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RECENT POSTS IN THIS TOPIC

amrit: on 1/19/10 at 19:32pm UTC, wrote Dear Hans In the universe there is no spacetime. Time is run of clocks in...

Author Frank Martin DiMeglio: on 1/5/10 at 21:52pm UTC, wrote Farrin and Hans/Thomas: Farrin, you said: "A very nice article and...

Farrin Payandeh: on 12/24/09 at 22:52pm UTC, wrote Dear Thomas, A very nice article and wonderful idea about the deep...

Frank DiMeglio: on 11/29/09 at 19:25pm UTC, wrote Hi Hans-Thomas. The following cuts to the fundamental core of reality and...

Eckard Blumschein: on 11/6/09 at 1:25am UTC, wrote Dear Hans-Thomas Elze, Thank you very much for your expert reply. My point...

Hans-Thomas Elze: on 10/29/09 at 14:03pm UTC, wrote Dear Eckard Blumschein, thank you for your message. It makes me curious...

Hans-Thomas Elze: on 10/29/09 at 13:42pm UTC, wrote Dear Lawrence B. Crowell, thank you for your message and the hint about ...

Eckard Blumschein: on 10/28/09 at 18:56pm UTC, wrote Dear Hans-Thomas Elze, I apologize for not having read your essay yet...


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FQXi FORUM
September 19, 2017

CATEGORY: What's Ultimately Possible in Physics? Essay Contest (2009) [back]
TOPIC: Spacetime and Matter - a duality of partial orders by Hans-Thomas Elze [refresh]
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Author Hans-Thomas Elze wrote on Oct. 2, 2009 @ 09:45 GMT
Essay Abstract

A new kind of duality between the deep structures of spacetime and matter is proposed here, considering two partial orders which incorporate causality, extensity, and discreteness. This may have surprising consequences for the emergence of quantum mechanics, which are discussed.

Author Bio

Hans-Thomas Elze is a theoretical physicist. - Phd at University of Frankfurt (1985), followed by positions in Berkeley, Helsinki, and 3 years spent at CERN. Professorships in Bremen, Regensburg, and Tucson (Arizona). Professor at Brazil's renowned Universidade Federal do Rio de Janeiro (1997-2004). Affiliated with Universita di Pisa (since 2004). - Several Fellowships, notably Heisenberg Fellow Award (German science foundation, DFG) for quantum transport theory in gauge theories. Organizer of biannual DICE (foundations of physics) conferences in Italy since 2002. Present interests include: entanglement entropy, decoherence, emergence of quantum mechanics.

Download Essay PDF File




Leshan wrote on Oct. 2, 2009 @ 15:47 GMT
Dear Hans-Thomas Elze,

I have found another essay, which admits the real existence of space-time. (There are many essays at competition that denies the existence of space-time.) My theory also is based on quantum structure of space-time. I agree that space-time and matter must reflect each others atomistic structure.

Imagine a space-time consisting of atoms (elementary volumes dV) that appears and disappears continually. If the elementary volume disappears then a vacant place must appear (a hole in space-time). This hole must collapse quickly because one does not possess extension and duration properties. In other words, a hole is filled by surrounding atoms. Since the speed of motion is limited by the speed of light, the environment cannot fill hole instantly. Therefore the lifetime of hole is non-zero. Holes in space-time must really exist if space-time has quantum structure.

Sincerely, Leshan

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Ben Baten wrote on Oct. 2, 2009 @ 16:14 GMT
Dear Hans-Thomas,

I was glad to see your essay submission to the FQXi contest.

Oddly enough, the end of your essay has some resemblance with my essay. In my essay, based on A.P. Kirilyuk's fundamental work, you can find a state equation (2.1), which resembles your equation (7). However, (2.1) does not presuppose space or time, or known details of the Hamiltonians or the (attractive) interaction potential. Even without assuming any detailed knowledge of those entities, analysis of the state equation shows that quantum behavior dynamically emerges/exists. In particular, discrete time and space emerges in a unified continuous dynamic process that is described quantitatively by the relativistic invariant expression (2.2).

I must admit that my essay is probably not the best format to describe a theory. Consequently, I had to limit myself to highlight particular aspects only, resulting in some artificial shortcuts. However, the details of the theory can be found in the quoted references, on my website, and extra notes on the page where you can find my essay.

