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Zbigniew Modrzejewski: on 11/20/12 at 23:15pm UTC, wrote Thank you, Roger. And I forgot to add. Yes! I agree with you. You are...

Roger Schlafly: on 11/19/12 at 22:31pm UTC, wrote Thanks. Well put.

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CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: Nature Has No Faithful Mathematical Representation by Roger Schlafly [refresh]

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Author Roger Schlafly wrote on Jun. 15, 2012 @ 12:24 GMT
Essay Abstract

Much of modern theoretical physics assumes that the true nature of reality is mathematics. This is a great mistake. The assumption underlies most of the paradoxes of quantum mechanics, and has no empirical justification. Accepting that the assumption is wrong will allow physics and mathematics to progress as distinct disciplines.

Author Bio

Roger Schlafly has a BSE from Princeton U, and a PhD in Mathematics from U California Berkeley, under I. Singer. He blogs at DarkBuzz.com.

Florin Moldoveanu wrote on Jun. 15, 2012 @ 19:49 GMT
Congrats on a well written essay. Hope you will win one of the prizes.

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Pentcho Valev wrote on Jun. 15, 2012 @ 20:38 GMT
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

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James Putnam replied on Jun. 15, 2012 @ 21:26 GMT
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

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Author Roger Schlafly replied on Jun. 15, 2012 @ 21:28 GMT
It is true that Einstein did not appreciate the Michelson-Morley experiment, as explained in those papers. But the experiment was crucial to Lorentz in 1895, and crucial to many other physicists as evidence for special relativity.

Pentcho Valev replied on Jun. 15, 2012 @ 22:10 GMT
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

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Robert L. Oldershaw wrote on Jun. 15, 2012 @ 22:51 GMT
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

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Robert L. Oldershaw wrote on Jun. 16, 2012 @ 00:37 GMT
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

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Armin Nikkhah Shirazi wrote on Jun. 16, 2012 @ 09:08 GMT
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

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Author Roger Schlafly replied on Jun. 16, 2012 @ 16:38 GMT
I say that it is a mistake to equate ignorance with not having a mathematical representation. Physics is what is really going on, not mathematics. We are not ignorant of the physics, as we have many great theories.

Paul Reed replied on Jun. 17, 2012 @ 06:10 GMT
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

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Azzam AlMosallami wrote on Jun. 16, 2012 @ 14:28 GMT
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.

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Constantinos Ragazas wrote on Jun. 17, 2012 @ 01:22 GMT
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,...

view entire post

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Pete wrote on Jun. 20, 2012 @ 05:33 GMT
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.

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Author Roger Schlafly replied on Jun. 20, 2012 @ 06:53 GMT
I think that you are misunderstood the paper. I am not denying that there is a structure to math, or that math is real, or that math is an essential truth. I have no quarrel with the Quine-Putnam indispensability argument or the symplectic camel. I do not write that the uncertainty principle undermines mathematics. I am not trying to rid mathematics from its place in describing the world. Math is very useful in physics and other sciences.

J. C. N. Smith wrote on Jun. 20, 2012 @ 22:05 GMT
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

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Author Roger Schlafly replied on Jun. 21, 2012 @ 00:10 GMT
Yes, I see you wrote that in response to someone else saying not to "confuse language with reality". I agree that a description can be different from reality, as the ancient Greeks realized. Your paper mainly challenges the sufficiency of the operational definition of time. I would just add that the definition is entirely due to H. Poincare, as explained in the Wikipedia article on synchronization. He introduced it to relativity theory.

Paul Reed replied on Jun. 21, 2012 @ 05:41 GMT
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.

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J. C. N. Smith replied on Jun. 21, 2012 @ 13:35 GMT
Roger,

"Your paper mainly challenges the sufficiency of the operational definition of time. I would just add that the definition is entirely due to H. Poincare, as explained in the Wikipedia article on synchronization."

