Kelvin,

I looked at your essay, it has some very nice illustrations and the narrative gives a rough idea of what you are trying to convey.

Unfortunately you make a number of very strong statements of fact without showing how they follow from the mathematics associated with your idea. For example, you write:

"It [i.e. your theory] effortlessly merges all the tested features of...

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Kelvin,

I looked at your essay, it has some very nice illustrations and the narrative gives a rough idea of what you are trying to convey.

Unfortunately you make a number of very strong statements of fact without showing how they follow from the mathematics associated with your idea. For example, you write:

"It [i.e. your theory] effortlessly merges all the tested features of Classical mechanics with the statistical probabilities of quantum mechanics and scales up to the cosmological scales of General Relativity."

without showing any equations to substantiate this claim.

I know that in your post thread you said that you are not a mathematician, but, for better or for worse, mathematics is the language of science and for no science is this more true than for physics. In fact, our most fundamental theories of nature tend to bear a greater resemblance to mathematics than to physics because they often involve concepts that are beyond our ability to visualize. One is left in those instances to fall back on mathematics to provide an unmatched level precision of expression, an ability to check the implications of a given relation as well as the consistency of an conceptual structure.

I came, like you, into this area from outside mainstream physics, but I have attempted to take the lesson to be taken from this to heart. The paper in which I presented my full theory contains a mathematical derivation of the Feynman path integral for the simplest situation, a single free particle, from my ideas. My derivation might be imperfect in the sense that involves only a special case and that the expression of some of the ideas could benefit from greater precision, but given an attitude which accepts that mathematics plays a fundamental role in any theory that models nature (which is an inducement to improve one's mathematical abilities, these issues will likely be resolved over time).

I would suggest that you either reduce the strength of your statements, in which case you might frame them more as philosophical speculations, or to present the mathematics that back up your very strong claims.

Finally, I would strongly advise against including any statement like the concluding remark of your essay ["This is my gift to our Planet and all future generations"]

Good luck and take care,

Armin

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Hi Jerzy,

Thank you for your feedback. Would you care to elaborate why you did not find it a very easy task to read my essay? Was this also because of overly long paragraphs? Having seen some of your work I suspect that instead it may be that my paper is not nearly as mathematical and precise in the expression of some of the core concepts as one would expect of a mathematical paper. But I'm...

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Hi Jerzy,

Thank you for your feedback. Would you care to elaborate why you did not find it a very easy task to read my essay? Was this also because of overly long paragraphs? Having seen some of your work I suspect that instead it may be that my paper is not nearly as mathematical and precise in the expression of some of the core concepts as one would expect of a mathematical paper. But I'm not sure, and your feedback would certainly help me improve my writing style.

I completely agree that mathematics bridges the separate domains, just as the concept of area does not suddenly become meaningless in three-space. It is just the entities that are the subject of the theory and described by it which are confined to those domains.

As for your question about the relationship between the pictures, I take it that you are asking me about the relationship between the object in fig. 3 and that in fig.4 and how it relates to quantum theory. I think you understand the analogy correctly: fig. 3 is an analogy for a an eigenstate immediately after it has been 'measured' and fig. 4 is an analogy for the superposition state just before the measurement (also fig.5 which is an analogy for the 2-state system). the attribution of an interval along z is an analogy for a 'measurement'. note that the analogy can even to a limited extent accommodate a change in basis: Instead of 1 unit length along z, we could chose 2 or n unit length to attribute to the column, in which case fig. 4 would turn into a superposition of an infinite number of objects with unit width and depth but n-unit height.

The purpose of these pictures and analogies is just to help develop intuition for the basic idea, which is simply that an object (really a worldline) in areatime manifests itself to spacetime observers as a superposition of spacetime worldlines which however do not have the same quality of existence as the worldlines of spacetime objects., and that a 'measurement' is what happens when the superposition of worldlines collapses to just one actual one.

I hope I was able to answer your questions. if you have more feel free to let me know.

take care,

Armin

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Dear Jerzy,

I want to give you a fuller response, but my work week starts today (I work midnights 7 nights on and 7 nights off while going to school) so a more elaborate version will have to wait until next week.

For now, let me just say that you are basically correct. The QM operator corresponds in my analogy to the operation "add an interval of length z" and the eigenvalue...

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Dear Jerzy,

I want to give you a fuller response, but my work week starts today (I work midnights 7 nights on and 7 nights off while going to school) so a more elaborate version will have to wait until next week.

