Relativity Is Not About Spacetime by Edward J. Gillis

[deleted]

nmann,

(First, thank you Ed, for your kind indulgence. Since the reference is to my essay, I would feel more comfortable moving this discussion to my site.)

The difference between Joy's proposed experiment and those that validate quantum nonlocality is that Joy's is a constructive alternative explanation of quantum correlations. It is exceedingly easy to show that Bell's proof is by double negation, and thus only means to validate what it assumes in the first place. In fact, I don't think there is any way that it *can* be made constructive.

Because there is no probability measure in Joy's hypothesis, only the sort of statistical inference that attends the classical case of a measurement function continuous from an initial condition, the correspondence between theory and experimental prediction is a 1 to 1 complete closed judgment. In fact, it would have to be, because Joy's framework is fully relativistic.

Tom

[deleted]

Tom,

If BT proves out, as it does, and brilliantly, in macroscopic logical tests and physical experiments, it's relativistic. And professionals have known since the get-go that the theorem involves double-negation. That only seems to bother people who don't like BT for ideological reasons. It kind of resembles sqrt-1 in that regard.

Anyway, you're right. Your thread.

Joy Christian

nmann,

The question is not about liking or not liking BT, or liking or not liking entanglement, or liking or not liking non-locality. The question is about whether these ideas, or unicorns or UFOs, have any relevance for the real physical world, or for the future theory of physics. We had a perfectly cogent concept known as phlogiston---a truly beautiful concept. Unfortunately it turned out that it had absolutely no relevance for the real physical world. Similarly, BT, entanglement, or non-locality has no relevance for the real physical world. As Tom says in different words, in the real physical world what matters are the correlations among a set of measurement events---or among the clicks of a set of detectors.

Now Bell claimed that for local functions of the form

A(a, L) = +1 or -1 with 50/50 chance for any a in R^3

and

B(b, L) = +1 or -1 with 50/50 chance for any b in R^3,

together with

AB(a, b, L) = A(a, L) x B(b, L) = -1 when b = a,

it is mathematically impossible to construct a model that can reproduce the correlation

E(a, b) = -a.b.

It turns out that Bell was wrong (but not trivially so). It *is* possible to mathematically reproduce the correlation E(a, b) = -a.b if we take the physically and mathematically correct co-domain for the functions AB(a, b, L), A(a, L), and B(b, L), namely a unit parallelized 3-sphere. The proof can be found in the attached paper.

It is scandalous to continue to believe in BT despite this explicit one-page proof showing exactly what Bell thought was mathematically impossible. Further details and implications of the proof can be found in my book.Attachment #1: 18_disproof.pdf

[deleted]

Joy,

The issue here is whether some individual or group out there with the money to spare might consider you a potential Lavoisier and you and that person or group could then obtain the cooperation of a reputable and qualified team of credentialed experimentalists who judge your proposed physical experiment to be in fact do-able and then conduct it.

I'm sorry, but I can't help you there. If I could I well might. Not so much to help you personally, mind, but simply to get the issue sorted and savor the drama. Having followed your recent online career, however, one has to wonder if you'd accept an experimental verdict that went against Christian's Theorem.

Steve Dufourny

Ironical their strategy, sad, and without universality. a real comedy.

[deleted]

Not sure I agree about the "universality" part.

Steve Dufourny

not sure , not sure, it is important to be sure you know.

Me for example I am sure about my theory of spherization.

Joy Christian

"Having followed your recent online career, however, one has to wonder if you'd accept an experimental verdict that went against Christian's Theorem."

Here too you are mistaken. I don't mind you insulting me personally (many have done worse in my "online career"), but I do mind you insulting me as a scientist. Here is what I wrote on Scott Aaronson's blog in May, to give you just one example:

Scott wrote: "The obvious question is: if such an experiment were done and Bell/CHSH were not violated, would you admit that you were wrong?"

And I replied: "Yes, I would. Do this experiment (http://arxiv.org/abs/0806.3078) and prove me wrong. Let no man but Nature bestow her verdict on herself."

So, nmann, stop wondering. I am a scientist, period.

[deleted]

Okay, sorry, and I'd fund your experiment. If only I could. At the very least it'd be interesting. Hypothetically ... do you think you'd be able to round up a first-class team of experimentalists? I mean IQOQI or U of Geneva or MIT or Cavendish or Livermore Lab etc. class? Nothing along the lines of those Utah guys who gave the world cold fusion.