You're correct that my challenge is to the sufficiency of the operational definition, but the operational definition far predates Poincare and relativity. In fact, I'd say it dates back to the invention of the first clock. It's deeply ingrained into our thinking and psyches, and therefore not easy to alter or augment, as I believe will be necessary if we are to move forward.

jcns

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Alan Lowey wrote on Jun. 21, 2012 @ 11:29 GMT
Dear Roger,

Yes, I totally agree with your opening sentence! The last FQXi contest of "Is Reality Digital or Analog" is also relevant to your essay. My entry featured the imagery of the creation of structure from the starting point of a void. You may find it a useful read. Cheers

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Jonathan Burdick wrote on Jun. 21, 2012 @ 13:07 GMT
Our friend Rog needs 10 pages to opine that "the map is not the territory"? :-)

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Pete wrote on Jun. 21, 2012 @ 17:21 GMT

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Author Roger Schlafly replied on Jun. 21, 2012 @ 19:55 GMT
Pete, I do believe that mathematics is real, but my essay is about physics, not philosophy of math. My point is like the above succinct comment, "the map is not the territory". Yes, the map is real, and the territory is real, but they are not the same.

You mention string theory, and say "At the most fundamental level, it all boils down to mathematics." I say that is a faulty premise of string theory. No one has any way of observing those Calabi-Yau manifolds. Those manifolds are part of a fanciful, desperate, and misguided attempt to salvage a faith in a faulty premise.

Yes, there are mathematical patterns seen in nature. You could regard these as hints that the universe is fundamentally math. Nearly everyone accepts that premise, and agrees with you. The purpose of my essay is to point out that there are also hints that the universe is NOT fundamentally math, and to argue that the premise is wrong. I fully realize that I am going against conventional wisdom.

Pete replied on Jun. 22, 2012 @ 15:16 GMT
Alright I think I understand, you're trying to play devil's advocate in a sense. As you have a mathematical background and think that mathematics exists, would you say that the mathematical universe and the physical universe are two real but distinct entities. I know I'm delving into philosophy a bit and your paper is about physics, but I just wanted to understand your metaphysical worldview. Do the two realities interact at all or are they mutually exclusive?

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Author Roger Schlafly replied on Jun. 22, 2012 @ 18:31 GMT
Pete, I am not just playing the devil's advocate in the sense of showing that there is an argument against conventional wisdom. I firmly believe that the conventional wisdom is wrong.

The realities interact in all the ways that math is useful in physics. Just look at the formulas in a textbook. There are far too many to list. I do not dispute any of that.

Sridattadev wrote on Jun. 21, 2012 @ 18:36 GMT
Dear Roger,

Mathematics is a language to express the universal truth, so is science of theoritical physics (SR, GR, Quantum mechanics) and spirituality. One can arrive at the universal truth with in one self, the path chosen is not important and all paths are equal to the one who has attained the singularity.

Please see the true mathematical representation of the universal i, zero = i = infinity, in the following topic Conscience is the cosmological constant.

Love,

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Peter Jackson wrote on Jun. 22, 2012 @ 08:17 GMT
Roger

Excellent essay, thank you. Paul Dirac agreed the limit of maths, saying;

"There are, at present, fundamental problems in theoretical physics...(which)...will require a more drastic revision of our fundamental concepts than any that have gone before. ...these changes will be...beyond the power of human intelligence to get... by...mathematical terms. (and we must try to find and) ...interpret...in terms of physical entities."

I will identify some specific supporting evidence in my own essay. I believe these will show that maths is simply not yet well enough developed to accurately describe nature, and that we are lazy with it, assuming that it's 'abstractions', of 'points and lines' can produce results with REAL physical meaning without bothering to 'renormalise' the abstraction. Is it simply blind faith?

Congratulations on challenging one of the most damaging assumptions in physics.

Peter

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Author Roger Schlafly replied on Jun. 22, 2012 @ 15:12 GMT
Thanks for the Dirac quote and the comments, but I very much doubt that Dirac would have agreed with me. The quote is from his 1931 paper proposing anti-electrons and magnetic monopoles on the grounds that they are mathematical possibilities. He argues that advances in physics will come from increasingly abstract mathematics. His approach has been an inspiration to unified field theorists and others who argue that nature is fundamentally mathematical. My essay takes a contrary view.

