Nature Has No Faithful Mathematical Representation by Roger Schlafly

Congrats on a well written essay. Hope you will win one of the prizes.

Roger,

There is a wrong statement in your essay:

"The crucial experiment was by Michelson-Morley in 1887, showing that the speed of light was the same in different frames of reference."

In fact, in 1887 (the ad hoc length contraction hypothesis is not yet introduced) the Michelson-Morley experiment shows just the opposite - that the speed of light varies in different frames of reference as predicted by Newton's emission theory of light:

http://www.pitt.edu/~jdnorton/papers/companion.doc

John Norton: "These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."

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/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

Pentcho,

Pentcho: "There is a wrong statement in your essay:"

Roger: "The crucial experiment was by Michelson-Morley in 1887, showing that the speed of light was the same in different frames of reference." "

Pentcho: "In fact, in 1887 (the ad hoc length contraction hypothesis is not yet introduced) the Michelson-Morley experiment shows just the opposite - that the speed of light varies in different frames of reference as predicted by Newton's emission theory of light: ..."

How did it do that? I have seen the quotes. I am not asking for more of the same. I stopped trying to check your references months ago. I am asking if you will explain in your words how the Michelson-Morley experiment shows ... that the speed of light varies in different frams of references ... ?

James

Below is the original calculation based on the assumption that the speed of light is independent of the motion of the light source:

http://www.berkeleyscience.com/relativity.htm

"Michelson and Morley designed an experiment to detect the ether and measure its influence on the speed of light. (...) Let's do the math. Assume light travels at a constant velocity c in the ether. Suppose the apparatus is moving through the stationary ether with velocity v. In the direction of motion, the time for the light to reach the mirror and come back is T=L/(c-v)+L/(c+v). In the direction perpendicular to the motion, the time to reach the mirror and come back is calculated by solving (cT)^2=L^2+(vT)^2, so T=(L^2/(c^2-v^2))^(1/2). The experimental results did not match this calculation. Instead T was the same for both directions (T=2L/c )."

Alternatively, one can assume that, in accordance with Newton's emission theory of light, the velocity of the light, as measured by the observer, is c±v, where v is the velocity of the light source. Suppose the apparatus passes the observer with velocity v. In the direction of motion, the time for the light to reach the mirror and come back is T=L/c+L/c=2L/c. In the direction perpendicular to the motion, the time to reach the mirror and come back is calculated by solving (c^2+v^2)T^2=L^2+(vT)^2, so T=2L/c. The experimental results did match this calculation (for both directions T=2L/c).

Conclusion: In 1887 the Michelson-Morley experiment unequivocally proved that the speed of the light is c'=c±v, as predicted by Newton's emission theory of light, and refuted the assumption that the speed of light is independent of the motion of the light source.

Pentcho Valev pvalev@yahoo.com

Pentcho,

I will not be invading Roger's space, so I need to keep this short.

You said: "Suppose the apparatus passes the observer with velocity v. ..."

Please find another thread to respond and I will pursue this at least until I am clear about the value of what you are claiming. If you respond here, even though I appreciate that you did respond, I will not follow up here.

What apparatus passes the observer with velocity v? Also:

You said: "Conclusion: In 1887 the Michelson-Morley experiment unequivocally proved that the speed of the light is c'=c±v, as predicted by Newton's emission theory of light, and refuted the assumption that the speed of light is independent of the motion of the light source."

How did the experiment show that :...it refuted the assumption that the speed of light is independent of the motion of the light source."?

I guess this seems clear to you but it is not clear to me.The experiment showed null results and the follow-up experiments showed null results. How can you say anything more than that the experiment showed that 90 degrees between tubes showed no difference in the local speed of light? The followup experiments say the same. I am asking these question strictly with regard to the empirical results. Thank you.

James

I have always loved the wit and wisdom of Albert Einstein's take on the relationship between mathematics and the actual physical world:

"Insofar as the propositions of mathematics refer to reality, they are uncertain; insofar as they as they are certain, they do not apply to reality."

