Imagination and the Unreasonable Effectiveness of Mathematics by Armin Nikkhah Shirazi

Hi Adel,

Thank you for your comments. I vaguely remember some of my criticisms, the one which stands out most clearly in my mind was whether you could account for the fact that the wave function is a probability amplitude. During the last 1.5 years that I have been more focused on mathematics, I have noticed that some of that "thinking like a mathematician" has rubbed off on me, in the sense that I tend to now be a lot more careful with certain statements that would have seemed obvious to me before. I mention this because your assertion that "your theory is mine" strikes me as something which is not immediately obvious to me, especially because I do not recall that you made a formal distinction between actuality and potentiality, on which essentially my entire framework is based. However, I will read your essay and give you further feedback in the next few days.

Thanks again,

Armin

Dear Mary Ann,

Thank you for you complement on my writing. I invite you to let me know what your specific objections are; many times it was precisely because of the objections of others that l was led to deeper understanding.

Best wishes,

Armin

Dear Akinbo,

Thank you for your feedback. Regarding your comments:

"Your "actual" and "actualizable" are a continuation from your previous ideas. I can't recall if we agreed then that these can be representable as binary digits 1 and 0. Is there an agreement?"

No, I don't think that the distinction can be put in a 1 to 1 correspondence with the digits 0 and 1. If 1 denotes actual existence, then the natural interpretation of the denotation of 0 would be non-existence. One move to save the correspondence would be to attempt to put actualizable existence in a correspondence with some fraction between 0 and 1. To some extent, it works: For example, the outcome of obtaining a 6 in the throw of a fair die could be put into correspondence with the fraction 1/6. To that extent, the concept of actualizable existence maps into probability, and I did mention this in my essay. The problem appears with events described by a probability of 1. If the correspondence worked, then this would always correspond to something that actually exists, but this is false. A simple counterexample is the loaded die which always and no matter what, whenever it is thrown, gives an outcome of 6. Then, even though the probability of obtaining that outcome is equal to 1, it is not true that when I have the die in my hand without having thrown it that this would be equivalent to the actual outcome of a throw. This is exactly the distinction between pro-actuality and actuality that I explain in my paper. It gums up the 0 to 1 correspondence between ontological states and the binary digits, and it is responsible for a what is in my opinion a widespread misunderstanding of an implication of quantum mechanics, namely that correlated phenomena of distant objects covered by Bell's theorem are evidence of non-locality.

"can something represented by mathematics perish or is it eternally existing? "

It think the question, as you ask it, has a definite answer, and it is yes, it can perish. We can, for example, represent people mathematically by numbers, and it is certainly not the case that they exist eternally. From your comments elsewhere, though, I get the sense that what you really are asking is whether the numbers themselves, like 1 or 2 can perish.

I would say that in the absence of saying anything further, this question reflects a category error. It is sort of like asking whether truth could ever be yellow colored, or whether snow flakes could ever be ticklish. Without saying anything further about them, numbers are not the sort of things to which "being able to perish" applies.

However, the question could conceivably be salvaged by saying something more, like, "Given X, could numbers perish?" Where X is a statement or set of statements which make the concept of perishing applicable to numbers. Two examples I can think of which could possibly make this question sensible are as follows:

X_1: Suppose numbers are abstractions of everything that has that property (sort of like Frege thought about numbers, "3" would then be the set of all things which have "threeness" in common, like 3 apples, 3 atoms, etc.)

X_2: Suppose we supplement Peano's axioms with some axiom A (where this axiom has something to say about the the perishing of a number).

So, I would say that if you really want to investigate this questions seriously, your starting point is too meagre. You need to stipulate more before such questions make sense, in my opinion.

"*I still recall your 'photon existence paradox' for the photon and regret that you recanted on it. It was a paradox that SR would have found almost insurmountable. "

I find your statement surprising for two reasons: 1) what led you to believe that I have recanted the paradox? In fact, in a more recent paper I elaborated on this more

http://vixra.org/abs/1306.0076

That paper essentially drives at the same sort of conclusions as I do here, but from the point of view of special relativity. 2) What leads you to believe that the paradox is an "almost insurmountable" challenge to SR? In fact, in the paper in which I introduced it,

http://fqxi.org/community/forum/topic/329

I used it to derive the invariance of the speed of light, so it seems to me as far removed from a challenge as it could be.

I will read your essay and give feedback in a few days.

Best wishes,

Armin

Dear Akinbo,

I find it amusing that you interpret my results as a defense of "illogicalities" of special relativity, while I interpret them as support of a unifying idea between quantum theory and SR. Of course, they have already been combined in quantum field theory, but not in a manner in which they can be said to be "unified".

In this contest entry, I presented some theoretical support for the idea that quantum objects prior to a measurement cannot be said to exist in space-time (due to an incomplete embedding), so the SR arguments suggesting that objects characterized by v=c do not exist in space-time would not only be congruent with it but, because in my speed of light postulate paper I already showed how this idea can be taken as a fundamental starting point for SR, could serve as an initial assumption for both SR and QT.

I read your paper on dark matter as a possible ether, but I must say I still don't see why the photon existence paradox would be a problem for relativists. Note that I am using the term "paradox" here in the way it is usually used in the context of SR, namely, as a puzzle which seems like a paradox but is not a paradox at all if one understands the implications of the theory correctly.