For now, let me just say that you are basically correct. The QM operator corresponds in my analogy to the operation "add an interval of length z" and the eigenvalue corresponds to the length of the side of the cube wherever it 'actualizes'. I did not mention probabilities in my paper, except very indirectly when I said that being 'actualizable' corresponds to an intermediate state of existence. Some time ago, I replied to another person what I meant and for the sake of time I will just paste my response because it may help understand better. (The person to whom I responded was an educated layperson, not someone like you who understands the implications at a very deep mathematical level, so the tone of my exposition was meant for a different audience).

here it is:

"The more challenging concept to understand is what I have called 'actualizable'.

Before I attempt to explain it, let me acknowledge that it is not your fault for having this conceptual difficulty. In all of my papers about my theory and the talk, I have so far described the concept of actualizability only within a very limited context, namely how it is different from "actual". But to get a deep understanding of what this concept really means one needs more than an understanding in terms of what it does not mean. The fact that I have not been more specific is not entirely an accident.

You see, I have found that when in discussing my ideas with others I introduce too many unfamiliar ideas at once, the risk that they will be dismissed as being too far "out there" dramatically goes up (you can even see that in this thread), so I have tried to be strategic about it: I try to introduce just enough so that it becomes evident that one can reframe quantum mechanics in a novel way that no longer seems mystical (as in my talk), leaving more subtle clarifications of the conceptual basis which have truly radical implications for later, after the basic picture painted by my theory is at least somewhat understood and it becomes clear how the radical implications of the novel concepts are required in order to form a self-consistent worldview (which is different from the present one). Describing precisely what I mean by "actualizable" is one of these concepts (but unfortunately not the only one).

I take it that you have perused the references I provided and that therefore you are ready for the more precise definition:

My concept of 'Actualizablity' refers to an intermediate state of existence.

I mean it in the following way: According to our current worldview, existence is a binary concept, which means you can assign one of two values to the ontological status of anything

0- it does not exist

1- it exists

end of story

The notion that something could have an ontological status somewhere in between, which is what I mean by "intermediate state of existence", at first sight seems absurd. If one is going to claim such a thing, one better have a darn good reason for doing so. Well, my reason for doing so is that this definition is required to provide a consistent conceptual basis for a framework that seems to make sense out of a lot of the seemingly mysterious parts of QM.

So, does that mean that something could have an ontological status of, say, 0.3? Yep. 0.6? Yep. And that the latter in this sense twice exists "twice as much" as the former? Yep.

I can appreciate how bizarre this must seem to you, but I would argue that a large part of this is just due to the fact that since you were a little kid you have been conditioned to think of existence as binary and you are reading this for the first time. If this idea is generally accepted, future generations will find it a lot less strange. If you doubt this, just ask yourself how strange you find the idea that the earth goes around the sun? Well, today almost nobody finds this strange, even though it is exactly opposite to what our sense experience tells us. That is why if you had suggested that to someone in the 16th century before Copernicus, they would have considered it an extremely bizarre idea.

We actually already have way for quantitatively expressing actualizability, but we have not yet recognized it as such. It is called the Born Rule. I am certain that you don't see the connection, so I will try to be more specific.

First, let me review how the need for "squaring the wave function" arises in my theory. As you should recall, I postulate a symmetry that serves as a mechanism by which the passage of time for an areatime object (its proper time) can be matched or "translated" into the proper time for each actualizable object that traverses an actualizable path in space. Upon a simple transformation, the symmetry can be decomposed into two complex conjugate phase factors which are associated with each actualizable path, and upon appropriate substitution become e^plusminus(iS/hbar). Since the areatime object manifests itself in spacetime in terms of a superposition of all possible actualizable paths, and each is associated with the phase factors, the proper representation of the areatime object in spacetime is the Feynman path integral.

Now, in transforming from the Lagrangian to the Hamiltonian Formulation, the exponent of the phase factor changes but there is still a direct link between it and the phase factor of the Wave function Psi. This implies that Psi only represents the square root of all the spacetime manifestations of the areatime object in a specified region of space (Each phase factor represents 1/2 of the symmetry associated with the angle in the exponent, and 1/2 in the exponent is the square root). To represent it fully, you must multiply it by its complex conjugate, which is to say that you must take the absolute square.

