Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

John Merryman

Tom,

What if there are issues that really are that ingrained? Do they just get grandfathered in? What if we held that view for politics, or religion, or medicine, or other sciences? The situation with math is it isn't conceptually as flexible as those other fields, so if an idea gets accepted that does cause issues, it can take a very long time to create enough problems to be reopened. Now that multiverses is establishment theory, it many be time to go really, really deep into these questions and see what might have been put in centuries ago, that could lead to where we are now.

Regards,

John M

Thomas Ray

John, is it really asking too much to stay on topic?

John Merryman

Tom,

I realize this strays from Joy's argument, but this is the 'Foundational Questions' website. If there are those who question the premises on which an idea is based, such as Akinbo's observation that what is mathematically accepted might be a physics shortcut that obscures further issues, should they be dismissed as not on topic? Obviously if every point is open to question, we would never get anywhere, but given the increasing confusion and untestability of many of the ideas currently arising in modern physics, how will the flaws be found, if certain assumptions are not open to question?

And when it comes to dimensionless points, they are assumptions, even if they have been around for millennia.

Regards,

John M

Joy Christian

Neither the axiom of choice nor the Banach-Tarski theorem is needed to prove that there are as many points on the real line as in the plane. These are elementary concepts. There is no issue here. It is counterproductive to make up issues when there is none.

John Merryman

Joy,

"Neither the axiom of choice nor the Banach-Tarski theorem is needed to prove that there are as many points on the real line as in the plane. These are elementary concepts."

So what is the difference between a line and a plane, if it isn't the number of points?

Space?

It would seem points are not consequential to the line, or the plane, since they seem to serve no function. It seems measures of space are what is relevant.

Regards,

John M

John Cox

Math emerges to the extent one produces any.

Dr. Christian has produced the math which is topical to the question of non-locality, whether I can follow it or not. The implications are what I find intriguing, given that since Galileo the history of science has been one of proofs of causality but without proof that if something happens without a causal link, it is purely blind luck. The underlying question is to what degree of certainty can it be shown that math is capable of generating a true random dispersion of points. Whether a point can be dimensionless is irrelevant to the math because the point in question is essentially abstract, axiomatically so.

jrc

Thomas Ray

"So what is the difference between a line and a plane, if it isn't the number of points?"

The number of dimensions. Line = 1 dimension. Plane = 2 dimensions. Complex plane = 2 complex dimensions -- in the complex plane, points are analyzed as lines (a pair of points). And as Joy said, unrelated to the elementary proof in Euclidean geometry that the line contains as many points as the plane.

Please, we cannot even talk about topology without some basic background in geometry. This is an even more serious obstacle than the lack of understanding of classical mechanics so prevalent here. My suggestion is that one be prepared with the requisite knowledge before commenting. It isn't much, but it is important.

Joy Christian

John,

Let me try to answer your question differently from how Tom has answered:

Points, lines, planes, and volumes are primitive concepts is geometric algebra. For example, a line is represented by a symbol, say s, and a plane is represented by a symbol, say s /\ t, where t is another line. What distinguishes lines from planes is how they act on other points, lines, planes, and volumes. These actions are themselves defined as primitive concepts. There is no need to invoke even the idea of a dimension (or any other concept that you will undoubtedly would want to argue against).

In any case, all of this is completely irrelevant to the issue at hand. Bell used standard mathematical concepts to claim that within his proposed framework certain type of correlation among certain type of local functions is impossible. His claim has profound implications for all of physics. Using the same mathematics and his own framework I proved that his claim is false. Therefore it is completely irrelevant whether the mathematics we both used is well-founded or not. It most certainly *is* well-founded, but even if it were not, it does not matter, as far as the issue of locality is concerned. Bell's claim is simply false. End of the story.

Joy

John Merryman

Joy,

I applaud your effort to tie up Bell's loose ends and am sorry for the interruptions, though your opponents are currently absent.

