Can Differentiable Description of Physical Reality Be Considered Complete? by Wang Xiong

WANG Xiong

Essay Abstract

How to relate the physical \emph{real} reality with the logical \emph{true} abstract mathematics concepts is nothing but pure postulate. The most basic postulates of physics are by using what kind of mathematics to describe the most fundamental concepts of physics. Main point of relativity theories is to remove incorrect and simplify the assumptions about the nature of space-time. There are plentiful bonus of doing so, for example gravity emerges as natural consequence of curvature of spacetime. We argue that the Einstein version of general relativity is not complete, since it can't explain quantum phenomenon. If we want to reconcile quantum, we should give up one implicit assumption we tend to forget: the differentiability. What would be the benefits of these changes? It has many surprising consequences. We show that the weird uncertainty principle and non-commutativity become straightforward in the circumstances of non-differentiable functions. It's just the result of the divergence of usual definition of \emph{velocity}. All weirdness of quantum mechanics are due to we are trying to making sense of nonsense. Finally, we proposed a complete relativity theory in which the spacetime are non-differentiable manifold, and physical law takes the same mathematical form in all coordinate systems, under arbitrary differentiable or non-differentiable coordinate transformations. Quantum phenomenon emerges as natural consequence of non-differentiability of spacetime.

Author Bio

WANG Xiong has obtained his B.Sc. majoring in math from the Shanghai Jiao Tong University, China. Currently, he is a research student at City University Hong Kong at the Centre for Chaos and Complex Networks. From undergraduate time, he continue an independent solitary quest for a unified foundation for mathematics and physics.

Download Essay PDF File

Patrick Hutchinson

Hello Wang Xiong

Thank you for a stimulating article. I have a feeling that it will need some work to make some mathematicians content with it. Somewhere it seems to be assuming something about a measure on space-time. Anyway there seems to be a deep idea in it.

Regards

Alan H.

WANG Xiong

Hello Dear Alan H.

Thank you for reading my article. I have the same feeling that it will need some work to make some mathematicians content with it.

There is really a deep idea in it, this paper just a draft picture

Regards

Wang Xiong

Jonathan Dickau

Hello Wang Xiong,

I gravitated to your paper because of my familiarity with the work of one of the authors you cite. In section 4.4 you mention that Laurent Nottale did promising work in a similar direction, but did not arrive at a satisfying conclusion.

He has since published his book "Scale Relativity And Fractal Space-Time" which delves into some of the questions you raise with considerable rigor.

The new book repairs most of the deficiencies in the Math of his earlier works, attempting to both correct errors and expand upon the earlier work you cite. I was privileged to see the book in manuscript form, and the published version is quite the Magnum Opus for Nottale - over 750 pages in all! It is obviously recommended reading, considering your subject. You will find many points of agreement.

I read your paper very swiftly, and I will need to re-read it to make meaningful comments. Best of luck!

Jonathan

WANG Xiong

Oh, thanks Jonathan,

Nottale is really a great physics with lots of great promising idea,

I believe some of his idea is really on the right way

I feel like to look at the new book you mentioned, thanks very much!

Jonathan Dickau

One more thing;

Nottale suggests that a continuous but non-differentiable spacetime is necessarily fractal. Do you agree, or assume this?

All the Best,

Jonathan

WANG Xiong

Dear Jonathan,

In fact, there lacks a rigorous definition of fractal.

So what we really means is continuous but non-differentiable spacetime

also there is a subtle issue about continue, there are also discussion about to give up continue, such as levy flight kind of path.

We still need some new math for this problem.

Thanks

Regards,

Xiong

[deleted]

I like your essay. It was very informative, and not too difficult to understand. Your point was very clear.

[deleted]

Thanks, physics should be as simple as possible

simple but profound.

[deleted]

Dear Wang Xiong,

"All weirdness of quantum mechanics are due to we are trying to making sense of nonsense." Let me admire first your excellent style of writing. I also found out that non-differentiability is an important issue. I would merely appreciate if you could explain more in detail:

"But by analogy, we can say that quantum equation must of order 1.5 as for x. So there is less than two, but more than one independent variables. This is why the x and dx/dt are somehow not independent to each other, but are conjugate variables with uncertainty relation between them."