Peter Jackson replied on Jul. 7, 2012 @ 17:39 GMT
Roger

Are we perhaps too kind to and trusting of maths? A novel view here; http://9gag.com/gag/4689183

Peter

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Anonymous wrote on Jun. 28, 2012 @ 14:07 GMT
Dear Doctor Schlafly, in my essay, Reality Identification, which was published in the 2011 FQXi contest, I did opine that reality had nothing to do with digital or analog mathematical concepts although I did not specify why this should have been so. I have restated that belief in my essay, Sequence Consequence, which has been published in this year’s contest. This is the problem, a symbolic 1 as seen here would have to be minutely different in appearance and physical constitution not only to any other 1 that has ever appeared on this or any other computer, this manifestly singular number 1 would also have to be minutely different from any other number 1 that will appear on any computer screen ever to be built on this or any other planet. This number 1 would have to be different from every other number 1's that have ever been produced or imagined ever. All immutable mathematical laws have been fixed and must be adhered to. Reality has not been completed and it will never be completed. Reality is an ongoing experience. Reality has no shape, no size, and no duration. Your essay was superbly written.

Joe Fisher

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Author Roger Schlafly replied on Jun. 28, 2012 @ 15:44 GMT
Thanks for your correction. Among those who say that reality is analog, some would say that a physical 1 is minutely different from every other 1 because they are all real numbers that are likely to differ in the 10th decimal place. Your essays make somewhat different arguments.

Joe Fisher replied on Jun. 29, 2012 @ 16:02 GMT
Respectfully Doctor Schiafly, reality is a singular condition that can only occur once. A person cannot measure a singularity by using a plurality of numbers. 1 is only a symbol. The only real Universe occurring once in one place for one eternity should ever be accorded the accurate symbol of 1. Parts of the real Universe and parts of reality can be entertainingly speculated upon by using thoughtful abstract methodology; however, one must never stray from identifying any singularity and try explaining its existence and nature with the forced application of pluralistic insertions. Light is singular. Particles and waves are pluralistic conceptions. There is no way to isolate a single particle or a single wave of light. One can theorize that a certain number of accumulated particles or a certain continuous number of waves ought to cause light to move from place to place, except one has then to assume that all of the accumulated particles and/or all of the waves of light are identical. One has then to assume that the intervening spaces between the quantity of particles and/or the repeatable occurrences of tidal light waves are also identical. All you have to do then is explain how and why light from the sun and from a glow worm and from an incandescent lamp seems to differ so much.

Joe Fisher

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Paul Reed replied on Jun. 30, 2012 @ 06:09 GMT
Joe

Correct. For any existence to occur physically, and then alter, it can only have one physically existent state at a time. This applies to anything that has physical existence, elementary particle, light, cathedral, you, whatever. Change involves more than one, with the new one replacing the old one. There is no change within any given reality (existent state-a preent).

Paul

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Frank Makinson wrote on Jun. 28, 2012 @ 17:03 GMT
Roger, Typically, the parameters of a physical law concept are identified and then a mathematical algorithm is developed that fits the parameters. The resulting algorithm allows a resultant to be obtained with varying parameters. There is no argument that the mathematical algorithm is artificial relative to the physical law concept, the physical reality. Specific information had to be known before the mathematical algorithm was developed, such as unit sizes and a measured resultant.

The distinction between physical reality and mathematics became a little blurred when a physical law concept was applied to a pair of right triangles and the resultant produced information that was not known to begin with. A paper titled, "A methodology to define physical constants using mathematical constants" was published in the July/August 2011 IEEE Potentials.

Methodology-IEEE

Methodology-postprint

Creating a conventional physical law algorithm uses predefined units of measure and a measured resultant. The methodology produced the sizes of the required units of measure and numerical resultants that match the measured physical law. The methodology reveals that properly matching a mathematical technique to a physical law concept provides a better fit to reality, that is, a more faithful representation of nature.

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Author Frank Martin DiMeglio wrote on Jun. 29, 2012 @ 16:21 GMT
The purpose of vision is to advise of the consequences of touch in time -- per Bishop Berkeley. This has direct, fundamental, relevant, and important significance and meaning when it comes to what are the sensible manifestations (and understandings) of physics. Really think about it.

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Thomas Howard Ray wrote on Jul. 5, 2012 @ 16:12 GMT
You packed a lot into 9 pages, Roger! It was a good read. However. I'm curious about something that you didn't mention -- if mathematics is not a faithful language of reality, does that obviate *any* formal representation, e.g., Lev Goldfarb's ETS formalism?

If you get a chance to read it, my essay "The perfect first question" addresses issues that you raise about hidden variables and Bell's theorem.

Good luck in the competition.

Tom

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Author Roger Schlafly replied on Jul. 5, 2012 @ 16:51 GMT
You refer to Lev Goldfarb. As I understand his approach, it might describe observations or knowledge, but cannot be a true representation of reality.