But just as in my Euclidean analogy a point in 2-space manifests itself as an infinite line in 3-space, the representation of the areatime object in terms of the squared wave function extends over all of space (in the non-relativistic limit at least. In the relativistic limit, I believe, it extends only to the boundaries of the light cone originating from where the paths started).

So if you integrate the absolute square of the of the wave function over all of space, you have finally obtained a complete spacetime representation of the underlying areatime object under the Hamiltonian formulation. Under the Born rule, this is set equal to one and interpreted as a probability.

Let us suppose that the the wave function represents a particle. One often finds a statement to the effect that the above reflects the fact that the particle is certain to be somewhere in space. Under my interpretation it means that if a "measurement" is performed everywhere in space, one is certain to detect a particle somewhere (Since a "measurement" is the mechanism by which a spacetime object emerges out of areatime).

At first glance, the two statements might seem equivalent but they are not: The first assumes that there is a particle out there, independent of whether you are trying to measure it, whereas the second does not. Prior to a measurement, you still have merely the representation of an areatime object in spacetime, not a particle in space. You can hopefully see my interpretation comes closest to the Copenhagen interpretation, but unfortunately the CI tends to substitute mysticism for genuine gaps in understanding.

Alright, after this basic review, let me now get down to how the Born rule can be interpreted as a reflection of "partially existing objects" ('actualizable' sounds much better to me) .

Suppose a quantum state in a particular basis consisted of only two eigenstates. Each of the eigenstates has a coefficient which tells you how much it contributes to the total state. In standard QM, the coefficent has a purely operational interpretation. What I mean is this: The coefficient is ideally determined by running measurements on a large number of identically prepared states, and the frequency of the two different possible outcomes is recorded. Since the calculation of the expectation value for the measurement outcome involves both the wave function and its complex conjugate in a product, the coefficients are the square roots of the relative frequencies. For example, if both outcomes are equally likely, then, the coefficients become sqr (1/2)=1/sqr(2). Since, as far as I know, there is in standard QM no "deeper" interpretation of this, the coefficients must be interpreted purely operationally, as mentioned.

In my framework, the coefficients have an ontological interpretation: The coefficients tell you how much each actualizable eigenstate contributes to the total representation of the areatime object in spacetime, and their contribution is a measure of the extent to which the areatime object "fractionally" exists in spacetime in that particular manifestation.

The problem is that when you do 'measurement', you cannot detect "fractionally existing" objects, only ones that fully exist in spacetime, hence the ontological status of the eigenstate you detect upon a measurement must change from some value less than 1 to 1. This is consistent with the fact that if you immediately repeat a measurement, you will obtain the same outcome, and directly connects this to the probability interpretation, since under a the latter, being certain of obtaining a particular result is equal to a probability of 1.

So let us now examine the bizarre notion that one eigenstate could exist "twice as much" as the second. Well, it just means that the coefficient of the first is sqr (2/3) and the coefficient of the second is sqr(1/3). Because both states are associated with some form of existence, in a small number of runs you might measure one or the other in some different proportion, but in the limit in which the number of runs on identically prepared systems goes to infinity you recover the fractional existence of each state. This is essentially the definition of the (frequentist interpretation of) probability.

"Conservation of probability" then is really conservation of existence. Unfortunately, existence is not currently considered a physics concept but I strongly believe it needs to be. As you might imagine, this makes the idea all the more difficult to accept. I had written a paper a while back called "Ontology and the Wave Function Collapse" where I hinted at this problem.

Alright, if you have really read my papers and watched my talk, I hope that you will see how this fits in with everything and have a better understanding of what I mean by actual vs. actualizable, but if you have not done so, I doubt that the above will make much sense to you. "

hope you found this useful,

Armin

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Hi I went back to your post and saw that it contained some questions I did not see. Ok, here is my best attempt to answer your questions:

You said: "When I read your DFR concept, it again brought me to essentials like "a square has only one side" or is two sides ? for a flatlander it has only one side , and a moebiusring does not exist in his 2 dimensional universe. On page 5 you are...

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Hi I went back to your post and saw that it contained some questions I did not see. Ok, here is my best attempt to answer your questions:

You said: "When I read your DFR concept, it again brought me to essentials like "a square has only one side" or is two sides ? for a flatlander it has only one side , and a moebiusring does not exist in his 2 dimensional universe. On page 5 you are creating the column of squares, just as a straight line , a fixed z coordinate, however the Z coordinate can take any value, so that any form is "actualizable".

