

Quite apart from the contest and FQXi community, do you know of any scientists who are likely to take an interest on essays like ours concerning fundamental problems of physics. If you feel it appropriate I request you to let me know.

My email: virajplf@yahoo.co.uk

Best regards,

Viraj

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Hi Ben,

Quite an ambitious essay indeed! If we ever meet, I suspect we will have many interesting discussions.

I applaud your courage for trying to reject so much structure and still try to reproduce the rich structures of GR and the Standard Model. It is certainly not an easy task as is evidenced by the efforts of the Causal Sets people. However, I have always found that these approaches are well motivated. Good luck with your approach and in this competition!

Sean.

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Author Benjamin F. Dribus replied on Sep. 20, 2012 @ 19:22 GMT

Dear Sean,

Thanks for your kind remarks. I think you have characterized the obvious advantages and disadvantages of an approach like mine quite correctly: it's well-motivated and would be terrific if it worked but may fall well short of the level of structure necessary to describe the real world.

One remark I will make (I said something similar on Daniel Alves' thread) is that perhaps one way to think about the relationships among approaches such as causal sets, causal dynamical triangulations, shape dynamics, and my approach, is to consider the symmetry, antisymmetry, or asymmetry of the relations involved. Shape dynamics seems to involve symmetric relations, since separation does not specify order. Causal sets involves strictly antisymmetric relations because of the acyclicity hypothesis. Causal dynamical triangulations uses both symmetric and antisymmetric relations, and my approach uses mostly antisymmetric relations, although I admit the possibility of cycles. Of course, shape dynamics assigns weights (separations) to the symmetric relations, which gives more information. Anyway, maybe this is wrong, and I'm certainly a fool to talk about shape dynamics two weeks after first learning it existed, but it seems on the surface that there might be dualities among appropriate versions of some of these theories. Oh well, just a wild thought. Take care,

Ben

Member Sean Gryb replied on Sep. 21, 2012 @ 14:17 GMT

Interesting thought.

I don't know much about the difference between symmetric and anti-symmetric relations so I can't comment much. However, I would just point out that, in shape dynamics, the conformal factor of the metric is pure gauge, up to a constant. Because of this, the causal structure is really the main information that we are keeping aside from the total volume. Thus, I suspect that there is a way to map causal structure onto shape space. Indeed, this could have something to do with the isomorphism between the de Sitter group and the conformal group. Probably there is a way to map the conformal structure of de Sitter to the isometries of the conformal sphere in one less dimension. Then one could use a framework similar to what Flavio and I are discussing the paper we're about to post to understand this better in gravity. The discreteness is another issue but I have some ideas about that as well. There may be a way to make some connections.

Cheers,

Sean.

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Author Benjamin F. Dribus replied on Sep. 21, 2012 @ 15:40 GMT

Sean,

I believe it's precisely because of the conformal factor that Rafael Sorkin incorporates the (constant discrete) measure in his "order plus number equals geometry;" i.e., because "order" by itself is not enough to recover the metric. That was part of what interested me about shape dynamics, because throwing in the scale seems artificial. You note that I have to keep repeating "up to a scale factor," in my own essay. Take care,

Ben

Sean,

Also, Lawrence Crowell (who seems capable of instantly making precise remarks about almost any subject) has made some comments on Daniel Alves' thread along the same lines (possible duality/complementarity of symmetric/antisymmetric relations). I'm sure you are following Julian Barbour's thread; there is some relevant discussion there as well. Take care,

Ben

Member Sean Gryb replied on Sep. 21, 2012 @ 16:47 GMT

I'll take a look. I haven't had much time to check the discussions but I will but we just posted our new paper so I will have some time next week. I think there is definitely a connection. It would be nice to make this more rigorous though!

Cheers,

Sean.

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Heaven Breasts and Heaven Calculus

http://vixra.org/abs/1209.0072

Since the birth of mankind, human beings have been looking for the origin of life. The fact that human history is the history of warfare and cannibalism proves that humans have not identified their origin. Humanity is still in the dark phase of lower animals. Humans can see the phenomenon of life only on Earth, and humans' vision does not exceed the one of lower animals. However, it is a fact that human beings have inherited the most advanced gene of life. Humans should be able to answer the following questions: Is the Universe hierarchical? What is Heaven? Is Heaven the origin of life? Is Heaven a higher order of life? For more than a decade, I have done an in-depth study on barred galaxy structure. Today (September 17, 2012) I suddenly discovered that the characteristic structure of barred spiral galaxies resembles the breasts of human female essentially. If the rational structure conjecture presented in the article is proved then Sun must be a mirror of the universe, and mankind is exactly the image on earth of the Heaven.

http://galaxyanatomy.com

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Author Benjamin F. Dribus replied on Sep. 22, 2012 @ 18:20 GMT

Dear Jin,

Thanks for informing me of your paper. Take care,

Ben

Hi Ben --

I'd just like to register my support for your viewpoint on foundational assumptions. For reasons probably unrelated to yours, I think the "causal set" approach has a lot of promise, and I wish you every success in working out your hypothesis. I find it very impressive that a mathematician would approach physics by doubting the validity of continuous manifolds at a fundamental...

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Hi Ben --

I'd just like to register my support for your viewpoint on foundational assumptions. For reasons probably unrelated to yours, I think the "causal set" approach has a lot of promise, and I wish you every success in working out your hypothesis. I find it very impressive that a mathematician would approach physics by doubting the validity of continuous manifolds at a fundamental level! And I've appreciated the very clear and sensible comments you've made to many of the other contest essays.

My own interest is in learning to describe the physical world that can actually be experienced, whether by us or a measuring device or any other local entity. Traditionally this "view from inside" is treated merely as a means for gaining knowledge of an objective reality that exists in itself. While that's obviously reasonable, I tried to argue in my essay ("An Observable World") that fundamental physics also need to deal with the context-structure of the physical environment that makes information observable. I argue that regardless of the nature of any background reality, the ability of the world to communicate about itself is a basic feature we need to understand.

So for me, what's important about "the binary relation generating the causal order" is that it describes an element in the structure of observable interaction, in contrast with background-structures like spacetime manifolds, fields and particles.

I do have one comment on the "causal metric hypothesis" and the problem of the "recovery of established physics at appropriate scales." A basic point made in my essay is that any physical parameter is only measurable in a context defined by other measurable parameters. This suggests that an observable world like ours has to be based on several essentially distinct types of interaction-structure. We can imagine that some of these are more basic than others -- for example, it seems significant that electromagnetic field-structure is largely independent of the metric, and so perhaps reflects a more "primitive" structural layer. But I suspect a successful theory won't just reduce every kind of interaction to a single elementary structure that explains everything at one shot. More likely it will focus on the differences between interaction-modes, explaining what each contributes to the emergence of an observable environment, and perhaps sort them into some sort of evolutionary sequence.

Again, best wishes for success with your theory -- you have a lot going for you.

Conrad

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Author Benjamin F. Dribus replied on Sep. 22, 2012 @ 18:19 GMT

Dear Conrad,

I appreciate the kind remarks. You make several distinct and important points, so let me itemize my reply.

1. Regarding the general theory of observation and its importance, my impression is that one reason why it is often neglected even in new theories is simply because the problem is so difficult, and is in some ways unlike the types of problems that physicists and...

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Dear Conrad,

I appreciate the kind remarks. You make several distinct and important points, so let me itemize my reply.

1. Regarding the general theory of observation and its importance, my impression is that one reason why it is often neglected even in new theories is simply because the problem is so difficult, and is in some ways unlike the types of problems that physicists and mathematicians are used to solving. This remains true in spite of the attention the "quantum measurement problem" has received over the last generation. I am somewhat guilty of this myself; in my "secret papers" I have written down a lot of thoughts about this subject, but haven't felt sufficiently justified or confident to say much about it publicly.

2. I am glad you alerted me to the presence of your essay; I have read a fair number of them, but I am sure there are many good ones that have escaped my notice. I will be sure to read yours carefully. I think I agree with what you said in the paragraph above, but I hope to be able to say more after reading it. Let me repeat that I regard the problem as very difficult, however.

3. One of the aspects of the manifold assumption that bothers me is precisely that it postulates an entity that cannot possibly be observed, even with arbitrarily advanced technology. However, what bothers me even more is the extremely special structure ("too good to be true"), which makes the mathematics convenient at the expense of assuming a number of properties (least upper bound property? nonmeasurable subsets?!?) that seem obviously irrelevant to physics. In my mathematical work, I spend a lot of time studying things like complex manifolds and algebraic schemes, which constantly reminds me how very special, uniform, and "idealistic" such mathematical objects are. I get the impression that many physics students still get the impression that the shifts of paradigm from Euclidean spacetime to Minkowski spacetime to Riemannian manifolds represent vast and perhaps final generalizations of what is possible, when in fact all these constructs are perched on a tiny ledge over a vast gulf of models that might be relevant at much smaller scales.

4. I think that your expectation that the observable world "has to be based on several essentially distinct types of interaction-structure" is perfectly reasonable; indeed, it appears this way at ordinary scales, and the radical position, requiring the greater justification, is to assume otherwise. However, there are hints that a simpler picture might be possible. We seem to observe one arrow of time, not several, and to the extent that the arrow of time can be identified with the direction between cause and effect, it seems reasonable to ascribe causality to a single binary relation. If "essentially distinct types of interaction-structure" correspond to multiple distinct binary relations, then from this point of view you would expect "multiple time dimensions," which seems dubious, at least to me. There are several ways in which this chain of reasoning could be wrong, however.

In any case, I won't remark further on this until I have read your essay! Take care,

Ben

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Conrad Dale Johnson replied on Sep. 30, 2012 @ 16:43 GMT

Hi Ben,

I realize you wrote the above before the exchange we had that's posted with my essay, but I'd like to respond to your last comment.

I agree with your first points exactly -- the issue of observation is inherently very difficult, and also quite different from the types of issues physicists normally deal with. I certainly don't blame physicists for ignoring this issue as...

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Hi Ben,

I realize you wrote the above before the exchange we had that's posted with my essay, but I'd like to respond to your last comment.

I agree with your first points exactly -- the issue of observation is inherently very difficult, and also quite different from the types of issues physicists normally deal with. I certainly don't blame physicists for ignoring this issue as unlikely to be productive, even though QM makes it hard to ignore.

As to your last paragraph -- it's true that we have one "arrow of time", but it may not be as simple as we usually suppose. For example, the "acyclic" aspect of interaction that lets us conceive of time as linear does not yet distinguish a "direction" in time, but I think your causal structure does. So even with your primitive "binary relation" we have at least two levels of structure on a randomly connected interaction-web. And this doesn't yet give any definition of a metric, which I would guess may involve several kinds of structure. And then there's still more structure in the physical "present time" we experience, which involves the availability of "measurement-contexts" that can create new facts, and pass them on to participate in defining new measurement-contexts.

I would guess that the complexity of our interaction-rules is essentially mirrored in the complexity of spacetime structure, each rule contributing something different to making spacetime meaningful and measurable. It's just a holdover from the classical viewpoint that lets us imagine a simple, given spacetime background distinct from what happens in it. But I don't think of this in terms of multiple basic "binary relations" co-existing with each other.

I'd guess the causal-set structure defines very basic topological restrictions on the web of interaction, which provide a structural context in which certain higher-level constraints can define themselves, corresponding to other laws of interaction. Each level selects out part of the graph defined by previous levels, and gives new constraints that makes new selection-rules definable.

Incidentally, in case this conjecture makes any sense to you -- I have in mind your discussion of "covariance". I agree that symmetries in physics aren't fundamental -- I think of them as reflecting this kind of layering of information. Essentially a symmetry indicates a boundary between levels, where one kind of information is already definable but another is not. E.g. you get a circular symmetry if you can define a central point in a plane and the length of a radius, but angles and directions aren't yet definable. (I'm very vague about what the levels actually are, in physics, but given the way QM operates, I would guess that angles are more primitive than lengths.)

Needless to repeat, "there are several ways in which this reasoning could be wrong"!

Thanks -- Conrad

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Author Benjamin F. Dribus replied on Sep. 30, 2012 @ 18:39 GMT

Dear Conrad,

Thanks for the follow-up. In the future, please just go ahead and write a new post on the bottom of my thread. I have no problem remembering our previous conversation, but great difficulty in locating new posts somewhere up in the middle of the thread!

I am interested in your remarks about symmetry in physics. I included my rejection of the symmetry interpretation of covariance in my essay with some reluctance, because even though I believe it is true and important, it has become nearly unquestioned in physics that more and more symmetry must be invoked, and that symmetry is the most basic and important type of unifying principle. Your conjecture sounds very similar to my idea that covariance (and possibly other "symmetries") involves partitioning privileged information from unprivileged information. However, your conjecture sounds more general in two ways: first, "layering" admits the possibility of more than two layers, and second, you seem to be suggesting that perhaps all symmetries should be viewed this way. I don't know if this is true; for instance, the "gauge symmetries" of the standard model may "really" be group symmetries, although perhaps not Lie group symmetries (i.e. continuous symmetries). In any case, I predict that the de-emphasis on group symmetry will be viewed 50 or 100 years from now as one of the most important conceptual advances from this generation of physicists. If you have any further thoughts on the matter, I'd be interested. Take care,

Ben

Dear Benjamin F. Dribus

I have liked your essay and I agree with your abandon of the ordinary concepts of symmetry, conservation laws, covariance, and causality in a spacetime context.

Effectively spacetime is emergent, not fundamental and, therefore, the above assumptions have to be abandoned during the development of a fundamental theory. For instance, the conservation of dynamical...

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Author Benjamin F. Dribus replied on Sep. 23, 2012 @ 00:57 GMT

Dear Juan,

I appreciate the details. Actually, I need more details on this subject, because the Liouvillian approach that you describe is something that largely escaped my notice in my program of physics self-education. Let me ask a few more questions:

1. Where can I read about the derivation of spacetimes in the Louivillian approach?

2. I am not sure what you mean between t-causality and tau-causality. Is it related to what I call the "causal order" and refinements of the causal order given by "frames of reference?"

By the way, I downloaded 5 or 6 papers of yours from viXra, but haven't got a chance to read them yet. Perhaps some of the information is there.

Thanks again, and take care,

Ben

Juan Ramón González Álvarez replied on Sep. 26, 2012 @ 11:02 GMT

Dear Ben,

I will prepare an article on detailed derivation of spacetimes from generalized formulation in Liouville space.

Here t-causality is associated to the approximated Hamiltonians used in general relativity and quantum field theory, whereas tau-causality is associated to the fundamental Hamiltonian. The distinction between "tau" and "t" is mentioned in my essay. A more detailed discussion of both and of the limits of the use of coordinate time "t" is given in the monograph by Pavsic --reference [3] in my essay--. E.g., Pavsic denotes the fundamental Hamiltonian by H and the approximated Hamiltonian used in quantum field theory by H_0.

Regards

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Author Benjamin F. Dribus replied on Sep. 27, 2012 @ 00:35 GMT

Dear Juan,

Thanks for letting me know. I will be sure to look out for that article.

I feel silly for overlooking the distinction between t and tau causality in your essay. My only excuse is that I have read a lot of physics papers in the last few weeks! Of course you mentioned tau as the "fundamental concept of time" in the Liouville space at the very beginning. Many people do not associate time and causality so closely, so I did not put two-and-two together even though I view the two concepts that way myself. Oh well... if one talks or writes for long enough, one is bound to make a fool of oneself eventually!

Thanks again for keeping me in the loop on this. Take care,

Ben

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Dear Benjamin,

I have an idea that I hope can be of some interest to you. Nothing mathematically fancy, I find that the zero spin quantum field can be reconciled from a system with vibrations in space and time. The model has some unique features that seem to be extendable to gravity and non-locality of quantum theory.

Is there really no reality in quantum theory

Best wishes for you in the contest.

Hou Yau

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Author Benjamin F. Dribus replied on Sep. 23, 2012 @ 01:06 GMT

Dear Hou,

Thanks for pointing out your essay to me. As it happens, I had already seen from reading the abstract that your essay was interesting and had it highlighted to read more carefully. I will post some remarks about it over on your thread in a day or two when I have looked at it in detail. Take care,

Ben

Dear Ben,

i now read your essay and it is indeed interesting. You begin with very clear and well-ordered introductions to the whole problem fields of modern physics and you clearly write what are rejected assumptions for you and what you consider as working hypothesis. I enjoyed reading your essay, albeit not understanding every line of reasoning you made during your elaboration.

I...

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Dear Ben,

i now read your essay and it is indeed interesting. You begin with very clear and well-ordered introductions to the whole problem fields of modern physics and you clearly write what are rejected assumptions for you and what you consider as working hypothesis. I enjoyed reading your essay, albeit not understanding every line of reasoning you made during your elaboration.

I found it intelligent to explicitely write about some phenomenons in the way that the community "interprets" them as "...". This clears up a lot and makes the whole argumentation of yours very easy to follow.

As i understood it at this point of my reading, your approach is in some way a reinterpretation - surely with the important! fact of abandoning some "fundamental" principles and adding! some interesting new ones - of large parts of the common deduction sheme that is incorporated into classcial physical thinking.

In some way you "play" - in combination with thoughtfull reasoning - with the building blocks of the classical physical framework and this is exactly what seems interesting and creative to me.

Nonetheless, in my opinion, wether we interpret some building blocks as "universes", as "virtual Feynman paths" or something other, it seems to me that the ontological meaning of the whole building blocks stays somewhat ambigious for the reader. Therefore i would prefer to explicitely state that the very foundation of your framework is in its essence a logical (mathematical) and therefore "non-physical thing". For me i understood it as an informational theoretic approach that is at its core deterministic in the same sense the Everett worlds are. Moreover, at the end of your essay you outline the difficulty to decide/test the hypothesis, - please don't get me wrong - your approach deserves further examination, surely more examination than my own approach/interpretaion does. I write this to be intellectually honest and because i know the problem of reinterpreting the commonly used framework and at the same time give some reasonable proof of the exclusiveness of such a reinterpretation.

All in all, i wish you good luck with your work and because you gave me some inspiring new points to think about, i thank you having visited my page and left a commment.

All the best,

Stefan

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Author Benjamin F. Dribus replied on Sep. 23, 2012 @ 11:29 GMT

Dear Stefan,

I appreciate your kind remarks! Regarding your impression of my approach as largely involving reinterpretation, I would prefer to think of it in the way you describe than to think of it in terms of simply throwing out all that we've learned over the last 500 years and starting over. There are often many steps separating original physical ideas from the formal theories eventually used to describe them, and I think that a lot of the great scientists of previous eras had many physical ideas more or less perfectly correct without necessarily having the tools necessary to make them precise.

Regarding the mathematical nature of my approach, through my many discussions here I have come to realize that to some extent I have failed to communicate what I view as the proper perspective on the relationship between the physical and mathematical ideas involved. As a mathematician trying to do physics, my goal is to not allow mathematics to be a limiting factor in the expression and description of physical ideas. In other words, I have tried not to be influenced by the mathematical convenience of particular models, but rather by which models I feel express the physical ideas in the purest way and with the least baggage. One possible result of abandoning mathematical convenience is, of course, that the mathematics can become very difficult and can lead into mathematical fields and topics that most people, including myself, have never heard of before. For this reason, the whole approach can create the false impression of focusing too much on the mathematics itself. The intention, however, is just the opposite: to begin with the simplest of physical ideas (such as cause and effect) and then simply bring to bear whatever mathematical machinery is necessary to adequately describe the resulting theory. Take care,

Ben

Dear Ben,

You have gone through my paper extentsively. Thanks. Pls give me some time to go through yours once again and make my comments.

I will have to respond to your comments part by part, since the posts cannot be too long. In this post I will take up your comment about “Lorentz invariance”.

You wrote: “5. I agree that Lorentz invariance as Einstein conceived it is...

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Author Benjamin F. Dribus replied on Sep. 24, 2012 @ 00:10 GMT

Dear Viraj,

Thanks for reposting this here. Since this part of the discussion is about your work, I will post any further remarks about it over on your thread. Take care,

Ben

Hello Ben,

I thank you for the gracious comments you left on my essay forum page. I'll answer your queries shortly. Your points are well taken and very much appreciated. Unfortunately; I've been sidelined with unexpected responsibilities, but I do hope to get to read your essay soon and respond to your comments sooner. However I am still catching up elsewhere, so it may be a little bit.

All the best,

Jonathan

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Author Benjamin F. Dribus replied on Sep. 25, 2012 @ 15:07 GMT

Jonathan,

Thanks. I would be grateful your feedback, both on my questions and on my own work. However, I do see that you have a few messages piled up on your thread, so I won't be impatient! Take care,

Ben

Hi Ben and thanks for a very interesting essay.

I realise I share your view of the universe in some key aspects of your hypothesis and must read it once more to give you some useful comments on it. Here is a first:

"...the metric properties of classical spacetime, up to overall scale, arise from a binary relation, which I will call a causal relation, on a set..."

Well formulated !

The problem I have in accepting it is not that it contradicts observations, but the mind-nuking number of "binary relations" involved. Intuition tells me this cannot be right and that there has to be a simpler model, but then again, I do not trust intuition very strongly in these matters.

If you have an hour of lesure time, I think you would enjoy this youtube-video:

http://www.youtube.com/watch?v=YfYon2WdR40

PS.

M
y first impression of you, extrapolated from your written posts on several essays, was that you were 60+ years old. But since you present yourself as a Ph.D student, I suspect that is not the case.

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Author Benjamin F. Dribus replied on Sep. 25, 2012 @ 15:05 GMT

Dear Andreas,

Haha... well, actually I'm 32, which I admit is a bit long in the tooth for a graduate student, but I've had a rather interesting and non-traditional journey to this point.

Thanks for the feedback and the video suggestion...I will be sure to take a look!

Regarding the number of relations, one must make a distinction between "binary relation," of which there is...

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Dear Andreas,

Haha... well, actually I'm 32, which I admit is a bit long in the tooth for a graduate student, but I've had a rather interesting and non-traditional journey to this point.

Thanks for the feedback and the video suggestion...I will be sure to take a look!

Regarding the number of relations, one must make a distinction between "binary relation," of which there is precisely one for each classical alternative in my approach (and a single higher-level binary relation for the entire quantum picture), and "relation between elements," which refers to a particular ordered pair of elements which are "related" by the binary relation.