Best regards,

Ben Baten

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amrit wrote on Oct. 2, 2009 @ 17:30 GMT
Dear Hans-Thomas

You mention in your essay "slices of space-time".

I do not see and no one has provided experimental data slices of space-time being physical reality. Might be this is merely a math model. Recent research on brain shows that space-time is a brain map, we can talk about neuronal space-time.

According to my research we have to distinguish between math space-time, neuronal space-time and timeless quantum space that is physical reality in which clocks run.

yours amrit

attachments: 3_MATHEMATICAL_SPACETIME__NEURONAL_SPACETIME_AND_TIMELESS_QUANTUM_SPACE_arXiv.doc

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Mohammed Sanduk wrote on Oct. 2, 2009 @ 23:11 GMT
Dear Hans-Thomas

Yes, it is interesting article. I agree with you, about the deep structure of space-time. I think there must be a deep space-time, and this deep structure is responsible for the existence of the complex wave and the particle features in Quantum mechanics. In other word, that hidden existence may be the unified foundation for both Quantum mechanics and Special relativity. The standard Model of elementary particle is quantum version of Mendeleev element periodical table. The discovery of the atom structure has revealed the secret of the periodical table. So if there is no deep space-time, what is behind the particle-wave duality and the standard model? This may be a blasphemy for van Neumann gospel.

However, owing to that probing problem, physics confronts the ultimate limit, and all works beyond that will be speculative. Please note my essay.

Mohammed Sanduk

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Author Hans-Thomas Elze wrote on Oct. 3, 2009 @ 08:56 GMT
Dear Leshan, Ben Baten, Amrit and Mohammed Sanduk,

thanks for your affirmative responses to my article. I see from your notes that you have thought about QM and its potential relation to the deep structure of spacetime in various ways. I will check out your articles.

Best regards,

Hans-Thomas Elze




amrit wrote on Oct. 3, 2009 @ 10:05 GMT
Dear Hans-Thomas

A limit of physics we have to pass is idea of space-time being physical reality. Quantum space is timeless. Gravity is result of curvature of timeless quantum space. More mass is in a given volume of quantum space more space is curved. Curvature of quantum space depends on its density. More mass is in given volume of quantum space, less space is dense and more is curved....

view entire post


attachments: 1_TIMELLESS_QUANTUM_SPACE.doc

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Narendra nath wrote on Oct. 3, 2009 @ 15:08 GMT
i feel fascinated by the curvature aspect of space time continuum where singularities signify the generation of matter and energy associated with it. What may happen if the curvature smoothness gets distorted temporarily? Does it not generate mass/energy. Thus, the concept of space and time becomes fundamantal in the understanding of the physical universe. It simply does not matter wheather it is real or imaginary to a human being inside or outside of the physical universe.

Another aspect i wish to be enlightened by the author concerns the speed of light and its constancy aspect. In homogeneous space it is considered holy. Hwever, if a space ship is built with a technology that can make the spave ahead of it contract and the space behind expanded, the vehicle can certainly exceed the speed limit of c, as it is true only for homogeneous space.

Another point concerns some of the authors in this forum who consider irrelevance of time as essential to picture the universe. Timelessness to them is the truth about the universe, it is ony the objects within that chnage their position and it is there that the speed of change gets involved , not otherwise.

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Author Hans-Thomas Elze wrote on Oct. 3, 2009 @ 15:45 GMT
Dear Amrit,

thanks for your further comments. It would be nice to discuss these in person, with a blackboard nearby ( ... perhaps at next year's DICE conference). I am afraid that you throw in so many ideas in a few lines that I cannot pin down what you really have in mind. In particular (cited from your last post):

"In a centre of neutron stars and black holes density of space is...

view entire post





Author Hans-Thomas Elze wrote on Oct. 3, 2009 @ 16:00 GMT
Dear Narendra Nath,

concerning speed of light and its potential dependence on spacetime structure,

my understanding is that locally(!) you can always transform your description of physics such that it appears as if you were in Minkowski space with c being fixed, as is.

Furthermore, the story is different, if you are in a physical medium. It is known from condensed matter physics (experimentally verified) that the speed of light can deviate from the bare value c. Whether there are reasonable ideas about media that would produce an effective speed of light exceeding c, I do not know. You might ponder about geometries that are expanding exponentially fast (inflation) etc.