I did not realize until now that you have some problems with the invariance of the speed of light. I invite you to read the short but excellent paper by Ralph Baierlein called "Two Myths about Special Relativity" and focus on the second myth:

http://www.uio.no/studier/emner/matnat/fys/FYS-MEK1110/v06/MythsSpecRelativAJP193.pdf

Einstein's assumption regarding the constancy of the speed of light was only that it was independent from the motion of the source, and only in conjunction with the principle of relativity does it turn into the independence from moving frames. It is worth to quote Baierlein on this point:

"To take as a postulate that the speed of light is constant relative to changes in reference frame is to assume an apparent absurdity. It goes against common sense. No wonder, thinks a student, that we can derive other absurdities, such as time dilation and length contraction, from the premises. Far better to start much closer to where Einstein started and to derive the logical consequence that the speed of any given light pulse has the same value in all inertial frames. The derivation can be accomplished with one simple diagram."

Notice how the first part of the paragraph could have been exactly one of the many posts by Pentcho Valev around here. It means that if you want to deny the constancy of the speed of light, it is not enough to just show invariance in different frames, you also have to show how it implies that either the principle of relativity is wrong, or how the assumption that the speed of light is independent of the motion of its source is wrong, both of which seem eminently reasonable.

Let me make a final remark on your question about the perishability of numbers. I already mentioned that at least in my opinion, you have to overcome the hurdle of making sure that enough is stipulated for such questions to make sense. It occurred to me that there is also a possible second hurdle, namely, to make sure that even if the question makes sense, it is not just a variant of another question which gets to the heart of the matter more directly and therefore is more useful. For example, if you ask, "Given X_1 (see above), could numbers greater than one perish?" you are really asking, "is there a point in our future in which the entire universe collapses to a single point (i.e. a big crunch)?" And I think the second question is a better statement of what is being asked than the first. This is not to say that there is no useful question of the sort that you are interested in, but it does mean that you should be careful to make sure that you are not asking really asking something different in disguise.

Best,

Armin

Dear Ed,

Thank you for your comments, and for the Epicurus quote, with which I was not familiar (I am, however, planning to take a course in ancient Greek philosophy later this year, so hopefully I'll be more informed).

I will take a look at your paper and leave a comment,

Best wishes,

Armin

Dear Jayakar,

Thank you for your comment, although I must admit I could not parse what you mean by the axiom being "imaginary".

Best,

Armin

Dear Leo,

Thank you very much for your feedback. Regarding Feynman, he did not say that no one "should" understand quantum mechanics, but rather that no one does. See the short clip below to see how he meant it:

https://www.youtube.com/watch?v=w3ZRLllWgHI

Also, "shut up and calculate" is widely attributed to Feynman but was actually said by N. David Mermin, see his article here:

http://www.gnm.cl/emenendez/uploads/Cursos/callate-y-calcula.pdf

As far as new paradigms are concerned, I still have a lot of work to do, but I hope that this is a solid step in that direction.

I will read your paper and give feedback shortly, thank you again,

Armin

Dear Gordon,

Thank you for your comments. I understand that you consider yourself a local realist. Then how can you at the same time assent to Bohr's statement that "the result of a 'measurement' does not in general reveal some preexisting property of the 'system', but is a product of both 'system' and 'apparatus',"?

It seems to me that the hallmark of realism is the assumption that generally the system has pre-existing properties. I think if you can explain to me how you reconcile the two, then this will go a long way towards me being able to understand your point of view.

Armin

Dear Akinbo,

I can only tell you how I think about this issue, and it is as follows:

The problem is with your assumption 1. It does not apply to light. Although we express the speed of light in terms of meters/second it is *not* fundamentally defined in terms of distance per time. It is defined in terms of wavelength times frequency (note they end up having the same dimensional units). In any other situation this distinction would not matter, because you can express wavelength in terms of ruler lengths and periods (inverse frequencies) in terms of clock ticks, but for light this difference does matter.

Think about it this way: If it really was the case that you could fundamentally express lightspeed in terms of some units of distance per time, then there would be logically nothing preventing you from expressing it in terms of the passage of zero units distance per time; in other words there would be nothing preventing you from finding a rest frame for light.

While it might seem very strange that your obvious and reasonable assumption cannot apply to light, it only seems so because back in your mind you are thinking of light as something that is traveling in space. But if it were traveling in space, then that would mean that it has a definite trajectory. From quantum mechanics we know that this is not the case. I believe it is reasonable to infer from the fact that photons do not have definite trajectories that they do not travel in space. If they do not travel in space, then, once again, you cannot apply the notion of distance per time to the speed associated with their "travel".

None of this is very controversial, but what I consider to be the fundamental insight here that "unties" all these conceptual knots in one fell swoop is: the idea that photons do not exist in spacetime. If you are willing to accept this for a moment, then you will have a natural explanation for every single one of the above conceptual difficulties.

As for my alleged mathematical talents, I honestly do not see myself as particularly talented in math. Whatever skills I might have built up came from a lot of toil, sweat and pain. I do wish, however, I was mathematically talented because it would make my life a lot easier.

I briefly looked at Gordon's paper, and I think the reason it has been rated so low is that he could have made it hardly any more uninviting to read. It will take some self-discipline on my part to go through it, but before I even make the attempt, I first want to find out what exactly his position is (see my comment to him below).

Best,

Armin