Saying that to a flatlander a square has only one side is like saying that to us a cube (when looked at face-on) has only one face. Do you see that you are conflating perspective with dimensionality? A flat lander can go around the square and thereby establish that it has four sides and that it is not just a line segment. A moebius ring like region in flatland could exist in principle: cut at two places into sheet of paper to make a long strip without separating the strip, then twist that part between the cuts (the strip) by 180 degrees and glue the ends of the strip to the edges. You won't be able to glue the entire strip, but if it is long and narrow enough, you can glue that part that is the closest to where you started to cut. For us, this would be like a region in space for us in which if you go in and come out in a certain directions everything is mirror-reversed, but that is just exotica that I don't think is relevant to my idea. The last part of your paragraph seems to agree with my idea.

You said:"Your page 6 is in fact the same as the theory of the collapse of the wave function, even the comparision to the Feynman path, I like your description of area time as "it manifests itself to spacetime observers as asuperposition of two actualizable matter distributions describable by ....". The only remark here is that you accept already the existance of the "observer" (!)"

Indeed, I do already accept the existence of the (spacetime) observer. this is required by the fact that quantum mechanics goes in the (2,3) box (refer to the appendix). I could have also not accepted the existence of a spacetime observer; that would be a theory of areatime interactions when spacetime has not yet emerged, and this theory goes into the (2,2) box, such a theory is only metaphysical for us, since we cannot observe in 2+1 dimensions, so I see no problem.

You said:"On page 7 you mention "two or more objects described by the same non-factorizable wave function who share the same wave-function, share common wave factors", I came to a different interpretation (with almost the same result) and introduced the Objective Simultaneity Speres, together forming a foam being the origin of "decoherence".

No, in my paper I stated that"... two or more objects... described by the same non-factorizable wave function...share common *phase* factors." This is a big difference that can only be appreciated if you know something about the mathematical structure of the wave function. Also, I would be very careful in claiming that a an idea you have corresponds to a well-defined concept like "decoherence" without showing how it exactly does that. To understand decoherence you will already have to know quite a bit of quantum mechanics. Using a technical term like "decoherence" in your theory without actually showing how your theory corresponds to it will damage the credibility of your theory.

You said:" I liked very much you schema of the "METATHEORY OF NATURE", very good , the only thing you could think about is that the dimensional frames could also go to the negative side and perhaps there all the dark energy and so on can be found."

We use negative dimensions already all the time, they are called *densities*. For example, mass density is mass per volume or mass times length^(-3). If you look at the schema, you see that, for example area=length ^2, so a negative dimension has to be a density. If you meant negative signs in front of a dimension i.e. as a coefficient, then I don't know what that means, other than perhaps a direction in an arbitrarily defined coordinate system.

While Dark Energy indeed appears to be a negative energy density, I don't think your suggestion will help understand it any better, because "negative" in this context has a completely different meaning:it refers to the energy not to the density.

You said:"I hope that you take the time to comment also on my essay, this tile I took also at heart your posts wher you gave me indications how to be more clear."

Well I did and as I said, you have greatly improved how you communicate your ideas. Communicating one's ideas is very important but it is not enough: You also have to make sure your ideas match what we know, and the only way to be certain that you can do this is to learn what we already know. I was in your situation several years ago, but I have made a sincere effort to learn what we know, and continue to do so. I am sure that you are making some effort to learn what we know, but to be effective, it should not be from a science popularization but a text book. Also, in response to our exchange I suggested to Max Tegmark that FQXi add a physics resource section, and they did. Have you seen it? If not, go to the community page and look at the upper left corner.

Thanks for your comments and good luck in your endeavors,

Armin

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Mi M.V.,

Thank you for the critique and for listening. I had planned to upload more music but reading all these essays has caused me to fall behind.

Yes, I had heard some of its pieces but not "In a monastery". I did find the link below:

http://youtu.be/ix1t4AsQXdo

I find Borodin's music has a very unique quality which I like a lot. Very few composers have such a...

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Mi M.V.,

Thank you for the critique and for listening. I had planned to upload more music but reading all these essays has caused me to fall behind.

Yes, I had heard some of its pieces but not "In a monastery". I did find the link below:

http://youtu.be/ix1t4AsQXdo

I find Borodin's music has a very unique quality which I like a lot. Very few composers have such a distinctness pervading their work. The other composer like that who comes to mind is Chopin, whose music is also very beautiful.