You must admit, though, that you don't come on all that scientifically objective sometimes. My snarkiness wasn't 100% unprovoked.

Joy Christian

"Hypothetically ... do you think you'd be able to round up a first-class team of experimentalists? I mean IQOQI or U of Geneva or MIT or Cavendish or Livermore Lab etc. class?"

If I were to guess from this question, you are not a professional scientist. You cannot just go and ask a first-class team of experimentalists and hope to get a decent response. With a controversial idea like mine you have to do a lot of ground work, sociologically speaking, before anyone can take your idea seriously. Lacking this, I did take a leap of faith and wrote to David Wineland last year to have a look at my experiment. And, lo and behold, he replied: "I did take a look at your proposed experiment, and although it seems straightforward and doable, we probably couldn't realistically make such an undertaking."

No matter. I now have someone else's ears and we are thinking about how to make the experiment more doable and less expensive. We shall see how that goes. It is not going to be an easy task.

Robert McEachern

Joy,

In an earlier post you stated that

"Similarly, BT, entanglement, or non-locality has no relevance for the real physical world. As Tom says in different words, in the real physical world what matters are the correlations among a set of measurement events"

I believe your first statement to be true. But not the second. A purely classical experiment is known, demonstrating that even the correlations are irrelevant. Furthermore, you can repeat the experiment yourself, on the table in front of you.

Over thirty years ago, Bernard d'Espagnat, writing in Scientific American (Nov., 1979) identified two conditions, that he labeled an "extension" and a "conclusion", that had to be true, in order for Bell's Theorem to be true.

The desktop experiment demonstrates that they are not.

[deleted]

I've dealt with funding of experiments (more often biotech related) and understand the complexity of the process on the ground. "Round up" is clearly shorthand. I'm also painfully aware that it's a problem at the present time for labs to maintain personnel, with resulting understaffing, not because qualified people are unavailable for training but because the institutions lack the funding to guarantee steady employment. (I believe the problem's particularly acute at the moment in the UK.) An enormous amount of training is necessary. You don't assemble teams ad hoc. There's no Hiring Hall down the street for experimentalists.

But still ... "straightforward" is a decent description. As I understand the experiment it's room-temperature. You undoubtedly realize the immense budgetary burden which is lifted right there. Some of the precision equipment probably needs to be custom-manufactured or at least existing equipment needs to be modified. But there's nothing insurmountable involved. It'd require time. And cash. But hey, in our imaginary perfect world we just write a check.

One suspects that some of the feed-in to "...[W]e couldn't realistically make such an undertaking" was plain fear. Science politics can be deadly and that's nothing if not a realistic concern. A certain amount of toxicity may be attached to your person. Also of course you probably had no independent funding to offer and they weren't properly equipped. Anyway, I hope "someone else's ears" are first-class ears and the experiment, if and when conducted, is resultingly loophole-free: as near to perfection as reality permits.

Joy Christian

Robert,

I read d'Espagnat's 1979 article exactly 30 years ago, in 1982, and that set me up on the path I am on today.

Independently of Bell's theorem or quantum mechanics, correlations among measurement events are observed. They are the only facts we know and have to account for. So I do not understand your statement that correlations are irrelevant. How do you account for the fact that "stronger-than-classical" correlations are observed in experiments?

In any case, can you please provide some more details about the desktop experiment you are referring to?

Thanks,

Joy

Robert McEachern

Joy,

I read d'Espagnat's 1979 article in 1979. Read what he said on page 166. Or you can find the quote in the comments under my essay, if you no longer have the article.

Correlations between components cannot exist, when there are no components.

Single bits of information do not have components, by definition.

Unlike an entangled pair of gloves, in which "handedness" is an actual attribute of a glove, "Heads-or-Tails" is not an attribute of a coin.

Stand two coins, on edge, anti-parallel.

Then really look at them.

And think about d'Espagnat's "extension" and "conclusion".

Thomas Ray

Robert,

You wrote to Joy,

"Stand two coins, on edge, anti-parallel.

Then really look at them.

