Nature Has No Faithful Mathematical Representation by Roger Schlafly

Dear Roger Schlafly,

I think, adaptations of wave mechanics with strings as particles, emerges with faithful mathematical representation that demonstrates the function of group homomorphism for this particles of strings.

With best wishes,

Jayaker

Roger,

An excellent essay which I fully agree with. Math is the map(s) of reality, not the bedrock on which it rests. There is though a further argument that might help to support your point:

What is the function of a map? To isolate out and distill the salient points one wishes to focus on. Necessarily many different maps can be created of the same or adjacent territories; road, topographic, butterfly ranges, algebra, geometry, calculus, QM, GR, etc. Each having their advantages. To paraphrase The Lord of the Rings; Why don't we have a math to rule over all the other maths? and give a complete description of everything?

Because that defies the function of math! Which is to focus, isolate, distill out that particular aspect of reality which best serves the purpose at hand. This goes to the nature of perception. It is inherently subjective. Information tends to cancel out other information. Consider a camera. To get the clearest photograph of an object in motion, we use as short a shutter speed as possible. Yet actually we gather much more light and thus information, if we were to leave the shutter open longer, but the result would blur the image. Not only is information very much a function of perspective, but even the creation and destruction of information is itself information. Can't have your cake and eat it too. There is no God's eye view and a theory of everything is seeking that God's eye view. The problem goes to the concept of God. The absolute is the elemental from which reality rises, not an ideal form from which it fell. Everything and nothing are the same, because everything cancels itself out. The happy medium is a big flatline on the universal heart monitor.

You want a theory of everything? "Stuff happens."

Good luck in the contest. You get a high mark from me.

Thanks for your reply dear Roger Schlafly,

Linearity of faithful mathematical representations that describes group homomorphism is applicable when there is holarchial clustering of the matters of universe.

With best regards,

Jayakar

Roger: I appreciate the way you handled quantum mechanics (QM)in your essay. I quote your statement and questions. My position is all explained in my essay, A Challenge to Quantized Absorption by Experiment and Theory.

"It is rare in science for an 80-year-old theory to be so relentlessly challenged by theorists, and yet be so accurately confirmed by experiment."

ER: Until now. My experiments test QM at its most fundamental level, and QM fails. This was all Very difficult to develop.

"Does quantum mechanics have some flaw, or do the challengers have some conceptual misunderstanding?"

ER: Yes to both. The precursor to QM was the loading theory (LT), but it was prematurely rejected. QM will model a wave function associated with a particle. LT is a two state system, a wave state and a particle state. It seemed impossible for an atom to turn into a wave, spread out, and then load up and turn back into a particle. The particle is a contained wave structure. LT needed to be developed to make this picture reasonable, and LT needed to work for our key experiments that led to QM; I did all that. Physicists stopped considering LT because it was given false witness by quantum supporters in our literature and textbooks; I describe all that in detail. My experiments show one gamma-ray can split and cause two gamma detection pulses to appear. I also show one alpha-ray can split and cause two full alphas to appear. By experiment, QM fails and the loading theory works.

"Why are physicists so fond of quoting R.P. Feynman and saying that no one understands quantum mechanics?"

ER: Feynman and quoters understand that by embracing duality, QM is not understandable. Particles cannot cause wave patterns, and waves cannot not magically collapse from everywhere into a particle. They stuck with QM because it worked and there was no experimental challenger. We will only understand QM when we overcome it.

Thank you, Eric Stanley Reiter, August, 2012

Hello to both of you,

Where is the limit between the reason of maths and the rationality of physics....perhaps anywhere in fact :)

ps interesting discussion .

Regards

Roger. Very good essay. Mathematics involves relatively narrow thinking. Math, if it can, truly follows the very greatest ideas in a relatively inferior fashion/role.

Mathematics is certainly more limited in the description of physics as it applies to the body. A very significant limitation of mathematics indeed.

If we only had to/could describe physics in mathematics/mathematical terms/mathematical language, how far could/would we get?

Roger,

I agree with your view. Mathematics cannot be a faithful representation of the physical world. To describe a physical world, we require physical laws, and to explain how the physical world changes we need mathematical laws. This fine distinction between mathematics and physics is often neglected nowadays, and mathematical models having no physical meanings are often brought out as the real representation of physical world.

I dunno - "mathematics" is an awfully big subject, and one can cook up all sorts of ideas that have nothing to do with why the world is the way it is. So ? we already know that. But it appears that we can not really disentangle the Math we need to make sense of phenomena, and Physics. They are not, in any realistic sense, "distinct disciplines" when it comes to subjects like Spin. Physics seems to use only a small part of math - it boxes in the sort of math that is crucial, and leaves open a lot of stuff we can not make sense of - like why it looks like there are 3 generations of fermions. Does anyone really think the explanation is NOT mathematical - probably algebraic ? All the speculation is no surprise - hopefully we learn from mistakes.