Perhaps you will be among those who are rather shocked by my very basic criticism. It seems unlikely to me that we will easily agree on the logical consistency of SR. Nonetheless I invite you to challenge in detail what I wrote here and also here .

Regards,

Eckard

WANG Xiong

Dear Eckard,

Some of these ideas are explained in more details in my ongoing book but not in English, I will try to write some paper with more details in the future.

Thanks for your interesting paper. will discuss after my reading

Xiong

[deleted]

Wang Xiong,

I found your essay interesting, as it has a relationship with my own. Whereas you state a solution may exist examining non-differentiability, my essay postulates that we have been anti-differentiating the Newtonian field incorrectly, which leads to the incorrect form of the Einstein field equation. If a function F1 is Newtonian field strength, then F1' is gravitational force. I state that we have probably been mistaking F1' for (C-F2)' so that the Einstein field equation with the cosmological constant should read similarly, i.e. [math]G_{\mu\nu}=\Omega g_{\mu\nu}-L_{\mu\nu}[/math] where the constant term is equated to a potential for energy of the vacuum and Luv is equated to a residual dynamic stress energy tensor. This would allow a large magnitude for the constant while still appearing like attractive gravity but also allowing a repulsion after a certain radius. Solves the old and new cosmological constant problems.

I will peruse your paper more in depth to see if there are places from which I can learn.

Regards,

Jeff Baugher

WANG Xiong

Thanks Jeff Baugher,

It may take some time to enjoy and digest your paper,

personally, I don't like the cosmic constant term, ;-)

Xiong

Benjamin Dribus

Wang,

Interesting essay. I agree that differentiable manifolds are probably "too good to be true," and are assumed mostly because they are easy to work with mathematically. I also agree that the path integral formulation of quantum theory provides key insight, and that fractals, scale-dependent phenomena, self-similarity, etc. deserve more attention. I have a couple of questions.

1. What exactly do you mean by a "nondifferentiable manifold" and a "fractal manifold?"

2. How do time and causality fit into your picture?

To see what is motivating these questions, you might look at my essay

On the Foundational Assumptions of Modern Physics

I also reject differentiable manifolds and emphasize path integrals, but there are some differences too. Take care,

Ben Dribus

WANG Xiong

Dear Ben Dribus,

I am very happy to have math background reader like you,

your questions are very important!

1. What exactly do you mean by a "nondifferentiable manifold" and a "fractal manifold?"

this is a big problem,indeed a big subject of math, impossible to address in such a short paper,

roughly, you can think nondifferentiable manifold just as manifolds without additional differentiable structure.

Because we add this differentiable structure without physical reasons, so as to allow calculus to be done on manifolds.

2. How do time and causality fit into your picture?

this is an important problem, which I still need to clarify.

I think the first step is to get this picture fit with SR

Xiong

[deleted]

Wang,

Please read Nobel lecture Gerardus t' Hooft

http://www.nobelprize.org/nobel_prizes/physics/laureates/1999/thooft-lecture.pdf

p.360 about same problem.

WANG Xiong

Thanks, but the link is broken? please send me a copy to my email, if possible, thanks!

WANG Xiong

yes, thanks for this paper,

like he said in p361, everything......has to be reexamined

[deleted]

More details please...

WANG Xiong

For the math issue, please see my paper

Fractional Geometric Calculus: Toward A Unified Mathematical Language for Physics and Engineering

http://vixra.org/abs/1206.0005

thanks

[deleted]

Have you read my essay with my Appendix-comments?

http://fqxi.org/community/forum/topic/1413

[deleted]

What is your opinion concerning my essay?

[deleted]

Hello, Wang Xiong! Profound dialectical essay. But: "the truth is to be drawn and is provided an unlimited number of viewers" (A.Zenkin "Scientific counterrevolution in mathematics"). You could draw and ontologically justify the structure of space-time by Wang Xiong? Sincerely, Vladimir Rogozhin

WANG Xiong

Dear Vladimir Rogozhin,

Thanks very much for your interest.

Your question is very important, ontological groundlessness is essential for Einstein to build his theory of relativity

and things become very subtle in GR, some problem still remain, I still try to quest for a clear construction

Xiong