Robert L. Oldershaw

http://www3.amherst.edu/~rloldershaw

Discrete Scale Relativity

Some Platonists argue that mathematics is eternal, exact and perfect - that its truths are discovered by humans rather than invented. A corollary of the Platonist paradigm is that nature is a somewhat imperfect approximation to the eternal mathematical truths. Although many are swayed by these arguments, it is possible that the Platonist philosophy has things backwards.

An alternative paradigm asserts that it is nature that is an eternal magnificent perfection, and that pure mathematics is an inherently abstract and imperfect enterprise. According to this alternative philosophy, when mathematics is applied to modeling nature, the analytical models are:

(1) Artificial (in the non-pejorative sense of the word, and more in the sense that the models are invented rather than discovered), and

(2) Approximate (in the sense that they cannot in principle provide a complete representation of nature's infinite complexity).

The Platonist paradigm seems to be motivated by a fervent hope that mathematics offers exact answers and absolute truths. Unfortunately, it seems more likely that such things as exact answers and absolute truths will always remain beyond human reach. Perfect circles and absolute certainty probably exist only in the "world" of the imagination. We would do well to be mindful of the distinction between what is real and what is an abstraction.

Mathematics is a truly sublime subject of study and it plays an extremely important role in modeling nature. Yet perhaps applied mathematics is significantly more limited than the Platonists and the Bourbaki physicists are willing to acknowledge.

RLO

http://www3.amherst.edu/~rloldershaw

Fractal Cosmology

Dear Roger,

I just read your essay and have a couple of questions: If mathematics is not a faithful representation of reality, is there any other way to obtain such a representation, or are we forever doomed to ignorance about what "really goes on" in the world, according to your view? Also, can you give an example in which you see physics progressing independent from mathematics?

Thank you,

Armin

Roger

Michelson 1881: "The result of the hypothesis of a stationary ether is thus shown to be incorrect...This conclusion directly contradicts the explanation of the phenomenon of aberration which has been hitherto generally accepted, and which presupposes that the earth moves through the ether, the latter remaining at rest"

Michelson & Morley 1886: "The result of this work is therefore that the result announced by Fizeau is essentially correct; and that the luminiferous ether is entirely unaffected by the motion of the matter which it permeates"

Now, in 1892 (not 1895), Lorentz writes: "I have sought a long time to explain this experiment [M&M] without success, and eventually I found only one way to reconcile the result with Fresnel's theory. It consists of the assumption, that the line joining two points of a solid body doesn't conserve its length, when it is once in motion parallel to the direction of motion of Earth, and afterwards it is brought normal to it...Such a change in length of the arms in Michelson's first experiment, and in the size of the stone plate in the second, is really not inconceivable as it seems to me...Anyway, it seems undeniable that changes of the molecular forces and consequently of the body's size of order of 1 - p2/2V2 are possible. Michelson's experiment thus loses its verification power for the question at which it was aimed. If one assumes the theory of Fresnel, then its meaning rather lies in the fact, that we can learn something about the change of dimensions".

By 1895 Lorentz is writing: "Thus we see, that the phase difference expected by the theory could also arise, when (during the rotation of the apparatus) sometimes one, sometimes the other arm would have the greater length. From that if follows, that they can be compensated by opposite variations of the dimensions...If we assume, that the arm lying in the direction of Earth's motion, is shorter by p2/2V2... than the other one, and simultaneously the translation would have an influence which follows from Fresnel's theory, then the result of Michelson's experiment is fully explained... Consequently we have to imagine, that the motion of a rigid body, e.g. a brass rod or of the stone plate used in later experiments, would have an influence on the dimensions throughout the aether, which, depending on the orientation of the body with respect to the direction of motion, is different... As regards the experimental confirmation, it is to be noticed at first, that the relevant elongations and contractions are extremely small... it would cause a contraction in the direction of motion in the ratio of 1 to √(1-p2/V2). In reality the molecules of a body are not at rest, but there exists a stationary motion in every "equilibrium state".

