The Myth of a Theory of Everything by Armin Nikkhah Shirazi

Dear Peter,

Thank you for your remarks and I look forward to your comments (should you be inclined to make any), especially since you have a particularly broad perspective on the history and philosophy of physics.

Armin

Dear Inger,

Thank you for your kind remark, you are of course under no obligation to make any comments or ask any questions, just the fact that you read it twice is an indication that some of my ideas were found to be worthwhile and I find that is a reward in and of itself.

Thanks again and all the best,

Armin

Dear James,

Well, in the generality you stated it the superposition principle could already be applied to the classical physics, such as Maxwell's or Newton's theories. In fact, your second sentence indicates to me that this is what you had in mind.

What makes quantum superposition quite distinct is the fact that a state of a system is a linear superposition of 'measurement outcome states', and this something you just don't find in any classical theory.

There is a quantum mechanical version of 'Force' which you can either derive in terms of a change in the expectation value of a system's momentum over time using Ehrenfest's theorem, or (in certain cases only) as as the change in the expectation value of the Hamiltonian of which the wave function is an eigenfunction with respect to a coordinate using the Feynman-Hellman theorem but these are nothing like classical forces because they do not refer to definite objects.

I don't dispute the validity of either General Relativity or Quantum Theory, which actually makes my stance the most conservative one could take. The entire point of my essay was to show that if we realize that quantum theory and general relativity are fundamentally about different objects, then the seeming contradiction between them vanishes.

As for your paper, I will leave an honest comment on your thread.

Thank you for your remark and your question.

All the best,

Armin

Hi Ben,

I'm glad to hear that you came out alright (I somehow missed this post, hence the late post). Given that you have composed so many works, perhaps you might be inclined to share a few with world? I'd be certainly looking forward to hearing them.

On the Toccata and Fugue, well, given that you are a mathematician perhaps it is not so unexpected that (occasionally) complex interlocking melodic patterns might sound pleasing to you. I find this style very challenging to emulate, btw. It is truly astounding that Bach could compose (and by some accounts even improvise (!!!)) contrapunctal works with 5 or 6 independent voices.

All the best,

Armin

Dear Peter,

When you say that you have tested the idea that there are no clear distinctions between areas of human activity, I take it that you have thought about several concrete examples that serve as an epitome of such division and then come up with specific counterarguments to refute that view.

To help me understand your perspective better, it would be helpful if you could give one or two examples in which the division seems especially obvious and in which you have found that this was ultimately due to lack of sufficiently deep understanding or other factors.

Let me give one example that at least in my mind clearly divides the sciences and the arts, and you can provide a counterargument if you are so inclined.

In my view, the correspondence principle as the general idea that subsequent frameworks or theories in science need to subsume the domains of previous theories in addition to providing explanations for new ill-understood phenomena marks as a division between the arts and the sciences. I see no comparable compulsory requirement for an analog to the correspondence principle in the arts. Incidentally, should you be interested, several years ago I wrote a paper in which this was a key point, so if you like a greater elaboration of this argument, you can find the paper here:

http://hdl.handle.net/2027.42/79042

All the best,

Armin

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

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

Ah, I think I better understand your perspective. It seems to me that you are saying that if a practitioner of the arts and/or the sciences can see aspects in his practice that appear to fall equally well into either domain, then this is a reflection of the inherent unity between those subjects.

From this point of view, the issue becomes a bit tricky, because a lot depends on how you define 'the arts' or 'the sciences'. Let me state my belief that it is always possible to find a definition for either field that is broad enough that you will always find examples that validate your point of view. So in this sense, we agree.

The danger I see, however, is that if a field is defined overly broadly, the definition becomes less meaningful, and in the most extreme situations it could become meaningless.

If I, say, mix some kool aid in water, am I doing physics? Well, again, I believe you can always find a definition in support of affirming this question. After all, in order to achieve the desired result, I might have to precisely weigh a quantity of powder and/or measure out a precise quantity of liquid. Perhaps to achieve the right kind of temperature I could also calculate how much ice to add using the specific heat capacity of ice and water. I might try to be careful not to add too much energy to the system via mixing (after all, this was basically the method Joule used to estimate the mechanical equivalent of heat) and so on.

The point is, yes, you can defend this point of view, but it just seems a lot more reasonable to me to say that I am not doing physics, I'm just mixing some kool aid. If I did consider this as doing physics, then, yes of course, by the same reasoning, everything becomes everything.

This is certainly a very unified point of view, but does it really add any deeper understanding?

Thanks for sharing your perspective,

Armin

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