I see Bell's theorem as just one of many arguments against hidden variables. People want to believe in these hidden variables for some reason, but I say that all the evidence is against the whole concept.

Thomas Howard Ray replied on Jul. 5, 2012 @ 17:03 GMT
The evidence, yes. When the evidence is, however, identical to one's expectation of experimental results, how can one determine that the evidence (data) is a "true" representation of reality? Without a principle of correspondence between a formalized theory and physical experience, we would -- like Mach -- never accept the reality of atoms. Now suppose that atoms are only approximate, sure -- at least, the theory gets us from the naive Bohr orbital model to something more.

Roger, do you agree that science is progressive? If so, what role does language play in that progress? If not, what's the point of doing science?

Tom

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Author Roger Schlafly replied on Jul. 5, 2012 @ 18:17 GMT
Yes, I agree that science is progressive. T. Kuhn is famous for saying the opposite, with his paradigm shift theory of science, but he was wrong. Not sure what you mean about language. Sometimes it is useful to have new terminology or language to describe ideas.

Peter Jackson wrote on Jul. 5, 2012 @ 17:40 GMT
Roger

Your essay was so refreshing I've had to re-read it. A small issue on your point about last years essays. I flagged up the role of maths and took a wholly ontological approach to expose and overcome a measurement methodology problem in handling 'discrete' kinetics (2020 'Vision'). It was a top 10 finalist but I was disappointed the judges seemed to miss or avoid the important conclusion.

Indeed I strongly applaud your suggestion that relativity is "a theory about something that would be due to our methods of measurement." I'm reasonably sure I've identified a serious misunderstanding about measurement methodology which has broad and deeply fundamental implications (the essay should pop up any time now). I really look forward to your comments.

For now, can you comment on this; As motion is an invalid concept in geometry, and geometry is the basis of vector space, can we assume that motion is validly and adequately described by vector space algebra?

Peter

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Author Roger Schlafly replied on Jul. 5, 2012 @ 18:18 GMT
Vector spaces are ideal for describing motion of particles. If the moving particle is really a wave, then the situation is more complicated.

Peter Jackson replied on Jul. 6, 2012 @ 18:39 GMT
Roger

When a photon in a medium interacts with an electron moving laterally (i.e. at the refractive plane of a moving medium), the interaction time is non zero (say 6.5x 10^-24s for c and a classic electron radius) so there must be a 'kinetic' effect from the evolution of interaction. This is consistent with recent findings at a larger scale, i.e. from astronomy (i.e. Emsellem, E., et al., Atlas 3D. MNRAS 414 2. 888-912. June, 2011) which derives a kinetic term for the interaction with halo matter which matches observation (also finding galaxy rotational velocities quite accurately).

Yet Cartesian co-ordinate systems and 'point' particles can't even 'see' any such effect mathematically. When using Propositional Dynamic Logic instead of simple maths an ontology emerges, but this would point at vector space and overlapping inertial 'wire' frames as inadequate to model reality ('time stepping' maths can also do it after a fashion). Could it possibly be so? And would that be just tooo heretical?

Peter

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Paul Reed replied on Jul. 7, 2012 @ 07:19 GMT
Peter

This is a specific example of the generic point I have just made above (and have made many times before). It is not the intrinsic validity of the model which ultimately counts (though it is a good start to create one which works in accord with the rules!), but its extrinsic validity vis a vis that which is being modelled.

Paul

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nmann wrote on Jul. 12, 2012 @ 19:09 GMT
"[T]he ... fermion minus sign problem ... is often misconcieved as a technical detail frustrating the careers of numerical simulators. It is much more. It is the nightmare of modern physics. At the moment one is dealing with an infinity of interacting fermions, it is a tragic fact that no methodology is available to handle the problem in a systematic, controlled fashion. The standard escapes are to either declare the non-interacting fermion gas to be the universal truth, or to suppose that fermions are completely eaten by collective bosonic fields. The devastating influences of the minus signs are most clearly felt in high Tc superconductivity, the subject of heavy fermions, and adjacent areas like the 2d metal-insulator transition. However, it permeates all of fundamental physics, from the nature of the core of neutron stars up to string theory. When you still think it is a non-existent problem, I am interested to hear your answer to the following simple question: can a state of matter exist, characterized by an irreducible sign problem in the scaling limit (i.e. it cannot be absorbed by an appropriate transformation) which cannot be adiabatically continued to the Fermi-gas?"