With the important proviso: "When I developed the present theory, I hoped at first to be able to explain this difference, but soon I found myself disappointed in my expectation" & "Everything taken together, the question is forced upon us, whether it might be possible to adapt the theory to observations, without ceasing to explain the other phenomena discussed in this work. I haven't succeeded in this, and I must therefore leave the whole question open, in the hope that others might overcome the difficulties that still exist".

The original argument is about the constitution and effect of ether. Correct assumptions about light, ie its independence and constancy, were already in place because this was the basis upon which the result of the M & M experiment was considered. Leading to the conclusion that it proved that matter had a certain 'elasticity'. The calibration of light speed (ie its speed wrt) will of course vary depending on the reference point. Lorentz dissasociates ether from having any effect, eventually. At first (as above 1892) he hypothesises the actual physical alteration of matter as a function of ether. But that becomes problematical (see above). By 1899 he is trying to resolve the problem (of differential movemnt and an associated effect on dimension) with "such small differences" having the "same local time". Under pressure from Poincare to 'propose a coherent theory and not keep adding to the current one', and bearing in mind his principle "that many electromagnetic actions are entirely independent of the motion of the system", by 1904 he puts one forward with "The only restriction as regards the velocity will be that it be smaller than that of light".

Essentially, Lorentz suggests that the alteration in dimension in the line of motion is a function of the flattening of electrons: "I shall now suppose that the electrons, which I take to be spheres of radius R in the state of rest, have their dimensions changed by the effect of a translation, the dimensions in the direction of motion becoming kl times and those in perpendicular direction l times smaller... Our assumption amounts to saying that in an electrostatic system, moving with a velocity, all electrons are flattened ellipsoids with their smaller axes in the direction of motion".

As Einstein later said (Ether & Relativity 1922): "He [Lorentz] achieved this, the most important advance in the theory of electricity since Maxwell, by taking from ether its mechanical, and from matter its electromagnetic qualities. As in empty space, so too in the interior of material bodies, the ether, and not matter viewed atomistically, was exclusively the seat of electromagnetic fields. According to Lorentz the elementary particles of matter alone are capable of carrying out movements; their electromagnetic activity is entirely confined to the carrying of electric charges.

Light was deemed, correctly, to always start with the same velocity, which will not alter unless impeded in some way. This is obvious, because light is just another entity. Forget that it enables organisms to 'see'. It results from an atomic interaction (ie always has the same start speed) and, like anything else, will continue to travel at that speed unless acted upon in some way. Furthermore, observation cannot affect reality.

The bottom line here is that, according to the theory, the variable is a quality in matter which results in an alteration in one particular dimension when a differential force is incurred, ie one which also causes it to speed up/slow down. So in the context of comparison, one must be aware of this, because an 'it' which is undergoing changing momentum does not have the same dimension as one which is not. It has nothing to do with light, observation, timing and any other spurious explanation which has been alluded to. Of course, whether this dimensional alteration does actually occur, and if so, why and what is its magnitude, are different questions.

Paul

As Einstein said "imagination is more important than knowledge". Same as if you have a big imagination and you are a writer and know language and letters well, you can build very fascinating and beautiful novels, stories, and poems. Same as in physics, if you have big imagination and you know mathematics well, you can describe and understand how the natural laws are working. Math is the language of the natural laws in physics. All of us know the language, letters and math, but we don't have an imagination like Shakespeare,Picasso, Einstein, Heisenberg or Newton.

Dear Roger Schlafly, you write

"The 2011 FQXi essay contest asked, "Is Reality Digital or Analog?" The answers

accepted the premise that reality had to be one or the other, and no one admitted the possibility that it might be neither because both are mathematical."

Though your quote is generally true, it is not entirely true. Specific to my FQXi 2011 Contest Essay, "A World Without Quanta?" (http://www.fqxi.org/community/forum/topic/908) below are some quotes to the contrary ...

"To the question, "Is the Universe Continuous or Discrete? ", we argue that we cannot know 'what is' and strike a philosophical balance and answer, "it is neither and both"."