I do see a broader issue of mathematical patterns being taken as more fundamental than the physical processes and forms they model. With everything from multiworlds to multiverses, it does seem there are many more dragons left to slay, than only Bell's non-locality.

In these debates, I try making the argument that time is simply an effect of action and the problem is that since we linearly experience it as a sequence of events from prior to succeeding and physics further distills this to measures of duration, it completely overlooks the actual physical process by which the changing configuration of what exists is turning future into past, not that some point of the present is manifest/traveling along some dimension. The earth doesn't travel from yesterday to tomorrow, tomorrow becomes yesterday because of the spin of the earth.

If time really were a progression from past to future, you would think the faster clock would move into the future more rapidly, but the opposite it true. It ages/burns/processes quicker and so recedes into the past more rapidly. Nor is there any need for the cat to be in a super-position, because probability precedes actuality. Future potential collapses into present actual and past residual. It is the physical occurrence of events that determines the cat's fate.

This makes time much more like temperature, than space. Time is to temperature, what frequency is to amplitude. Duration is simply what is physically happening between the crests of the waves, or any other occurrences. It does not exist as a dimension external to the present.

On the other hand, geometry does not create space, only delineates form within it. Which is why I take issue with the notion that dimensionless points create a line. No matter how many points you have, if they have zero dimension and you add them together, they still have zero dimension. Action does not create a physical line from a point, or a plane from a line, only a narrative of its encounters. Just the residual effects and memories. Only the story/history.

Models are tools, not gods.

Safe to say, I've made little progress as well.

Regards,

John M

Joy Christian

John,

You are entitled to your own ideas about time, or about any other issues in physics. But ideas are dime a dozen, and the days of armchair punditry are long gone. It would impress me more if you came up with a concrete physical theory of time which not only explains existing physical phenomena without contradictions, but also makes predictions of new physical phenomena that can be tested by experiments.

As you may know, I myself have such a theory of time. It is in fact a theory of becoming, in line with some of your own ideas about time. You may not like my theory, but at least it is an actual physical theory that makes testable predictions. Until you come up with such a concrete theory, all you have are empty words. No one in the physics community is likely to be impressed by them. Many in the physics community are well aware of the fact that we are going through a deep crisis in fundamental physics. But they also know that this crisis is unlikely to be resolved by empty words.

Joy

Eckard Blumschein

Joy,

"there are as many points on the real line as in the plane. These are elementary concepts." To me it is obvious who fabricated these concepts and why. May I remind of Salviati (Galileo), Spinoza, Peirce and others whose arguments were not refuted but arbitrarily defined away. Common sense use of bijection tells us that there is an unlimited and uncountable amount of points within every piece of a Peirce continuum. You seem to fear a radical discussion that could fundamentally shutter a castle in the air a part of which you have been successfully attacking.

I agree on that practical benefits are good conformations of a theory. Can you already provide an example where your ideas are used in engineering? I know, the establishment will anyway hardly admit your success. When I suggested that nature does not perform complex calculus, and cosine transform is the natural one in hearing, I faced rejection, although application of cosine transformation has proved not just possible but favorable in MP3 coding.

I don't deny your work. I am looking for allies.

Eckard

John Merryman

Joy,

"That is to say, far from being an illusion, our sensation of that sumptuous moment now,

ceaselessly streaming-in from nowhere and slipping away into the unchanging

past, happens to reï¬‚ect a truly objective feature of the world."

Lol. We seem to be of similar opinion, but my thoughts are empty words? I'm used to being dismissed with such condescension, but it would actually be more interesting for someone to refute my point. Having someone in general agreement dismiss it is ego.

Like Eckard, I'm more interested in congruence than conflict. If you think about what we are discussing, you would as well. As your paper observes, this is a debate going back millennia and it seems doubtful either side will concede, so I'm not sure your purpose in dismissing me without thought.

