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Sergey Fedosin: on 10/4/12 at 5:40am UTC, wrote If you do not understand why your rating dropped down. As I found ratings...

Yuri Danoyan: on 9/25/12 at 11:01am UTC, wrote See my discussion with George Ellis ...

Constantinos Ragazas: on 9/24/12 at 16:29pm UTC, wrote Dear Wang Xiong, You raise an interesting issue: differentiability in...

Peter Jackson: on 9/23/12 at 19:41pm UTC, wrote Wang I appreciated your approach to finding a unified foundation. I found...

Hoang Hai: on 9/19/12 at 13:48pm UTC, wrote Dear Very interesting to see your essay. Perhaps all of us are convinced...

Yuri Danoyan: on 9/17/12 at 19:49pm UTC, wrote For better clarification my approach I sending to you Frank 3 keen ...

Pentcho Valev: on 9/15/12 at 4:54am UTC, wrote Wang, In your "road toward a complete theory of relativiy" (Table 1), in...

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FQXi FORUM
July 18, 2019

CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: Can Differentiable Description of Physical Reality Be Considered Complete? by Wang Xiong [refresh]

Author WANG Xiong wrote on Aug. 31, 2012 @ 12:06 GMT
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.

Patrick Alan Hutchinson wrote on Aug. 31, 2012 @ 19:57 GMT
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.

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Author WANG Xiong replied on Sep. 1, 2012 @ 01:11 GMT
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 J. Dickau wrote on Sep. 1, 2012 @ 00:49 GMT
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.

Jonathan

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Author WANG Xiong replied on Sep. 1, 2012 @ 00:57 GMT
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 J. Dickau wrote on Sep. 1, 2012 @ 00:52 GMT
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

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Author WANG Xiong replied on Sep. 1, 2012 @ 01:02 GMT
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

Anonymous wrote on Sep. 1, 2012 @ 04:30 GMT
I like your essay. It was very informative, and not too difficult to understand. Your point was very clear.

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Anonymous replied on Sep. 1, 2012 @ 06:36 GMT
Thanks, physics should be as simple as possible

simple but profound.

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Eckard Blumschein wrote on Sep. 1, 2012 @ 06:51 GMT
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

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Author WANG Xiong replied on Sep. 2, 2012 @ 13:33 GMT
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.

Xiong

Jeff Baugher wrote on Sep. 2, 2012 @ 02:52 GMT
Wang Xiong,

I found your essay interesting, as it has a relationship with my own. Whereas you state a solution may exist examining non-di fferentiability, 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.
$G_{\mu\nu}=\Omega g_{\mu\nu}-L_{\mu\nu}$
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

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Author WANG Xiong replied on Sep. 2, 2012 @ 13:36 GMT
Thanks Jeff Baugher,

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

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

Xiong

Member Benjamin F. Dribus wrote on Sep. 2, 2012 @ 08:41 GMT
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

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Author WANG Xiong replied on Sep. 2, 2012 @ 13:48 GMT
Dear Ben Dribus,

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

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

Yuri Danoyan wrote on Sep. 2, 2012 @ 17:23 GMT
Wang,

http://www.nobelprize.org/nobel_prizes/physics/laureates/199
9/thooft-lecture.pdf

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Author WANG Xiong replied on Sep. 2, 2012 @ 22:45 GMT
Thanks, but the link is broken? please send me a copy to my email, if possible, thanks!

Author WANG Xiong replied on Sep. 2, 2012 @ 23:11 GMT
yes, thanks for this paper,

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

Yuri Danoyan replied on Sep. 2, 2012 @ 23:20 GMT

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Vladimir Rogozhin wrote on Sep. 2, 2012 @ 18:46 GMT
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

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Author WANG Xiong replied on Sep. 2, 2012 @ 23:16 GMT

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

Torsten Asselmeyer-Maluga wrote on Sep. 4, 2012 @ 19:43 GMT
Dear Wang Xiong,

interesting essay, in particular I like your style.

We disagree about the importance of differentiability (see my essay). I would also ask the same questions then Ben.

As I understand your approah in a right sense, then fractal means non-smooth. But from the math point, it is wrong. Consider Alexanders horned sphere: it is a wild embedding of the 2-sphere with fractal dimension (between 2 and 3). But it is a smooth embedding inducing a smooth metric (from the embedding space).

Therefore I think one can save differentiablity and the concept of a manifold.

4-manifolds have special properties.

Best

Torsten

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Author WANG Xiong replied on Sep. 8, 2012 @ 13:16 GMT
Dear Torsten,

I don't think we need to save differentiablity by that way...

anyway

YES,4-manifolds are special.

Best

Xiong

Michael James Goodband wrote on Sep. 11, 2012 @ 17:19 GMT
Dear Wang Xiong

The assumption that space-time is a smooth differential manifold is a convenient but fundamentally metaphysical assumption that you are right to identify as an implicit assumption made in physics. It is an assumption that I make in the theory mentioned in my essay and I am happy to explicitly acknowledge that it is metaphysical. After all, the search for new physics theories has an element of looking for a set of metaphysical assumptions that reproduce known results - we just need to be willing to be explicit about those assumptions.