I'm not sure what could be simpler than cause and effect as a basic building block for physical interactions. Of course, there are going to be a huge number of cause-and-effect relationships, but this will be true in practically any model you can think of, whether that model takes causality to be fundamental or not. In particular, if the universe is infinite, its hard to imagine how there could not be an infinite number of causal relationships.

If you mean that the number of "classical universes," each with its own binary relation, is large, then yes, there is an infinite number of such binary relations, representing the infinite number of possible histories. I call these "classical universes" not in the sense of "THE Universe," but in the sense that each is self-contained as a classical causal network. Then entire ensemble of these possible classical histories is a way of talking about THE Universe in my view.

Again, on the subject of simplicity, I believe that the sum-over-histories view is by far the most conceptually simple view of quantum theory. Without it, you have to take for granted mathematical objects like Hilbert spaces and operator algebras. Of course, many people would still like to believe that quantum theory is somehow wrong, and that a single deterministic picture underlies everything. While I can understand and sympathize with this view, my own opinion is that quantum theory really does play a fundamental role,and that trying to do without it raises much worse problems, particularly in the philosophy of science.

Anyway, thanks again for the feedback! Take care,

Ben

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Dear Ben

Thanks so much for your comments on my submission discussing Riemann’s concept of density. I believe everything in your submission, up to its last sentence on “energy density,” reflects rigorously much of what I discuss at a different level. And it does so a hundred times better.

I’ve also often wished that Einstein had met Riemann. Einstein and Planck borrowed a...

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Juan Miguel Marín replied on Sep. 26, 2012 @ 01:19 GMT

…From my European Journal of Physics article perhaps you could guess that I would find exciting any research concerning your “universal Schrodinger equation.” Keep it up!

“Mathematical tools necessary to implement these ideas include a synthesis of multicategory theory and categorization in abstract algebra, involving interchangeability of objects, morphisms, elements, and...

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…From my European Journal of Physics article perhaps you could guess that I would find exciting any research concerning your “universal Schrodinger equation.” Keep it up!

“Mathematical tools necessary to implement these ideas include a synthesis of multicategory theory and categorization in abstract algebra, involving interchangeability of objects, morphisms, elements, and relations.” The seeds of those tools are in Gauss Disquisitiones Arithmeticae and Riemann’s “Natural Philosophy.” I believe Grothendieck’s use of category theory re-discovered a few ideas already present in Gauss, and even more, Riemann.

“For example, zeta functions, and hence the Riemann hypothesis, are connected to

quantum field theory via noncommutative geometry and the theory of motives “ You’ve read the book “Zeta and Modular Physics (2010)”? Maybe the link to relativity is there. I would link their discussion to Riemann’s approach to Dirichlet.

Thanks for the reference to Connes. I’ve only read his earlier work on Riemann’s hypothesis. If you ever want to win a million dollars you should try to prove Riemann’s hypothesis. You could apply your ideas to Connes’ proof and/or your paper’s “complex Hilbert spaces whose elements represent probability amplitudes of point particles, self-adjoint operators whose eigenvalues are interpreted as the possible values of measurements, and time evolution according to the Schrodinger equation.” I would approach the Hilbert-Polya conjecture through Heisenberg/ Von Neumann’s “mathematical causation” and Von Neumann/Wigner’s “observational algebra.”

Riemann wrote down he proved “Riemann’s hypothesis” and only needed to “simplify the expression.” But from my paper you know what he meant by “expression.” Still, if you pay close attention to what Riemann thought about his hypothesis, i.e. pay attention to the historical-foundational context, you could come up with the proof. You certainly have the required talent.

Hope at least some of this helps. I’ll give it more thought and send you comments that are not half-baked. I look forward to read more of your work. Best, Juan.

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Author Benjamin F. Dribus replied on Sep. 26, 2012 @ 19:48 GMT

Dear Juan,

I appreciate the kind remarks. I'm beginning to feel as if it is difficult to be a competent physicist or mathematician without being a rather avid historian! Your comments are particularly valuable to me because you evidently possess a rare grasp of historical context in regard to foundational issues. The phrase "before his time" is overused, but it undoubtedly applies to...

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Dear Juan,

I appreciate the kind remarks. I'm beginning to feel as if it is difficult to be a competent physicist or mathematician without being a rather avid historian! Your comments are particularly valuable to me because you evidently possess a rare grasp of historical context in regard to foundational issues. The phrase "before his time" is overused, but it undoubtedly applies to Riemann. In many cases, the most fertile period for an idea seems to occur shortly after its inception, before certain arbitrary choices have hardened into orthodoxy, and if the community is unready to use an idea at the time it is introduced, it may be many years before it is fully exploited. I believe this has occurred with many of the ideas of Gauss and Riemann, and I'm only dimly becoming aware that the potential seeds of new advances may be lying dormant not in the last few generations, but a hundred years earlier!

I will certainly read your European Journal of Physics article with interest. For myself, I have several volumes of unpublished work on foundational topics in physics, but this is my first small effort to make any of it public. I prefer Gauss's philosophy of "few, but ripe" to the current creed of "publish or perish." Also, I am coming from the mathematical side, and don't yet feel comfortable with my grasp of what is already known.

I was unaware of the close connection between Cantor and Riemann, but Cantorian ideas do arise unavoidably in the approach I have been working on. I even named an important counterexample the "Cantor graph." The axiom of choice and the continuum hypothesis also become significant.

I will have to look at the early notions of causality you mention. One thing I have learned from reading Grothendieck is the importance of properly organizing local and global data, and in regard to causality, this has led me to define things somewhat differently from the usual notions. In particular, "interpolative" properties like "interval finiteness" and transitivity play less of a role than legitimately local properties.

Thanks again for the helpful comments! Take care,

Ben

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Great Article. I will reread again -

Regarding the ending, quoted as follows:

"Finally, the dimension of space as well as its curvature might vary

with \energy density," though the effect might be immeasurably small"

This appears consistent with CIG: www.CIGTheory.com in that the volume of Space (i.e. dimension of Space) is tied to energy density / / / Full curvature = black hole; no curvature = vacuum energy/Dark Energy; partial curvature = Dark Matter, and each is all %"c" dependent

THX

doug (comments still welcome)

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Author Benjamin F. Dribus replied on Sep. 26, 2012 @ 20:00 GMT

Dear Doug,

I'll take a look! Thanks for the comment. Take care,

Ben

Hello Ben,

Thank you again for your comments on my essay, which to me are among the most valued of all the comments I've had.

I saw your recent point about objects ageing, in relation to the point I made about the residual effects of time dilation. The emphasis in my essay is simply to set out the clues we have, and draw broad conclusions from them, rather than going into detailed...

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Hello Ben,

Thank you again for your comments on my essay, which to me are among the most valued of all the comments I've had.

I saw your recent point about objects ageing, in relation to the point I made about the residual effects of time dilation. The emphasis in my essay is simply to set out the clues we have, and draw broad conclusions from them, rather than going into detailed attempts to interpret them. Because I think it's possible to arrive at a conclusion that way, and to reject block time via simple deduction, it seemed a good way of keeping the essay simple. But of course these questions can be examined in far more detail, and from there it's a case of choosing between two or three initial avenues.

I've read your essay today, will read it again, I found it excellent in a number of ways. The overview of the whole landscape of physics you give in the first half is important and very useful, particularly at a time when things are getting a bit fragmented. It not only helps that you've summed up the landscape as a whole, but - like myself and not too many others - you've included comments on the mindset of the physics community over the 20th century, which helps with understanding about attitudes, and how and why the general view has shifted over time.

In relation to the second half of your essay, what I'll say now is simply a personal opinion, not a criticism of your particular view. And I tend to agree on the assumptions you reject. But I suspect that the way forward, when we find it, rather than involving shuffling the underlying principles and making some go from fundamental to emergent, while others go from emergent to fundamental - which several essays here do, though none better than yours - will instead involve finding some truly new concepts. However, it may be that rearranging the bits of the puzzle we have will also be needed, and I do see that you bring in new principles, and that you may recover established physics from them. So it's certainly too early to tell, and I very much wish you luck with it, and with your essay.

Best wishes, Jonathan

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Author Benjamin F. Dribus replied on Sep. 26, 2012 @ 20:10 GMT

Dear Jonathan,

Thanks for the feedback! I understand that your essay doesn't represent the whole of your thinking about fundamental physics, and I agree that the ideas you consider are sufficient for the point you are making. Conciseness and clarity are particularly important in the present context.

Nevertheless, I am interested to know what your ideas about the fundamental structure of spacetime are. You say that you "suspect that the way forward, when we find it... will instead involve finding some truly new concepts." Do you have any favorite conjectures for what those "new concepts" might be? Take care,

Ben

Hello Ben,

well thanks for asking - it's more a book that's needed to answer that. I saw you mention somewere the other things that you 'ought to be doing' at the moment, well I have the same... I would be putting the finishing touches to my book if I wasn't on this site, the publisher is expecting it - but am enjoying the discussion here and learning a lot from hearing other people's views. In the book I compare and explore some different avenues, and different kinds of answers to these questions, and try to use rational thinking to estimate what kind of answer is the most likely. It seems to me that I narrow down the possibilities well, but I'll wait to see what others say. I'd very much value your opinion when it's out, will let you know.

Your contribution here has been enormous, I find your posts in many places, helping to pull people's thoughts together, and helping to focus the general attempts to crack these puzzles. Thanks again, and good luck to you.

Best wishes, Jonathan

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Author Benjamin F. Dribus replied on Sep. 27, 2012 @ 00:22 GMT

Jonathan,

Thanks. Be sure to let me know about your book. My email address is on my essay. Take care,

Ben

Dear Ben,

Your comments all over the place have been a joy to read. I particularly admire your habit of asking 4 to 6 detailed and relevant questions on each essay, and am most impressed with the mental power and will power that drives your output.

In most cases I find myself in agreement with you, and certainly when you state:

"...in any case, the physical ideas ought to come...

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Author Benjamin F. Dribus replied on Sep. 27, 2012 @ 00:20 GMT

Dear Edwin,

Thanks for the kind remarks. You are, I believe, even more prolific than I am on these threads, and you always maintain a high standard of reason, civility, and circumspection.

I hope I'm not too far down the path of causal binary relations to reconsider things! I'm 32 years old, and have been working on this idea for about 2 1/2 years. As I've mentioned before, most...

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Dear Edwin,

Thanks for the kind remarks. You are, I believe, even more prolific than I am on these threads, and you always maintain a high standard of reason, civility, and circumspection.

I hope I'm not too far down the path of causal binary relations to reconsider things! I'm 32 years old, and have been working on this idea for about 2 1/2 years. As I've mentioned before, most of my mathematical work involves manifolds, varieties, schemes, and objects of that nature, so I am quite friendly with them in general. In addition, a lot of what I have read here has taught me features of manifold physics that I simply did not know. I have read about a lot of things, but my education in physics is not standard. I never had the usual graduate curriculum. Hence, there are bound to be gaps in my knowledge that most professional physicists don't suffer from, and the only way to fill them is to keep an open mind.

I have your ideas filed away for further consideration, partly because I tend to suspect that you will be willing to continue to engage in conversation after the contest is over. I suspect that a number of authors will check out after the next few weeks, so I have been trying to gather information while everyone is still engaged.

The action principle you mention does interest me. Besides your arguments, the specifically "pro-manifold" contributions that have made the biggest impression on me are those by Torsten and Jerzy involving exotic smoothness structures, those by the shape dynamics folks (Sean, Flavio, Julian, Daniel), the essay by Abhijnan Rej, and a few others. The questions I asked these people were serious, and the answers were quite convincing in some respects. There is no reason to limit oneself to working on a single idea.

In any case, I appreciate your remarks and will always welcome any sincere effort to challenge my point of view. Learning which of my opinions are mistaken as quickly as possible saves a world of trouble! Take care,

Ben

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Edwin Eugene Klingman replied on Sep. 27, 2012 @ 00:39 GMT

Dear Ben,

Thanks for pointing out the other 'pro-manifold' authors. I have not read most of them yet.

And of course I'll be happy to communicate with you after the contest ends and things settle down.

Best wishes,

Edwin Eugene Klingman

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Dear Benjamin F. Dribus

Your opinions is very specific and specifically impression.

You might consider and make suggestions for "a draft for proposal of T.O.E " of me in this topic (topic/1417- out side of my essay)

Kind Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Author Benjamin F. Dribus replied on Sep. 27, 2012 @ 13:04 GMT

Dear Hoang,

I would not presume to propose a "Theory of Everything;" my belief is that all such attempts will look a bit silly a thousand years from now. Even if we succeed in developing a theory that seems to explain all natural phenomena of which we are currently aware, there is nothing to prevent us from making new discoveries in the future. Don't you think a "Theory of Everything" would be a bit depressing? What would be left to do?

However, I will take a look at your essay! Take care,

Ben

Hoang cao Hai replied on Oct. 6, 2012 @ 00:45 GMT

Dear Benjamin F. Dribus

It is the work that we must do.It is inevitable.

With all the confidence that has found it, I found that: still a lot of hard work we must do.

It simply means: we no longer have to "groping" more.

Many thank.

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Dear Benjamin,

Your CMH opens a lot of new perceptions and universes. I liked it very much. You also mention : "The initial family evolves to the terminal family", so in your view every universe was in facto initial and becomes terminal, also the conglomeration of universes that forms our "reality".

In "THE CONSCIOUSNESS CONNECTION" I go back to the initiality and limit our universe by the Planck length and time. So "reality" emerges from our consciousness, that is why I appreciate your "thought experiment".

I also saw that Eric verlinde had your attention, his perception of gravity is also in accordance with my idea that only materialistic reductionism is not the only way to research our questions about existence.

I hope that you will read my attribution in the contest, especially your opinion about my "causality" perception.

best regards

Wilhelmus

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Author Benjamin F. Dribus replied on Sep. 27, 2012 @ 16:38 GMT

Dear Wilhelmus,

Thanks for the kind remarks. I have seen some interesting comments of yours on other threads, but so far missed reading your submission, probably because you are near the bottom of the alphabetical list! In any case, I will be sure to take a look. I do think that consciousness is a very difficult topic and one that I would not have attempted myself, though I have thought about it a fair bit. I'll be interested to see what you have to say. Take care,

Ben

Ben,

Thank you for stopping by. I am very interested in reading your works. I will be writing to you later today.

James Dunn

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Author Benjamin F. Dribus replied on Sep. 28, 2012 @ 17:18 GMT

Dear James,

Thanks. I got your email, and sent you some questions back. I also posted again on your thread. Take care,

Ben

Ben,

Thank you for the nice comments over on my essay. I responded over there. While your essay is way over my head in terms of math, the points you made that I think (?) I understood were very good! A few comments are below, but take them with a grain of salt because, as I said, it was kind of over my head. Anyways, they are:

1. I think your way of thinking as illustrated...

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Author Benjamin F. Dribus replied on Sep. 28, 2012 @ 17:49 GMT

Dear Roger,

Thanks for the kind remarks. I took a look at your website, but unfortunately only the top of the page would load; I don't know if this is a site issue or a browser issue.

In any case, even if some of the mathematical content was a bit unfamiliar, it seems that you understand quite well what I am trying to do conceptually. In particular, I'm trying to give a precise description of something very like what you mentioned in your point 5, with the clarification that I think each "element" generally has multiple "parents." In particular, by "causal relation," I mean almost exactly what you said.

One difference we might have is that I think dimension (like "space" and "time" themselves) is just a "way of talking about what actually happens." For instance, in three-dimensional space you can "go in six different directions," forward, backward, up, down, left, right. If you turn this around and start with a bunch of events that are related to each other in this way (each having "six neighbors" in an obvious sense), then you would get a "three-dimensional network." This is all a very rough and imprecise way of describing things, but hopefully gives the right picture. I think that the dimensionality of the universe is telling us something about how interconnected the structure is at the fundamental scale: how many "direct neighbors" each "fundamental element" has, and how they are arranged. All this ignores the quantum-theoretic version, of course.

Anyway, thanks again for the feedback! Take care,

Ben

Roger Granet replied on Sep. 29, 2012 @ 04:20 GMT

Ben,

Hi. For my website, maybe try:

https://sites.google.com/site/ralphthewebsite/

and then click on the third link which is called " Why do Things Exist and Why is there something rather than nothing?" The section related to my point 5 was the last one before the conclusion; although, it helps to read the whole thing.

On the dimension thing, I would just say that for "events" or "structure is at the fundamental level" or geons or causal sets or anything to physically exist, which I think they have to if the universe is to be made of them, then I personally have trouble imagining how they could physically exist without having 3 dimensions. If one of the three is actually zero, then does this really exist in the non-mind, physical universe?

Anyways, no need to reply on this since it's good to have some differences in opinion (we don't want no groupthink!) and I know it kind of takes some time! Good luck at school and in the contest!

Roger

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Hi Ben,

Thank you for your kind comment on my essay. As you say, it's good to see alternatives explored, and a fresh view of causal set-type structure is welcome.

Best wishes and good luck,

Peter Morgan.

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Author Benjamin F. Dribus replied on Sep. 28, 2012 @ 18:16 GMT

Dear Peter,

Thanks. I left another remark on your thread... I imagine you will see that remark before this one. Take care,

Ben

Ben,

The best thing about these contests is they give an opportunity to brain storm on a range of possibilities. The questions concerning physical foundations, particularly with respect to cosmology and quantum gravity, require different ways of thinking. I sometimes think that our educations have a disservice. While of course a graduate student needs to know classical and quantum...

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John Merryman replied on Sep. 28, 2012 @ 17:53 GMT

Lawrence,

Not to butt in here and while we have discussed this before, I usually avoid getting in the conceptual ring with you, but;

You make the two observations that prior knowledge can blind our thinking and that physics treats time as an interval.

That goes to my repeated observation that by treating time as a measure, physics only re-enforces the effect of sequence, rather than considering the cause of change, that is action. That it is not the present moving from one frame to the next, but action replacing configurations of the same material. Not the earth traveling a fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates.

Duration doesn't transcend the present, but is the state of the present between observations, so there is no physical extension, only action.

If time were simply a dimension consisting of those intervals, wouldn't a faster clock rate move into the future more quickly, yet the opposite is true, as it ages/burns quicker, it moves into the past faster. Witness the twin in the faster frame has died, when her twin in the slower frame returns.

I feel like a frog on the road when I make this point, but while it only seems to be ignored, no one bothers to refute it.

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Author Benjamin F. Dribus replied on Sep. 28, 2012 @ 18:55 GMT

Lawrence,

Thanks for gathering these ideas here at the bottom of my thread. I have been saving the pieces of this particular conversation for more careful consideration after I have finished reading everyone's ideas.

In regard to the potential disservice of formal education, I have a generally low opinion of many aspects of the educational system myself, so this is probably not a good topic for me to get started on! One thing I can't resist adding, however, is that there is a great deal of pressure to specialize and little or no incentive to learn or care about what anyone else thinks. I cannot count the number of times I have gotten the answer "that's not what we do" in reply to a question about using a certain mathematical theory or technique in a novel way.

Coming from outside physics proper, I'm not sure if I'm more crippled by ignorance of certain "standard material" that most physics graduate students probably know, or advantaged by being largely oblivious to any sense of commitment to any established school of thought I knew about before I started thinking about these things myself.

Maybe the information age is a partial antidote to the problems you cite, since information about technical subjects is available without the necessity of dependence on an individual or institution, along with the pressure to conform that such dependence often entails, despite the best of intentions. Of course, this information is generally a few years delayed, but major foundational problems often take much longer than this to solve anyway. In any case, I'm sure more than a few people have wasted their talents because they were "too nice" to reject the avenues suggested to them by others. Hopefully the wide availability of information will increasingly permit intellectual independence without the necessity to be antisocial! Take care,

Ben

Author Benjamin F. Dribus replied on Sep. 28, 2012 @ 19:09 GMT

John,

I will have to read your essay to better understand what you are proposing. You seem to reject the existence of an independent time dimension, which is also one of the assumptions I reject in my essay. In particular, you seem to reject the idea of block time. Jonathan Kerr has written an interesting essay on this that you may enjoy reading.

The general idea of time being a way of describing actual change sounds like Mach's view; I don't know if you encountered this idea by reading about Mach, or if you thought of it independently. I would like to think of time as a way of talking about cause and effect, which is similar but not identical. In any case, I will have more to say after I have read your essay. Take care,

Ben

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Ben & John,

When it comes to time, I have no particular objective concerning its ontology. I find the idea that one want to can remove time and then say that objects in motion move through space with a velocity which we interpret as time as just another way of defining time. I find there is a sort of epistemological “dog chasing its tail” issue going on here. Space and time may...

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John Merryman replied on Sep. 29, 2012 @ 03:17 GMT

Lawrence,

I'm thinking of your observations about tmi(too much information), as I'm reading this. Part might be distraction and part might be that the information is so dense as to be impenetrable by anyone not intensely versed in it to begin with.

While I certainly agree we are drowning in oceans of information, I see there are lessons to be learned there as well. Think in terms...

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Lawrence,

I'm thinking of your observations about tmi(too much information), as I'm reading this. Part might be distraction and part might be that the information is so dense as to be impenetrable by anyone not intensely versed in it to begin with.

While I certainly agree we are drowning in oceans of information, I see there are lessons to be learned there as well. Think in terms of how you process information as sequence, yet what you are getting is masses. What principles apply to mass? Temperature, weight, velocity, pressure, magnetism, etc. Now how would your instinctive, non-linear right brain process these masses of information? Are they stable, ie. does it seem like the parts don't fit together, etc. Is it something attractive or repulsive to you? Does it have weight, ie, gravitas, or too much gravitas? Think of financial bubbles in terms of waves and how when lots of them line up, you get a very large one. Consider how energy manifests information and information defines energy and how our bodies have distinct systems to process both, with the central nervous system dealing with information and the digestive, respiratory and circulatory systems processing energy. The hemispheres of the brain are thermostat and clock.

See, this is why I both like physics so much and am so frustrated by physicists. The opportunities to explore and examine all aspects of reality are there, but physics is way off in the extremes of the very small, very large and very obscure, not to mention off on a number of wild goose chases. As well as insisting static models can really describe dynamic processes.