Finally, concerning timelessness, there are experts on this issue who are represented among the authors of essays. Better to consult them. In the causet approach, in particular its dynamical versions, there is an intrisic notion of time related to "events happening", i.e. new causet elements being added (or being lost? I tend to believe that there is such a "forgetting mechanism" as well ... ).

Best regards, Hans-Thomas Elze




amrit wrote on Oct. 4, 2009 @ 07:54 GMT
Dear Hans-Thomas

Quantum space is 4-dimensional, matter is 3-dimensional. Material objects exist and are somehow “captured” into quantum space in a similar way as 2-dimensional geometrical objects exist in 3-dimensional geometrical space. Presence of material objects is diminishing density of quantum space that is increasing its curvature. Curvature of quantum space generates gravity....

view entire post


attachments: 3_TIMELLESS_QUANTUM_SPACE.doc

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Author Hans-Thomas Elze wrote on Oct. 4, 2009 @ 11:46 GMT
Dear Amrit,

I see your point. - Just a friendly suggestion, concerning the arXiv:

try to publish your paper first in an appropriate physics/philosophy

journal. From there, you will find the appropriate forum to discuss

and have discussed your ideas.

Best regards, H-T Elze




amrit wrote on Oct. 4, 2009 @ 13:57 GMT
Dear Hans-Thomas Elze

My essay is not about philosophy, it is about fundamental elements of physics that are two:

1. energy

2. change (motion)

Energy of the universe cannot be created and not destroyed. Energy is in a permanent change. IN AGN Energy of quantum space transforms into elementary particles, into energy of matter in black holes and neutron stars matter...

view entire post


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Philip Vos Fellman wrote on Oct. 4, 2009 @ 18:09 GMT
A very enjoyable, readable technical essay which moves us, in important ways, cloaser to understanding the endogenous generation of time, space-time and matter within the light cone. An excellent step on the road to better understading what have been historically difficult epistemological or ontological aspects of quantum mechanics (or quantum electrodynamics). I particularly liked the degree of precision here which did not demand an excessive reliance on either conventional wisdom or received doctrine and which nonetheless provided an innovative approach to deep problems.

Cheers,

Phil Fellman

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Ray Munroe wrote on Oct. 5, 2009 @ 21:58 GMT
Dear Hans-Thomas,

This is an interesting essay. I only skimmed it today. I need to reread it and think about it more. My essay defines all known fermions and bosons (plus many additional states consistent with your described transition from course-grained to finer-grained spacetime) within a multi-dimensional atomistic structure. Interestingly enough, I have also corresponded with some of the other authors on this blog site (Mohammed and Leshan) about how their ideas and my ideas may be complementary. Specifically, Leshan is dealing with "holes" in spacetime that must also have an atomistic structure. The natural assumption would be "if holes in spacetime have an atomistic structure, then spacetime itself must have an atomistic structure".

Let me think on your ideas for a couple of days - I may have more questions or observations.

Good luck in the contest!

Ray Munroe

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Author Hans-Thomas Elze wrote on Oct. 6, 2009 @ 09:08 GMT
Dear Phil Fellman, Dear Ray Munroe,

many thanks for your appreciative responses. Concerning the theme of essay contest, in general, it seems to me that bears a seductive trait to get authors carried away. Therefore, I tried hard to pin down things, while keeping a speculative note. I am glad that you seem to like the outcome.

I will check out your articles, when I get to it, besides daily obligations ...

Best regards,

Hans-Thomas Elze




Ray Munroe wrote on Oct. 9, 2009 @ 15:41 GMT
Dear Hans-Thomas,

You talk about randomly stacking 1+1-D sheets together.

My geometrical TOE models also build on even numbers of dimensions, but they aren't randomly stacked, they are based on products of close-packing simplices (a simple example is: the tetrahedron is a 3-simplex, and this is the underlying structure of a Face Centered Cubic (FCC) close-packing lattice).

Reciprocal and dual lattices are also important in my models.

The 1+1-D base structure may be related to the quantions that Emile Grgin and Florin Moldoveanu have been talking about. Somehow this 1+1-D base structure pairs up (like twistor theory) to form a 3+1-D spacetime.

