Patterns in the Fabric of Nature by Steven Weinstein

I think you may have meant to send this to George Ellis?

Hi Steve,

Nice essay! I was glad to see that you've also entered an essay into this competition. I can certainly sympathize with the possibility of non-localities lurking in the fabric of spacetime. What I'm trying to understand is what precisely you mean by "non-locality" or even "non-local constraints". For example, your opening statement, taken literally, is not true: many (or most) theories have derivatives, which couple neighbouring points in a manifold. But I assume that a finite number of derivatives is suitably "local" by your definition. However, in shape dynamics, we have a Hamiltonian that has powers of the inverse Laplacian, which is highly non-local in some sense. Yet, shape dynamics is dynamically equivalent to GR.

I've always found locality in GR a tricky issue. The field equations and the constraints can be written "locally" (i.e., with a finite number of derivatives) but observables are non-local. So how "local" is GR really? As you know, constraints can expressed locally but may have global obstructions for solving them. Would this kind of non-locality be good enough or are you looking for something deeper?

Cheers,

Sean.

Dear Steve,

I cannot agree more with you about your statement: "...the possibility that there is a more fundamental theory possessing nonlocal constraints that underlies our current theories. Such a theory might account for the mysterious nonlocal effects currently described". I have a different approach that I am investigating. It appears only in the "Disuccsion and Conclusion" of my essay but hope to see if you think it is possible.

In my essay Is there really no reality beneath quantum theory?, I am able to show that the properties of a boson can be reconciled by assuming matter has vibrations in space and time. The system has an unusual propery that the vibrations are generating a probability and not real energy at the deterministic level. The Einstein's mass-energy relation is a constriant that matter field must be quantized and follow all laws of relativity at the standard model scale. However, the properties of the vibrations at the high energy level may not be local. I hope I can get your feedback.

Sincerely,

Hou Ying Yau

Thanks, Sean. I've just printed your essay, and am looking forward to reading it.

As for your questions, the primary concept in the paper is that of a nonlocal constraint, not about "nonlocality" in general. The Gauss Law constraints are local, by my usage, even though they are expressed in terms of derivatives. E.g., the Gauss Law for the electric field insists that the charge density at a point is equal to the divergence of the electric field at that point. What makes it local is that all the quantities we're concerned with have to do with an infinitesimal neighborhood around each point. On the other hand, if the electric field were sensitive to charges a finite distance away, we would have an example of a nonlocal constraint.

There's a somewhat more interesting example of a nonlocal constraint in the paper, in which one has a universe with timelike compactification. Spatial compactification will also do, and has in fact been studied. Either way, the periodicity one finds in these models means that the matter configuration at one point may determine completely the matter configuration at other points. That is a kind of nonlocal constraint.

In GR, I think the nonlocality is of a different sort, though I'm not sure I follow the question entirely. Offhand, I'd say that the nonlocality of the observables has to do with the diffeomorphism invariance (hence the physical meaninglessness of talking about properties "at a point"), but that the solvability of the constraints would be distinct. In any case, I'd say that GR is local in that if you're giving data on a Cauchy surface, it can be freely varied from point to point (at least as long as it's sufficiently differentiable).

Dear Steven,

Splendidly written! You discuss many important issues from a very original perspective. A few comments and questions:

1. I am wondering what, if anything, the possibility of nonlocal constraints says about causal structure. Quite naively, it seems as if making a local change to a system involving a nonlocal constraint would "cause" suitable adjustments elsewhere to satisfy the constraint. I'm not sure if this would have any implications for signaling, etc., since the "effect" might be distributed in such a way as to prevent any conclusions from being drawn at any particular remote point.

2. I wonder if you have read Ken Wharton's essay. I believe the type of constraints he invokes is somewhat different, but there seem to be some analogous points.

3. Have you looked at Donatello Dolce's submission? He uses a timelike compactification. (For instance, compare his figure 4 with your figure 1).