You covered a lot of history there. A very entertaining and informative essay.

Roger,

One of the best essays on here! (although I may be a bit biased)

When you speak of first principles, it seems to me that we also have been ignoring a first principle which describes the limits of one of our main mathematical tools. I am speaking specifically of the arbitrary constant of integration from anti-differentiation. The human senses are normally only good for determining differences, and not absolute magnitudes. When we anti-differentiate gravitational force, we can certainly map out a gravitational potential but our calculus tools tell us that while F'=gravitational force, there is no way to know if F=f1 or F=C-f2, or any other combination where the spatial derivatives (gradients) are equivalent). We simply chose the simplest. Thus the "map" of reality is only true up to the limits of what our mathematical tools can tell us. I bring this up because the Einstein field equation, using a much more mathematically logical unimodular approach, could easily have the Einstein tensor substituted such that [math]G_{\mu\nu}=\Omega g_{\mu\nu}-L_{\mu\nu}[/math], which seems a better fit for being able to have a large vacuum energy which appears small.

So this leads me also to the question of choosing which mathematical reality I see from the evidence, and your positivist one strikes the right chord.

You can find my essay here. Comments welcome.

Regards,

Jeff

Dear Roger,

I read your essay and found it very interesting and well written. I highly appreciate and share your viewpoint.

Just as any spoken or written language is an indispensable tool for describing and representing physical reality, mathematics as a symbolic logic system is also an extremely valuable tool for representing and analyzing physical reality. In my essay I have written, "Apparently, growing complexity of mathematical models developed to represent physical reality, often obscure the physical reality to such an extent that the difference between the two is lost in the specialist jargon. In the process however, we have lost our intuitive guide, the common sense, to judge whether these abstract representations do really describe physical reality or simply lead us to a world of fantasy".

As you know, with arbitrary assumptions we can build wonderful fantasies. But to come close to building a model of reality, we must use barest minimum of assumptions and such assumptions that are used must be plausible and compatible with physical reality. For this reason I think FQXi has chosen a most appropriate topic for this contest.

You are also requested to read my essay titled,"Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space". Kindly do let me know if you don't get convinced about the invalidity of the founding assumptions of Relativity or regarding the efficacy of the proposed simple experiments for detection of absolute motion. However, you are welcome to disagree with me regarding my proposal for fundamental research in 'Physical Space' because, possibly, that idea may be still ahead of its time!

Best Wishes

G S Sandhu

Roger,

You fight Einstein's relativity in a way that will please Einsteinians - you will get many points from them. You wrote:

"The crucial experiment was by Michelson-Morley in 1887, showing that the speed of light was the same in different frames of reference. G. FitzGerald was the first to make the logical deduction from the apparent contradiction, in 1889, by saying, "I would suggest that almost the only hypothesis that can reconcile this opposition is that the length of material bodies changes..." H. Lorentz made a similar deduction..."

Quite the opposite happened. Originally the Michelson-Morley experiment showed that the speed of light varies with the speed of the light source, as predicted by Newton's emission theory of light. However at that time the emission theory was totally forgotten and the ether theory's tenet that the speed of light is independent of the speed of the light source was universally accepted. So FitzGerald and Lorentz had to advance the ad hoc length contraction hypothesis in order to reconcile the ether theory's tenet with the null result of the experiment.

Pentcho Valev pvalev@yahoo.com

Yes, Roger, at the time there were physicists immeasurably cleverer than Einstein. Walther Ritz for instance:

http://www.datasync.com/~rsf1/crit/1908a.htm

Walther Ritz 1908: "The only conclusion which, from then on, seems possible to me, is that ether doesn't exist, or more exactly, that we should renounce use of this representation, that the motion of light is a relative motion like all the others, that only relative velocities play a role in the laws of nature; and finally that we should renounce use of partial differential equations and the notion of field, in the measure that this notion introduces absolute motion."

Einstein came to the same conclusion in 1954 but it was too late:

http://www.perimeterinstitute.ca/pdf/files/975547d7-2d00-433a-b7e3-4a09145525ca.pdf

Albert Einstein (1954): "I consider it entirely possible that physics cannot be based upon the field concept, that is on continuous structures. Then nothing will remain of my whole castle in the air, including the theory of gravitation, but also nothing of the rest of contemporary physics."

Clues:

http://arxiv.org/ftp/physics/papers/0101/0101109.pdf

"The two first articles (January and March) establish clearly a discontinuous structure of matter and light. The standard look of Einstein's SR is, on the contrary, essentially based on the continuous conception of the field."

http://www.pbs.org/wgbh/nova/einstein/genius/

"And then, in June, Einstein completes special relativity, which adds a twist to the story: Einstein's March paper treated light as particles, but special relativity sees light as a continuous field of waves."

http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768

Relativity and Its Roots, Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

Pentcho Valev pvalev@yahoo.com