Good luck in the contest!

Ray Munroe

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Author Hans-Thomas Elze wrote on Oct. 10, 2009 @ 09:30 GMT
Dear Ray Munroe,

thank you for your comments! - Yes, I appreciate very much that this combination of objects of lower dimension to form a decent (1 plus 3)-dim. spacetime seems an essential ingredient. (1 plus 1) is a reasonable starting, since it is the minimum you need, in order to incorporate causality and what I call extensity, i.e. a primordial sign of the presence of matter.

But note that dimensions will only arise as a "measurable" property of causal /extensional sets with large numbers of elements.

Of course, in order to have this give rise to a dynamical "toy model", interactions are all important. They have to produce, last not least, a sort of crumpling transition between a dilute phase of effectively (1 plus 1) objects and a phase that is most appropriately described as (1 plus 3).

Obviously, there remains much to be tried out.

Thank you again, with best regards,

Hans-Thomas Elze




Andreas Martin Lisewski wrote on Oct. 10, 2009 @ 17:58 GMT
Dr Elze,

an noteworthy elaboration on causal sets. But I see two questionable points in your work. I would appreciate your comment on these.

1. You say it is difficult to believe that space-time can exist deprived of matter, but doesn't general relativity (GR) allow such solutions? In other words, your proposed duality cannot account for a full description of GR because it cannot lead to vacuum solutions in GR. To this end, even a Schwarzschild solution is a vacuum solution which certainly has a wide range of physical implications.

2. It's hard for me to understand your conceptual leap from a classical statistical ensemble described by a Liouville equation to a quantum mechanical state described by a von Neumann equation. Wasn't the main conceptual step of quantum mechanics the departure of the classical ensemble toward rays in Hilbert space? In general, such as for the movement of a charged particle, both lead to totally different and dynamics.

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Author Hans-Thomas Elze wrote on Oct. 10, 2009 @ 19:34 GMT
Dear Andreas Martin Lisewski,

many thanks for the very detailed and interesting questions. -- Let me begin with the second one:

The whole point of "emergent" quantum mechanics is to show that there is not necessarily such conceptual leap between quantum mechanics and "classical" theories; but that quantum mechanics appears to us in an analogous way, through coarse graining, as hydrodynamics emerges from atomic physics. This point of view has recently found much attention by, for example, L Smolin and F Markopoulou, S Adler, G 't Hooft, G Vitiello with M Blasone and P Jizba, myself, and others. Papers can be found online in the "arXiv". In the present article I show, as a result, and with reference to more detailed work, that the Liouville equation and the von Neumann equation do not need a different conceptual starting point, but that they are related to each other by a unique set of tranformations -- AND -- differ from each other, in a suitable representation, by one characteristic term.

The aim of the rather condensed last section in the present paper is to discuss that the causal / extensional set perspective provides heuristic arguments which allow to understand under which conditions the Liouville equation does go over to the von Neumann equation, by eliminating the term by which they could differ. This is NOT to say that this is all of QM! I indicated this, open questions in particular concerning Born rule, the danger or interesting aspect of negative probabilities etc., some of which are discussed in more detail in the references given. What is obtained here is the dynamical equation of QM, in the usual Hilbert space language.

To the first question: Once interactions are introduced, in order to continue the present first step by providing a dynamical "toy model", one certainly should be able to see under which conditions the duality is sort of maximally broken, which would provide a causal set theory of a spacetime -- as much studied by R Sorkin and collaborators, see references in the article. One of the aims of the causal set research program, then, is to understand how large dynamical causal sets may approach a continuum limit, and particularly one which is described by GR.

Thus, concerning both your questions, QM and GR possibly arise as limiting cases of a more encompassing theory, in which causality and extensity, besides discreteness, are believed to be essential ingredients.

I hope, these remarks help to place my article in perspective of currently active research topics.

Thank you again and my best regards,

Hans-Thomas Elze




Narendra nath wrote on Oct. 11, 2009 @ 07:01 GMT
The author postulates layers of space time. How the layers can be distinguished from one another. Is there a non-homogeneity in space or how one can separately treat these layers. i often wonder about distortion in space and time that may be shortterm or longer term. May be such distortions are not taking place in the universe now.But these may have taken place closer to the birth of the Universe. Thus it will be very significant to do such cosmological experiments for the early universe. he secrets of unknown physics to me are tied up with what happened in the universe closer to its birth. The Particle Physics appraoch for the same kind of experiments is fraught with huge cost and difficulty in execution ( LHC accelerators).