However, my assumption of a smooth differential manifold turns out to perhaps not quite be what it seems in physically measurable terms. This is because in my extended GR manifold (S3*S7) the compactified S7 dimensions effectively provide the discrete physical units in which spatial distances and times are measured - a unit system of the Planck scale. Other theories with smooth space-time and compactified dimensions can have the same feature. Although the limit dx->0 is technically possible for the assumed smooth manifold, in measurement terms the limiting procedure runs into the finite Planck scale in which the distances are measured. Have you considered such scenarios where even the assumption of a smooth manifold may not fully transfer to physically measurable terms?

Michael

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Author WANG Xiong replied on Sep. 14, 2012 @ 11:46 GMT
Dear Michael,

Thanks for your question, it's very important question

even the assumption of a smooth manifold may not fully transfer to physically measurable terms,

yes, but I think there is no need to limit it to smooth case

anyway, the general manifold will be very complicated and rich in content

Xiong

Author WANG Xiong replied on Sep. 14, 2012 @ 11:47 GMT
anyway, one thing we believe in common is

Quantum Theory is not As Fundamental As It Seems

;-)

Don Limuti wrote on Sep. 13, 2012 @ 03:58 GMT
Dear Wang,

Our languages are somewhat different. I am not highly trained in math. However I can see your points clearly.

You explain non differentiability as the reason why gravity theory cannot come to grips with quantum phenomena. Yes, I agree completely, only I would phrase it differently: The common assumption that an object can have a velocity at a point is a fallacy, v can never be dx/dt no matter how many epsilons are thrown at it. It is great math and rotten physics.

You seem to favor a fractal picture of reality, do yo think this can be related to Feynman's sum over histories approach?

I like your thoughtful clearly written essay.

Don L.

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Author WANG Xiong replied on Sep. 14, 2012 @ 11:35 GMT
Dear Don L,

Thanks,

Yes, the math behind is quite subtle, but I tried to express the idea as clear as possible.

yes, Feynman's sum over histories approach indicate that the quantum path is fractal.

Best Regards,

Xiong

Yuri Danoyan wrote on Sep. 17, 2012 @ 19:49 GMT
For better clarification my approach

I sending to you Frank 3 keen articles

http://ctpweb.lns.mit.edu/physics_today/phystoday/Ab
s_limits393.pdf

http://ctpweb.lns.mit.edu/physics_today/physt
oday/Abs_limits393.pdf

http://ctpweb.lns.mit.edu/physics_toda
y/phystoday/Abs_limits400.pdf

All the best

Yuri Danoyan

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Hoang cao Hai wrote on Sep. 19, 2012 @ 13:48 GMT
Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regard !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Peter Jackson wrote on Sep. 23, 2012 @ 19:41 GMT
Wang

I appreciated your approach to finding a unified foundation. I found one from a different approach, but will need validation from yours. I hope you might give me your view. I do not feel well qualified to comment in detail on yours, but was anyway impressed with the parts I fully followed.

Best wishes, and thanks

Peter

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Constantinos Ragazas wrote on Sep. 24, 2012 @ 16:29 GMT
Dear Wang Xiong,

You raise an interesting issue: differentiability in Nature. But whereas you resort to non-differentiable manifolds of Spacetime to correct existing mathematical models of the Universe, I argue in my essay, “The Metaphysics of Physics”, all mathematical models of 'what is' the Universe are in essence metaphysical and will ultimately fail. Knowing truly 'what is' the Universe is like knowing another person; what they think, how they feel and how they will behave. We can only know ourselves truly. All knowledge in this sense is therefore self-knowledge.

The question of differentiability in Nature can be considered in the following very simple context, for example. When we take a thermometer reading, is the final reading on the thermometer “asymptotically approximated” (as would be the case if the underlying physical processes were differentiable) or will the final reading be exact (up to the limits of our instruments).

In my view, there is a simple explanation that does not require differentiability and is able to explain the reading we get would be exact and not asymptotic. The physical view here can be described as follows: “energy propagates continuously as a wave while it manifests discretely in interactions”. Thus, we can view Nature as being 'continuous' and explain the 'manifestation' of Nature (as readings in our instruments, for example) as being 'discrete'.

Constantinos

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Yuri Danoyan wrote on Sep. 25, 2012 @ 11:01 GMT
See my discussion with George Ellis

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 05:40 GMT
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is
$R_1$
and
$N_1$
was the quantity of people which gave you ratings. Then you have
$S_1=R_1 N_1$
of points. After it anyone give you
$dS$
of points so you have
$S_2=S_1+ dS$
of points and
$N_2=N_1+1$
is the common quantity of the people which gave you ratings. At the same time you will have
$S_2=R_2 N_2$
of points. From here, if you want to be R2 > R1 there must be:
$S_2/ N_2>S_1/ N_1$
or
$(S_1+ dS) / (N_1+1) >S_1/ N_1$
or
$dS >S_1/ N_1 =R_1$
In other words if you want to increase rating of anyone you must give him more points
$dS$
then the participant`s rating
$R_1$
was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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