We also loose sight of temperature when we try to measure it to arbitrary accuracy. If time is an effect of action, there can be no dimensionless point in time, as that would mean no action and thus no time. Like a temperature of absolute zero.

I think it is a mistake to lump space and time together. When we measure time, we are measuring change, as caused by action, but when we measure space, be it distance, area, or volume, we are measuring space. While I agree space is occupied by fields of energy, no matter how weak, I still don't think it should be define entirely in terms of what occupies it. Consider that centrifugal force is the relation of spin to inertia, not some outside reference to the spinning object. Being aphysical, space cannot be bound, bent, accelerated, etc. Only what occupies it can be so defined. If there is no "fabric of spacetime," then possibly space is the real frame, so that C is determined by the rate at which all nuclear energy is converted to velocity, due to moving through that inertial space, with clock rates slowing as the velocity increases.

As for gravity, this is very simplistic, but if releasing energy from mass creates pressure, wouldn't energy condensing into mass create a vacuum? That way, it wouldn't be a force, but an effect. Gravity waves would be the energy released by fusion. Sunlight. They can't find any dark matter, but if gravity is not simply a property of mass, but an effect of energy condensing into mass, then the excesses of cosmic rays in galaxies and lots of interstellar gases might hold the clue. Could the conditions in parts of the galaxy make this transition from one to the other possible? It's not like we can run experiments outside the heliosphere.

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Dear Benjamin,

Thank you for reading my essay and giving good opinion. It is beneficial to me that one Ph. D. student gives good opinion about my essay. It is also a favor that someone reads it precisely and comments, this is what our amateur theories lack. So it is well to obtain any opinion, still better if it is professional or skilled one. It gives new ideas.

I hope that we will further exchange some physical opinions, also after this contests.

Because I cannot read all essays until Friday, can you recommend the best ones by your opinion.

I will read your essay tomorrow. I will give comment below of your essay.

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Author Benjamin F. Dribus replied on Sep. 30, 2012 @ 19:16 GMT

Dear Janko,

Thanks. I will look forward to seeing your comments. I emailed you again as well. Take care,

Ben

Janko Kokosar replied on Oct. 1, 2012 @ 20:08 GMT

Dear Benjamin,

I am going through your essay, but I have not yet finished. (It is interesting that there is no one formula in the body of essay, but it is very demanding mathematically. :) )

It is interesting that you "reject the symmetry interpretation of covariance", You reject "space time is a manifold", and you have similar ideas. Can you, please, attach your ideas with my...

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Dear Benjamin,

I am going through your essay, but I have not yet finished. (It is interesting that there is no one formula in the body of essay, but it is very demanding mathematically. :) )

It is interesting that you "reject the symmetry interpretation of covariance", You reject "space time is a manifold", and you have similar ideas. Can you, please, attach your ideas with my interpretation of special relativity, that space-time does not exist in empty space, although space-time of Minkowski means space-time coordinates in empty or non-empty space? I need still some time to understand your ideas, so I please you for help.

You wrote that matter-antimatter asymmetry might indicate a problem with QFT. It is an interesting idea, and it is linked with the last paragraph in this post.

It is interesting that such basic idea, as that of Weizsacker one why three dimensions exist, was not presented to me in University. I suppose that others also mainly have not hear this in University courses. I ask why they hide such interesting idea.

You asked, why my theory is against Higgs boson. I defined that Black holes exist whose are superpositions of Planck's mass and mass zero. They are not against uncertainty principle (UP), I suppose. Their mass can be equal or smaller than masses of elementary particles. (So they can be elementary particles) So their masses are defined, so they need creation of mass by Higgs boson. If CERN will show that 125 GeV particle creates masses of particles, my theory will be rejected, probably. Besides, if my superposition is against UP, my theory will also be rejected. But, who know. (But my rejected theory will be more successful that superstrings, which cannot be tested. :) )

You said "proof is lacking antimatter interacts in the same way as ordinary matter gravitationally". It seems to me, that you are wrong. Feynman wrote about this in, it seems to me, in "QED: the strange theory of light and matter".

Other my important idea in the essay is that wave functions are less fundamental than UP. Thus, in curved space, UP is changed, but definition of wave functions is also changed. And this fact has consequences as I wrote. This Idea is not forbidden by Higgs boson. (I regret that I had not enough time to study Higgs mechanism.)

Best regards

Janko Kokosar

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Author Benjamin F. Dribus replied on Oct. 2, 2012 @ 05:45 GMT

Dear Janko,

Thanks for the comments. Regarding your interpretation of special relativity, I agree with your conclusion that "spacetime" does not exist in the absence of "matter-energy," and my approach says the same thing, but in my approach this is a direct consequence of a hypothesis about what "spacetime" and "matter-energy" really are at the fundamental scale (the causal-metric...

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Dear Janko,

Thanks for the comments. Regarding your interpretation of special relativity, I agree with your conclusion that "spacetime" does not exist in the absence of "matter-energy," and my approach says the same thing, but in my approach this is a direct consequence of a hypothesis about what "spacetime" and "matter-energy" really are at the fundamental scale (the causal-metric hypothesis), not deduced from an argument on the basis of an existing theory (such as your argument involving the trolley and the rocket in special relativity). Arguments like yours are encouraging for such a hypothesis because they reach downward from existing theory toward a more fundamental theory, while my ideas are trying to reach upward to recover existing theory in some approximation.

The strong form of the causal metric hypothesis treats what we call "spacetime" and "matter-energy" as manifestations of causal structure. Neither has an independent meaning at the fundamental scale; they emerge together. Other "causal theories" (such as causal set theory and causal dynamical triangulations) sometimes impose "matter fields" on causal structure, essentially by adding "weights" to the edges or vertices of a causal graph (the weights might be numbers or various types of mathematical objects such as spinors or elements of SU(2)). There might be some use in trying this, but I would prefer to try to use only the graph-theoretic structure.

This might seem to contain too little information to describe things like particles in the standard model, but I think there might be enough information present after all. Metric recovery theorems show that causal structure can give a metric up to a conformal factor, and this can be supplied by appropriate volume information, which can also be associated with the causal graph by an appropriate rule (Sorkin uses the simplest possible rule: a constant discrete metric in his "order plus number equals geometry" motto in causal set theory).

Many of the properties of the particles of standard model come from the representation theory of the Poincare group of symmetries of Minkowski spacetime, so already there is enough information in causal graphs to recover these properties. But there is more information: not only are other metrics recoverable as well, but the microstructure contains local information which has not yet been used. Also, the causal graphs I use are more general than causal sets; for instance, a given causal set corresponds to an entire equivalence class of "degenerate" non-transitive causal graphs, each of which specify information that is lost when taking the transitive closure.

At the most naive intuitive level, the reason why no spacetime exists in the absence of energy is because energy involves causal relations; i.e., "things are happening" in an energetic system. As the energy goes to zero, all interactions (relations) cease; there is no causal structure because "nothing is being caused." Hence, there is no emergent geometry and no spacetime.

Bear in mind, though, that all this is based on the hypothesis that spacetime is only a way of talking about causal structure. If this hypothesis is wrong (e.g. if there is a "background manifold") then this whole idea falls through. Take care,

Ben

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Author Benjamin F. Dribus replied on Oct. 2, 2012 @ 05:52 GMT

Dear Janko,

By the way, regarding the gravitational behavior of antimatter, a lot of money is currently being spent to test this experimentally. Here is one of many popular news articles; the paper itself is behind a pay wall.

If this has already been proven, then a lot of people should be fired for wasting money!

By the way, I would personally be shocked if antimatter had antigravitational properties, but some people still hold out hope that "gravitational segregation" may account for local absence of antimatter. In any case, I think it should be conclusively tested. Take care,

Ben

Janko Kokosar replied on Oct. 2, 2012 @ 12:29 GMT

Dear Benjamin

I see that we both intuitively believe that space-time is background free. You also understand my conclusion about my derivation of special relativity, a referee only wrote that Minkowski spacetime is so defined that time flows also in empty space. :) He also claimed many time repeated words that "derivation with relativistic mass does not give anything new". (I admit that this version needs some corrections about Duff's claims.) I hope that someone will generalize my derivation into general relativity, that influence of diffeomorphism will be easier explained.

I agree with Machian rule, which is in one version advocated by Barbour. I think that causal relations are based on Machian rule. If we said that spin of universe is zero, then Newton's bucket do not contradict with Mach. Do you agree?

You write that you hope that your theory will give SR and GR at large scales. It seems to me that such theories need be so clear, that we will see this without long calculations. But, who knows. Thus, for instance, I more like Weizsacker explanation of 3D than with triangulation of Loll. Maybe the theory still needs clarification about foundations, and then quantum graphity will be easier.

I you can see I avoided causal metrics to give masses to Planckian black holes, but it will be necessary some day.

Probably we disagree about consciousness. It seems to me that the money which enables Higgs boson, will enable also physical explanation of consciousness. Then we will see, how it is important for physics.

Those are some my disagreements, but because of your right intuition (I hope) and because of your big mathematical knowledge I give you 10.

Best regards Janko Kokosar

p.s.

I wrote the wrong book of Feynman. Feynman has a Lecture book on gravity available. Here I found his explanation why gravity of anti-particles is not negative. I do not remember it precisely, but it is worth to read it.

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Author Benjamin F. Dribus replied on Oct. 2, 2012 @ 15:03 GMT

Dear Janko,

Thanks for the feedback. I will see if I can find what Feynman said about this... I always appreciate his point of view.

Regarding Machian ideas and shape dynamics, a number of us (me, Lawrence Crowell, Sean Gryb, Flavio Mercati, Daniel Alves) have been discussing the possibility of a duality or complementarity between causal theory and shape dynamics. Shape dynamics derives an arrow of time essentially from an asymmetry in configuration space, whereas I take it to be fundamental, but these two ideas need not necessarily contradict each other. Part of that discussion is on my thread, and part of it is scattered about on the other threads.

Regarding the recovery of relativity, many the ideas specific to relativity (as opposed to Newtonian mechanics) are clear in causal theory; in fact, causal theory is more a generalization of relativity than anything else, since it is in relativity that the primacy of the causal structure and the ideal of background independence are clearly embodied. The technical difficulty comes in recovering manifold structure, and the point of view is that this is really unnecessary to all the important physical ideas of relativity. This will take work, because these ideas are currently expressed in geometric language. If Riemann had been around to advise Einstein rather than Minkowski and his friends, he might have showed him that there are many possible formalisms for expressing his physical ideas that don't involve continuum manifolds.

I don't know enough about consciousness to agree or disagree with anyone about it, though I think it can't be deterministic. I like to read about it, though! Also, I appreciate the rating! Take care,

Ben

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Ben,

I thought I would repost this response to your observations :

I wouldn't describe time and sequence as purely mathematical, but as features of action. If I may use an example, it would be that time is frequency and temperature is amplitude. While one wave/cycle/step doesn't cause the next in the series, it does lead to it from the perspective of the dynamic manifesting the...

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Ben,

I thought I would repost this response to your observations :

I wouldn't describe time and sequence as purely mathematical, but as features of action. If I may use an example, it would be that time is frequency and temperature is amplitude. While one wave/cycle/step doesn't cause the next in the series, it does lead to it from the perspective of the dynamic manifesting the series. Cause is wholistic and the sum total cause of any event cannot be known prior to the event, because the lightcone(to use a spacetime concept) of input isn't complete until the event occurs. A bolt of lightening or bus might hit you before you make that next step and the energy manifesting you would be disrupted from its progression. It is just that we exist as a particular point of reference/one molecule of water in that tea kettle and so encounter a series of events within the larger dynamic.

As for entropy, it seems everyone always ignores that it only applies to a closed system. In an open or infinite system, energy lost by one system is gained by others. We are absorbing light that was radiated by other galaxies billions of lightyears away. It is only because the universe is presumed to be finite that it gains such prominence. Yet even in that model, this energy is simply being dispersed over an expanding area, not eliminated. I think the larger reality is a form of universal convection cycle of expanding energy and contracting mass. These galaxies drawing in mass and radiating energy, until that energy condenses back into mass and falls back into the closest galaxy.

You are quite right that "energy" defies clear definition, but think about that; Definition is structure and order and energy is constantly manifesting and dissolving structure and order. It's hard to put something in a box, when even the box is an aspect of what you want to put in it. Think of energy as what is physically real, whether radiant, potential, spin, attraction, repulsion, inertial. Even the absence of energy is a form of energy, in the vacuum. Energy manifests, information defines. Information arises from the interaction of different forms and degrees of energy. Such as that mass is a balance of positive and negative energies. We try to measure reality by banging energies into each other. Whether it is light from distant stars onto our telescopes, or ions in a particle collider. Or even cavemen banging one rock into another to see how it breaks/flakes.

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Author Benjamin F. Dribus replied on Sep. 30, 2012 @ 18:49 GMT

John,

Thanks for the followup. I posted a few more remarks about this over on your thread. Take care,

Ben

Dear Ben,

I read your essay. Your field being mathematics, as I expected, your remedy is also mathematical.In your comment about my essay, you mentioned about mathematical convenience. I agree. But convenience is more related to practical work than theory. Mathematical convenience may lead to (has already led to many) technology. The foundational question is more of theoretical nature, the question what matter actually is.

Let us suppose a lump of matter (whatever it may be) devoid of any motion. It will remain the same even after billions of years. So it is motion that causes changes. Motion is a space- time relation that can be mathematically stated, and any change can be mathematically interpreted. That is the role of mathematics.The cause- effect explanations based on mathematics need not necceesarily help us understand what that lump we call matter is. For that we require some physical assumptions about matter.

I have some assumptions about matter, and I think that it agrees with all observations, though it disagrres with the existing cause- effect explanations. However, there may be loop holes in that. So what I suggest is that the main stream scientists propose some physical assumptions about matter and verify whether these agrees with all the recorded observations.

Your suggestions regarding new mathematical approach and new experiments may sometimes lead to new technologies. The experiments can provide proof to the theory. But before that, you have to decide what physical assumption regarding matter is to be proved.

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Author Benjamin F. Dribus replied on Oct. 1, 2012 @ 13:07 GMT

Dear Jose,

Thanks for the remarks. I agree that reducing physics to mathematical concepts is not necessarily very satisfying; the question of what makes the real world "real," rather than another of the myriad mathematical possibilities, has plagued scientists and philosophers for as long as there have been scientists and philosophers.

However, I don't think that causality is a mathematical concept. Nothing causes two plus two to equal four, it just does. While you can describe a network of cause-and-effect relationships mathematically, there is nothing intrinsic to the resulting mathematical structure that identifies it as cause and effect; this is a physical interpretation.

The point I was trying to make about "mathematical convenience" is that it can lead you to get the wrong answer. Choosing to describe physics in terms of mathematical objects whose theory is well-developed and easy to work with shifts the focus from what the physical universe really is like to what we wish it were like for the purpose of calculating things.

I agree that ideas leading to technology don't necessarily lead to illumination. However, one could hope for both! Take care,

Ben

Benjamin,

Like Julian Barbour, you create theories in which the "old" concepts cannot be found at all. This is a winning strategy in contests like this one but detrimental for science.

Earlier you wrote: "Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales. (...) You'll have to remember that my background is mostly mathematical, and therefore I'm inclined to consider the possibility of things that most physicists "know" are wrong. This might be useful in some cases; in others it only reflects my own ignorance."

Pentcho Valev

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Author Benjamin F. Dribus replied on Oct. 2, 2012 @ 07:30 GMT

Dear Pentcho,

Thanks for the feedback. Causality is a rather "old" concept, at least according to Aristotle. In any case, to paraphrase an "old" proverb, "mathematics is a good servant but a bad master." Regarding the "bad master" part of this phrase, you might have noticed that I've repeatedly expressed the opinion that physical theories should not substitute convenient or "elegant" mathematical constructs (such as manifolds over the continuum) for clear, motivating physical principles. Hence, my own ideas are based on the simplest physical principles you can imagine: order, cause, and effect. However, regarding the "good servant" part, one cannot afford to do without the mathematical tools necessary to implement these simple principles. The physics comes first; the mathematics must be whatever is required to get the job done. Nature demands no less. Take care,

Ben

Pentcho Valev replied on Oct. 2, 2012 @ 13:40 GMT

Any theory dealing with (or rejecting) spacetime should be able to provide an EXPLICIT DERIVATION of the constancy/inconstancy of the speed of light, or at least advance either the constancy or the inconstancy as an assumption and then derive conclusions from it. I am afraid your confession:

"Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales. (...) You'll have to remember that my background is mostly mathematical, and therefore I'm inclined to consider the possibility of things that most physicists "know" are wrong. This might be useful in some cases; in others it only reflects my own ignorance."

...shows that your approach is incommensurable with the speed of light problem. So is Julian Barbour's Shape Dynamics.

Pentcho Valev

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Author Benjamin F. Dribus replied on Oct. 2, 2012 @ 14:51 GMT

Dear Pentcho,

Well, you will have to give me time (no pun intended). I have never represented the ideas I discuss in my essay as a complete "theory." The causal-metric hypothesis is just that, a hypothesis, and the ideas so far I term an "approach." A physical theory must eventually make predictions and connect with known physics, or it is not worth the paper it is written on. However, this takes time. I have been thinking about this for three years. Your criticism might be perfectly valid if 1000 people had been thinking about it for 30.

You seem delighted with my admission of possible ignorance, so I have given you an even better quote above: "A physical theory must eventually make predictions and connect with known physics, or it is not worth the paper it is written on." Feel free to repost it as many times as you wish. No one knows very much about physics compared to what there is to know.

The problem we were asked to address was "which of our basic physical assumptions are wrong?" It was not, "analyze the implications of the Michelson-Morley experiment." I will opt to interpret your interest in the foundations of relativity in a positive light, as a reflection of your zeal for the integrity of natural philosophy. But please bear in mind that it is counterproductive for everyone to be forced to work on the same problem. Cause and effect is more fundamental than the speed of light, or any speed for that matter, yet I don't insist that you make any definitive statement about causality. Feel free to work on any problem you wish, and please suffer me to do the same. Take care,

Ben

After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.

Cood luck.

Sergey Fedosin

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Author Benjamin F. Dribus replied on Oct. 2, 2012 @ 15:06 GMT

Dear Sergey,

250 is quite impressive; I have not managed to understand that many so far. At this rate, you will have read every entry in the contest within another week or so. I appreciate the rating. Take care,

Ben

Benjamin,

If "The central new principle I propose is the causal metric hypothesis, which states that the metric properties of classical spacetime, up to overall scale, arise from a binary relation, which I will call a causal relation, on a set, which I will call a universe... Mathematical tools necessary to implement these ideas include a synthesis of multicategory theory and categorification in abstract algebra, involving interchangeability of objects, morphisms, elements, and relations; a version of graph 11 dynamics more sophisticated than versions involving uniform probabilities;and the theory of noncommutative algebras over sets with partially defined operations"

Then your attempt to introduce Some sort of Set-theoretical /Category-theoretical Evolution of Minkowsky spacetime Without Complex Numbers can faced with unavoidable necessary of destruction of some advanced areas of established mathematics and quantum physics... I know you understand it, but pure mathematical doubts on Minkowsky-Einstein complex( number) theory of time can suggest more elegant way to prove some your intuitions...?

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Author Benjamin F. Dribus replied on Oct. 2, 2012 @ 15:25 GMT

Dear Michael,

Thanks for the feedback! The complex numbers are undoubtedly the workhorse of much of modern physics, and avoiding them, if it's even possible to do so, will certainly require a great deal of work to achieve the same explanatory power, let alone surpass it. You might ask, "why, then, abstain from the complex numbers at all, if they are so useful?" The important word here is "useful." Many of the properties that characterize the real number continuum, and by extension the complex numbers, are mathematically "useful" without having any clear physical meaning. Even if there were not physical reasons to doubt that spacetime is infinitely divisible (of which there are many), properties like the least upper bound property of the real numbers would never be directly relevant to physics. Even worse, paradoxes like the Banach-Tarski paradox (you can pull apart a solid sphere into nonmeasurable sets and reassemble them into two spheres identical to the original sphere) show that the real and complex numbers have properties that are not only physically irrelevant, but also physically absurd.

But I am not sure if this answers your question? (I suspect it doesn't!) In any case, I see that you have an essay here about an interesting subject, so I will read what you wrote before making any further remarks. Take care,

Ben

Author Benjamin F. Dribus replied on Oct. 2, 2012 @ 19:17 GMT

Dear Michael,

I realize after reading your essay that my answer to you above was mostly irrelevant. Hence, I have left some additional remarks on your thread. Take care,

Ben

Benjamin,

Since you want Minkowski spacetime to emerge from your "causal relations", you will have to assume, additionally, constancy of the speed of light:

John Norton: "That the speed of light is a constant is one of the most important facts about space and time in special relativity. That fact gets expressed geometrically in spacetime geometry through the existence of light cones, or, as it is sometimes said, the "light cone structure" of spacetime. (...) So if we mean a spacetime that also behaves the way special relativity demands, then we have a Minkowski spacetime."

Then it may turn out that your "causal relations" are superfluous - Minkowski spacetime emerges from the assumption that the speed of light is constant and that's it.

Pentcho Valev

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Author Benjamin F. Dribus replied on Oct. 2, 2012 @ 18:46 GMT

Dear Pentcho,

I have heard of a certain company that offers to name distant celestial objects after its clients in exchange for a fee. Calling the causal relations of the universe "mine" would be an even more absurd presumption of ownership.

I'm afraid that suggesting that causal relations are superfluous because spacetime is a large-scale manifestation of them is like suggesting that the pixels on your screen are superfluous because they form a picture. Try doing without them!

Regarding the constancy of the speed of light, "speed" means "change in distance per unit time." Distance and time are both metric concepts. When one begins with something other than a metric, "speed" must be viewed as a secondary, rather than a primary, concept. No assumption must be made about it whatsoever. Take care,

Ben

Pentcho Valev replied on Oct. 3, 2012 @ 08:52 GMT

Benjamin,

I thought your theory was deductive. That is, "causal relations" can be formulated as an assumption (analogous to Einstein's 1905 assumptions) from which (and possibly from other assumptions) you are going to deduce conclusions, Minkowski spacetime in particular. Now I see I was wrong: there is no deductive theory.