-- Jan Zaanen, http://www.lorentz.leidenuniv.nl/~jan/

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Georgina Parry wrote on Jul. 13, 2012 @ 00:29 GMT
Dear Roger Schlafly,

I enjoyed reading your essay. It is really clearly written and thoroughly accessible, even to someone without a maths or physics background. You have set out your arguments very clearly and I might have been convinced had I not previously given this subject quite a bit of thought.

You wrote "It is time to accept the non-mathematical nature of reality, just as it was time to accept the non-Euclidean geometry of spacetime when H. Poincare proposed it in 1905." I'm sorry that I must disagree. In my opinion it is not that the universe can not be described mathematically but that the structure of reality has been inadequately comprehended, so that the mathematics when applied are inadequate to describe all of its facets in their correct relationship. That might sound like nonsense but it is explained more methodically in my essay and accompanying diagrams.

I also think that mathematical relationships are inherent to the structures and patterns of the universe and those relationships are also the forces for change. Mathematics "in vivo" is not identical to the mathematics modelling our observed reality. That does not make the unobserved reality non mathematical. This view does open up new possibilities for mathematical representation and new considerations of how numbers and sets relate to a broader view, the physics of the entirety of reality.

Having disagreed with you, I would like to say that there is a lot in your essay that I do like, it is very good, well constructed and thought provoking. Good luck in the competition.

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Author Roger Schlafly replied on Jul. 13, 2012 @ 01:47 GMT
Thanks for your comments. I see your essay argues that space-time is emergent, and does not exist externally. These essays go against conventional wisdom, so I don't expect many people to be convinced.

Georgina Parry replied on Jul. 13, 2012 @ 02:06 GMT
Dear Roger,

I hope that my essay and accompanying explanatory framework diagram do give a convincing argument. However I agree that a quick glance at the list of false assumptions is not in itself convincing at all.It is a pity if people's minds are closed so easily. It is unconventional, I agree, and requires some thought to see how it functions and overcomes so many problems. I have a higher resolution file of diagram 1. if the quality is a problem. I'm not saying I'm right and you are wrong. We are both giving sensible, well reasoned arguments from our own viewpoints, in my opinion. Which argument is ultimately more useful for science time will tell.

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Anton W.M. Biermans wrote on Jul. 13, 2012 @ 01:02 GMT
Dear Roger,

If we assume that we live in a universe which creates itself out of nothing, then conservation laws say that everything inside of it, including spacetime itself, has to add to nil.

The universe then is that unique, paradoxical thing which has no physical reality as a whole, no 'exterior', but only exists as seen from within.

The universe therefore isn't only not a mathematical object, it isn't even a physical object.

By treating it as an object which, as a whole, has particular properties even though there's nothing outside of it, nothing with respect to which it can have properties, physicists have made an awful mess of physics.

For details, see topic 1328.

Regards, Anton

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Jason Wolfe wrote on Jul. 13, 2012 @ 03:28 GMT
Hi Roger,

Quoting your essay, "The most puzzling quantum experiments are the double-slit experiment and the spin measurement of entangled particles. Quantum mechanics predicts these outcomes without difficulty, but these experiments have been described as impossible to understand or as proof that there is no reality."

I'm still writing my paper, but I came to the conclusion that the double-slit experiment makes perfect sense and is perfectly natural, provided that you make one assumption. You have to assume that an aether exists, but not just any aether. You have to assume that an aether made of waves exists, perhaps even probability amplitude waves. In the two slit experiment, a single photon or particle can be fired at the two slits. It's not the particle that interferes, it's the wave-function that describes its pathway. The pathway/quantum wave/aether wave is what interferes, not the particle. The particle only exists as an excitation of the waves of the aether. The aether waves interact with the slits as interfereing waves (no suprise there). The particle is just an excitation of the waves of the aether. The information about which slit it went through just doesn't exist.

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Author Roger Schlafly replied on Jul. 13, 2012 @ 03:34 GMT
If the particles are really waves, then yes, there is nothing confusing about the double-slit experiment.