I thought that probably many readers here are familiar with flatland, and that it would not be a bad idea to start from familiar place to launch some ideas that are no doubt highly unfamiliar to many.

About your question: I will give a mathematical and a conceptual answer.

The mathematical answer is that if in a given coordinate system you wish to specify a lower-dimensional "surface", you just specify that part of it that you want to assign a position in space and leave the rest unspecified. Thus, x=3, for example, specifies an infinite plane that intersects the x-axis at 3. r=3 in a spherical coordinate system specifies a sphere of radius 3, and so on. So when you leave certain properties of the surface unspecified, they mathematically take on all possible values for that property.

The conceptual answer to your question is that when you leave the property unspecified, it attains an "empty slot" for that value. This means that you cannot assign it any definite value (that would be filling the slot with a definite value), but you still wish to represent it somehow in the higher-dimensional space. If you think of an empty slot as one that is "waiting to be filled" then the representation would include all possible values, since any of those could eventually fill the slot.

I don't know if my conceptual explanation made any sense to you, but I would appreciate your feedback on whether it did or not. I believe it is important to be able to communicate my unfamiliar ideas clearly to others, so your question is received with much gratitude.

Thank you also for the final comment.

All the best,

Armin

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Dear Juan,

I just re-read your essay (I had read it once soon after it came out but wanted to refresh my memory).

I agree with several of the eight points you made, and indeed some of them are quite close to the arguments discussed in my paper.

In particular, the idea that spacetime is not fundamental (or "special" as I like to say) would seem to be an unavoidable...

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Dear Juan,

I just re-read your essay (I had read it once soon after it came out but wanted to refresh my memory).

I agree with several of the eight points you made, and indeed some of them are quite close to the arguments discussed in my paper.

In particular, the idea that spacetime is not fundamental (or "special" as I like to say) would seem to be an unavoidable consequence of attributing quantum phenomena to the spacetime manifestation of objects that actually exist in lower dimensional analogs.

Also, I agree with the notion that unitarity is not fundamental, but it appears to me that this is for a different reason than given in your paper: In my framework, the mathematical requirement of unitarity arises ultimately from a simple symmetry that serves as a mechanism for comparing two distinct proper time dimensions: the proper time of the underlying onject in areatime, and the proper time associated with each path that is part of the path integral. Since objects we observe in spacetime do not require this "comparison mechanism" this would seem to refute the notion of unitarity being fundamental.

My knowledge of black hole thermodynamics is insufficient to be able to give sound evaluation of your argument, but let me just say that I am a bit suspicious about whether any of the seemingly reasonable assumptions that had to go into combining quantum theory with general relativity will in the end turn out not to be reasonable.

You raise an interesting point under your "quantum state vectors are not fundamental" section: If one has a multiparticle entangled state, how sensible is it to consider each describable by its own "state"? Probably due to my own prejudices, I tend to shy away from claims that descriptions that are even more mathematically abstract than this as being the "fundamental" description (such as the state operator in Liouville space) because at least in my view, whenever one abstracts, one loses some part of the thing one tries to model, and the extent of that loss defines how much less fundamental the abstraction becomes. To me, path integrals are the most fundamental description. They may seem abstract, but as far as I can tell, they are the most concrete models of quantum object in that they describe objects directly in spacetime rather than in some abstract phase, state or configuration space.

The point that GR is not an ordinary field theory is congruent with that presented in my paper, although again for different reasons. In my view, the notion of a quantum field captures in the greatest generality the idea that there is some lower-dimensional fundament from which spacetime is continuously emerging, and that close to that limit where, as it were, the "phase transition" occurs, there is a constant flux between the "phases" perhaps not so unlike what can observe in certain thermodynamic regimes. Since GR is about "equal dimensional" objects in relation to the observer's dimensional frame of reference, GR cannot, according to this view, be an ordinary (quantum) field theory.

Finally, I suspect that dark matter may be related to gravity somewhat as gravity is related to electrodynamics: In the proper limits there may be some similar or even formally identical relations (say, Newton's vs. Coulomb's law) which may confound our observations and lead us to believe that there is a gravitational explanation for it, but these might reflect totally different underlying conceptual entitities.

Milgrom's relation does not seem in contradiction with this view, for one could imagine an analogy in which Newton's law was replaced with a special kind of "Coulomb's law" that holds only under certain circumstances (e.g. it is only noticeable at very large scales, it is always attractive, it even holds for entities in which all electrical charges cancel etc. etc. ). I suspect that Milgrom's relation is something like this special "Coulomb's law".