Smothness between classical and quantum physics also bothers me. The universe evolution is a wonderful example of high logic intelligence. The processes we study appear random in nature as these can not be studied as individual events. But wherein we consider the logic intelligent design. That can not be random in nature and completely probabilistic. Thus truth may be considered to possess an illusion associated with it. We need to sharpen our minds to isolate the 'tricks' nature is playing with us, a challenge for 'smart ' human beings who profess to do high-brow Physics using intelligent Mathematics.

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Author Hans-Thomas Elze wrote on Oct. 11, 2009 @ 09:41 GMT
Dear Narendra Nath,

thank you for your thoughtfull comments on my article. I will make a few remarks in return, citing appropriate parts from your statements:

"The author postulates layers of space time." -- This I do not understand. In my article, as well as in others' recent work on causal sets, and in any microscopic theory of spacetime, there is the *reductionist* assumption...

view entire post





Frank Martin DiMeglio wrote on Oct. 11, 2009 @ 12:10 GMT
Greetings Hans-Thomas. Balance and completeness go hand-in-hand in theory and in life. This can include a sort of "neutrality" involving the unification/merger of opposites. You touch on this to some extent.

Do you agree that the fundamental union of gravity and electromagnetism/light necessarily/ideally involves balancing scale by making gravity repulsive and attractive as electromagentic energy/light? Given the pervasive effects of electromagnetism/light, closely consider: 1)No time at light speed. 2)One cannot catch up to a photon. 3)No feeling of gravity in outer space. 4)Our relative/natural immobilization in outer space (and in reference to photons). 5) Now look at the extremes of size/visibility/energy/brightness involving electromagnetism/light (the Sun and photons).

Our essays discuss many similar and very important issues. My essay is the fourth one listed.

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Author Hans-Thomas Elze wrote on Oct. 11, 2009 @ 12:15 GMT
ADDENDUM:

Dear Narendra Nath,

in order to avoid misunderstandings, let me emphasize that I am not a sole, if not lost defender of *accelerator physics* -- this was just meant as an immediate reply to your concerns. Instead, I believe strongly that research into the foundations of quantum mechanics, which is still at the level of *table top experiments*, as compared to (astro-)particle physics, promises to be one of the most fruitfull, near-future *gardens of Eden* to explore. Crises are imminent, by experience, whenever one (field of research) dominates the others ...

Best wishes, Hans-Thomas Elze




Author Hans-Thomas Elze wrote on Oct. 11, 2009 @ 12:37 GMT
Dear Frank Martin DiMeglio,

thank you for your comments! I am not sure, I fully get what you want to express by points 1) - 5) of your message. Concerning the philosophical remark on the merger or, let us say, interplay of opposites, I find this as teasing the mind as you. The problem is to make such ideas concrete, i.e., to locate them WITHIN physics.

The problem of antigravity that you mention has come up time and again in research, without a definite outcome, as far as I know. An interesting twist on this story are works by Kaplan and Sundrum, Hossenfelder, myself, and others, which discuss a related energy-parity symmetry in various contexts (papers onine at the arXiv). Most attractive feature of this would be a zeroth order cancellation of the particle physics contributions to the cosmological constant.

Your mentioning of dreams, with a loose bridge to physics notions or experiences, I find interesting -- but beyond physics, at this time. Are you aware of the extensive correspondence between W Pauli and C G Jung on these matters; it is inspiring to read but difficult to get something *tangible* out of it ...

Thank you again, and best regards,

Hans-Thomas Elze




Frank Martin DiMeglio wrote on Oct. 11, 2009 @ 13:33 GMT
Hello Hans-Thomas. You are very welcome, and thank you for your reply.

Antigravity fundamentally relates to the balancing and unification of gravity and electromagnetism/light (in dreams, that is): 1)Our relative immobility therein 2)Being in a larger and smaller space at once -- i.e., gravitational expansion/contraction 3)Dreams of falling and flying 4)The varaible distance/size of space...