The following wisdom of yours is breathtaking:

"Regarding the constancy of the speed of light, "speed" means "change in distance per unit time." Distance and time are both metric concepts. When one begins with something other than a metric, "speed" must be viewed as a secondary, rather than a primary, concept. No assumption must be made about it whatsoever."

Pentcho Valev

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Anonymous replied on Oct. 3, 2012 @ 12:54 GMT

Dear Pentcho,

You were right the first time. I do assume the causal relations to be fundamental. Minkowski space is not "deduced," but recognized as a large-scale approximation. No assumption is made (or needed) about the speed of light because it is not a fundamental concept. Take care,

Ben

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Pentcho Valev replied on Oct. 3, 2012 @ 15:47 GMT

Then don't mislead the reader by saying in the essay that you will "recover" established physics from your new principles:

"Recovery of established physics at appropriate scales from these principles is a challenging problem due to their parsimony, with the standard model likely more dicult to recover than general relativity. (...) Emergence of Minkowski spacetime is the first step toward the standard model as well as toward relativity..."

At least in my understanding this means that you first state your new principles and then physics, Minkowski spacetime in particular, somehow emerges from them. This is tantamount to deduction. If it is not, you will have to justify your original (euphemism) theoretical approach.

Pentcho Valev

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Author Benjamin F. Dribus replied on Oct. 3, 2012 @ 16:25 GMT

Dear Pentcho,

I appreciate that you are spending so much time trying to understand my essay, and I am sorry if you are struggling with aspects of it. You must keep in mind that we only had 12 pages in which to explain our ideas. "Emergence" in physics is not tantamount to deduction. Recovery of established physics means that whatever existing theory describes or explains must also be described or explained by new theory. It does not mean that every detail of every mathematical model appearing in the original theory must appear in the new theory. If this were so, the new theory could not improve on mistaken aspects of the old theory. Take care,

Ben

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Dear Benjamin,

I found your essay to be one of the most all-encompassing in the contest. The paper paints a fairly complete picture of the current state of things and yet it is not lacking in details. It surely merits the high rating it has received.

One comment I can pick out that especially triggered a response is:

"Causality is often formalized at the classical level as...

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Dear Benjamin,

I found your essay to be one of the most all-encompassing in the contest. The paper paints a fairly complete picture of the current state of things and yet it is not lacking in details. It surely merits the high rating it has received.

One comment I can pick out that especially triggered a response is:

"Causality is often formalized at the classical level as an irreflexive, acyclic, transitive binary relation on the set of spacetime events."

I agree. Though the approach I wrote about is classical or semi-classical, and therefore embedded solely in U(1) topology, the rigorous consideration of rotations really requires formulation in SU(2) or higher topologies because of the difference in rotational characteristics of the electric and magnetic fields, path dependencies and the cyclic nature of waves. Then the algebra accommodates reflections and cyclic relations. And there the non-commutative nature of the algebra naturally leads to quantization.

It's hard to picture just what you mean when you make this intriguing statement:

"I will call the relation induced by these transitions the universal relation, and each of its subrelations a kinematic scheme. Under suitable assumptions, a pleasing fractal picture emerges, in which kinematic schemes share most of their abstract properties with the causal relations of their constituent universes, and quantization becomes an iteration of structure, at least locally"

Perhaps that is related to the point made in the essay at note 1. The statement conjured up reflections on an interesting but perplexing book "Fourier Analysis on Finite Groups and Applications" by Audrey Terras. I've not yet fully fathomed its nuances but the author demonstrates how Fourier Analysis and associated sets can be used in a surprisingly general series of applications where the domain can be interpreted as having some type of cyclic basis. She doesn't mention Quantum Mechanics, as I recall, but maybe there is a natural fit there.

Congratulations on a fine essay,

Steve

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Author Benjamin F. Dribus replied on Oct. 3, 2012 @ 05:26 GMT

Dear Steve,

Thanks for the kind remarks. I will have to find a copy of the book you mentioned. Regarding my two-sentence statement that you quote above (regarding kinematic schemes), this is based on some hundreds of pages of unpublished papers, and hence is an amusingly short abbreviation. Conceptually, it boils down to a precise statement of the point Robert Spekkens makes in his essay, that kinematics and dynamics in causal theory cannot be separated.

At any rate, you can see now why your discussion of Lorentz invariance interested me! Take care,

Ben

Dear Ben,

Earlier today I made a short comment (hard for you to to find) related to your conversation with Daniel Burnstein. Forget about it. What I wanted to say was that I'm hopefully beginning to begin to grasp your very interesting ideas. As you already know, I'm neither a physicist nor a mathematician. But re-reading your essay today, and following the above conversation, has been most instructive. It also gave me an idea, which I will come back to later, after more reading and thinking. I very much look forward to follow this conversation further. I have so much to learn!

Best regards,

Inger

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Author Benjamin F. Dribus replied on Oct. 3, 2012 @ 05:17 GMT

Dear Inger,

Thanks for the kind remarks. I found your essay interesting too, and have read it more than once. Don't forget to pass that idea along when it is ready! My email address is on my essay. Take care,

Ben

Inger Stjernqvist replied on Oct. 3, 2012 @ 21:16 GMT

Dear Ben,

I have been so busy not understanding your causal metric hypothesis that I have forgot to tell you about my growing understanding of your essay. The first four sections are very well structured and have all the more emerged as chrystal clear. I just needed some re-reading. My troubles arrive when entering section 5. But today I started to once again follow the above conversation, to see what I can get out of it. At present I understand too little to be able to ask you any meaningful questions. Hopefully that will come, because it is part of my idea. I will tell you about it by e-mail.

Best regards!

Inger

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Hi Benjamin,

I think I made an interesting discovery. Check out my post of 9/19/12. Let me know what you think!

Regards,

Steve

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Author Benjamin F. Dribus replied on Oct. 3, 2012 @ 05:12 GMT

Dear Steve,

Thanks for bringing this to my attention. I had checked your thread a couple of times after I posted there originally, but there are so many to look at that I missed seeing this. I don't know if you saw the discussion about antimatter antigravitation in my thread above or my brief mention of the possibility in my essay, but this is something I find very interesting. Take care,

Ben

Hello Ben,

I finally responded to your comments on my forum page. I have also started reading your essay, which looks very interesting so far. I shall try to finish up quickly and have a few proper comments once I am done. I noted Lawrence's comments about the Fermi and Integral experiments above, and I think that addressing that data is going to be a crucial step for showing the viability of your theory.

Causal structures can be problematic, in terms of Lorentz invariance. CDT may have been ruled out by Fermi and Integral and I had thought it was quite promising. Most of what you see for that subject in Wikipedia was written by me, largely unchanged though now in need of an update. I had interesting discussions about this topic with Gerard 't Hooft at FFP10 and with some Loop Quantum Gravity people at FFP11.

I commented on my essay page that - concerning the summing over paths approach - you may want to learn about Hamiltonian Phase Space Path Integrals. The conventional Lagrangian PIs treat particles as things, in effect, or deal with them kinematically. Re-casting the problem in the Hamiltonian form focuses instead on the dynamics and allows for the uncertainty to be factored in up front, but reduces calculations to a simpler functional integral later on.

See the attached paper.

Regards,

Jonathan

attachments: 0912.0006v2.pdf

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Anonymous replied on Oct. 3, 2012 @ 12:56 GMT

Dear Jonathan,

Thanks for the feedback! You raise some excellent points that give me an excuse to talk about certain technical issues that might otherwise have been considered overkill. I must hurry to go teach my class, but will get back to you later today. Thanks also for the paper. Take care,

Ben

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Dear Benjamin,

I tried to read your essay but despite my interest in what you had to say by the time I got to new principles, the really interesting part, it was no longer at all comprehensible to me. I recognise it as English but not much more than that. That is not meant in an unkind way but an honest reflection of my personal experience. You seem to be doing very well in the ratings so perhaps it is only a reflection of my own intellectual shortcoming. You also appear to have had a lot of feedback on your essay, so you are obviously doing something right. Kind regards Georgina : )

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Anonymous replied on Oct. 3, 2012 @ 13:04 GMT

Dear Georgina,

Thanks for the message. The last two sections were a little compressed because of the length requirement, and I could only state short versions of my ideas in a rather formal way without much explanation. That part represents several hundred pages of my own work. You certainly should not feel any personal shortcoming from not understanding the details, because by itself that part raises more questions than it answers. Since the topic of the essay contest was which existing assumptions are wrong, I didn't feel justified in spending more than a few pages at the end introducing new theory. Anyway, thanks for persevering through it! Take care,

Ben

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Hello again Ben,

I have a lot of thoughts to share about causal structure, though I have not finished my first read-through of your essay yet. So I figured I should cross post a comment I left on Robert Spekkens' forum, regarding how we look at kinematics and dynamics. To wit..

The notion that kinematic states and dynamic evolution are separable seems to carry over from the subject-object distinction in English and other European languages.

It is a peculiar left-brain dominated preoccupation, which necessitates measures like Korzybski's "the word is not the thing." In Chinese, by contrast; one cannot describe a thing apart from its process, and even the individual strokes in a character tell the story of how that pictogram evolved.

So this gives you one more thing to reflect on. I'm just returning the favor, since you gave me a lot to think about - in terms of thoughtful questions about my essay content. I have been very busy, this past week or so, but I shall be interested and available to engage on this subject matter as long as there is something worth talking about.

All the Best,

Jonathan

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Dear Ben,

You've got my highest note!

I hope you keep the first place and win the contest, 'cause you deserve it!

Good luck.

Gene Alexandrescu

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Author Benjamin F. Dribus replied on Oct. 4, 2012 @ 06:37 GMT

Dear Eugeniu,

Thanks! I don't expect to win... particularly after the ratings chaos yesterday morning, but I appreciate the vote of confidence. Take care,

Ben

Eugeniu Alexandrescu replied on Oct. 6, 2012 @ 04:39 GMT

Dear Ben,

See? I told you and I'm glad you did it!

Congratulations!!!!!

Gene

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Author Benjamin F. Dribus replied on Oct. 6, 2012 @ 05:32 GMT

Dear Gene,

Thanks, I'm quite amazed and humbled by the current results. I don't think any official announcement has been made, so I won't take it for granted that these are the final standings for this round, but in any case the degree of hospitality and positive feedback has been very heartening. Thanks again, and take care,

Ben

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Hello yet again, Ben and everyone;

I'm following my muse, by sharing a few more thoughts before reading further, as they respond to comments you left on my essay forum and Ian's. First, yes; Twistors are way cool, because they address the objection of Grothendieck, that geometric points omit too much essential information. In twistor theory, rays are more fundamental than points, which I...

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Hello yet again, Ben and everyone;

I'm following my muse, by sharing a few more thoughts before reading further, as they respond to comments you left on my essay forum and Ian's. First, yes; Twistors are way cool, because they address the objection of Grothendieck, that geometric points omit too much essential information. In twistor theory, rays are more fundamental than points, which I believe are a special case. This strongly suggests a causal element, and incorporates the idea of forward motion in time, revealing that the fabric of spacetime is emergent. As I understand it; the paper by Witten - after his meeting of the minds with Penrose - showed connections with String Theory, but mainly proved the concept and paved the way for others. Work by Nima Arkani Hamed and Freddy Cachazo involving twistors and S-matrix theory has been especially productive.

But my intuition is that the emergence of spacetime and structure proceeds most simply or elegantly from the octonions, as I mentioned in my essay. One paper by Connes emphatically states "Noncommutative measure spaces evolve with time," but I came to believe that as the Planck scale is approached, geometry becomes non-associative as well - so we must examine the implications of this to have a full understanding of dynamism at the smallest spatial scales and at the universe's time of origin. We know that the octonions are the most general number type, where the quaternions, complex numbers, and reals are a subset thereof. If we assume, as suggested by my departed friend and colleague Ray Munroe, that the imaginary dimensions in octonionic space are at the outset space-like, and the real dimension is time-like - some things fall into place nicely IMO.

If we interpret the imaginary components of octonions as the freedom to vary by a specified amount, it is natural to consider those dimensions as space-like extents. But making the observation (ontological?) that structures must have a duration in time in order to exist; the last sentence of the preceding paragraph can be seen as a kind of procedural formula. In octonionic space, things can evolve through seven dimensions in sequential relation - as possible directions afforded by a specific range of play - but the next step is always time-like, and this creates specificity or definiteness. Briefly stated; non-associativity makes the octonions not only evolutionary (a la Connes' comments about NCG) but also procedural. Multiplying or dividing with octonions is sort of like putting together or taking apart a watch - where you have sub assemblies that must fit together in a specific way.

Intriguingly; I've been working on a universal theory of measurement or determination, and some of the behaviors noted above appear to be emergent. For example; the postulates of projective geometry have a connection or can be a generator...

More later,

Jonathan

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Author Benjamin F. Dribus replied on Oct. 3, 2012 @ 21:16 GMT

Dear Jonathan,

I'm grateful that you have chosen to post this on my thread! Feel free to post thoughts here at any time.

Your observations raise many important points. As soon as I can, I will get back to you about Fermi/Integral, CDT, causal sets, the missing conformal factor, constant discrete measures, configuration space versus phase space, the Lagrangian as an infinitesimal path functional, path summation over general directed structures, relation and morphism functions as abstract Lagrangians, the generality of (twisted) multiplicativity for phase maps (owing to a cohomological vanishing theorem for noncommutative algebras over sets with partially defined operations), special algebras in quantum information theory, nonassociativity in general relativity...

But my students are killing me at the moment! Hope to continue this discussion/synthesis soon...

Take care,

Ben

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is

$R_1$

and

$N_1$

was the quantity of people which gave you ratings. Then you have

$S_1=R_1 N_1$

of points. After it anyone give you

$dS$

of points so you have

$S_2=S_1+ dS$

of points and

$N_2=N_1+1$

is the common quantity of the people which gave you ratings. At the same time you will have

$S_2=R_2 N_2$

of points. From here, if you want to be R2 > R1 there must be:

$S_2/ N_2>S_1/ N_1$

or

$(S_1+ dS) / (N_1+1) >S_1/ N_1$

or

$dS >S_1/ N_1 =R_1$

In other words if you want to increase rating of anyone you must give him more points

$dS$

then the participant`s rating

$R_1$

was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Dear Benjamin,

I have read your essay with great interest (even if I am not sure if I fully understand your causal metric hypothesis idea). I think you might like to read something that was once intended to be my diploma thesis (in a quiet longer and more complicated version). : About the length of world lines … (my essay)

My abstract could be like this:

There is a way to test if the metric (based on the notion of distance, given by the Minkowski norm) tying space and time to space-time really exists.

By using an assumption that is (WLOG) weaker then the assumption that has been used to derive Minkowski norm, we can see that reversed triangle inequality (one of the three conditions that have to be met for space and time to be a four-dimensional metric space) is violated. Thus space and time can not be seen as a four-dimensional metric space.

I would be happy to hear what you think about it.

Kind regards,

Frank

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Author Benjamin F. Dribus replied on Oct. 4, 2012 @ 19:38 GMT

Dear Frank,

This looks very interesting. Thanks for pointing it out. I'll try to look it over in detail today or tomorrow and post some remarks on your thread. Take care,

Ben

Dear Ben,

I'm glad to have finally read your essay. Frankly, I'm most impressed that your clear and insightful discussion of established theories in the context of their "explanatory and predictive power." There are a few of observations I'd like to discuss more fully. Unfortunately I've never been a student of physics or mathematics - although I have isolated and corrected critical...

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James T. Dwyer replied on Oct. 5, 2012 @ 10:12 GMT

Dear Ben,

Quantum Gravity?

Their of course does seem to be a distinct differentiation in the dynamics of interactions at quantum scales. As you discuss in your essay, foundational theories are evaluated by their explanatory and predictive success. While many think that general relativity's primary advantages over classical gravitation is its predictive accuracy and it's ability to...

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Author Benjamin F. Dribus replied on Oct. 5, 2012 @ 16:55 GMT

Dear Jim,

Thanks for the kind remarks and the extra references. There's much more to discuss here... but I'm currently in the lab on a lousy connection. I forget if you have an email address on your paper... if not, do you mind sending me an email at bdribus@math.lsu.edu so I have your address for future contact? Thanks, and take care,

Ben

Ben,

Although I didn't manage to come up with any insightful questions about your essay, I have to say your participation in this contest has been invaluable.

You have an incredibly keen mathematical sensibility, combined with the rare ability to frame and ask concise, direct questions. I would often read your questions and the author's replies in other essays posted here *before* reading the actual essays. Since the essays here ranged across so many fields of expertise, your questions often helped to provide a middle ground for understanding.

Between your essay and Wharton's, whose Lagrangian perspective really threw me for a loop, I have considerable subject matter to catch up on.

I look forward to watching as your career unfolds.

Dean

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Author Benjamin F. Dribus replied on Oct. 5, 2012 @ 17:06 GMT

Dear Dean,

I appreciate the kind remarks. I have learned a great deal over the last couple of months and have thoroughly enjoyed the experience. I hope that thinking over everything I've read will give me some useful new perspectives. It's wonderful to be able to access such a broad cross section of scientific thought! Take care,

Ben

Dear all,

Everyone has noticed the ratings volatility over the last few days. Obviously one would rather focus purely on the science, but I know everyone is on edge about this. There has been some discussion on the forum (topic 1263) about this today. I repost here two general posts I made over there this morning. Take care,

Ben

Dear all,

Something I've noticed, in...

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Dear all,

Everyone has noticed the ratings volatility over the last few days. Obviously one would rather focus purely on the science, but I know everyone is on edge about this. There has been some discussion on the forum (topic 1263) about this today. I repost here two general posts I made over there this morning. Take care,

Ben

Dear all,

Something I've noticed, in addition to the recent volatility, is that the mean community score seems to be distressingly low. Every time I rate an essay below the top 100 it seems to jump 20-30 places, and I have not given many 10's, though I've given a lot of 6's and 7's. I am glad to hear that the recent ratings chaos is due to a glitch rather than deliberate manipulation, but I do wish more people would follow the contest guidelines that request a "supportive atmosphere of scientific conversation rather than a judgmental atmosphere of critical scoring and evaluation."

Most people have put a lot of sincere effort into their work, and it threatens the whole nature of the contest if a large percentage of the contributors are playing "gotcha," either with comments or with ratings. Participation isn't a right, and we'd all be nowhere if FQXi and the sponsors took their ball and went home. It's amazing how some folks behave when afforded anonymity. Anyway, I'm probably preaching to the choir here, because most of the recent comments are by people who have made a major constructive and encouraging contribution on many threads. Take care,

Ben Dribus

***

Dear all,

By the way, on an amusing note, I have watched my pathetic "public rating" of 4.9 accumulate and hence know that it consists of something like four 10's, a 9, 7, 6, 3, 2, and six 1's (this may not be exact, but it is close). Most of the 1's have been accompanied by a drop in community rating, so this implies certain participants have been childishly bombing others with low community ratings, logging out, and then giving a public rating of "1" as well. If you look at the public ratings overall, most of them are awful except for those with a very large number of ratings, likely from friends. I suppose this is just human nature, but it augurs badly for our ability to ever escape this planet without blowing ourselves up. Take care,

Ben

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Hi Ben,

D-Wave Systems just got a huge cash injection from the CIA (In-Q-Tel) and Jeff Bezos. That and the previous Lockheed-Martin injection makes the industry all but giant. So, just for fun maybe you could apply to these funding sources (or to D-Wave itself) to see if you can get help with your work on quantum computing. You never know. They might like it.

- Shawn

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Author Benjamin F. Dribus replied on Oct. 5, 2012 @ 17:39 GMT

Dear Shawn,

Thanks for bringing this to my attention. The only difficulty is that would probably prove to have seven thumbs in regard to experimental work; my lab time/expertise is quite limited, which probably doesn't surprise you, seeing my bio! I would need to have some competent experimentalists on board. Take care,

Ben

S Halayka replied on Oct. 18, 2012 @ 15:17 GMT

Hi Ben,

Looks like I spoke just a bit too soon: The FQXI grant program was announced, as I'm sure you've heard. Surprise! :)

- Shawn

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MAX PLANK:

An important scientific innovation rarely makes its way by gradually winning over and converting its opponents; it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning.

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Author Benjamin F. Dribus replied on Oct. 7, 2012 @ 01:06 GMT

Dear Jin,

Unfortunately, this seems to be true more generally, not only in science. The fact that each new generation tends to repeat the whole process over again shows that to know history is not the same as to learn from it! Take care,

Ben

Ben,

Congratulations !!!!!

Edwin Eugene Klingman

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Author Benjamin F. Dribus replied on Oct. 6, 2012 @ 05:37 GMT

Dear Edwin,

Thanks for the message, and more generally for your cordial and constructive approach to the whole contest! The numbers have moved around a bit since they were first posted, so I won't take it for granted that these are the final standings for this round, but I'm nonetheless quite humbled by the hospitality and positive feedback I've found here. Take care,

Ben

Dear Sir:

Sergey G Fedosin is bombing entrants' boards with the same "why your rating has dropped" message. They are all dated Oct. 4... same message.

WTH? I've seen one fine essay drop 89 (eighty-nine) positions, in "Community Rating" in the past 24 hours, and “Sergey’s note” came BEFORE it plummeted. Hmm.

The vote/scaling of this contest is quite nebulous.

"Hackers Rule!", I suppose!

Well??? What else is one to think? The General Public is... Watching…

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Author Benjamin F. Dribus replied on Oct. 7, 2012 @ 00:42 GMT

Dear Concerned,

I noticed at least three different major shake-ups in the ratings, the first one around 11 AM EDT Wednesday, when most of the essays at the top (including mine, which was #1 at the time) fell around 15 places and were replaced at the top by entries from as far down the list as 30 or lower.

Sergey Fedosin's message came after this, and I can't see any reason why someone intent on manipulating the vote would choose to draw attention to himself. When I first saw the message, before even seeing who had sent it, I interpreted "why your rating dropped" as some childish person gloating over down-voting my essay, but after reading it I realized that he was just trying to explain his displeasure with the voting procedure, and that the way in which the message was expressed was merely a reflection of the fact that English is not his first language.