Incidentally, if you did not see the appendix to my paper, you may find it interesting to see the proposed schema of the metahteory.

So, overall it seems that we agree on many of the points albeit for substantial different underlying reasons. Thank you for reading my essay,

All the best,

Armin

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Dear Armin,

Thank you for emphasizing the analogies on our arguments. It is a good notice for science when two or more lines of reasoning converge at the same point. This increases the confidence of each one of them.

Let me emphasize that my reasons against unitarity are general and apply as well in cases when proper time is not even defined.

There is not problem in defining...

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Dear Armin,

Thank you for emphasizing the analogies on our arguments. It is a good notice for science when two or more lines of reasoning converge at the same point. This increases the confidence of each one of them.

Let me emphasize that my reasons against unitarity are general and apply as well in cases when proper time is not even defined.

There is not problem in defining the state of a particle in a multiparticle entangled state. Of course, in this case the state cannot be given by a state vector as Dirac first noticed. Observables for each particle are computed in the ordinary way using the state operator for the particle.

Path integrals are not fundamental, they are derived as special case for a restricted class of systems. Moreover, in quantum field theory the spacetime associated to the path integrals is dummy and has no physical meaning:

"Every physicist would easily convince himself that all quantum calculations are made in the energy-momentum space and that the Minkowski x^\mu are just dummy variables without physical meaning (although almost all textbooks insist on the fact that these variables are not related with position, they use them to express locality of interactions!)"

--------

H. Bacry

"It is important to note that the x and t that appear in the quantized field A(x, t) are not quantum-mechanical variables but just parameters on which the field operator depends. In particular, x and t should not be regarded as the space-time coordinates of the photon."

----------

J. Sakurai

Regarding GR, my point is not that "GR cannot, according to this view, be an ordinary (quantum) field theory". What I am emphasizing is that GR fails to satisfy dynamical and energetic consistency even at the classical field theory level. This is the reason which GR is plagued with a number of serious difficulties as described in textbooks. Such difficulties are absent in the Field Theory of Gravity (FTG).

The idea that Milgrom law can be reproduced by a scale modification of some existent law is not new. It has been explored by many but it does not work, because Milgrom law is an acceleration scale modification of Newtonian mechanics. It does not predict deviations from Newtonian gravity for certain distances (.e.g. galactic scale), but deviations for certain accelerations below the Milgrom one. In my own work I derive all observed phenomena plus the value of this acceleration scale.

With my best regards.

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Dear Hector,

Thank you for raising some extremely interesting questions. I would love to discuss them without the restraints of space and time, but this is not always possible, so I will attempt to give reasonably concise answers.

1. Re: Information theory. Given that I don't have much knowledge in this area, I am agnostic on your specific question, mainly because I don't trust...

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Dear Hector,

Thank you for raising some extremely interesting questions. I would love to discuss them without the restraints of space and time, but this is not always possible, so I will attempt to give reasonably concise answers.

1. Re: Information theory. Given that I don't have much knowledge in this area, I am agnostic on your specific question, mainly because I don't trust myself to know what has yet to be imagined in the future.

I can perhaps give a more satisfactory answer about my point of view on the interpretation of information as a foundation for reality, a view one does find occasionally, particularly in the area of quantum foundations (If I am not mistaken, Anton Zeilinger is a prominent proponent of such a view). I am sympathetic to this view, for if this turns out to be true, then, it seems to me, it would effectively unify mathematics with physics.

There are, however, two profound problems that I see, and I'm not sure due to my lack of a deep understanding of the subject matter whether these are genuinely original objections or problems solved a long time ago, or even worse, non-problems or reflections of my personal misunderstanding. Should the latter be the case, please do let me know, so that I can correct my mistakes.