Jason Wolfe replied on Jul. 13, 2012 @ 05:19 GMT
But I think the physics community might be reluctant to embrace wave phenomena as an aether medium. For one, a lot of people have had the Michelson-Morley drilled into their heads. So now it's more of a reflexive answer: "No there's no aether!" than it is a well contemplated answer.

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Paul Reed replied on Jul. 13, 2012 @ 07:07 GMT
Jason

But what are waves, what is the physical reality of them? And a wave sounds like a sequence of different physically existent states. So one cannot talk of a wave as if it is one physical reality.

Paul

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Peter Morgan wrote on Jul. 14, 2012 @ 19:04 GMT
I'm somewhat in sympathy with Jonathan Burdick's pithy response, but of course in ten pages you do more that say that the map is not the territory. I take you also to say that the territory (reality) is not mathematical. I suppose that as a positivist, albeit I think you are too influenced by the post-positivists to really claim the name, you might accept that Physics is the systematic description of reproducible experimental results. Whatever systematization we use would then seem to be a part of mathematics, which leaves me wondering what principle or postulate you are proposing, or critiquing, to speak to the theme of the competition? [An empirical principle is, I take it by definition, a systematic view of some large body of experience, which to be successful must allow the construction of a tractable mathematics, whereas a postulate is something more in the realms of convention. Interesting that the competition is phrased in terms of postulates rather than principles.]

It is true that there are some parts of Physics that are apparently less systematized --more empirical or phenomenological, one might say-- than other parts, but where there is chaos there is the presumption that a better systematization might be possible if a good enough mathematician comes along. What is left to do is very hard, in the usual story of all the low-hanging fruit having been picked, but we have made better tools than our forebears. It is also possible that there is some part of the territory that only ever happens once, so that it cannot be subject of Physics taken to be a repeatable experimental subject. Indeed, the irreproducibility of quantum mechanical phenomena at the finest level of detail precisely underlies the turn to statistics, where there is reproducibility, and the idealization of statistics as probability.

In any case, there has been a constant interplay between Mathematics and Physics, a "battle" that has recently been going relatively less well for the Platonists, which I think many creative theoretically-inclined Physicists continually renegotiate in their attempts to construct new models, sometimes stepping into high theory, sometimes stepping into phenomenology, anything that helps in the construction of a new systematization of experimental data.

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Author Roger Schlafly replied on Jul. 14, 2012 @ 19:50 GMT
Peter, I like your phrase "construction of a new systematization of experimental data." Yes, that is a laudable goal and mathematics is a terrific tool. I also "accept that Physics is the systematic description of reproducible experimental results."

My purpose is to better understand the limits to mathematical reasoning in physics. For example, consider the No-cloning theorem. If a physical state is perfectly representable by some numbers or other mathematical objects, then it is very hard to understand why a perfect copy cannot be made. Perfect cloning of mathematical objects is axiomatic. I say that the quantum state is great for systematizing experimental data, but when you take it too literally as being reality then paradoxes result. It is better to step back, and admit that our mathematical models may be necessarily imperfect.

Elvira Colburn wrote on Jul. 27, 2012 @ 04:42 GMT
"I will love the light for it shows me the way; yet I will love the darkness for it shows me the stars."- Og Mandino

We keep shining a brighter light ( mathematics ) looking for the stars ( answers ). My interpretation of Roger’s essay is to consider radically revising the approach to answering the big questions about the nature of reality. Could it be as simple as metaphorically turning out the lights to see the stars? The answer is surely that simple, and no doubt all around us. We may be blinded to seeing seeing the answer by the bright light of academic thinking. As the daddy goldfish said to the baby goldfish as they swam in circles around the tiny fishbowl: “ Even though you can’t see it, I assure you water exists”. The great mystery of reality and existence can be torn down to it’s basic components through the language of mathematics, but can only be understood by seeing the deepest truths we are already experiencing by our very existence.

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Dirk Pons wrote on Aug. 8, 2012 @ 09:20 GMT
Roger

A great essay, thank you. Well-written and accessible.

You tackle the assumption that mathematics is always a faithful representation of reality, and find it wanting. As you say, 'hardly anyone distinguishes between scientific realism and some sort of mathematical idealization of the world.' Indeed, physics journal papers are invariably stuffed full of mathematics but devoid of interpretation, and often don’t even show the courtesy of providing a conclusion. Apparently most authors do not see that they have any responsibility to explicitly communicate the implications of their work for interpretation of the natural world. Your essay incisively identifies the tacit premises and underlying mental models that lead to this kind of mathematical idealisation.