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Frank Martin DiMeglio wrote on Oct. 11, 2009 @ 14:41 GMT
In addition to the questions/points in my last post to you, do you agree that the fundamental union of gravity and electromagnetism/light necessarily or ideally involves balancing scale by making gravity repulsive and attractive as electromagentic energy/light? Are you still considering this question (from my first post to you)?

This is a very relevant and important question. Thanks. ...

view entire post


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Author Hans-Thomas Elze wrote on Oct. 11, 2009 @ 16:49 GMT
Dear Frank Martin DiMeglio,

since it is fun to discuss and I have a free day ... let me just add few more remarks / questions.

I do not see why unifying electromagnetism and gravity necessarily says something about the need to have antigravity. The only model of this kind, which seems to have survived as a platform for discussion for a number of decades is the Kaluza-Klein idea...

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Author Hans-Thomas Elze wrote on Oct. 11, 2009 @ 19:12 GMT
Dear Frank Martin DiMeglio,

I am sorry that I obviously did not find the right words to communicate serious concerns with you. In any case, it was fun, and I thank you for your rating.

Best regards, Hans-Thomas Elze




Terry Padden wrote on Oct. 14, 2009 @ 01:33 GMT
Thomas

A fine essay on a very important subject.

In fact I include some of your underlying issues among the points of my essay - in a rudimentary and elementary way suitable for non-physicist general readers (at least those with a sense of humour). My conclusion is that an ultimate limit on physics is the (in)effectiveness of its formalisms (maths and logic). My other conclusion is that we need new foundations for our formalisms.

There are physical principles but no empirical content in your paper. That is not a criticism (even if Uncle Al is watching us). I see it as necessary when examining conceptual foundations. So your work, as i see it, uses a new formalism - but one using concepts derived from existing foundational ones. I think that may be the hidden limiting variable in your work.

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Terry Padden wrote on Oct. 14, 2009 @ 01:36 GMT
Thomas

Addendum: I wanted to refer you to the final quote (from Gershwin) of my essay !

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Jose Isidro wrote on Oct. 14, 2009 @ 09:48 GMT
Dear Hans-Thomas,

I enjoyed reading your essay. I have some

questions/comments.

1. If I understand correctly, you have contributed the notion of "extensity" as

a way to implement matter within the causet framework. Previously this

framework existed only for spacetime, w.r.t the property of "causality".

2. Spacetime-matter duality follows. I liked the...

view entire post


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Author Hans-Thomas Elze wrote on Oct. 14, 2009 @ 21:16 GMT
Dear Tony Padden,

many thanks for your comments and putting our articles in perspective. And yes, of course, I try to make a suggestion for a little next step. - I will look at your paper over the weekend, since a piece of humour in a lot of meta-physical considerations that one encounters sounds really like a promise of wellcome "refreshment"!

Thanks again and my best regards,...

view entire post





Author Hans-Thomas Elze wrote on Oct. 18, 2009 @ 10:21 GMT
Dear Jose Isidro,

thank you for your detailed and thoughtful comments / questions for my article. Let me reply, following your points:

1. Yes, to introduce "extensity" is an attempt to have a primordial trace of matter, when trying to build up a theory of spacetime-matter following the successful layout of the causal set approach. Invariably, discreteness is an ingredient from the outset.

2. Duality is a symmetry which may or may not be realized. Since there are two partial orders introduced, it is natural that they somehow influence each other: this must be the role of dynamics.

3. Yes, as I mentioned in the article, QM and GR depart from the experience that empty space or weak gravitational fields are excellent approximations under the conditions that have been accessible to us. However, the suspicion cannot be refuted that this also conditioned both theoretical constructs, which resist to be embedded in a more encompassing structure and understanding, for technical reasons that have been related in many ways to their formulation, as it is.

4. This is hard to say before various dynamical toy models have been studied, in order to get a feeling how the apparent asymmetry can arise. I have two possibilities in mind: matter, as we know it, may present a perturbation on top of a perfectly dual state, or the asymmetry is due to a sort of phase transition breaking the duality. Other possibilities are not excluded.

5. Yes, interactions will be essential. I do not think that this raises doubts, on the contrary: the two partial orders form a "pre-geometrical" picture. In the causal set program, for example, geometry is produced only in the limit of sufficiently large causal sets.