I would take you to task on an aspect of your paper though. I think you should consider the solidity of the past as you have the future. As relativity makes clear, the order of events can be subjective to spatial positions and I would observe, so would interpretations and perspectives on them. Think how participants on opposite sides of a battle might have different views of the same events. So those events, which quickly recede into the past, are very much a construct of perception and interpretation in the first place. Meanwhile the physical components would have changed positions and the information contained in their order would be rearranged anyway, with any stored information to be absorbed by continuing circumstances.

So, given this constantly changing perspective of receding events that were based on perspective, it would seem the past is not quite written in the hardest stone.

Then consider the future: It can often be predicted. Why? Because the residue of those past events possesses trajectory and momentum. It is the events of yesterday and their physical consequences, which inform and form the events of today.

What I'm getting at here, is that in real, physical terms, time is much more of a cycle or circle, in which the present is a tapestry being woven of threads pulled out of what was previously woven.

It is only in our projection of these transient events, that are passing configurations of what exists, that time seems a line or arrow, either of past to future, or of future becoming past.

Regards,

John M

Akinbo Ojo

Dear All,

I hope everyone has had a look at the figure and re-arrangement using Banach-Tarski's celebrated theorem in the Wikipedia link... Same celebration must apply to Bell's theorem and Joy's disproof, given the underlying assumptions they don't want to look at, that there must be a physical , (even if not mathematical) limit to the divisibility of geometric objects. Given Tom's answer to "So what is the difference between a line and a plane, if it isn't the number of points?" and his response: The number of dimensions. I now reformulate the question to make it more difficult for escape, since dimension will not be an issue: What is the difference between a line and its segment?

John M, I want to predict the answer Tom or Joy will give us: "these are elementary concepts", "It is counterproductive to make up issues when there is none", "It most certainly *is* well-founded (that they are the same and contain the same number of points), but even if it were not, it does not matter, as far as the issue of locality is concerned", prolonged arrogant silence or "for &^%$'s sake"! So John M, if you want to take a bet, you are welcome.

Akinbo

*I must commend Joy. For even bothering to answer once in a while, he seems to be one of the less arrogant members we have around here.

Joy Christian

A segment of a line is compact, whereas line itself is not. It is elementary, Mr. Watson.

Thomas Ray

John, I don't think Joy is the one guilty of ego and condescension.

In the face of all we objectively know about the world, which is overwhelmingly counterintuitive, you condescend to say or imply that your naive notions of past and future are not only worthy of science, your personal intuition is the very foundation of knowledge. If science were done that way, it would be nothing more than opinion.

In order to comprehend Joy's beautiful paper on relative becoming, one must be grounded in relativity and classical mechanics. From the abstract:

" ... the inverse of the Planck time at the conjunction of special relativity and Hamiltonian mechanics, which necessitates energies and momenta to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values."

This isn't opinion; it is in principle testable in objective terms. Joy goes on to say how this differs from the Minkowski model of spacetime "prone to a blocktime interpretation" -- which you abhor -- and he offers up an experimental protocol to support the point. Instead of picking up on that similarity of thought, however, you go into another egoistic tirade about having not been refuted by those ivory tower types. John, what is meant by "empty words" is that you don't offer up anything -- a theory -- that *can* be refuted by scientific method. That's the thing that gives words, and equations, scientific value.

Best,

Tom

Thomas Ray

While I'm on a rampage about scientific method, allow me to point out that the assumptions of nonlocality and linear superposition that support Bell's theorem are not themselves falsifiable. The theorem merely proves, by the technique logicians call double negation, that which it assumes.

Remove those assumptions, and the theorem collapses. Analogously, remove the axiom of choice from set theory, and many well known theorems cannot be proven.

John Merryman

Joy,

First off, I want to say having an ego is not a crime. Simply that lacking a refutation, it seemed your dismissal of my observations was based on assumptions of intellectual inferiority, quite possibly correct, but assumptions none the less.