4. Since many approaches to quantum gravity involve breakdown of manifold structure at small scales, it seems worth considering how locality should even be defined in such a context, since the definition usually involves metric structure.

5. For example, a model (such as a graph) with less structure than a manifold might have a single "short path" between two points, while every other path between them is "long." At large scales, the two points would seem distant, and interaction over the "short path" would seem "nonlocal" when in fact the effect arises from a nonmanifold microstructure. It seems that this sort of consideration might be relevant to the horizon problem.

Thanks for the great read! Take care,

Ben Dribus

Okay, I understand what you mean by non-locality. It was in the text but it didn't pop out at me right away (probably my fault)! Do you have a particular model in mind for cosmology (like the quantum graphity stuff)?

I can see that the non-locality in GR is definitely a bit different from what you're talking about so I don't want to distract too much but I would say that the FREELY specifiable data (i.e., non-gauge) on a Cauchy surface is non-local. That's because you have to solve the constraints which are partial differential equations and the inversion of a partial differential equations does depend upon data over the whole manifold. I can't tell if this is something deep or trivial.... maybe trivial?

Hi Steve,

I really enjoyed your essay - it's a fascinating topic.

I'm curious how the kind of nonlocality you discuss fits in with the nonlocality that results from the holographic principle, for instance in AdS/CFT?

Thanks for a great read!

All best,

Amanda

"Cosmic Solipsism"

Do you think that the constraints in GR are any different from the constraints in Maxwell theory with regard to nonlocality? My guess is no, and that the nonlocality you're referring to has to do with the fact that, e.g., the flux of the electric field through a boundary tells us the total charge within that boundary, but does not determine or even constrain the charge density at any particular point.

Nonlocal constraints of the sort I'm talking imply that the range of values a field can take at a point (or in the infinitesimal neighborhood around that point) is dependent on what the facts are at other (spatially separated) points.

If I'm missing something, please let me know!

Thank you, Ben, for the compliment and also for the questions and comments. Here are some brief replies.

1) This is a subtle and interesting question you raise. The short answer is that the causal structure is unaffected. The reason is that if the world operates in this way, then any local "changes" to the data at one point, corresponding to a causal intervention of some sort, are subject to the constraints as well. In the EPR context, this has led some commentators to claim that violation of Statistical Independence (which is a consequence of the presence of nonlocal constraints) means that we would lack "free will". (See my "Nonlocality without non locality" paper for more discussion and references to related papers by 't Hooft, Conway & Kochen, and others.) My reply in brief is that there is no more of a problem for free will than there already is in our ordinary, fully local theories, in which we typically understand our actions to be constrained or determined by what has occurred in our casusal past.

2) I've been meaning to read Ken's essay - he's done some really interesting work - and I will do so ASAP.

3) Have not seen Dolce's paper, but will print it out and take a look. Thanks for bringing it to my attention!

4) Excellent question. I think that if one has a discrete graph, one has at least a hope of defining locality, though even there it is not clear how to treat neighboring points. My thinking is less radical, hoping that consideration of nonlocal constraints in classical theory will enable us to understand better how to think about quantum theory in general, and quantum gravity in particular.

5) Right - with a metric of some sort defined on a graph, we could have shorter and longer paths. It's not immediately obvious to me why two points with a short path between them might seem to be far apart when viewed at large scales, since this seems similar to the case in ordinary space where two points (Boston and New York, say) are connected by a short path but also by many longer ones (Boston east to Paris to Beijing to LA to New York). In that case, as in this, we'd say they're close together, despite the fact that there are long routes as well. All that said, your point (4) above raises real questions about the general notion of locality once one starts messing around with the spacetime background.

5a) Fractal spaces would seem to exhibit the phenomenon you mention: scale-dependence of distance.