6. I am not sure that I understand your statement. --

Yes, I am aware of your work that you mention. However, I have not thought about a possible relation to what is said here. If I remember correctly, your ideas do not invoke discreteness as a fundamental feature, but discuss this as a result of "quantization"?

Your 'last thought' "... that a symmetry-breaking mechanism in the discrete picture actually becomes a manifestation of the symmetry itself in the continuum ..." is intriguing. -- Certainly, one has to account for, say, Standard Model symmetries somehow (Kaluza-Klein?), of which there seems to be no trace in the underlying discrete structure. You can find hints in the literature that people working along these lines are quite aware of the need to have symmetries "emerge" in discrete theories (R Sorkin, G 't Hooft, F Markopoulou, S Adler, O Dreyer, D Oriti, G Vitiello, B-L Hu, F Girelli, ... ).

Thank you again for giving me the occasion to expand on these matters here.

With best regards,

Hans-Thomas Elze




Member Tobias Fritz wrote on Oct. 27, 2009 @ 14:19 GMT
Dear Hans-Thomas,

I need to admit to having a hard time understanding your 'extensity' relation. What does it mean, intuitively, when u is extended by v? My first mental explanation for this was something along the lines: "well, it's like with Russian dolls, chunks of matter are nested inside each other, so that the partial order records the successive fine-graining of matter". However, now I think that this cannot be what you mean, for two reasons: the first reason being that the elements of a causet are supposed to be the smallest entities of spacetime, its points, and therefore cannot stand for whole chunks of matter nested inside each other. The second reason being that parity reversal also reverses the extensity relation, as equation (6) and the resulting explanation seem to show.

Another explanation I pondered was that 'u is extended by v' could mean something like 'u and v belong to the same piece of matter'. But then, this relation should be an equivalence relation, and not a partial order!

Can you clear up the confusion? Sorry for being slow in understanding.

Last but not least, a minor technical point: your symmetry group doesn't contain time reversal by itself, and neither does it contain parity reversal by itself, although both are symmetries of the kinematics. Why? Wouldn't it be better to consider the full 8-element symmetry group generated by time reversal, parity reversal, and spacetime-matter duality?

best wishes, Tobias

PS: it's good to see familiar names here in the essay contest! (Växjö)

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Author Hans-Thomas Elze wrote on Oct. 27, 2009 @ 20:37 GMT
Dear Tobias Fritz,

it is good to hear from you! And thank you for pondering about my article. - Let me reply to your comments:

The Russian doll idea you mention is interesting in itself, a sort of "bootstrap" mechanism to introduce matter, perhaps? However, indeed, I have not thought about this. Instead I depart from the reasoning that matter should be present but distinct from entities related to spacetime (I mention some current ideas in the causal set literature that attach aspects of matter to the "spacetime atoms", which obscures simplicity and beauty of the picture).

Your second interpretation is closer to what I propose, namely that the only "place" naturally left empty "in between" events in the causal set approach is on the spacelike relations. They can carry matter, which is represented by the extensional relation.

There are two reasons for a partial order here: a) matter is assumed not to exist pointlike but extended; b) the order introduces a notion of direction. One could also say that matter introduces an asymmetric correlation between spacelike events.

Concerning the symmetry group, I agree with you. I introduced only the most rudimentary idea, for simplicity. In particular, when it comes to interactions, one likely has to enlarge the set by operators which interfere with the present symmetry, but could be embedded in a larger group, as you indicate.

I hope, these remarks clarify the points you make.

With my best regards,

Hans-Thomas Elze

PS: Perhaps we meet at Vaxjoe 2010 again, or at DICE2010 here in Italy!




Lawrence B. Crowell wrote on Oct. 28, 2009 @ 01:12 GMT
I will have to read your paper again I think. You do seem to make the point that a duality between matter and spacetime can be obtained from a causal net structure based rather much on logic. I have been working on how spacetime is similar in ways to solid state physics, in particular with tesselations and quantum error correction codes.

Cheers LC

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Eckard Blumschein wrote on Oct. 28, 2009 @ 18:56 GMT
Dear Hans-Thomas Elze,

I apologize for not having read your essay yet because I do perhaps not agree with you in important issues. Nonetheless, I would like to ask you: What does the notion "causal set" mean with reference to the very moment?