As you pointed out, more grotesque changes in the rankings continued after this. I noticed yesterday that essays I knew I had already rated displayed the "do you want to rate this essay?" message at the top. A number of submissions went unrated by me at the end because I did not want to risk double-voting. I am sure others felt the same way, and this itself affected the process.

It would be too great a demand on human nature to expect those near the cutoff who were left out in the end not to feel cheated, particularly if they appeared above the cutoff when the clock ran out. In my opinion, there were many more than 35 deserving essays, including two or three in particular that did not make the final round, yet will likely prove to contain some of the most important ideas of any in the contest. Take care,

Ben

James Putnam replied on Oct. 7, 2012 @ 01:13 GMT

Ben,

I have read several complaints and analyses about the voting system since this morning. I think that the others could have been anticipated both from the rules and the wide range of expertise allowed. Perhaps not all of it for first timers. This is the fourth year and those kinds of effects on the ratings are known and need to be learned. I accept them because if things were tightened up I might not be permitted to participate. My lowly finish this year was consistent with my finishes in each of the previous three years. Personally I don't think that it reflects the value of my work. But it does reflect how these contests rate my work. So be it. However, This one that you mention concerns me:

" I noticed yesterday that essays I knew I had already rated displayed the "do you want to rate this essay?" message at the top. A number of submissions went unrated by me at the end because I did not want to risk double-voting. I am sure others felt the same way, and this itself affected the process."

It shows that the system did not work as could have been expected. I care very much that the results be correct however they turn out. Your words tell me that it didn't happen that way this time, and, I think that nothing can be done to make it right. I think it has to be accepted knowing that the administrators will have it in mind for future contests. I am confident that high quality essays will be selected by the juding system as has been the case in the past contests.

James

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Author Benjamin F. Dribus replied on Oct. 7, 2012 @ 02:58 GMT

Dear James,

Thanks for the thoughts. I certainly don't wish to level blame at anyone, I just feel a bit sick for those who saw their submissions drop out of the top 35 after the clock ran out. I believe that the administrators tried to do the best they could under the circumstances, and I agree that doing anything further now would probably just open another can of worms. Something I do wonder about is how many additional authors actually saw their entries fall below the cutoff sometime after midnight. If it were only three or four, I would wish that these could be added to the list. But I know that in this case, anyone currently ranked above one of these would feel cheated. Anyway, this is my first year of participation, and I'm sure no one needs or wants my advice on the subject! Take care,

Ben

Well done Ben, you deserve it. Not just for the essay, but also for pulling the discussions together and focussing people's thinking.

As 'Concerned public' says above, some essays have shot down - mine dropped from 31 on thursday, after 2 weeks in the top 35, to somewhere I can't count to! I don't know why, but whatever. It was a very good forum, and I think most of us have learned a lot from the exchange of ideas.

Good luck in the finals....

Best wishes, Jonathan

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Author Benjamin F. Dribus replied on Oct. 7, 2012 @ 01:01 GMT

Dear Jonathan,

It's a little hard to understand. Whenever I wanted to look at your thread over the last few weeks, I clicked on the "community rating" link because you were up near the top. I lost track of this when the chaos started on Wednesday (my essay fell from #1 to #13 in a few minutes, having been in the top five for much of the last two weeks). It's true, as Brendan pointed out, that one would expect heavy voting in the last few days, but it still would have taken multiple very low ratings to push you down so far.

Anyway, I appreciate your kind words. We have had some good (and I trust mutually enlightening!) discussion, and I hope we can stay in touch. I don't see an email address on your paper, but mine is bdribus@math.lsu.edu. Take care,

Ben

Jonathan Kerr replied on Oct. 7, 2012 @ 09:01 GMT

Thanks Ben,

Well it may be that the positions up to the last 24 hours are more indicative, but that's all in the margin in some ways anyway. My email address is on my thread but I forgot to put it on my essay, it's jonathan.kerr@to-gl.net . Have a well earned rest!

Best wishes, Jonathan

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Benjamin,

thank you very much for the explicit support in topic/1263 and congratulations by your first position

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Author Benjamin F. Dribus replied on Oct. 7, 2012 @ 00:48 GMT

Dear Juan,

Thanks for the message. I am glad to see you in the finals! Take care,

Ben

Congratulations Ben!

It is good to see you with a top ranking. You had kind things to say about my essay, and I am pleased to report also being among the lucky few (assuming there are no more oscillations). Now you can impress your students with the fact that you ended the qualifying round scoring above a scientist who co-authored a book with Stephen Hawking. But I digress.

Yours was a very interesting essay, which demonstrated a deep understanding, and it will be intriguing to see what other ideas you have to share - and compare notes.

More later,

Jonathan

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Author Benjamin F. Dribus replied on Oct. 7, 2012 @ 03:13 GMT

Dear Jonathan,

Thanks for the kind remarks. I actually wrote the message just below this one before I refreshed the page and saw yours... "comparing notes" was exactly what I had in mind! As I said there, however, I expect no one will be reading this for the next day or two anyway, so I'll hold off until early next week. It's good to see you in the final round as well... thoroughly deserved! Take care,

Ben

Dear All,

I appreciate the opportunity I've had over the last two months to read your essays, which represent a broad cross section of current scientific thought. I have attempted to assimilate the principal ideas by disciplining myself to try to understand your papers well enough to engage in at least rudimentary discussions about the main points. With very few exceptions, you've been unfailingly hospitable, and have in many cases given me significant extra clarification and references. You've also been very open-minded concerning my own ideas about fundamental physics, which I admit take some getting used to, and which will require significant further development to determine their scope of applicability to the real world.

What I'd like to do in the coming weeks is respond more adequately to some of the important points that have been raised by some of you on my thread and in conversations we've had on your threads. First I would like to address some of the points raised in this thread by Jonathan Dickau on October 3. However, I imagine that no one will be paying much attention over the weekend, so I’ll hold off on this for a day or two. Take care,

Ben

Inger Stjernqvist replied on Oct. 9, 2012 @ 20:35 GMT

Dear Ben,

My warmest congratultions to your first - and most well deserved - rating in this contest.I have spent a few days in rural southern Sweden, hardly within reach of the Internet. But today I have re-read the above conversation, and learnt more from it. Now, when everything is settled about the final essays, I look forward to the possibility of a more peaceful converstation, in which I have a slight chance to catch up.

Best regards!

Inger

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Dear Ben,

Thank you a lot of for your attentions and comments. Please accept my apology for delay.

As you correctly mentioned, we reviewed all non-local hidden variable models which simulated quantum singlet state by non-local hidden variables. We derived inequalities which are based on these models and showed that they violated by quantum correlation function.

Unfortunately, my essay has typos at first paragraph of page 5 (is equal to one…), however, equation 6 and fig. 3 are correct.

As you mentioned at your essay, there are some physical models which are based on the Extra Dimensions and compactification of extra dimensions. However, please pay attention that these models take place at high energy physics (about 10^{18} Gev). I can accept your opinion if you find rationalization for it. In other words, how space-time microstructure is changed at low energy physics (about 1 kev)?

I am ready to see your work at more detail.

Thank you in advance

Sincerely yours.

Akbar

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Hello again Ben and Friends,

I'm taking up your invitation to post at any time, with due respect to John Baez, who is not my cousin in real life.

A story:

They say my uncle is crazy, and cousin John tells me some family members wanted to lock old Uncle Octonius up in the attic, but I think he is only eccentric because he's seen the universe, and knows its secrets. For years...

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Hello again Ben and Friends,

I'm taking up your invitation to post at any time, with due respect to John Baez, who is not my cousin in real life.

A story:

They say my uncle is crazy, and cousin John tells me some family members wanted to lock old Uncle Octonius up in the attic, but I think he is only eccentric because he's seen the universe, and knows its secrets. For years we thought he just wouldn't associate with the other family members at all, but somehow we worked out how to do it safely. You see; Octonius is very persuasive, and can make people do almost anything - so he can't be trusted, or rather no one person can ever see him alone. And when we send two, they always disagree on what was said. Therefore; we always visit Uncle Octonius in committees of three. But; the first time a group of us visited, he insisted that he must see all the family members - with equal frequency - and that there always be someone in common between any two visits. Luckily; this worked out, because there are seven of us.

The thing is; Octonius is incredibly wealthy and knows the secrets of the universe, but we were all so afraid of him that we never knew why he seemed so crazy. You see; he always liked to break the laws of algebra - or insist on things being backwards sometimes - whenever we tried to use the associative and commutative rules to simplify expressions for him. But we never understood why that was, until we attempted to rank ourselves - thinking that both the greatest and slightest within our family needed to be included, within each committee, to assure trust. Then Octonius explained that committees follow a rule that is non-commutative, and then if you include everyone at once things become non-associative, because there can be disagreements between members or committees - but there is also a hierarchy or ordering of and within any committee.

Though we are still not sure we can trust him, Uncle Octonius tells us this is as fair as it can be, and now he is teaching us the secrets of the universe. So who could complain? I'm glad cousin John didn't let the others lock him up in the attic, or we would never have learned of his vast wealth and untold secrets.

end of story

Jonathan

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Steve Dufourny replied on Oct. 19, 2012 @ 12:58 GMT

ahahah learn french and read my poems ahahah uncle spherical gives you a lesson.and you know it.Don't try with the faith and the spherization. You are not really relevant in fact.a simple sockpuppet player is your name,in fact you are only good for the computing, the rest oh my god but what is your foundamentals. ahahah in fact you are only good for these kind of play.not for the gnerality.You...

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ahahah learn french and read my poems ahahah uncle spherical gives you a lesson.and you know it.Don't try with the faith and the spherization. You are not really relevant in fact.a simple sockpuppet player is your name,in fact you are only good for the computing, the rest oh my god but what is your foundamentals. ahahah in fact you are only good for these kind of play.not for the gnerality.You repeat always the same in fact. ahahah frustrating no? me I have faith, you no.It is there your error sockpuppet inventing false names. Even your maths are always the same. In fact several people fear for their funds. They fear that their institute looses a little of their credibility.So they utilize the competition like excuse, but in fact they are just pseudos. They prefer the publicity instead of generalities. They are simply people lost in the meanders of the society. You confound a little the things in fact.You do not evolve, you just make a pub because you fear for your jobs perhaps I don't know.Or it is just the taste of monney who interests you.In all case, it is not a good parameter that you utilize. You have just simply profitted about a discovery, revolutionary and you try simply to prove to yourself that your hormons are ok. Have you probelms in the bed with women or What ? if you want I can give courses. I am understanding your hate.You can evolve, buy a bibble I don't know me. I can also give courses of maths, piano, physics, theaters,poesy,guitar,taxonomy of evolution,indeed I class all.You know animals and vegetals I suppose. And you try with what ? the spherization, ahahah let me laugh.I have quantized the mass me, you no. I am arrogant I agree but it is the reality. The story begions dude, you know the evolution and its optimization spherization, we are young, we are aged of 14 billions years dude, I have time to explain you the spherization.I am going to explain you what are the maths of spheres of light and its uniqueness giving the singularities. You think really that my soul of spheres of light is going to accept your play.You can even kill me you know.We are eternal my friend, you shall be head in the soil in front of the infinite light poor thinker. Uncle what? make surf dude, and pray for your soul. All is said in fact. Jesus Christ and Siddartha Gottama Buddah are with me.Ahahah I have the syndrom of the elected. and what ? what is the probelm, put me also on a cross also if you want, I will laugh in front of your face, I will resist with universal love and faith.you can even burn me if you want,I will resist poor dude.

You are already in the bad boat.

Spherically yours band of comics.

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Steve Dufourny replied on Oct. 19, 2012 @ 13:56 GMT

sockpuppets-play....conclusion, anybody of the familiy has right.

Results....easy to see the truth.

You do not understand what is the universal love. So why you insist ?

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Dear Ben - first of all I want to thank you again for your supportive remarks on John and my submission! Thankfully, after checking my records, I found your essay in the list of ones I loved as well. I am happy to see that enough people also loved your essay. Honestly, the rating and voting was overwhelming to me, and I admire your thoroughness in this essay contest. Hopefully you win a prize,...

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Rick Lockyer replied on Oct. 10, 2012 @ 04:55 GMT

Jens,

While I am interested in Ben's answers to your questions, I would like to assert that the belief an "electromagnetic observer space" is "(Minkowskian)" is one of the fundamental assumptions needing review, the subject matter of this essay contest. As you know, my essay promotes a contrary opinion.

Rick

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Dear All,

I am suffering a bit of a backlog of deep and important points raised by a number of different people here over the last two weeks. Each of these points requires a careful and somewhat involved response, to whatever extent I am intellectually capable of providing one!

This is midterm week at my university, and I have a throng of needy calculus students tugging at my coattails at present. It may well be the weekend before I am able to catch up on some of these communications. Some of the main priorities are the following:

1. The implications of experimental results constraining certain types of nonmanifold structure/covariance breaking.

2. The proper application of path summation in general contexts.

3. Discussing what "particles" might look like in view of the causal metric hypothesis.

4. Discussing some special algebraic structures of particular importance...

In the meantime, please feel free to continue posting such remarks here; you're contributing to my education! Since this thread is at the top of the list, it's a reasonably convenient place for discussion. Many of you know more about some of these issues than I do, so feel free to post remarks in response to others' comments. While I will do my best to answer things myself, I am a bit greedy in the sense that my greater interest at present is absorbing, black hole-like, what everyone else is saying. I will endeavor to give off a little Hawking radiation, however!

Finally, I am trying to compile a coherent email list; my email is bdribus@math.lsu.edu, and I'd appreciate hearing from any of you. I have already contacted a number of you who included email addresses on your essays. Take care,

Ben

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Dear Jonathan,

The following three posts are in response to a point you raised in your post on October 3 05:33 GMT on my thread on the subject of “Lorentz invariance violation.” From reading your essay and from our other correspondence, I know that this is ground you have been well over, but I include some general details here for general interest.

My essay advocates an “order-theoretic interpretation of covariance,” which is an example of what is usually called “Lorentz invariance violation,” (LIV) or “covariance breaking.” I prefer to regard this as a “reinterpretation” of the covariance principle, to extend it to a domain where continuous group symmetries are of doubtful applicability. But that is merely a choice of terminology.

As you point out, there exist experimental means to test certain types of LIV, and some of these methods have placed tight constraints on these types of LIV in the last few years. In particular, you mention experimental results from the Fermi Gamma Ray Telescope and the INTEGRAL gamma ray observatory. For anyone who is interested, I link to a few references about this:

INTEGRAL[\link]

Fermi[\link]

Stecker[\link]

Popular INTEGRAL article[\link]

The first two articles are arXiv versions of recent papers describing the methods and results of INTEGRAL and Fermi in constraining LIV. The third is a somewhat general review of such methods, unfortunately dating from before the most recent results. The fourth is a popular article on the same subject.

(continued below)

(continued from previous post)

I botched up the above links with backslashes. They look absurd, but they all work except for the Stecker link, which is here:

Stecker

(continued below)

(continued from previous post)

The “popular simplification” of these results has been that “if Lorentz invariance violation exists, it must occur on scales much smaller than the Planck scale.” Of course, such conclusions are model-dependent; see for instance the discussion in section III of the first article to see how much conventional physics is being assumed.

As you point out, these results may be very problematic for the theory of causal dynamical triangulations (CDT), which is a much more constrained and structured approach to “quantum causal theory” than Sorkin’s causal sets or my causal metric hypothesis. CDT has nontrivial fundamental elements, namely Lorentzian 4-simplices, and this allows for the use of a lot of familiar machinery in the theory. I do not know exactly to what extent Fermi/INTEGRAL doom CDT, but my impression is that at least some of these methods apply more or less directly and have negative implications.

I don’t think this is true for causal sets, but I would like to ask Rafael Sorkin about this. There is a fair bit of literature on photon dispersion in causal sets, but I doubt if the machinery cited in the Fermi/INTEGRAL papers has a definitive causal set analogue at this point.

(continued below)

Dear Jonathan,

This is the last part continuing from above about Lorentz invariance violation...

Let me say a few words about why the Fermi/INTEGRAL experimental results don’t worry me from the perspective of my own work, though they certainly should be kept in mind as constraints on the details of nonmanifold models of fundamental spacetime structure.

1. Just to be clear, although I think locally finite causal graphs are the most physically interesting “causal-metric” models at present, I don’t think that “volume” arises from a constant discrete metric (a la Sorkin).

2. In particular, “nonmanifold” does not imply “discrete;” the two concepts are merely different extremes. Furthermore, “discrete” can mean several different things. There are several different topologies that are relevant for such models, and the discrete topology is perhaps the least interesting of these. There is also a measure-theoretic meaning of discreteness (e.g. Sorkin’s “order plus number equals geometry.”)

3. I doubt the arguments for the fundamental significance of the Planck scale.

What I am arguing is that experimental results like Fermi/INTEGRAL should serve as guides in pursuing nonmanifold models of spacetime structure, not discouragements. The most obvious objections to what I’ve said here is that my models are too vague and general at present to be either confirmed or falsified by feasible experiments. This is true… I need to do much more work. However, my feeling is that these results rule out only a tiny sliver of the universe of interesting quantum causal models.

Any additional thoughts you might have on this important point would be appreciated! In particular, I suspect you know more about exactly where Fermi/INTEGRAL leave CDT and other similar models. Take care,

Ben

The breakdown of the Lorentz symmetry is something which was advanced by loopvariable quantum gravity theorists. As Ben points out the observations of distant burstars has put considerable doubt upon these theories. Spacetime appears to be absolutely smooth down to scale of 10^{-45}cm or so. The graininess of spacetime that would result from violations of Lorentz symmetry should result in...

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Lawrence B Crowell replied on Oct. 12, 2012 @ 19:58 GMT

CONTINUED:

[equation]

where p^b_0 = e^b_0. For e^{aμ} the transformation involves {\cal G}^{-1}[p_0]. Similarly the differential operator

[equation]

transforms locally under the nonlinear Lorentz group. This then gives

[equation]

which for the local nonlinear transformation written according to indices gives the connection...

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Dear Benjamin Dribus,

Causal metric hypothesis is much applicable with the Tetrahedral-brane scenario of Coherently-cyclic cluster-matter paradigm of universe, in that time emerges with the eigen-rotational strings and a causality-effect continuum is expressional for an eternal universe and thus Causal cycles is descriptive with this paradigm. Causality of three-dimensional structures is the effect of tetrahedral-brane expressions by eigen-rotational strings, in that spacetime emerges from eigen-rotations of one-dimensional string-matter segments. Thus in this paradigm, the metric properties of spacetime is descriptive by the configuration space with string-length and time, in that the nature of spacetime is expressed differently.

With best wishes

Jayakar

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Thank You Ben and good Sir Lawrence!

Good summary and references Ben, and explication of the territory Lawrence. Lorentz invariance vilolation (LIV) is likely a problem for for some causally structured theories like CDT, but as LC pointed out, it first came out as a prediction by some LQG folks, as a possible means of validating the loops approach. Greatly summarized, the Fermi and...

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Thank You Ben and good Sir Lawrence!

Good summary and references Ben, and explication of the territory Lawrence. Lorentz invariance vilolation (LIV) is likely a problem for for some causally structured theories like CDT, but as LC pointed out, it first came out as a prediction by some LQG folks, as a possible means of validating the loops approach. Greatly summarized, the Fermi and INTEGRAL results detected the near simultaneous arrival of both very high and lower energy radiation pulses from the same distant gamma ray burstar event. This does greatly constrain things, but as you pointed out Ben - it does not close the door on all causal approaches. And my conversations with a couple of LQG researchers, would indicate that their approach is not ruled out either - only constrained.

As I understand it; the very thing which makes causal dynamical triangulation (CDT) work is what makes it problematic, in terms of LIV. The timelike lines must line up at the boundaries of each simplex, as the simplicial fabric evolves, and so there is a local discrete arrow of time that has a particular direction in space. The CDT approach has a fixed clock as well, yielding a very definite grain, but Smolin and Markopoulou showed that a varying clock yields similar results that show evolving dimensionality. One of the CDT authors (Loll or Ambjorn) pointed out in correspondence that they don't think it is an exact model anyway, but rather a discrete simulation of the way the spacetime metric evolves.

My guess is the CDT folks did not start with enough degrees of freedom, to end up with an invariant model, and that's where I think the Octonions come in. That would greatly increase the options at the outset. I have lots of ideas of how that would come together. I'll have to continue my comments on the morrow, though, as it is already very late here. I've downloaded the papers you provided links to, and also a few by Sorkin and colleagues on topics relating to this discussion. Though I think a lot of the work on the Causal Sets approach is entirely sound, I tend to believe that we are looking for something similar to - but not exactly like - it. I need to do more reading though, to see how far that program (CauSets) has come along, before I comment further.

All the Best,

Jonathan

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Lawrence B Crowell replied on Oct. 13, 2012 @ 12:59 GMT

Loop variable quantum gravity, causal sets or nets, causal triangulation theories and related ideas are themselves I think constraint systems. For instance, loop variable theory is a spinor, or spinor field, form of the 3 space plus 1 time form of relativity which has the Hamiltonian constraint NH = 0 and the momentum constraint N^iH_i = 0. The Wheeler DeWitt equation HΨ[g] = 0 is a...

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Loop variable quantum gravity, causal sets or nets, causal triangulation theories and related ideas are themselves I think constraint systems. For instance, loop variable theory is a spinor, or spinor field, form of the 3 space plus 1 time form of relativity which has the Hamiltonian constraint NH = 0 and the momentum constraint N^iH_i = 0. The Wheeler DeWitt equation HΨ[g] = 0 is a canonical quantization form of the Hamiltonian constraint, and loop variable theory is a spinor form of this type of theory. The vanishing of the Hamiltonian NH = 0 or the canonical quantization HΨ[g] = 0 is due to the fact the manifold is global and there is no boundary from which one can compute with Gauss’ law the mass-energy of the entire spacetime, or universe. It further have to be pointed out that loop quantum gravity (LQG) has yet to compute a one loop diagram properly. The reason is that if you have HΨ[g] = 0 it means you have ∂Ψ[g]/∂t = 0, and there is no dynamics! Computing a scattering amplitude, particles in --- > process --- > particles out, on a T-channel is not possible.