"I believe that mathematical models of 'what is' -- as with past metaphysical attempts -- are a never ending search getting us deeper and deeper into the 'rabbit's hole' [Ref. 15]. Physics reduces to Mathematics not through mathematical models but through mathematical identities that describe measurement, which is the essence of Physics. Though Mathematics provides logical certainties, it can not provide the Truth of 'what is'."

"Is the Universe continuous or discrete? In my humble opinion this is a false dichotomy. It presents us with an impossible choice between two absolute views. And as it is always the case, making one side absolute leads to endless fabrications denying the opposite side. The Universe is neither continuous nor discrete because the Universe is both continuous and discrete. Our 'view' of the Universe is not the Universe. The Universe simply 'is'. "

"So how are we to reconcile continuous vs. discrete? We can begin by being humble enough to acknowledge the hubris of knowing what is the Universe. Since we are limited by our measurements, we should consider these as the beginning and end of all our intellectual efforts in Physics."

"Mathematics is a tool. It is a language of objective reasoning. But mathematical 'truths' are always 'conditional'. They depend on our presuppositions and our premises. They also depend, in my opinion, on the mental views we use to think. We phrase our explanations the same as we frame our experiments"

"We can have beautiful mathematical results based on any view of the Universe we have. Ask the Ptolemy with their epicycles! But if the view leads to physical explanations which are counter-intuitive and defy common sense, or become too abstract and too removed from life and not supported by life, than we must not confuse mathematical deductions with physical realism. Rather, we should change our view! And just as we can write bad literature using good English, we can also write bad physics using good math. In either case we do not fault the language for the story. We can't fault Math for the failings of Physics."

"The failure of Modern Physics is in not providing us with 'physical explanations' that make sense. A 'physical view' that is consistent and confluent with our experiences. That will not put us at odds with ourselves, with our understanding of our world and our lives. Math may not be adequate. Sense may be a better guide."

Constantinos

Roger

The real point here is that mathematics is a representational device. And actually it is better, as such, than graphics or words, because it is more specific and has more opportunities for abstract construction. But, it must reflect how reality occurs. Otherwise, it is no more than a belief, ie it has intrinsic validity, but is extrinsically invalid. You allude to a number of flaws in presumptions about how reality occurs, which is the real problem.

Paul

This paper has done little to convince me that mathematics is not an essential truth that can describe how the universe works at a fundamental level. In philosophy there is something known as the quine-putnam indispensability argument, which states that because mathematics is necessary in order to describe aspects of nature, it follows that is must have an objective existence. In the paper you write that the uncertainty principle undermines mathematics, but there is no evidence for that at all. In fact, there is something known as the "symplectic camel," formulated by Maurice de Gosson, that describes the uncertainty principle in geometrical terms. In addition, the discovery of things in pure mathematics, such as Lie groups, that have found applications in physics many years after they were discovered also lends credence to the idea that we are not simply inventing things at will in mathematics. There is a structure to the entire body of math that is discovered, only our notations and symbols for math are invented. I find this article wanting, and I think that trying to rid mathematics from its place in describing the world is something that will never be successful. Mathematics, in a deep sense, is truth.

Roger,

Thanks for an interesting essay. I think we share some similar ideas about the relationship between mathematics and objective reality. Following is a quote from my essay, Rethinking a Key Assumption About the Nature of Time: ". . . please don't confuse what are mathematical descriptions of reality with the underlying objective reality itself."

If you find time to check it out I'd welcome your thoughts. Thanks.

jcns

JCN/Roger

But the differences can only be about 'detail', because no representational technique (and maths is the best one) can replicate all the intricacies of reality. In terms of logic, the essential mathematical components and relationships must correspond to how reality occurs and physically existent entities. Otherwise, it is just a belief system, ie it has no extrinsic validity as a representational model of reality. The fact that the maths 'works', internally, is irrelevant.

Paul

PS: yes Poincare was the essential source of the problem with his flawed concept of time and timing.