1) The problem of the "map": Suppose Wheeler's "it from bit" is true, it seems to me then that there is a "map" which leads one from "information" to "substance"(using this term to stand in for concrete physical quantities like matter, energy, space and time). The reverse "map" seems to be pretty well understood: we can think of "information" generically as some pattern of distinctions in otherwise formless "substance" , but I have difficulty envisaging the "map" that leads the other way around. Of course, an extreme proponent of "reality is information" might say that the map is a simple isomorphism, but to me that seems merely a case of "defining the problem away". What does it really mean to claim this? How does it contribute to the understanding that purportedly a quantity of "substanceless" information is equivalent to a quantity of "substance"? Moreover, if there really was such an isomorphism should it not be impossible to draw distinctions between the knowledge about a system and the reality of the system itself? The mere fact that we can easily conceive of situations in which such distinctions occur would seem to serve as a counterexample to this argument. One can also turn this around: Consider a scenario in which a quantum system has undergone one of those "measurements" in which the observer could "in principle" know the state of the system but in practice doesn't. The state collapses, and its information is known, but by whom? A hypothetical observer? If so, and information is reality, then a hypothetical observer, who only exists as an "informational construct", as it were, would seem to have to be every bit as real as an actual one. Is this a tenable position to hold?

I suspect that if we better understood the "map" that leads from information to substance (assuming it really exists) then many of these problems would suddenly become resolved in an obvious manner.

2) The information vs. Substance chicken vs. egg problem: Let us suppose the map exists and we are able to describe its nature satisfactorily. Then we would have grounds for claiming that there is a certain type of "fundamental" information (namely the kind which does not depend on any kind of "substance" in order to exist) which leads to "substance". But we know that there is also less fundamental information, namely the kind which does depend on substance for its existence. If so, could it not be the case that there exists also a more "fundamental" kind of substance which underlies our original "fundamental" kind of information? And if that is the case, is it not possible to continue this on in the manner of an infinite regress?

Again, I'm not sure how worthwhile these arguments are but they are at least the hurdles that strike me as the ones that need to be overcome before one can seriously consider information as a basis for reality.

Finally, on your question on whether the connections were completely unforeseeable. I'm not sure that this is completely right. Let's take E&M as an example: Oersted discovered the induced magnetic field in 1820, and Faraday surely had already a good conceptual picture of the relation between the fields at least in some settings well before Maxwell's treatise. So I would argue that the unification was, at least for over 40 years prior to its occurrence, not completely unforeseeable.

There is, however, a more interesting angle which adds some support to your point of view. It was only with the advent of special relativity that people could appreciate that it is not the fields that are the fundamental objects of the classical electromagnetic theory but the electromagnetic field tensor, for, as you know, that is the true spacetime object underlying the fields. I completely agree that before SR, this more unified understanding of the fields was indeed completely unforeseeable. Now, the irony here is that, since relativity is profoundly concerned with the concept of a reference frame, in this case, a deeper understanding of this concept led to a more unified picture.

But as I argue in my paper, our current conception of a reference frame is still not the deepest conception, and the unexpected nature of expanding this aspect leaves the door open for future developments in our understanding to be different from past ones in regards to unification.

Furthermore, as I pointed out toward the end of my essay, one can have multiple deeply significant trends in the history of science the resolution of one of which may well portend the termination of the other. It seems rather arbitrary to say that one trend is more important than the other, which is what would have to effectively do in order to ignore the consequences of this interplay between the trends.

I included the historical discussion in my essay precisely because I wanted to give the reader a greater sense for these broader considerations that surround the question of the existence of a theory of everything.

I hope that I was able to usefully address your questions,

All the best,

Armin

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Dear Inger,

Thank you so much for your interest, and your investment of time and attention. I am certainly happy to attempt to answer your questions.

You said:

"Does this mean that the smaller object is less acrual than the larger one, in a 3-dimensional frame of reference? This is how I intepret your schema. "

I suspect you might have meant "actual" (at least that way...

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Dear Inger,

Thank you so much for your interest, and your investment of time and attention. I am certainly happy to attempt to answer your questions.

You said:

"Does this mean that the smaller object is less acrual than the larger one, in a 3-dimensional frame of reference? This is how I intepret your schema. "

I suspect you might have meant "actual" (at least that way I can understand your question). Well, this is a bit tricky for me to answer because a full explanation depends on ideas that I have not yet publicly discussed or disclosed anywhere and introducing them here informally without detailed background information (as in a paper) does not seem such a good idea. I have already experienced the reactions of people who hear a really strange sounding idea without sufficient backing sufficiently often to know better.

Within the context of the paper and everything else I have discussed so far, the answer is no. The gradations in existence as I have discussed in my paper only apply to actualizable objects. For actual objects, existence is still binary: Either an object actually exists or it doesn't actually exist. Actualizablity, on the other hand can take on intermediate "ontological values", where by ontological value I mean this:

0- it doesn't exist

1- it exists

I did present a fuller description of this in my post above on Sept. 10th 18.36 in response to Jerzy Krol, and hope you don't mind if I refer you to that for more details as it was a bit long.