Heaven Breasts and Heaven Calculus

http://vixra.org/abs/1209.0072

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

http://galaxyanatomy.com

Dear Steve,

Thanks for the detailed replies, and I'll be sure to look up the references you suggested. By the way, I forgot to even mention my own essay On the Foundational Assumptions of Modern Physics. I fear you may find it too radical, but I would appreciate your thoughts nonetheless. Take care,

Ben

Dear Steve Weinstein,

Nonlocally of string-mattes in Coherently-cyclic cluster-matter paradigm of universe, is described with the continuum of stings in that the use of simplex is more commutative and quantitative to describe the fabric of nature in entirety, whereas the holarchy of universe is expressional as its factorizability in continuum.

With best wishes

Jayakar

Spelling error:

continuum of 'stings'

To be as,

continuum of 'strings'

Dear Steve,

Interesting essay. I think you may have overlooked that all "digital physics" theories are actually of the type you discuss, the kind of theories that prescribe determinism in the universe, and no free-will at all. Stephen Wolfram, for example, has proposed on several occasions what he calls the activity of "universe hunting", the idea of mining the "computational universe" of computer programs in order to find our own universe program and reproduce it. Zuse, Fredkin and Schmidhuber have also proposed fully deterministic theories of the universe. It would have been interesting to see a discussion in the context of quantum mechanics that you cover in your essay.

I agree with you.

Thanks for the comment, Hector. Actually, I think that the sort of theory I'm proposing does not preclude free will in any meaningful sense of "free will". There's more discussion of that very issue in my paper "Nonlocality without nonlocality", which may be found at http://arxiv.org/abs/0812.0349.

SW

Dear Steve,

The wave with space and time has an unique property. I am able to show in my essay that the wave generates probablities for quantization but with no real energy. Only the quantized oscillator carries energy. This seems to allow communication in the "sub-observational" level over distant locations through region that is "vacumm". Sudden changes e.g. wave collapse, shall not violate relativity because the wave has no energy except at the quantized locations. Although the approach seems different from your suggestion for statistical independence condition, your feedback whether this new idea is poosible will be very valuable.

Sincerely,

Hou Yau

"The divergence is a measure of the out‡ow of the fi…eld in the neighborhood of a point, and the two constraints tell us respectively that any such out‡ow of the electric …field is due to the presence of a charge at that point acting as a source, while the magnetic fi…eld can have no sources (there are no magnetic charges)."

In my work, I show there is a fundamental error in the assumptions of physics. First, charge is a dimension and not an object. Second, all charge is always distributed and is never a point. Even an electron has a surface. Third, there are, indeed, two types of charges. There is the electrostatic charge, and there is a quantifiable magnetic charge. Further, with the exception of electrostatic fields and magnetic moment, all other electrical units should be measured and notated in terms of magnetic charge.

The above understanding corrects numerous errors in physics, which lead to contradictory and unusual paradigms (like wave/particle duality and force particles). Further, the correct notation of charge as distributed, and the recognition of magnetic charge allows for a simple Newtonian unification of the fundamental forces. This is the subject of my paper:

http://fqxi.org/community/forum/topic/1531

Nobody would consider someone with only a high school GED to be able to make any meaningful contributions to physics. However, sometimes what the world needs is someone who can see things from a completely fresh perspective. I had the luxury of a clean mind, not polluted with incorrect assumptions, and was able to completely reconstruct the foundations of physics working only with known physical constants.

When I read your paper, and others like it, I can see valiant efforts to look beyond the mainstream, but you are still working within the fundamental assumptions of point charge and magnetism being quantified as moving point charge. These are fundamental errors, themselves.

I am certain that if brilliant minds, such as yours, could take the time to investigate the new foundations of physics I have formulated, you would be positioned to make significant and practical discoveries.

Dear Stewe

About false contradiction between free will and superdeterminism i would like reminding you :

As Yakir Aharonov's says: "...is somewhat Talmudic: everything you're going to do is already known to God, but you still have the choice." http://physicsworld.com/cws/article/news/2012/aug/03/can-the-future-affect-the-past

See my essay http://fqxi.org/community/forum/topic/1413