Regards,

Eckard

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Author Hans-Thomas Elze wrote on Oct. 29, 2009 @ 13:42 GMT
Dear Lawrence B. Crowell,

thank you for your message and the hint about

possible relations to your work! - Yes, a partial

order, as in the usual causal set approach, provides

a minimal structure to incorporate causality, assuming

this is fundamental (conjectured by philosophers and

physicists alike, even if not by all).

Invoking two such...

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Author Hans-Thomas Elze wrote on Oct. 29, 2009 @ 14:03 GMT
Dear Eckard Blumschein,

thank you for your message. It makes me curious to learn your point of view, in particular, since you mention to possibly disagree. - Do I understand your question correctly as referring to what corresponds to the notion of "now" in a causal set? If so, this can be answered: the "now", corresponding to a time slice, can be seen as the collection of last added elements in a growing causal set; in particular, these are all elements that do not precede any other element, according to the order relation.

For details and technical aspects, I recommend the works by R Sorkin and collaborators (all recent papers are available at arXiv.org, see arXiv:gr-qc/0309009 especially, which is a nice introduction and review), who introduced the modern causal set idea. My suggestion in the paper is to consider two partial orders, instead of one (the causal order) - and to explore the possibly surprising consequences.

Best regards,

Hans-Thomas Elze




Eckard Blumschein wrote on Nov. 6, 2009 @ 01:25 GMT
Dear Hans-Thomas Elze,

Thank you very much for your expert reply. My point was, the present time has strictly speaking no extension if it is not a slice but a Euclidean point sliding along a steadily growing Peirce-continuum .

I will check the hints you gave. Unfortunately I did not find the word extensity in my dictionary. Could you please translate it into German?

What about extensionality (in the sense of Bestimmtheit), I referred to the first axiom of set theory in my essay.

Let me briefly indicate the point of my somewhat hidden objection to Schulman's vote for the frontier in physics:

I am arguing that the a quantity in the past can have two quite different meanings:

It can either refer to the reality that utters itself as an unspecified manifold of traces, for instance the undeniable wrinkles to be seen in my face, or to a finite set copied or otherwise abstracted from it. The latter can be manipulated at will.

Future values of a quantity are always without a real background and therefore of finite quality. In other words there is not yet any real future. The future is partially uncertain because the extension of all influences is infinite while all models, records, or the like cannot consider all possible influences.

Laymen tend to understand this distinction between reality on the one side and prediction or plan on the other side better than physicists who still adhere Einsteins belief that the separation into past and future is merely an albeit obstinate illusion.

Just in order to indicate some consequences of this distinction: I am objecting to the absurd T-symmetry that allegedly only belongs to the wave function.

Best regards,

Eckard Blumschein

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Frank Martin DiMeglio wrote on Nov. 29, 2009 @ 19:25 GMT
Hi Hans-Thomas. The following cuts to the fundamental core of reality and physics, and it directly relates to the claims/core ideas of your essay as well. I would appreciate your detailed thoughts. Thanks.

According to Jonathan Dickau, my idea of "how space manifests as electromagnetic/gravitational energy" is "right on" as a central and valuable idea/concept in physics.

Since dreams...

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Farrin Payandeh wrote on Dec. 24, 2009 @ 22:52 GMT
Dear Thomas,

A very nice article and wonderful idea about the deep structure of space-time.Maybe the deep space-time is what is behind the particle-wave duality and ... .

Best regards,

Farrin Payandeh

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Author Frank Martin DiMeglio wrote on Jan. 5, 2010 @ 21:52 GMT
Farrin and Hans/Thomas:

Farrin, you said:

"A very nice article and wonderful idea about the deep structure of space-time.Maybe the deep space-time is what is behind the particle-wave duality and ... ."

My essay shows this. Does it not?

Your thoughts on this matter are appreciated.

Where do you two see common ground/ideas here?

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amrit wrote on Jan. 19, 2010 @ 19:32 GMT
Dear Hans

In the universe there is no spacetime.

Time is run of clocks in timeless space.

With clocks we measure motion in space.

Motion has no duration on its own.

Duration is result of measurment

Universe is timeless.

yours amrit

attachments: 3_In_what_way_are_related_psychological_time_and_physical_time__sorli_2010.pdf

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