Tom,

Maybe it is a tirade, but I would like to see an argument for why time is nothing more than the measure and effect of dynamic change. As Joy points out, it may well be bounded above and below, but then so is the effect of temperature.

As for scientific method, why have so many untestable theories been put forth and accepted, as well as patches between theory and observation, such as dark energy?

I simply state what amounts to an observation; That we experience time as a sequence of events, which physics distills to measures of duration between events, but this overlooks and subsumes the physical dynamic creating and dissolving those events. Then this geometry of spacetime is viewed as fundamental, rather than a modeling of activity. If Joy can present an effective rebuttal to the current paradigm, all the power to him, but it doesn't seem to be his primary focus.

Regards,

John M

Thomas Ray

" ... this geometry of spacetime is viewed as fundamental, rather than a modeling of activity."

It is fundamental and physically real, objectively so. I don't know how many times I have to repeat that "model" in the scientific meaning is the solution to an equation or set of equations, not simply what one imagines in one's own head.

In defending against early critics of special relativity, Einstein said,

"The theory of relativity is often criticized for giving without justification, a central theoretical role to the propagation of light. The situation, however, is somewhat as follows. In order to give physical significance to the concept of time, processes of some kind are required which enable relations to be established between different places. It is immaterial what kind of processes one chooses for such a definition of time. It is advantageous, however, for the theory, to choose only those processes concerning which we know something certain. This holds for the propagation of light _in vacuo_ in a higher degree than for any other process which could be considered, thanks to the investigations of Maxwell and H.A. Lorentz.

"From all these considerations, space and time data have a physically real, and not a mere fictitious, significance; in particular, this holds for all the relations in which co-ordinates and time enter, e.g., the relations (ref eqn. 21, the Galilean transformation). There is therefore, sense in asking whether those equations are true or not, as well as asking what the true equations of transformation are by which we pass from one inertial system K to another K' moving relatively to it. It may be shown that this is uniquely settled by means of the constancy of the velocity of light and the principle of special relativity."*

(*The Meaning of Relativity,* fifth edition, Princeton.)

John Merryman

Tom,

""model" in the scientific meaning is the solution to an equation or set of equations, not simply what one imagines in one's own head."

The solution to a set of equations is determined by the factors and functions of those equations. 2+2=4. Whether I'm adding abstractions in my head, or counting apples in a basket, the result is the same. Does this mean that the temporal dimension is "physically real," or is it an abstraction used to order events?

What would you consider as evidence time is an effect of action? When I point out as an example, that tomorrow becomes yesterday because the earth rotates, you dismiss it as naivete. Can you describe one example of measuring time that you are not using dynamical events that come into being and then recede, as your markers? It's not simply a matter of evidence, but whether it is accepted.

"From all these considerations, space and time data have a physically real, and not a mere fictitious, significance;"

This could be a matter of interpretation as well. Does it mean the 'data' have some foundational platonic reality, or does it mean the data is based on a solid physical foundation? I'm certainly willing to accept the dimension of time as abstraction; history, narrative, causal logic are all founded on this device. I'm not willing to accept blocktime.

Regards,

John M

Akinbo Ojo

Mr Watson, what is the difference between a segment of a segment? (Note that that initial line may have been a segment of another).

A line contains points as you say, and its segment contains points, and a segment of that segment also contains points. To a mathematician this can continue ad infinitum but physicists are coming back to their senses 2000 years after the epic dialectic between Aristotle and Plato, that there must be an end to divisibility ad infinitum, at the Planck length 10-35m.

I will read Joy's thoughts on time and see what Mr Watson is up to this time. But how I wish that Joy will do a 'what if...' for once and use his abundant talent to investigate the opposing view as well, instead of casually dismissing it. After all, Tom has said at the end of the day both views are based on axioms that are not directly provable, at least as at today.

Akinbo

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