And think about d'Espagnat's 'extension' and 'conclusion'. "

Demonstrably, he has. Joy's topological framework obviates considerations of probabilistic functions as well as the distinction between local realism and spatial separation. An ideal fair coin has zero thickness.

Tom

Edward Gillis

Joy,

This is in reply to your earlier post that included the attachment of your first chapter ("Origins"). Since the discussion seems to have progressed down here, I thought a response on this thread would be more visible.

Your representation of possible pairs of measurement outcomes is very elegant, but I do not see how this disproves Bell's theorem. On page 11 in Equation 1.31, you characterize the quantity used in the CHSH inequality as a sum of expectation values. That is NOT what the relevant quantity is. It is the expectation value of a sum. You cannot integrate (or average) over the individual terms of the expression before you add them. You must add all 4 terms, and then integrate (or average). When you do this the CHSH inequality follows immediately.

For each possible orientation of a and b your model associates a function on a 2-sphere that assigns an ordered pair of values (representing the possible outcomes of the 2 measurements on a and b) to each point on the sphere. You get the correct probabilities and expectations for a and b individually, and by associating each of these maps on a 2-sphere with a point on a 3-sphere (embedded in 4-d space) you are able to get the correct quantum expectation value for a*b when you integrate over the sphere. As you emphasize, this is not a trivial thing to do. You cannot do it in any natural way by just considering various orientations of 2-spheres in 3-space. If you integrate over the 2-spheres representing each of the 4 combinations individually (or if, as in equation 1.30, you take the sum of a large enough random sample of possible outcomes), and then add them, you can get the quantum expectations for the relevant orientations.

But the whole point of EPR is that all 4 possible measurement outcomes must possess definite values. This means that the addition of these values for the 4 terms, ab, ab', a'b, and a'b', must be done before taking the expectation value. As already stated this results in the CHSH inequality.

Thomas Ray

Edward,

You are a true gentleman and scholar for indulging this discussion on your page.

Without anticipating what Joy may say in response, I perceive that no assumption that suppports probability -- equally likely hypothesis, averaging of observed values a posteriori, etc. -- applies. Joy's continuous function domain assumes only topological initial condition and a measurement function continuous from that initial condition.

That one recovers all quantum correlations from this framework implies discrete local realistic measures from a continuous local-global range of measurement values. In other words, Bell's theorem can stand as an incomplete mathematical description of physical reality -- while complete quantum randomness in the classical domain predicts microscale quantum behavior by statistical inference, a completely classical measurement scheme.

Tom

Robert McEachern

Thomas,

d'Espagnat's use of the term "extension" has nothing to do with "thickness".

He is talking about an extension of logic. He extended himself too far.

Thomas Ray

Not true, Robert. Joy's mathematical framework is complete -- meaning that the logical judgments are closed.

Tom

Edward Gillis

Joy,

Sorry, my previous reply was written too hastily. I misstated the problem The integral of a sum is equal to the sum of the integrals, so my characterization of the problem is wrong.

But the point is that EPR's criterion of completeness claims that specific values of a, a', b, and b' must exist in every case. You must assign these definite values of either 1 or -1 for all 4 quantities, and then compute the averages. When you do this yo get the CHSH inequality. However, elegant your model is, the fact that you do not reproduce the inequality indicates that there is some errot in your calculation.

Joy Christian

Hi Ed,

Thanks for your reply. I am afraid you have misinterpreted my Eq. 1.31, which does not include the full calculation. The right hand side of that equation is a result of the expectation value of the sum, not a sum of the expectation values. Several other chapters of my book contain more details of the calculation---please see, for example, Eqs. (34) to (41) of the attached paper. As you can see from Eq. (41) of this paper, CHSH is violated by my model. What is more, all 4 counterfactually possible measurement outcomes, A, A', B, and B', possess definite values, albeit within a parallelized 3-sphere. The addition of the values for the 4 terms AB, AB', A'B, and A'B' is done before taking the expectation value, and this results in the violations of CHSH. The overall expectation value *has* to violate CHSH, because not only A, A', B, and B', but also AB, AB', A'B, and A'B' are all points of a parallelized 3-sphere, not the real line. The topological structure of the latter differs dramatically from the 3-sphere. Thus there are deep topological reasons for the violations of CHSH. Bell discovered something very profound, but he misinterpreted it completely.