What do these constrain? Frankly I think they constrain string theory. Ed Witten has found that within string/M-theory there is a form of twistor theory. This is the so called twistor “mini-revolution” that started a few years ago. Twistors are in some ways related to loop variables, but they have more spacetime content. I think this segues into thinking about these non-string approaches to quantum gravity as constraint systems. String theory uses a “time” τ that is a string time parameter along the string world sheet with the parameter σ along spatial extent of the string. This permits one to construct Hamiltonians of the form

H = (T/2)[(∂X/∂τ)^2 + (∂X/∂σ)^2], T = string tension,

for X the string variable. This contrasts of course with the LQG which has no explicit concept of time, because there is no way to define mass-energy in a global context. A Hamiltonian is the generator of time translations, which means the energy defined by the Hamiltonian is conserve (Noether’s theorem). In string theory this corresponds to level matching of string modes, but in LQG E = 0 and there is no time translation. However, the spacetime is a target map from the string, which should correspond to HΨ[g] = 0 for a wave functional over the spacetime metric. LQG is then some type of constraint system.

There are also some interesting possibilities for duality principles. Barbour and Alves have proposed a form of shape dynamics, which is a symmetrical theory. The spatial relationships between elements that define a shape in space are symmetrical. Causal sets involve asymmetrical relationships between nodes that are connected by lines or into graphs. These represent temporal ordering. The two approaches seem to represent something similar to Penrose’s tensor space of symmetric and anti-symmetric tensors in a type of duality. The duality in some work by Sparling and others is supersymmetry. I then conjecture that the correspondence between shape dynamics and causal nets (sets) is then a form of this duality or is a categorical equivalence to SUSY. This may then be another form of constraint, in particular the SUSY structure which exists in the AdS_n ~ CFT_{n-1} correspondence.

Cheers LC

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Dear All,

I want to thank Lawrence for the detailed info on deformed special relativity (DSR), Lorentz invariance violation, and the connection to the cosmological constant problem. His link to the original paper of Smolin and Magueijo does not appear to work; hopefully the following link fixes this:

Smolin and Magueijo DSR

I mentioned DSR briefly in my essay (it's one of the approaches involving noncommutative geometry). My understanding is that DSR has suffered a number of theoretical and experimental setbacks since it was introduced, but I think the issues it attempts to address are things which must be considered.

I'll also remark that a number of other authors who submitted excellent essays to this year's FQXi competition were instrumental in the development of DSR and related approaches involving a minimal fundamental scale. These include Sabine Hossenfelder and of course Giovanni Amelino-Camelia.

Paul Reed replied on Oct. 20, 2012 @ 06:58 GMT

Ben

At the risk of causing a riot, a problem with that Smolin/Magueijo paper is that it presumes SR includes gravitation in the first place. Which it does not. So in that sense, there is no issue to resolve. Einstein defined SR several times, and it is not 1905.

In 1905, the two postulates are “apparently irreconcilable”. Which is a bizarre statement when juxtaposed against...

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Ben

At the risk of causing a riot, a problem with that Smolin/Magueijo paper is that it presumes SR includes gravitation in the first place. Which it does not. So in that sense, there is no issue to resolve. Einstein defined SR several times, and it is not 1905.

In 1905, the two postulates are “apparently irreconcilable”. Which is a bizarre statement when juxtaposed against the assertion that “These two postulates suffice for the attainment…theory…electrodynamics of moving bodies”. The irreconcilabilty is because light is presumed to be in vacuo, whilst everything else is not, because they are subject to dimension and momentum variance. And the cause of that is subsequently revealed to be gravitational forces. In other words, light and matter cannot be co-existent and so 1905 is not a singular, cohesive, theory. So in expounding GR, where everything (ie including light) is subject to gravitation, Einstein refers to a special/entirely theoretical circumstance where there was no gravitation, ie SR. This is why SR only involves uniform rectilinear and non-rotary motion, light that travels in straight lines at a constant speed, and rigid bodies.

Einstein: Relativity 1916 section 18: “…the special principle of relativity, i.e. the principle of the physical relativity of all uniform motion…“

Einstein: Foundation of GR 1916 section 3: “…the case of special relativity appearing as a limiting case when there is no gravitation”

Einstein: Relativity 1916 section 28: “The special theory of relativity has reference to Galileian domains, ie to those in which no gravitational field exists…In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity”

Einstein: Relativity 1916, section 22: “Let us further investigate the path of light-rays in a statical gravitational field… Let us find out the curvature which a light-ray suffers. [equation (74) refers] …a curvature of rays of light can only take place when the velocity of propagation of light varies with position…

Paul

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Dear All,

Another point Lawrence re-raised is the possibility of duality between theories such as causal set theory, which involve anti-symmetric binary relations, and theories such as shape dynamics, which involve symmetric binary relations. This is one of the ideas arising from the discussion here (provided no one thought of it already!) that I hope will receive further attention and exploration.

The evolution of this idea here is worth reading, but it is unfortunately scattered around the threads and there is too much to repost in one place. I think the discussion began with my comments on Daniel Alves' thread about symmetric, anti-symmetric, and asymmetric binary relations in shape dynamics and causal theory. From there the discussion branches out in several places.

Lawrence has offered some important clues on making this idea precise. See his remarks on the axiomatization of space, Penrose tensor space theory, supersymmetry, fermionic and bosonic fields, etc. on Daniel Alves' thread, Sean Gryb's thread, and my thread. In particular, see his post of September 28 on my thread.

Lawrence B Crowell replied on Oct. 14, 2012 @ 02:04 GMT

I will write more on the Penrose tensor space, or what I think is also called a modular space. Shape dynamics is really a form of Regge calculus. One could think about this according to light rays. In this way there is no matter of time involved with the “motion” of a shape, for null rays have no proper time. I illustrate this with two diagrams I attach to this post. The first is a flat...

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I will write more on the Penrose tensor space, or what I think is also called a modular space. Shape dynamics is really a form of Regge calculus. One could think about this according to light rays. In this way there is no matter of time involved with the “motion” of a shape, for null rays have no proper time. I illustrate this with two diagrams I attach to this post. The first is a flat spacetime description. This is also pictured in 2-space plus 1-time spacetime in 3 dimensions. Two points on a spatial surface emit light pulses. These converge on three points on a subsequent spatial surface. These then define a triangle on that spatial surface. The two points then emit subsequent light pulses and map the triangle onto a third spatial surface. In Minkowsk spacetime this continues indefinitely.

In the curved spacetime situation null rays are curved. Since the metric

ds^2 = g_{00}c^2dt^2 – g_{ij}dx^idx^j

is such that for ds = 0 we can have

U^iU^j = (g_{00}/g_{ij})c^2dt^2,

and the optical path change due to curvature has a c^2 term. Hence we can assume the triangles on the spatial surface are flat. The deformation of null rays will then map the first triangle on the second diagram I attach into the second. The picture here is then completely described by null rays which have no proper time.

The time evaluated from the Jacobi variational principle

δt = sqrt{m_iδx_iδx_i/(E-V)}

is related to a proper time, or an interval. In the case of a null interval the spatial δx_i may be evaluated according to g_{00} and g_{ij} as above. The time computed by the Jacobi variation is then an “emergent” or computed quantity. This is a parameter which emerges from the “motion” of the triangle, or the map from the first to the second. This is related to Desargue’s theorem, where null geodesics are projective rays and these are used to “lift” a shape from one spatial surface to another.

The causal net or set approach is stranger to me. However, the ordering principle behind it seems to demand an antisymmetry due to one ordering A > B not equivalent to B > A. I ponder whether the two approaches have a relationship between each other. These two should have some matter of equivalency if they both predict the same spacetime physics. If this is so this seems to categorical relationship to this and supersymmetry. Penrose’s modular space of tensors is one way one can look at supersymmetry. The problem is that as yet I do not see a tensor structure to causal net theory.

Cheers LC

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Lawrence B Crowell replied on Oct. 14, 2012 @ 02:08 GMT

I forgot to attach my diagrams in the post above

LC

attachments: 1_light_rays_and_triangles.JPG, 1_null_rays_and_triangles_in_curved_spacetime.JPG

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Benjamin

I noiced your essay is top of the list, so I read it.

The first step is to understand how we detect existence, and hence what our reality is and how it must occur. We can only know our reality, as we cannot transcend our own existence.

“The first few assumptions I reject are… that systems evolve with respect to an independent time parameter”

Not so. The two fundamental knowns in respect of our reality (ie not some metaphysical conceptualisation) are that a) it exists independently of the sensory systems that detect it, b) it alters. This means our reality is existential sequence. Which entails:

1 It is comprised of elementary substances, these having physical existence which is not further divisible (there may be more than one type thereof).

2 These elementary substances have at least one innate property each which has a propensity to alter, of itself &/or under external influence, in its existent condition.

3 In any given sequence of physical existence, only one physically existent state (ie a reality) can occur at a time, and this has a definitive physical presence.

4 No phenomenon can have physical influence and not have physical presence.

5 There must be a particular relationship between a previously existent state(s) and a currently existent state for it(they) to be the cause, in terms of sequence occurrence and spatial position, as physical influence cannot ‘jump’ physical circumstance.

Now, what these simple rules mean ‘in practice’, is another matter. But one fundamental characteristic of our reality is that it is sequence (or system), timing being an extrinsic measuring system which calibrates the relative speed of changes. It is also easy, on the basis of the above, to discern, generically, what dimension can be, and indeed what any of the other concepts mentioned can be, if anything.

Paul

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Dear Paul,

Thanks for reading my essay and for your remarks. I think I can agree with part of what you say; the rest I am not quite sure about. Let me be more precise.

1. You say "we can only know our own reality." True enough; every observation is mediated by our interpretation, and every argument is mediated by our reason. But all of science is based on the assumption that...

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Dear Paul,

Thanks for reading my essay and for your remarks. I think I can agree with part of what you say; the rest I am not quite sure about. Let me be more precise.

1. You say "we can only know our own reality." True enough; every observation is mediated by our interpretation, and every argument is mediated by our reason. But all of science is based on the assumption that there exists an external reality with characteristics accessible to any competent observer; i.e., that competent interpretation and reason will converge on objective answers. I don't dispute this assumption; there is no use in doing science if one does.

2. I am not sure if your "not so" means you don't believe this is one of the first assumptions I reject (I assure you that it is!), or that you believe it should not be rejected. I will assume the latter.

3. Your first "fundamental known" is part of what I said above, that there exists an objective reality. I agree.

4. Your second "fundamental known" is less clear. What does it mean for "something" to "alter?" Well, you must have two different states, one you call "before," and one you call "after," but that is not enough. You must have some way of identifying the two states as representing the "same thing, only having altered." At the very least, this requires a relation pointing from the "first" state to the "second" state. The family of such relations is precisely a partial order as I described in my essay.

5. I am afraid that your points 1-5 seem to include many imprecise concepts and implicit time-related assumptions. For instance, what precisely is an "elementary substance?" Is it a set, or an element of a set, or a field on a manifold, or what? What precisely is an "innate property," and how is it connected to its corresponding "substance?" What precisely is a "propensity?" If a "property" "alters," how do you identify it as an altered form of the same property rather than an unrelated property? How do you define and model "influence?" When you say "only one state can occur at a time," you must already have an assumption about what "time" is for the statement to mean anything. Later you say that time "calibrates the relative speed of changes," but what does "speed" mean, and what are speeds "relative" to? What does "spatial position" mean? What does it mean to "jump?" And so on and so on...

You refer to these points as "simple rules," but I don't think they're simple. They sound simple in English, but if one tries to make them precise, one sees that they are quite complicated and include assumptions about the very things they are intended to define. This makes it hard to evaluate what you are actually claiming, and this is before one can even begin to think about whether or not the rules are likely to be valid or useful. Perhaps you could explain the meaning of these things a bit more clearly. Take care,

Ben

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Paul Reed replied on Oct. 16, 2012 @ 14:01 GMT

Benjamin

Thanks for you prompt response, and the constructive nature thereof.

Re 1: But this is not what I am saying. We can only investigate a specific form of existence. In short!:

Any form of existence invokes the possibility of an alternative, (ie if A, there is always the logical possibility of not-A). But, any form of existence other than our reality is inherently...

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Dear Paul,

Thanks for the clarification. I believe I understand much better now where you are coming from. Also, your view does not seem to be quite as much at variance with mine as I had thought from your original comments. In particular, I think we completely agree that time is a way of talking about sequence (i.e. order). However, each event (or observer) has its own local sequence, so the order is a partial order, not a single linear order.

You seem to be suggesting that it is the reality we perceive, not your principles, which is complicated, and this seems to be a valid contention. What I should have said is that it's complicated to translate your principles into meaningful statements about physics, but the same could be said of mine.

You write, "physics has failed to understand the fundamental nature of what it is investigating," and you're quite likely correct. My causal metric hypothesis is a guess about that fundamental nature. Likely it's too simple, but I hope it can explain some current conundrums when properly developed.

I chose not to write about observational and measurement-related issues not because I regard them as unimportant, but because there was simply not enough space. Also, these issues verge on the interface between consciousness and the physical world, which is something I regard as far beyond our abilities at present. I certainly don't feel confident writing about it! A few other brave contestants (Janko Kokosar, David and Julie Rousseau, Sara Walker, etc.) touched on some of these issues. Take care,

Ben

Paul Reed replied on Oct. 17, 2012 @ 05:27 GMT

Ben

I am not sure we do agree on the nature of time. Because you say, “However, each event (or observer) has its own local sequence, so the order is a partial order, not a single linear order”. And you reject the principle “that systems evolve with respect to an independent time parameter”.

But, the entirety of our reality is an existential sequence, one can, to maintain...

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Ben

I am not sure we do agree on the nature of time. Because you say, “However, each event (or observer) has its own local sequence, so the order is a partial order, not a single linear order”. And you reject the principle “that systems evolve with respect to an independent time parameter”.

But, the entirety of our reality is an existential sequence, one can, to maintain sanity! conceptualise constituent sequences. However, there is no time in a reality, because this concept is about the calibration of change anyway and is therefore non-existent, but more importantly, there is no change in a reality, otherwise it cannot exist, and then alter. Changes are occurring at different speeds, but that is irrelevant. Timing is an extrinsic measurement system, time being the unit of measurement. For this to function properly there can only be one time/one system, which is applicable to the entirety of reality. Put simply, there is only ever in existence what is commonly known as a present, ie our reality is only in one physically existent state (a reality) at a time. Timing just provides a reference to establish what that was, and a means of relating various disparate rates of change.

Furthermore, I noticed the sentence: “The fundamental structure of spacetime is the central focus of both the rejected assumptions and the new principles”. Now, as a representational device of our reality this model is invalid. As stated above, time is in no sense (ie even when properly expressed in terms of change) a factor within any given reality. This means that a reality has purely spatial properties. But, dimension has been misconceived. Three spatial dimensions is the absolute minimum number conceivable whilst maintaining ontological correctness at that level of conception, but not what is physically existent. In effect, dimension involves the concept of reality being divided into a spatial grid, the smallest unit of which equates with the smallest substance. The dimension, ie spatial footprint-size/shape, of any given entity being the relative spatial positions ‘occupied’ at any time (ie in its physically existent state). The number of possible dimensions in reality is half the number of possible directions that the smallest substance could travel from any given spatial point, because dimension relates to direction, either way.

I could ask rather superficial questions about the causal metric hypothesis, ie why are there two versions when there is only one reality, why a binary relationship in causality, but the more important issue is what is the model of reality which underpins this. Because that comes first, and then everything else follows, ie those 6 principles, once understood in grammatical terms, can then be translated into what they can mean in reality, given how that is fundamentally constituted.

Finally, one does not need to know about consciousness, etc, as such. These are just unfortunate(!) interference factors. The physics of our reality is unchanged. We, and all sentient organisms, receive a physical input. This exists whether we receive it or not. We create (ie the output) knowledge of reality, not reality. The trick is to discern (ie eradicate the interferences) what was received, and hence what caused that, given knowledge as to how the phenomena involved behave physically.

Paul

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Author Benjamin F. Dribus replied on Oct. 17, 2012 @ 07:28 GMT

Dear Paul,

Let me ask a few questions, since we seem to be at terminological cross-purposes...

1. Would you say, roughly speaking, that "time is a way of talking about change?"

2. How are the two statements "our reality is an existential sequence" and "there is no time in a reality" not contradictory? If time is unreal, why talk about it? In particular, why insist on its existence as an external parameter?

3. You say "Timing is an extrinsic measurement system, time being the unit of measurement. For this to function properly there can only be one time/one system, which is applicable to the entirety of reality." Why? Why make this assumption? What does "function properly" mean? In particular, how does this not contradict the relativity of simultaneity and everything we know about physics at large scales?

4. Regarding the reason for "two versions" of the causal metric hypothesis, the answer would be the superposition principle; i.e., because a single quantum-theoretic reality is built out of configurations we call classical alternatives. But what I can't understand is why you need both "sequence" and "time" in a purely classical picture. The sequence is what actually happens; your notion of "time" seems merely an artificial redundancy. Why not throw it out?

You have me more than a little confused! Take care,

Ben

Paul Reed replied on Oct. 17, 2012 @ 13:43 GMT

Ben

Re 1: Yes, but that answer would need an awful lot of caveats.

Re 2: Because the common assumption is that time is a characteristic of reality (specifically, a dimension), so one can end up using the same incorrect phraseology in refuting that!

The underlying point here being that, in terms of existence, there are only physically existent states (or realities) of...

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Ben

Re 1: Yes, but that answer would need an awful lot of caveats.

Re 2: Because the common assumption is that time is a characteristic of reality (specifically, a dimension), so one can end up using the same incorrect phraseology in refuting that!

The underlying point here being that, in terms of existence, there are only physically existent states (or realities) of whatever constitutes our reality. When compared, difference is revealed, which indicates alteration/change. Difference is not physically existent, neither is alteration/change. But these concepts reflect physicality, they are not an illusion. What they refer to are the characteristics of the difference between realities, not features of any given reality. So timing can only be an extrinsic measuring system, as its purpose is to calibrate the relative rates at which changes occur (by comparing numbers thereof within different sequences against a duration reference, ie time).

Re 3: It is not an assumption. By definition, ie given how our reality must occur, the identification of any given physically existent state (ie a reality) involves establishing what existed at any given time. There is no change in a physically existent state, otherwise it cannot exist, and then alter, because the incidence of change means there is more than one state involved. The choice of what time is irrelevant in that it does not determine the state, just what happened to exist then. But, as with any such form of comparison, having selected a reference this must be maintained in order to ensure comparability of different measurements. In other words, that same point in time would have to be used to discern what other physically existent states occurred at that time in other sequences. They do not have their ‘own time’. Only different times if they existed at different stages in the sequence.

[Just for the record! This misconception lies in Poincare’s flawed concept of simultaneity, and became the surrogate variable for dimension alteration (usually referred to as length contraction), which Lorentz, et al, were uneasy with, ie time variance seemed more rational. So the tail got pinned on the wrong donkey, so to speak. In repeating simultaneity in 1905 (the A-B example, 1st section), Einstein went a step further, thereby compounding a felony, by using light speed to assess distance, but this was effected in terms of A to B, and then (ie subsequently) back (B to A), thereby, again, reifying time as a feature (a variance) within a reality. Apart from inadvertently attributing light speed with some relationships which are non-existent. In the meantime(!) Minkowski reified time with his spacetime model, following through the flawed concept of simultaneity.

t = x/v is an expression of what timing is. The number always equals the sum on the other side, and the property is the same on both the top and bottom of that side. So it is an expression that timing is rate of change (1/t, per time). Which it is. Having understood this, one then has to be very careful how alternative variables are introduced into this ‘equation’.]

Re 4 To which I would say, does the concept of superposition have any existential substance? Sequence is different from time, and neither is this to do with a ‘classical picture’. The differentiation of classic/quantum is a false dichotomy, there is only one form of our reality, with distinct generic features. Sequence is how change occurs, ie one at a time. It is like a film. Time is about the speed of change. At the existential level, it might be that all change is a function of the same feature, or different features which function at the same speed. So however change eventually manifests, it is, at that level, occurring at the same speed, which then makes the concept redundant, at that level. But this needs to be proven first. And anyway, deconstructing physical existence to this level is probably impossible to achieve, and certainly does not help in understanding most situations. Try describing one physically existent state of the ‘object’ known as The White House. Trillions of dollars worth of equipment and a million years later, we would probably still be at it!

Paul

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Paul Reed replied on Oct. 18, 2012 @ 07:15 GMT

Ben

In scrolling down I noticed the post above on symmetry. After our first exchange I did have a think about those 6 key principles you refer to, and came to the immediate conclusion that symmetry (amongst others) was a meaningless concept, given the fundamental nature of our reality, but did not want to ‘overload’ the exchange. However, since you indicate above that this is...

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Ben

In scrolling down I noticed the post above on symmetry. After our first exchange I did have a think about those 6 key principles you refer to, and came to the immediate conclusion that symmetry (amongst others) was a meaningless concept, given the fundamental nature of our reality, but did not want to ‘overload’ the exchange. However, since you indicate above that this is important, I looked at your post (19/9 17.29) to David Alves. In it you say:

“Shape dynamics deals principally with symmetric relations, since the separation between two points has nothing to do with their order; X is a distance D from Y if and only if Y is a distance D from X”

Indeed, but this is just a truism determined by how existence occurs. There is no symmetry, or relations, involved. [Incidentally, this happens to relates back to my point about the AB example, which I threw into my last post]. Distance is a function of the relative spatial footprint, and the relative spatial position, of the physically existent states involved. It is an artefact and has no physical presence. One has to presume, until proven otherwise, that as at each subsequent point of time, a change will occur to one or more of the physically existent states involved which will impact on distance. But, in reality, the distance has not altered, the physically existent states have. In other words, it is no longer X &/or Y, it is a distance being different states. So, yes, by definition, X to Y must be the same as Y to X, but it is not a case of “only if”, because what must be under consideration here is an existent state which involves no change. The distance is just the distance is just the distance, as are the physically existent states which determine it.

