Nature Has No Faithful Mathematical Representation by Roger Schlafly

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, it is a fact that direct bodily experience is fundamental to physics and does not necessarily or fundamentally need or involve mathematics.

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

Stachel and Norton go as far as to accuse brothers Einsteinians of lying about the Michelson-Morley experiment but assure that Einstein, unlike "later writers", was honest and never cited the experiment as evidence for the principle of the constancy of the speed of light:

http://philsci-archive.pitt.edu/1743/2/Norton.pdf

John Norton: "In addition to his work as editor of the Einstein papers in finding source material, Stachel assembled the many small clues that reveal Einstein's serious consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost universally use it as support for the light postulate of special relativity. Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

http://www.amazon.com/Einstein-B-Z-John-Stachel/dp/0817641432

Einstein from 'B' to 'Z', John Stachel, p. 179: "Are there any common features to Einstein's mentions of the Michelson-Morley experiment? Yes: Without exception, it is cited as evidence for the relativity principle, and is never cited as evidence for the principle of the constancy of the velocity of light."

In fact, Einstein devised the lie, as can be seen from the New York Times 1921 article:

http://query.nytimes.com/gst/abstract.html?res=9806EFDD113FEE3ABC4152DFB266838A639EDE

The New York Times, April 19, 1921: "The special relativity arose from the question of whether light had an invariable velocity in free space, he [Einstein] said. The velocity of light could only be measured relative to a body or a co-ordinate system. He sketched a co-ordinate system K to which light had a velocity C. Whether the system was in motion or not was the fundamental principle. This has been developed through the researches of Maxwell and Lorentz, the principle of the constancy of the velocity of light having been based on many of their experiments. But did it hold for only one system? he asked. He gave the example of a street and a vehicle moving on that street. If the velocity of light was C for the street was it also C for the vehicle? If a second co-ordinate system K was introduced, moving with the velocity V, did light have the velocity of C here? When the light traveled the system moved with it, so it would appear that light moved slower and the principle apparently did not hold. Many famous experiments had been made on this point. Michelson showed that relative to the moving co-ordinate system K1, the light traveled with the same velocity as relative to K, which is contrary to the above observation. How could this be reconciled? Professor Einstein asked."

Pentcho Valev pvalev@yahoo.com

In 1887 the Michelson-Morley experiment UNEQUIVOCALLY confirmed the emission theory's tenet that the speed of light varies with the speed of the light source (c'=c+v) and refuted the ether theory's tenet that the speed of light is independent of the speed of the light source (c'=c). By advancing, ad hoc, his absurd length contraction hypothesis, Lorentz made the experiment confirm the false tenet (c'=c) and refute the true one (c'=c+v). That marked the beginning of the end of rational physics.

Pentcho Valev pvalev@yahoo.com

why ?

Hi Roger,

An interesting and thought-provoking essay! You write: "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. Does quantum mechanics have some flaw, or do the challengers have some conceptual misunderstanding?". I thik both, as can be seen from my own essay. However I will not recommend you to read it. Better, if you haven't already read Robert H. McEachern's essay "Misinterpreting Reality: Confusing Mathematics for Phisics" I strongly recommend you to do so.

Best regards,

Inger

Hi Roger.I am delighted with this passage in your essay

"The idea was described by the ancient Greek philosopher Socrates in about 400 BC, and written by Plato as the Allegory of the Cave. People in the cave see shadows, and do not appreciate the 3-D nature of the objects causing the shadows. They are seeing a 2-D projection of 3-D objects.

A photograph is also a 2-D projection of a 3-D scene. A measurement with a meter stick is a 1-D projection. Other observations can also be viewed as projections of some more complex reality."

In my essay i proposed where is need find out 2D world.

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