Having said that the answer is no, I will also mention that I believe that the answer is ultimately a qualified yes. I actually don't believe that actual existence is binary, but a quantity. Explaining my reasons for believing this at this point would take me too far. Suffice it say that if you can have quantitative gradations between actual existence, then of course it implies that some objects can be less actually existing than others, and you could create situations in which smaller objects are less actual than larger ones, but I would like to emphasize that in this case size is not the relevant factor, rather it is the energy-momentum associated with the object. Again, if this sounds really strange, just ignore this paragraph until I have had time to present my argument in a detailed paper at some future date.

What the schema does is to present a broad pattern into which we might be able to fit our current theories to obtain an overview of how they relate to each other. while there is a definite relation between size and dimensionality, the boundaries between the integer dimensionalities have to be abrupt to keep the domains of the theories apart. I envision this very much in analogy to phase transitions. As you heat, say, a quantity of water under constant pressure its temperature only increases up to a certain point, beyond that it becomes something that is macroscopically totally different, even though it is composed of the same basic building blocks.

You said:"

Analoguously, of two 2-D objects of same shape but different size, the smaller one has more units of length per unit of area than the larger one, which can be interpreted as the smaller object being more 1-dimensional than the larger one.

Does this mean that the smaller object is less actural than the larger one in Flatland - and even less actual in a 3-dimensional frame of reference? Would this be the reason behind quark confinement?"

Well, here I can only give a metaphysical speculation, but it does not seem unreasonable to me to believe that when 2-dimensional objects are observed in a 2-DFR, the same kinds of distinctions and relations apply as those between 3-dimensional objects as observed in a 3-DFR.

It would be very foolish of me to speculate on any direct relations between this framework at this stage of development and quark confinement. The task ahead to seriously answer this question is as follows:

1. Find the underlying physical description that gives rise to the SU(2) symmetry of the weak force and the SU(3) symmetry of the strong force (I believe that the mechanism I described, namely that the phase factor exp{tau/tau_A) arises from an indirect mechanism for comparing distinct proper times already gives an underlying physical description to the U(1) symmetry, as it can be directly related to the phase factor and a change in the gauge associated with the potential of the relevant field).

2. Once the underlying physical description for the symmetries is found, map the associated Lie Algebra to underlying physical processes in lower-dimensional analogs as observed by higher-dimensional observers.

3. Discover (hopefully!) a fundamental reason why quark confinement must arise as a direct consequence of this deeper physical understanding (rather than as a "patch" which one could uncharitably say how it was originally discovered).

So connecting my framework to quark confinement is far from a trivial task. It may well take me years (if it is even possible).

You said: "In your schema, you place dark energy in the fourth dimension of observed event (box 4.3). How would we, in our 3-dimensional frame of reference, experience a 4-dimensional phenomenon? I have read somewhere - but unfortunately forgot where - that we would experience its impact equally in all directions. The accelerating expansion of the Universe is equal in all directions. As is also the CBR.

Would placing the CBR in the same box as dark energy (4.3) facilitate an alternative to the Big Bang theory?"

As to how we would experience a higher dimensional phenomenon, the honest answer is that I don't know. However, I can offer a speculation based, again, on an analogy with phase transitions: From the perspective of a molecule sized observer it would seem very strange that above a certain average random motion, the molecules forming a substance suddenly seem to be a lot less constrained and literally fly off in all directions. An observer our size has no trouble with this: We might just say that the substance changed, say, from a liquid state to a gaseous state. In this analogy, one could imagine that we are like the molecule sized observer, and the human-sized observer is like the observer with a 4-DFR.

The point is, we might not see any direct "extra" objects, but instead unexpected behavior of objects we already have observed at very large scales, which indeed we do.

The CBR is most fundamentally an aggregation of photons, so it should properly be placed in the (2,3) box. However it can be a marker of what, in a sense, is going on in spacetime. The visual analogy of here might be that if you spill some paint on a balloon, and then expand the balloon, the paint spots will increase in size but become less dense.

i hope I was able to answer your questions, If you have more, don't hesitate to ask (It may take a few days for me to respond, due to my combined school and work schedule).

Thank you again so much for your interest,

All the best,

Armin

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