Best,

JoyAttachment #1: 9_1106.0748v6.pdf

Joy Christian

Hi Robert,

I reread d'Espagnat's article. It brought back some pleasant memories. I am, however, not convinced by your interpretation of what he is talking about. The example of two coins you give is just too simple. In my opinion, without the extension he is making one would be compromising the notion of realism, as understood, for example, by Einstein. I am therefore sceptical of your whole line of reasoning. As d'Espagnat says, the extension is subtle, but necessary and justified.

Joy

[deleted]

Ed,

FWIW, the heated set-to that a number of us engaged in on Scott Aaronson's blog back in May was largely focused on Scott's and Richard Gill's conviction that Joy's argument with Bell is based a few lines of arithmetic, and that he got the arithmetic wrong -- just as you imply in your assignment of values to sum and average. My reply on that blog:

"Consider the smallest NX4 array squared has a square root of 4. This is the least square integrable term > 1. Joy's bound of 2(sqrt2) = sqrt8, which I find significant in other ways than those he used to arrive at the term:

The integer 8 happens to be one unit less than the second least square integrable term. This suggests to me that there is more to the summation of terms on a simply connected compact surface than one finds by averaging terms on a one dimension interval oriented in the plane. For this reason:

It's a theorem of arithmetic that a point external to a set of points can approach any point of the set simultaneously, provided that the point is far enough away. (You can find this discussed in the introduction to Rozsa Peter's classic book, Playing with Infinity.)

From there, it's easy to prove that a point at infinity such as that which differentiates R^3 from S^3, maps to the entire set of points in R^3. In other words, the distance of one point to another is finite, except one. So when we speak of a dynamic physical system finite in space and unbounded in time, every time interval except one is identical to every other (as Leslie Lamport shows by Buridan's Principle: every measure function continuous from an initial condition in a bounded length of time contains a singularity of uncertain position).

Quantum mechanical descriptions of reality lack the feature of the point at infinity (thus the need for renormalization to restore the N - 1 physical measure result). Continuous function models based on Minkowski space or other tensor metric techniques prescribe arbitrary boundary conditions. So I think that mathematical methods that combine the best of algebraic and continuous function techniques (particularly Hestenes' spacetime algebra) are the best bet for mathematical completeness of a physical theory."

Tom

Steve Dufourny

we cannot violate the inequalities of Bell !!!

It is the same with the principle of equivalence.

The fact that we have hidden variables does not mean that we have bizare violations. The uncompleteness is not the problem. We are just simply far of our walls. But our universal laws are at all scales in 3D even far of us !

I don't understand sometimes why people can invest in bizare experiments. The monney is like the maths, they are tools. It is sometimes very bizare all that.

How can we harmonize if we do not use them with wisdom and a pure universal determinism. The improvement , harmonious is so essential, even necessary.

The Universal sphere .....spherization evolution........eternal physical sphere.......

Regards

Steve Dufourny

You see nmann, the world becomes completely irrational just due to these kind of comportments.

It is sad simply.

Regards

Lawrence Crowell

I reread your essay and a agree that nonlocality is commensurate with the Lorentzian spacetime theory. Nonlocal connections between entangled states only "communicate" noise, or no signal, because no experimenter is able to control what the outcome is. It does have to be pointed out that nonlocal connections can be between states anywhere in spacetime. This can include timelike separations. The Wheeler Delayed Experiment illustrates that a measurement at one time T can adjust the wave function at a time T' \lt T on a timelike separation.

Nonlocality only implies nondeterminism in the case of a measurement, and with recent developments on weak measurements and such experiments, this really means a "hard" measurement. Quantum wave functions for entangled states evolve by Schrodinger dynamics in a perfectly deterministic fashion. The role of nonlocality in nondeterminism focuses on the issue of measurement and various quantum interpretations.

In my essay I discuss a different from of nonlocality. In quantum field theory field amplitudes on a spatial manifold are local with respect to zero commutations of their operators. However, if spacetime itself is quantum mechanical, say with fluctuations and the rest, then quantum fields (including gravity itself) are nonlocal with respect to this definition. This means we need to refocus our definition of quantum field theory in a manner which remove locality, and even more unitarity. Unitarity must be replaced by modularity, or some structure which preserves quantum information.

Cheers LC

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