Then you say:

“Spacelike separation in relativity is similar. However, two events may also be causally related, and in this case the relation between them is generally asymmetric because the order matters; X is in the causal past of Y if and only if Y is in the causal future of X. In all but extreme cases, causal relations correspond to timelike separation”

Indeed, but again this is just a truism determined by how existence occurs. There is no asymmetry, just a sequential order of different states. Neither is there asymmetry in the sense that the other circumstance had symmetry, because there was none. In the first circumstance there was no sequential order, only one state within such an order. Now the circumstance involves more than one state of the order.

And, by definition, for any given physically existent state to have had a physical influence on any subsequent one, there must have been a specific relationship between the two in terms of both sequential order and relative spatial position. So, in terms of sequential order, a potential causal state must have been one of the immediate predecessors, because physical influence cannot ‘jump’ sequential order. Then in terms of relative spatial position, for any given state to be a potential causal factor, it must have been adjacent to, or in, the spatial position of the successor, because, again, physical influence cannot ‘jump’ spatial position. Given these criteria for potentiality of being a causal factor, in any given circumstance the causal factor could have stemmed from a) a previously existent physically existent state altering of itself, b) any combination of influence from all the other previously existent states, c) any combination of a & b.

Paul

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Author Benjamin F. Dribus replied on Oct. 18, 2012 @ 08:35 GMT

Dear Paul,

I think most of our mutual difficulties come from different conceptions and uses of the terms "existence" and "reality." In particular, this leads you to insist on one hand that a particular entity "does not exist," or "is not real," and at the same time insist that such an entity has particular properties and must be understood in a particular way.

For instance, you say, "Difference is not physically existent, neither is alteration/change. But these concepts reflect physicality, they are not an illusion." Similarly, you insist that time is "not real," yet insist that it is an "extrinsic measuring system!"

What I am trying to do is propose a model that may be useful in describing the physical world. Trying to argue about whether or not certain aspects of this model are a priori "physically real" on philosophical grounds is a waste of time. Ultimately, nature is the judge of whether or not a theory is useful. For instance, it's useless to argue against the superposition principle on the philosophical basis of whether or not it has any "existential substance." The fact is, it seems to describe how the world works. Similarly, the classical/quantum "dichotomy" is not really a dichotomy, but just reflection of archaic language. Again, "E pluribus unum" seems to describe how the world works.

Symmetry and asymmetry are not meaningless; they have very well defined meanings. The extent to which they are physically important is another matter. I argue that symmetry is slightly less physically fundamental than most physicists believe. To argue that it is physically meaningless, however, seems again to ignore the evidence of nature on philosophical grounds. Take care,

Ben

Paul Reed replied on Oct. 19, 2012 @ 07:39 GMT

Ben

I am not aware of any contradiction, although at times it is difficult to find an exact expression, because our very language incorporates a particular view as to how our reality functions. The differentiation is between something that is (or was) physically existent, and an artefact which reflects that, but cannot, of itself, be existent. Though your repeated reference to time is...

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Ben

I am not aware of any contradiction, although at times it is difficult to find an exact expression, because our very language incorporates a particular view as to how our reality functions. The differentiation is between something that is (or was) physically existent, and an artefact which reflects that, but cannot, of itself, be existent. Though your repeated reference to time is different from that, it being just a human devised measuring system, and therefore, obviously, has no physical existence.

And whilst that might appear to be somewhat pedantic or philosophical, it is not because it highlights the crux of the problem. And this is contrary to your assertion: “Trying to argue about whether or not certain aspects of this model are a priori "physically real" on philosophical grounds is a waste of time. Ultimately, nature is the judge of whether or not a theory is useful”.

The argument is not philosophical, but physical. Because, before any analysis can get underway as to what (ie content) is happening, we must first establish how existence is detected, and then how that (ie our reality) must occur generically (ie form). Form comes before content. And our reality has a definitive, independent, physical manifestation of its own, and there are physical processes which enable its detection. All of which is discernable, and thereby invokes a set of pre-conditions which must not be contravened in the analysis, construction of representational devices, etc. For example, given the fundamental characteristics of our reality (“nature”), the question then becomes, does the concept of superposition have validity? And the answer is: no, because it contravenes how our reality must function.

In respect of symmetry, again in the context of the form of our reality, I was pointing out that the first circumstance had no symmetry in it, there was nothing to be symmetrical with. And the second circumstance was not asymmetrical, it was just existential sequential order. Any concept of ‘a direction of progress’ (ie there is more than one possibility) is a fallacy. Which leaves me wondering, again, whether the concept of symmetry has any meaning. The more interesting point was about distance. This is another artefact. And there can only be distance between existent states which occurred at the same time. There cannot be a distance between an existent state and one that has ceased to exist, or indeed has not yet existed. All of which points to the necessity to understand the sequential order of the sequences and their relative status, otherwise we will have a jumble of hypothesised physical influences which actually could not have occurred. And since we depict a reality at a higher level than that at which it exists, and we have deemed that change (aka time) can be a characteristic of it, then it is highly likely we have that jumble.

Paul

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Hello Again Ben and friends,

On the subject of Lorentz invariance; a couple of brief conversations with Gerard 't Hooft about the Fermi results at FFP10 in 2009 gave me a lot of food for thought. Initially I simply asked how his newest CA-based QG theory fared, in light of the recent results, and his response was "it's too early to tell" and that considerable work still needed to be done...

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Hello Again Ben and friends,

On the subject of Lorentz invariance; a couple of brief conversations with Gerard 't Hooft about the Fermi results at FFP10 in 2009 gave me a lot of food for thought. Initially I simply asked how his newest CA-based QG theory fared, in light of the recent results, and his response was "it's too early to tell" and that considerable work still needed to be done (to make experimental predictions). But then I had another chance to speak with him later, and revisited the topic - naively stating that the microscopic time reversibility of any cell in his formulation avoids the local time arrow problem cited above (for CDT) - and he reiterated that Lorentz invariance is not that simple.

However, at FFP11 the following year; he had added 4 or 5 slides to discuss how desirable Lorentz invariance is to achieve, and how hard it is to accomplish with a CA-based theory. But many of his comments also apply in the case of CDT and likely Causal Sets. I still have not completely digested the Sorkin papers I downloaded, but one in particular directly addresses this issue, and says that instead of CauSets being Lorentz invariant, that type of graininess in spacetime induces a fuzziness to measurement instead. I think I like your approach better still, but I need to keep reading and digesting to be sure I understand. But there is one important matter you mentioned on George's thread.

The significance of action and reversibility thereof, was noted. Some of what was said there reminded me very much of ideas expressed by Phil Gibbs in his book Event-Symmetric Space-Time, which is worth checking out. Event symmetry may be important to developing Lorentz invariant formulations. I should also mention once more that I think that octonions hold a special place owing to their connection with projective space - and thus with the basis of object-observer relations in general. It seems that generalizing the ability to put things in perspective affords or possesses a natural embedding space that is octonion. Maybe that's part of the special magic of S7.

But again it is late, so I'll save further comments for another post. Sorry I have been too busy to post sooner. There is much to do.

Have Fun!

Jonathan

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Ben

Congratulations. Well earned. You said of mine; "Your ideas sound interesting" and "I'll be sure to have a careful look at your essay when I get back from my trip." (Sept 11th) . But seem not to have yet managed to do so. I do hope you can.

One thing I suggest is a limit to the domain of vector space for evolving kinetic systems, arising from the invalidity of motion as a concept in geometry. A simple and self apparent solution emerges, though from the viewpoint of current assumptions it seems not at first apparently simple at all!

You have to 'self built' an ontological construction from a kit of new elements, just like a dynamic Chinese puzzle, but with instructions and precisely following the structures of logic (from the basic 'nested' hierarchical structure of compound propositions in TPL upwards).

I think it represents the 'simple idea' Wheeler anticipated. But it needs help. I greatly look forward to your comments.

Very best wishes for the final judging.

Peter

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Author Benjamin F. Dribus replied on Oct. 17, 2012 @ 13:02 GMT

Dear Peter,

You're absolutely right... I did neglect to post my remarks on your thread. Things got a bit chaotic there for a while, and my own thread became rather busy, though not quite a busy as yours! In any case, I see you are near the top for the second year in a row, so I congratulate you.

I read your essay a couple of times before, but I should read it again before attempting to address you seriously. I do recall having a couple of questions about the scenarios involving multiple media in your scene 2, and the exact implications of the optical axis rotation on page 7. Also, I'm not quite sure in what context you refer to the "invalidity of motion in geometry," both in your essay and in your remark here. For instance, timelike curves in Minkowski space certainly "represent" motion in an obvious sense. I happen to agree that motion is derivative, but then of course I view geometry itself as derivative!

Anyway, thanks for the gentle reminder... I will certainly take another look at your work. Take care,

Ben

Peter Jackson replied on Oct. 18, 2012 @ 21:49 GMT

Ben,

Very wise to read again, and slowly. There are a whole related set of quite new assumptions to assimilate. The scene 2 (Act 1) media do have more different scenario's than we've assumed. I really needed a dozen more pages! Perhaps read my recent posts to Eckard & Pentcho.

But the concept is simple and physical. Six buses and six clouds of electrons flying round in space all...

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Ben,

Very wise to read again, and slowly. There are a whole related set of quite new assumptions to assimilate. The scene 2 (Act 1) media do have more different scenario's than we've assumed. I really needed a dozen more pages! Perhaps read my recent posts to Eckard & Pentcho.

But the concept is simple and physical. Six buses and six clouds of electrons flying round in space all represent different and mutually exclusive 'inertial frames', and domains for Maxwell's (near field) equations. Each then has spatial limits, with a boundary state and mechanism that absorbs and re-scatters to the local c precisely like a fluid dynamic coupling (as an auto gearbox torque converter). It is variously, magnetohydrodynamic shocks, surface charge/fine structure, the far field transition zone, the heliosheath, galactic halo, etc. It contains Boscivitch's 'sphere of influence' Einstien's 'spatially extended mass' and represents Galileo's states of motion, so, yes, derives discrete space time geometries, and at ALL scales, from a particle to a universe.

The structure is precisely that of Truth Functional Logic. Substitute 'frame' for 'proposition' and quantum relativity emerges. It's also continuous spontaneous localisation generalised to matter and systems in common states of motion at all scales.

The whole 'concept' of motion is of course invalid in geometry. Descartes tried a solution, but space and matter are 3D. It is the 'whole geometry' that moves, as a frame, not some unreal 'wire frame' where the wires have to cross. 'Getting wires crossed' may assume a new meaning!

Optical axis rotation was the last big piece that fell into place to complete the puzzle. If a plane wave in a medium hits ('charges') a beach ball or gyroscope (ion) at rest in the medium, which absorbs and re-emits it, the re-emission may be expected to be symmetrical (an ion/plasma is 'self focussing') and at c wrt the ion.

But if the ion is in motion through the medium fings appen! (effects from causes). Motion on the x (source) axis causes change to lambda L and, inversely, frequency f, (new but entirely obvious) which conserves c (c = fL).

Lateral motion v means the charge cannot be symmetrical. Ergo the re-emission is likely to be rotated, and in proportion to v. All of a sudden we find this maps atomic scattering direct to some of the most poorly understood physics we have; Stellar Aberration, Kinetic Reverse Refraction (the same thing). lensing, a whole host of related phenomena in optics and astronomy, and, yes, when we include harmonic resonance subject to f, and Huygens construction, apparently quantized refraction and 'curved space time.' Scary indeed. But it all needs clearer translation from English and logic into into physics and maths. It just needs someone who speaks both and also understands it.

That's almost another essay! but just scraping the surface. Do just ask every question you think of. I'll then link you to more if you can take it.

Thanks

Peter

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Dear all,

Some time ago, Jonathan Dickau raised the question of what the correct formulation of path summation is in various contexts. He attached a well-written paper by Steven Kauffman advocating a Hamiltonian phase space path integral approach and deprecating the Lagrangian approach. I would like to make a few remarks about this.

1. In causal theory, the natural version of path...

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Dear all,

Some time ago, Jonathan Dickau raised the question of what the correct formulation of path summation is in various contexts. He attached a well-written paper by Steven Kauffman advocating a Hamiltonian phase space path integral approach and deprecating the Lagrangian approach. I would like to make a few remarks about this.

1. In causal theory, the natural version of path summation involves paths defined by order morphisms from linearly ordered sets into the causal order. Assuming local finiteness and acyclicity, these may be identified with sequences of relations. In terms of acyclic directed graphs, such paths are just sequences of directed edges.

2. The natural object to sum over in this context is a “relation function;” i.e., a map from the set of relations to a ring, which conventionally is the complex numbers, but may be some other algebraic object. Finite fields, quaternions, octonions, etc. are interesting in this regard.

3. There is a technical information-theoretic reason why an “element function” won’t work: “antichains of elements are permeable.”

4. This relation function doesn’t correspond directly to a Lagrangian, but to a phase, which in Feynman’s Lagrangian approach is the exponential of the classical action. The action comes from integrating the Lagrangian with respect to time, but in the locally finite case, the integral is a sum, and a single relation represents the smallest subdivision of a path. In this sense, the relation function is an “infinitesimal path functional,” which is what a Lagrangian is in abstract mechanics. This is the sense in which the approach is “Lagrangian;” it need not have anything to do with conventional Lagrangians or actions.

5. Path summation over a single classical universe violates background independence, so the path sums I have in mind are over causal configuration space.

6. Conventional phase space involves “position” and “momentum” coordinates, and the Hamiltonian is an “energy function” on 2n-dimensional phase space. However, “momentum” is emergent in causal theory. As of now, I don’t know how one would could carry out background independent “phase space” path integration in the context of causal theory, or if this even makes sense.

So further thoughts on this would be appreciated! Take care,

Ben

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Lawrence B. Crowell replied on Oct. 21, 2012 @ 03:40 GMT

The relationship between position configuration variables and momentum can first be seen by looking at the diagram I attach. This illustrates a scattering process with 5 input momenta and 5 output momenta. The “blob” is the region with virtual or off shell processes, which can be realized by on shell processes by BCFW recursion. I will ignore that matter for the moment. The momenta labeled...

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attachments: scattering_polygon.GIF

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Paul Reed replied on Oct. 21, 2012 @ 09:30 GMT

Lawrence/Ben

Bear with me while I put up what may appear like a simplistic comment, but sometimes a person without all the background sees the ‘wood for the trees’. I have no idea how this could be represented as a model, let alone analysed in practice, but the logic of our reality must be:

In establishing what constitutes dimension, distance and space in our reality, it must...

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Lawrence/Ben

Bear with me while I put up what may appear like a simplistic comment, but sometimes a person without all the background sees the ‘wood for the trees’. I have no idea how this could be represented as a model, let alone analysed in practice, but the logic of our reality must be:

In establishing what constitutes dimension, distance and space in our reality, it must be recognised that we are, in effect, conceiving of any given physical reality (ie physically existent state) as if it was being divided into a grid of spatial positions. And in order to deconstruct it to its existential level, the ‘mesh’ size of this grid would have to be equivalent to the smallest physical substance in our reality. [Note: there is no form of change within any given state of physical existence within our reality, only spatial characteristics, because it can only occur in one such state at a time].

Only physically existent states exist, being comprised of physical substance. That is, concepts either reflect that physicality, or are an artefact of it. By definition (ie what constitutes physical existence within our reality), any given physically existent state must have a definitive dimension/size/shape (ie spatial footprint), this being a function of its constituent physical substance. That, with reference to the conceptual grid, can be defined as spatial positions ‘occupied’.

It could be argued that a direct comparison between states is possible, and therefore there is no need for the concept of a grid. But this is a fallacy, because logically the two circumstances are the same. The physically existent state used as a reference is just a surrogate grid. Indeed, in order to ensure compatibility with other comparisons, that state would have to be maintained as the reference (ie a de facto grid).

‘Mapping’ other states that were existent at the same given time, would reveal not only, obviously, both the spatial footprint of those states and their comparability with each other, but also, distance. That is an artefact, a function of the physicality of the particular existent states involved. It is a difference, defined by comparison. So, there cannot be a distance between physically existent states which existed at other times, because there cannot be a distance to a physically existent state which does not exist. Distance is usually measured between the two nearest dimensions of the existent states, but could include any combination of dimensions. And depending on the spatial relationship of the states involved, distance could involve a relationship in terms of separation of the states, or one within another, that again being with respect to specified dimensions.

Dimension is a specific aspect of spatial footprint (ie spatial positions ‘occupied’ when existent). It relates to the distance along any possible axis. So, three is the absolute minimum number of spatial dimensions that is still ontologically correct at the highest level of conceptualisation of any given physical reality. But is not what is physically existent. At that existential level, the number of possible dimensions that any given physical reality has is half the number of possible directions that the smallest substance in our reality could travel from any given spatial point.

Paul

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Lawrence B. Crowell replied on Oct. 22, 2012 @ 00:45 GMT

Largely what Dribus connects with is causal net, where physica can be established within a minimal set of postulates and is based on the causal succession of events. There is the shape dynamics which involves polyhedra in space and their dynamics. One involves time (causal nets) and the other involves space (shape dynamics), where I think there is some possible duality here between these pictures. I have suggested this might have some categorical relationship to supersymmetry.

Cheers LC

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Dear All,

Another idea I'd like to inject regarding the possibility of shape/causal duality occurred to me while trying to understand the "top-down causation" philosophy presented by George Ellis and others. I struggled with this a bit after first reading about it; in particular I seemed to run into trouble thinking about how one might make it precise. I recall Lawrence expressed some agnosticism about this on his thread too.

Anyway, it occurred to me that, very generically, it might be problematic to expect duality between a theory involving classical holism (e.g. shape dynamics) and a theory with complete reductionism at the classical level (e.g. causal sets). Ellis' top-down causation, suitably represented in a pure causal theory, might incorporate a degree of classical holism into causal theory and make the idea of duality more feasible.

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(continued from previous post)

Whether this idea would work or not, one might still wonder how top-down structure could be incorporated into pure causal theory in a sensible way, and what the actual quantitative differences would be. The answer, I think, is that top-down causation elevates the binary relation generating the causal order to a "power-space relation." The causal metric hypothesis still applies here, but the vertices of causal graphs no longer represent spacetime events. Below, I copy the relevant material from the post I made about this on George Ellis' thread.

(continued below)

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After initially struggling with the idea, I’ve been thinking a bit about

how your [George’s] top-down causation idea might look from the

perspective of nonmanifold models of fundamental spacetime structure that

emphasize the role of causality. It seems that top-down causation might

provide an interesting new perspective on...

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Lawrence B. Crowell replied on Oct. 22, 2012 @ 20:44 GMT

In later thinking about this, the top-down approach might make sense from the perspective of computation theory. It might be there simply is no way that one can compute complex structures at the top from the bottom. This may extend to matters of manifold compactification and the number of possible cosmologies in the so called multiverse. The possible number of windings in 6 dimensions is a...

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In later thinking about this, the top-down approach might make sense from the perspective of computation theory. It might be there simply is no way that one can compute complex structures at the top from the bottom. This may extend to matters of manifold compactification and the number of possible cosmologies in the so called multiverse. The possible number of windings in 6 dimensions is a large number, 10^{1000}, which can be estimated from topology. The "choice" of possible winding index is a set of Boolean procedures, such as a 0 or 1 in a tape slot. A search through all possible such configurations of Calabi-Yau manifolds could not be accomplished by any computer running at any speed that is physically possible.

The busy-beaver function or map is an extremization of algorithmic space or state change. This is an algorithmic variant of the calculus of variations, which pertains to trajectories in space with a continuum measure. A space that is evolving as a foliation or evolute in a de Sitter spacetime of inflation will exhibit nucleation bubbles and a vast array of possible CY manifolds and brane wrappings which construct local vacua are a manifestation of the possible outcomes that are not p-complete computable. The question then is how does the path integral of the universe in effect make the extremization, in a classical sense, or in a quantum setting the amplitudes of the various paths in the path integral?

In these cases, whether it is the halting problem or the busy beaver problem or the minimal compression problem, there is a computation that in principle can be done to look at the behavior of some algorithm. All one does is to track its performance step by step and record its computation or output. What does not exist is a single computable means to do this for all possible algorithms in each of these classes of algorithms. There does not exist a universal machine that can check if all possible algorithms of a certain type pass the test or not, such as halting or non-halting. In the above situation with CY manifolds, what is not computable in a p-complete setting are all possible discrete groups or orbifold configurations.

It has to be remembered that the "universe as a computer" is a model system one has in the "tool box." If we were to think of the universe as a computer or algorithm which evaluates a data stack that is the same algorithm, then we have some issues similar to a universal Turing machine emulating all possible Turing machines and itself. which means it emulates itself emulating itself and all other TMs and so forth. What can of course be done is to think of the universe as cut-off in a finite set of qubits. In that way the universe is not caught in a Godel loop, at least up to the limits of what we are able to observe.

As my essay here at FQXi references how there is only one electron in the universe, but which appears in multiple configuration variables that are holographic projections. The same holds for all other particles, quarks and leptons as well as gauge bosons and so forth. In this way the number of degrees of freedom in the universe is very small, 512 or 1024, instead of the vast number we appear to observe. The number of possible particles that emerges in the multiverse, and the complexity of internal configurations for them, grow faster than any ability to compute them from fundamental states. This means there is an element of "top-down" structure to the universe, where not all the states or configuration of states and structures can be computed from below.

We might consider there to be only 16 basic elementary particles, 3 lepton doublets = 6 particles, 3 quark doublets = 6 particles, the photon, Z and W^{+/-} for four gauge bosons. Again following the thread in my essay the graviton is the “square” of gauge theory. In particular the graviton is an entanglement between to gluons in a color neutral state. So we can ignore the graviton. This is a total of 16 elementary particles. We now consider these plus their supersymmetric partners, for a total of 32 elementary particles. Now divide 32 into 128, 256, 512 and 1024 for 4, 8, 16 and 32 respectively, corresponding to the number of supersymmetries. If we remove the weights of each of these, 4, 8, 16, 32 and the number of supersymmetries we have the root space dimension 120 (icosian quaternion space) 240 (the root dimension of E_8 or SO(32)) 480 (E_8xE_8) and 960. The last is more difficult to interpret.

I was going to get into adinkra diagrams and their possible functorial relationship with causal nets (sets). However, time probably prevents that. Adinkra diagrams are ways of looking at entanglements of states with supercharges. This has been worked for 4 supercharges. With 4 supercharges these are GHZ entanglements, which can be constructed from more elementary trinary (Cat state) and bipartite entanglements. I will defer that until tomorrow.

The NP-complete computation of all possible configurations means the de Sitter spacetime of inflation produces bubble nucleation regions (Coleman’s vacuum instability that results in so called pocket universes) according to an extremization principle. However, how this happens is strange, where the incomputatbility of a universal Turing machine that computes whether an algorithm is halting, or busy beaver, or in this case the computation of a winding topology, means there is no “extremization.” Yet by some means the cosmic wave function(al) does obey it.

Cheers LC

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Paul Reed replied on Oct. 23, 2012 @ 08:04 GMT

Ben

I would stop worrying about top down, oscillation, feedback, reaction, or any other concept that involves an hypothesised relationship which cannot occur.

What is physically existent is so at any given time. At the next point in time, at the existential level, ‘it’ will be significantly different. Which points to the ontologically incorrect way in which we conceptualise...

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Ben

I would stop worrying about top down, oscillation, feedback, reaction, or any other concept that involves an hypothesised relationship which cannot occur.

What is physically existent is so at any given time. At the next point in time, at the existential level, ‘it’ will be significantly different. Which points to the ontologically incorrect way in which we conceptualise physical existence, ie as ‘its’. Really these are sequences (systems) of physically existent states (ie an elementary and specific physical condition of substance), which when conceived by us at a higher level appear to persist in existence over time. But it is really only the superficial physical features which we deem to constitute any given ‘it’ that do so. St Paul’s Cathedral has a significantly different physical state as at each point in time, but it ‘looks’ the same, and we gradually notice the manifestation of alteration.

The more important point here is that at any given time only one physical state exists (aka present) in any given sequence, what did exist has ceased to do so (aka past) and there is no physically existent state commonly referred to as the future. Any concept which involves the notion of change to it, or that it can have some physical influence, is incorrect, because there is nothing in existence to affect, nor anything to invoke an effect. The notion of changing the future is properly expressed as the situation where a physically existent state occurred which is different to what which would otherwise have done so, had the causal factors been different. Which is meaningless physically, as by definition, any given state is a function of certain previously existent states.

At most there could be a repetition of a previously physically existent state as the sequence progresses, but this is still different because it occurred at a different time. Although even that is likely to be superficial, ie due to the level of conceptualisation (but possibly correct at that level). Physically, it is probably impossible that a configuration of any given physically existent state, in its entirety, will re-occur.

All this means that in any given instance of causality the cause must be from amongst physically existent states that exist concurrently, were the immediate predecessor of the subsequent state in sequential order, and had a spatial position which enabled a direct physical influence on the ‘changed’ state (ontologically it is a different state which when compared with a previous one reveals difference).

Paul

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Author Benjamin F. Dribus replied on Oct. 23, 2012 @ 08:30 GMT

Dear Paul,

The difficulty is that you and I have different assumptions about what is fundamental. I regard "what happens" as fundamental and view "spatial sections" or "antichains" or "Cauchy surfaces" as ways of talking about collections of events that don't interact. You regard "what is" as fundamental and regard "what happens" as a way of talking about "changes" in "what is." ...

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Dear Paul,

The difficulty is that you and I have different assumptions about what is fundamental. I regard "what happens" as fundamental and view "spatial sections" or "antichains" or "Cauchy surfaces" as ways of talking about collections of events that don't interact. You regard "what is" as fundamental and regard "what happens" as a way of talking about "changes" in "what is."

I don't know which view is right; maybe they both are! Surely the fact that I proposed the possibility of duality between the two (see my September 19 remark on Daniel Alves' thread) shows that I'm open-minded about the matter. However, I think that your view faces serious physical challenges.

The relativity of simultaneity invoked by Einstein seems to be a feature of the real world, and this seems to preclude a "naive" notion of an external time parameter. You can choose a time parameter, but it will be different for different observers, while the causal structure is invariant. Any number of different ways of slicing things spatially are equally valid, so taking a spatial slice to represent "fundamental reality" puts one on very shaky ground.

I use the qualifier "naive" because something like a preferred family of frames could arise from much more detailed considerations, and this is precisely the point of the whole discussion of Lorentz violation invariance. Once again, I'm open-minded about this; recall that I reject the symmetry interpretation of covariance (which puts all frames on an absolutely equal footing). But there's a big difference between rejecting the absolute equivalence of all frames and insisting on the priority of a single universal frame.

A lot of this comes down to philosophical or aesthetic choices about what "makes sense" or "looks right." Ultimately nature has no respect for such choices, however, so it's better to take very seriously what nature seems to be saying before making them! Take care,

Ben

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Paul Reed replied on Oct. 23, 2012 @ 09:39 GMT

Ben

But, to use your terminology, there can only be ‘what is’, because ‘what happens’ involves multiple ‘what is’. There can be no existence without ‘what is’. There can be no change unless a subsequent ‘what is’ reveals difference when they are compared. The first ‘what is’ having become ‘what was’.

“The relativity of simultaneity invoked by Einstein seems to be a feature of the real world, and this seems to preclude a "naive" notion of an external time parameter”

This concept is incorrect. I did put up a post on my blog about this (it could have been an alternative essay), but do not bother to read that. I have alluded to the odd point here, and there was something I said which triggered a much better explanation. So I am writing a better paper, which should not take long, but my knee is extremely painful as I cannot keep it straight whilst at the computer.

Suffice it to say that ‘time’ cannot alter as a function of observers, or more generally, physical reality does not alter as a function of observers. Observation of reality is precisely that, observation, it is not reality. The ‘spatial slice’ is a reality, what is existent at that time, one in the sequence. Or put the other way round, it is unique at that given time, no others exist. Neither was the Einsten/Lorentz notion about observation per se. The concept of ‘frames of reference’ was connected to the principle of relativity and the fact that any judgement must involve a reference point, the choice of reference is arbitrary, but having made the choice that one must be maintained in order to ensure comparability with other judgements. And before you say it(!) the concern about a relatively moving ‘frame of reference’ was that such a phenomena was also (allegedly) altering in dimension, because the factor that caused the movement also caused that. While it is not impossible, something that is altering in dimension is not the best of references.

Paul

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Author Benjamin F. Dribus replied on Oct. 23, 2012 @ 10:27 GMT

Dear Paul,

First, I hope your knee gets better!

You did not mention before that you have an essay here. I will take a look.

I don't think fighting the essential meaning of relativity will achieve anything in the long run, but science won't suffer any from independent thought, right or wrong. Take care,

Ben

Paul Reed replied on Oct. 24, 2012 @ 05:52 GMT

Ben

Had a scan on knee Sunday

Probably too late now but I would have said it's a slight waste of time because I have a better version of essay (well half of one!) and more importantly what I an saying here (and in the post above (13/10 13.31) about Einstein is not my essay. They are in posts by me about it at 11/7 19.33 and 13/7 11.24.

Paul

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Hello to both of you.

The computation begins to intrest me, :) perhaps it is due to you and Professor Ellis also. I am understanding better the 2d convergences. Thanks for that.

If we want to compute correctly the system of unqueness, so it becomes very relevant for the algorythms of superimposings and sortings.

The determinsim like an essential for all extrapolations. The...

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Author Benjamin F. Dribus replied on Oct. 23, 2012 @ 08:41 GMT

Dear Steve,

Just to be clear, I'm not proposing a multiverse in the sense of the string theory landscape, but only in the sense of the superposition principle. In ordinary quantum theory, the sum of any two states (e.g. particle states) gives you another state, but in a truly background-independent ("single substance") theory, the different particle states result in different "spacetimes." That's all I mean by the "classical universes." They interfere to give a single quantum universe. A relevant motto for this (and in some ways, quantum theory in general) is "E pluribus unum," i.e., "out of many, one." Take care,

Ben

Steve Dufourny replied on Oct. 23, 2012 @ 13:21 GMT

Hello Mr Dribus,

Thanking you.

The principle of superimposings also must be deterministic. I am understanding the difference that you make between the subjectivity and the objectivity. I beleive that the most important is to extrapolate with rationalism.

The spacetimes can be classed with the correct parameters of evolution and increasing of entropy. The states of particules...

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Hello Mr Dribus,

Thanking you.

The principle of superimposings also must be deterministic. I am understanding the difference that you make between the subjectivity and the objectivity. I beleive that the most important is to extrapolate with rationalism.

The spacetimes can be classed with the correct parameters of evolution and increasing of entropy. The states of particules...

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Dear Ben,

I've been procrastinating on making substantial comments, because your causal metric hypothesis is so close in principle to ideas I explored in a 2006 conference paper and in a 2008 preprint .

I hope that with your background in order theory and graph theory, you can make sense of these papers, if you choose and find time to read. I especially agree with the note in your essay: "Here an order is simply the transitive closure of a binary relation, which is said to generate the order. The transitive closure is the minimal transitive binary relation containing the original binary relation."

As you can see at the end of the discussion section of the 2006 paper, I arrived at the conclusion: "transitivity implies identity." This is the spark that lights the fire of the 2008 paper, a blaze which I am still trying to bring under control. :-)

All best,

Tom

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Author Benjamin F. Dribus replied on Oct. 23, 2012 @ 12:24 GMT

Dear Tom,

This looks very interesting. However, the link to the 2008 paper does not work. Could you repost it, please, or send it to me at bdribus@math.lsu.edu? Thanks, and take care,

Ben

Thomas Howard Ray replied on Oct. 23, 2012 @ 12:41 GMT

Sorry, I just cannot seem to ever get the link right on the first try!

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Thank you for the comment on my essay. I enjoyed reading yours and completely appreciate the amateur quality of my own. You know the ropes! Your paper, perhaps unrecognized by you, parlances with the establishment and flirts with boldness. I don’t mean to offend. We are supposed to be scientist here. Certainly many scientists have said spacetime tries to describe the interactions in the universe but scientist refrain from saying spacetime is an interaction. Some scientists refer to it as you do, dynamical, but do not purge it clean from fundamental phages: a still widespread, often subtle but resilient concept older then Kant. With even more ambiguity “spacetime is a way to talk about interaction” is certain to avoid contention. That said your essay describes the sociomorphic status of modern physics rather then a cornerstone to set in motion a new exodus in experimental science. As you hint at, discovery in science is likely to take a new direction after the Higgs and Standard Model are further confirmed but I think it highly unlikely new experimentation will elucidate a binary interpretation of the cosmos. No disrespect binary causal transitions are illuminating ideas. I believe new experimental results will establish a next stage of scientific inquiry leading to new levels of categorization not yet a catch all mathematical rationalization for everything. That does not seem to be relevant until the experiments are done and we have a better database for nongeometric interactions. After all Newton did not come before Kepler and Brahe.

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Author Benjamin F. Dribus replied on Oct. 30, 2012 @ 20:52 GMT

Dear Eric,

Thanks for the remarks. I would not worry about the "amateur" issue; the ideas are what matters. Anyone who neglects "amateur" contributions is only cutting off a source of potentially useful information. In any case, I wouldn't characterize your paper this way; it evinces plenty of familiarity with modern physics and knowledge of what the important questions are, in my opinion. Then again, I'm only a mathematician.

That said, I must say that I have absolutely no interest in political aspects of modern science. Your remarks such as "parlances the establishment," "certain to avoid contention," and "sociomorphic status" tend in this direction. In particular, I don't care a bit if my ideas are "bold," I care if they're right! If I were interested in establishment favor, I'd be doing string theory, not hanging out here.

Getting back to physics, what do you think is the best way to proceed experimentally post-LHC? Also, what do you think of Ellis' top-down causation idea? Take care,

Ben

Ben

In your post (Oct 23 08.30, 3rd para) you quite rightly pointed out that my view contradicts the ‘norm’. In a later you responded: “I don't think fighting the essential meaning of relativity will achieve anything in the long run, but science won't suffer any from independent thought, right or wrong”.

Indeed. So here is my reply. Apologies for the delay, apart from my...

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Author Benjamin F. Dribus replied on Oct. 30, 2012 @ 20:08 GMT

Dear Paul,

Thanks for compiling all this. As I mentioned below, I'm in over my head at the moment with other responsibilities, and can't do justice to the detail of your points at the moment. However, I will highlight one point you make repeatedly that might help explain where I'm coming from. You say (item 13, for instance), "the timing devices must be synchronised, otherwise the timings are meaningless." Fair enough, but how are devices synchronised? Well, by means of interaction. If two systems interact, it makes sense to compare stages of their evolution (e.g., "Bob held the door WHILE Janet walked through.") But if two systems do not interact, it is meaningless to compare their internal sequences to each other. They must exchange signals in order to establish a meaningful notion of common timing. This is the order interpretation of covariance. Take care,

Ben

Paul Reed replied on Oct. 31, 2012 @ 06:54 GMT

Ben

"Fair enough, but how are devices synchronised? Well, by means of interaction. If two systems interact, it makes sense to compare stages of their evolution"

It does not matter how these devices are synchronised, neither is this about interaction, it is just that timing devices must be, otherwise they are useless in their function. They just 'tell' the time, in other words...

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Ben

"Fair enough, but how are devices synchronised? Well, by means of interaction. If two systems interact, it makes sense to compare stages of their evolution"

It does not matter how these devices are synchronised, neither is this about interaction, it is just that timing devices must be, otherwise they are useless in their function. They just 'tell' the time, in other words 'time', the reference, is a measurement concept of tick rate. And therefore Einstein’s (Poincare’s) notion that they needed to reconcile these ‘local’ times against some ‘common’ time was a fallacy. If they were reconciling the timing of observations, then they could explain the difference by light speed, because that is what enables sight, and thereby causes a delay between the timings.

"But if two systems do not interact, it is meaningless to compare their internal sequences to each other"

No so. The determinant is not interaction, it is existence. Two systems/sequences can only be spatially compared as at any given time. In simple language, how do you compare the distance from ‘something over there’ with ‘nothing over here’? ‘It’ being ‘nothing’, in the sense that it existed in the physical state in the sequence being considered for comparison, at a different time from the state of the ‘it’ over there. The two systems do not have to physically interact, it is just a case of establishing what particular states in the sequence each was in at a given time. Your key word in Bob/Alice was “whilst”, ie as at the same time….it was not that there was an interaction. [Obviously there is more to compare than spatial attributes, but that is what is being concentrated on].

Then repeating that exercise will establish no only the substance of the sequence/system, ie what is changing, but the rate at which it is doing so. Timing, ie the quantification of rate of change, does not need a timing device. Systems/ sequences can just be compared directly, neither does the attribute being compared have to be similar. Bob cooked an egg whilst Alice did her homework. Timing is about the comparison of number of changes, irrespective of type, in order to establish the relative rate of change, ie the speed at which the changes are occurring. Neither does the ‘whilst’ have to be at the same time, it is a duration when n occurred in one sequence. Which is why we have a common denominator of tick rate. Then we can identify n occurred in x ticks, p occurred in y ticks, or at a particular tick…….

Paul

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Hello Ben, Paul and all others

The dialog between you two is especially interesting and detailed (amazingly detailed). I'd like to submit some observations particularly pertaining to the following comments:

"The relativity of simultaneity invoked by Einstein seems to be a feature of the real world, and this seems to preclude a "naive" notion of an external time parameter. You can...

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Hello Ben, Paul and all others

The dialog between you two is especially interesting and detailed (amazingly detailed). I'd like to submit some observations particularly pertaining to the following comments:

"The relativity of simultaneity invoked by Einstein seems to be a feature of the real world, and this seems to preclude a "naive" notion of an external time parameter. You can choose a time parameter, but it will be different for different observers, while the causal structure is invariant. Any number of different ways of slicing things spatially are equally valid, so taking a spatial slice to represent "fundamental reality" puts one on very shaky ground."

"I use the qualifier "naive" because something like a preferred family of frames could arise from much more detailed considerations, and this is precisely the point of the whole discussion of Lorentz violation invariance. Once again, I'm open-minded about this; recall that I reject the symmetry interpretation of covariance (which puts all frames on an absolutely equal footing). But there's a big difference between rejecting the absolute equivalence of all frames and insisting on the priority of a single universal frame."

As Paul mentioned, it was probably originally from Poincaré that the conception of the relativity of simultaneity arose. One could, of course, question whether that actually is a feature of the "real world". Or rather that the conceptualization of splitting the Universe into segmented unconnected pieces called "inertial frames" actually reflects what occurs in the "real world". And whether one has lost information common to the Universe as a whole by making that split. I won't argue that doing so has no validity but rather that alternate conceptions and mathematical models involving the Universe as a whole may well give us another picture of the "real world". One that is at least equally valid.

It may not have been fully noticed that the mathematics within one of the essays here does in fact rigorously demonstrate the validity of choosing a single common time parameter for multiple observers. One that is numerically equivalent in producing the observable wave effects elicited in special relativity. It appears that there is a mathematical homomorphism between that model and special relativity. One may therefore choose which paradigm one would like to work with. The application of force and the exchange of momentum is an area where the alternate paradigm is very much more explicit mathematically and physically.

I suppose that is a different way of considering things that falls outside of the comments that I've quoted above and in doing so doesn't so heavily contradict them.

Steve

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Paul Reed replied on Oct. 30, 2012 @ 06:58 GMT

Steve

The key flaw in that quote from Ben that you repeat, and I must stress that most people think-it is not a ‘Ben has got it wrong point’, lies in: “You can choose a time parameter, but it will be different for different observers, while the causal structure is invariant “

Observation of physical existence is just that, observation. Physical existence occurs in one...

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Steve

The key flaw in that quote from Ben that you repeat, and I must stress that most people think-it is not a ‘Ben has got it wrong point’, lies in: “You can choose a time parameter, but it will be different for different observers, while the causal structure is invariant “

Observation of physical existence is just that, observation. Physical existence occurs in one particular spatial configuration at a time. Observation always involves a time delay between time of existence and time of observation of that existence, because light has to travel and be received at the eye (apart from other factors which ‘interfere’). So, even in a ‘still frame of the film’ (ie what exists at any given time), observation timings are different. When the ‘film rolls’ (ie when existence changes) then variance in the momentum of individual observers has an effect. But, existentially, it is just a different ‘still frame of the film’, the others having passed. In other words, like with like is not being compared.

“Or rather that the conceptualization of splitting the Universe into segmented unconnected pieces called "inertial frames" actually reflects what occurs in the "real world".

This is the key point. We cannot deconstruct the entirety of any given physically existent state of our reality which exists at any given time, on the basis of observation. We can however conceptualise its constituent existent states which existed at that time. The problem is that we can only effect that by association with ‘its’, which is a higher level of conceptualisation, ie involves several existent states over time. Think on this: what you know as the monitor in front of you, is not in the same physically existent state from time to time. It just appears that way, because we are conceptualising what physically exists in terms of superficial physical features.

Timing is a methodology which, using a conceptual reference of tick rate, enables differentiation in terms of rate of change. Therefore it is a case of ‘choose a time’.

The notion of frames has nothing to do with observation, per se. It revolves around reference. To be able to effect any judgement there must be a reference, and if more than one is to be compared then the reference must be the same one (or adjusted to be so). The concern over inertial references is because it was believed that anything that was moving relatively was altering in dimension (a single force-gravity-being responsible for both effects). So, unless one factors in that supposed effect, then a moving reference is not a good one to use.

How one copes with this, if we can at that level, I do not know, but even if we consciously simplify it we must maintain the integrity of spatial and timing.

I will have a look at the reference in your post. However I note SR. Have a look at my post above in response to Ben 13/10 13.31. SR is not what everybody seems to think it is, but then you wouldn’t expect me to say anything else!!

Paul

PS: hopefully I can get the rest of the paper finished, which the response above is the front end of, very soon. But I have got to prepare for a Halloween party for the grandchildren today.

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Author Benjamin F. Dribus replied on Oct. 30, 2012 @ 20:20 GMT

Dear Steve,

Thanks for chiming in. As I mentioned in other recent posts, I'm swamped at the moment and can't say much in response. What I will say is that I absolutely agree that "alternate conceptions and mathematical models involving the Universe as a whole may well give us another picture of the "real world"."

It's a difference between "may," and "must." All I am contending is that the idea that we "must" use an interaction-independent notion of time is wrong. I certainly am not arguing that all models involving preferred frames should be rejected out of hand. I like your paper because it is mathematically precise and doesn't take Lie group symmetry for granted. Take care,

Ben

Paul Reed replied on Oct. 31, 2012 @ 07:42 GMT

Ben et al

It is the notion of frames which is causing a problem

A frame is a reference. Any judgement must have a reference. It is always comparison to reveal difference. And in order to ensure comparability of results, that reference must be consistent (or adjustments made on each necessary occasion to make it as if it was so). There is no such thing as a preferred frame (reference). There is a chosen one. And any one will suffice (it is just that some will present more practical difficulties than others).

Now, obviously, if there is some confusion as to the very nature of what is being analysed, then references could get confused. That is why it is best to establish first that physical existence has one physically existent state at a time, which alters, which results in a different physically existent state, and so on. Only one such state exists at a time, the predecessor must cease in order that the successor can exist. And, obviously, the next state in the sequence does not exist.

The two major references, not the devices used to operationalise them, are:

-tick rate (ie a concept of an omnipresent speed)

-spatial grid (ie a concept of a spatial mesh)

Spatial grid enables comparison of what is a fixed state of spatial relationships, ie what occurs in any given physically existent state, which only occurs at that time, and does not involve change. Therefore there is no tick rate.

Tick rate compares difference between physically existent states, ie rate of change.

The question is, given physical reality, rather than a metaphysical belief, can there be a relationship between these two? That is, is there a properly validated reference which enables comparison of spatial relationships over time. And if so, what it the unit of space to unit of change relationship?

Paul

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Sorry folks... I'll get back to this as soon as possible; at the moment I'm swamped with academic stuff. I've also got a few other papers that I promised to look at again and comment on. Feel free to keep up the discussion in the meantime. Take care,

Ben

Dear Benjamin Dribus,

There is an error in your essay: You propose the idea that the metric properties of spacetime arise from a causal relation. It is an error, the metric properties of spacetime depends only on energy-momentum tensor (gravitating matter), but not on causal relations.