As you point out, our current best theory of physics, quantum mechanics, uses mathematics to construct a representation of reality, but is unable to provide a descriptive explanation of reality. You also say that, 'It seems unlikely that mathematical structures would be suitable for a true physical reality.' What structures (or methods) would be, in your opinion?

Thank you

Dirk

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Author Roger Schlafly wrote on Aug. 8, 2012 @ 15:31 GMT
Thanks for your comments. As I see it, an electron is a physical object, not a mathematical one. We can measure things like position and momentum, but these are not intrinsic properties of the electron. You can use mathematics to describe it, and say that an electron is in a particular orbital or has a particular energy, but it is more mysterious than that. It is not really a particle and we do not even know whether it behaves in a deterministic way.

Saying that an electron is in a particular orbital is a very good description for some purposes. It allows predictions about chemical bonds, for example. So I am not saying that there is no description. I just think that there are limits to what you can do with a mathematical model.

Jayakar Johnson Joseph wrote on Aug. 8, 2012 @ 18:13 GMT
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

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Author Roger Schlafly wrote on Aug. 8, 2012 @ 22:38 GMT
Jayaker, please post a link to the published paper showing what you say. I do not believe it.

Jayakar Johnson Joseph replied on Aug. 12, 2012 @ 13:25 GMT
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

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John Merryman wrote on Aug. 11, 2012 @ 02:55 GMT
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.

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Eric Stanley Reiter wrote on Aug. 15, 2012 @ 07:46 GMT
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

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Author Frank Martin DiMeglio wrote on Aug. 21, 2012 @ 21:39 GMT
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?

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Author Roger Schlafly replied on Aug. 21, 2012 @ 22:50 GMT
You can go very far with math. That is what fills the textbooks today -- mathematical formulas to describe physics. And much more will be learned.

Author Frank Martin DiMeglio replied on Aug. 25, 2012 @ 20:38 GMT
Roger, it is a fact that direct bodily experience is fundamental to physics and does not necessarily or fundamentally need or involve mathematics.

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Author Roger Schlafly wrote on Aug. 25, 2012 @ 15:38 GMT
Bob Jones comments on my blog that I've "got the relationship between math and physics all wrong." I replied there.

Jose P. Koshy wrote on Aug. 29, 2012 @ 10:26 GMT
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.

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Anonymous wrote on Sep. 2, 2012 @ 15:40 GMT
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.

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Anonymous wrote on Sep. 2, 2012 @ 18:00 GMT
You covered a lot of history there. A very entertaining and informative essay.

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Jeff Baugher wrote on Sep. 2, 2012 @ 19:30 GMT
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
$G_{\mu\nu}=\Omega g_{\mu\nu}-L_{\mu\nu}$
, 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

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Gurcharn Singh Sandhu wrote on Sep. 3, 2012 @ 09:36 GMT
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

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Pentcho Valev wrote on Sep. 3, 2012 @ 11:42 GMT
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

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Author Roger Schlafly replied on Sep. 3, 2012 @ 13:55 GMT
Pentcho, you are correct that the Michelson-Morley experiment could have been interpreted as favoring an emission theory of light. Probably some physicists at the time said exactly that. But most everyone was sold on a wave theory of light, and Michelson-Morley was seen as crucial to Lorentz and others at the time, and in modern textbooks. So yes, Michelson-Morley was the crucial experiment. It is a historical fact that it led to relativity, whether or not it has an alternate interpretation.

Pentcho Valev replied on Sep. 3, 2012 @ 14:49 GMT
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...

view entire post

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Author Roger Schlafly replied on Sep. 3, 2012 @ 16:10 GMT
The Einstein biographers and historians (Holton, Stachel, etc.) now say that the Michelson-Morley experiment was of no importance to Einstein, and he might not have even known about it in 1905. Einstein relied on Lorentz's analysis of it. So I say that the experiment was crucial to relativity because it was crucial to FitzGerald, Lorentz, Poincare, and Minkowski. Einstein does not even talk about the importance of it until 1909.

Pentcho Valev wrote on Sep. 3, 2012 @ 16:37 GMT
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...

view entire post

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Author Roger Schlafly replied on Sep. 3, 2012 @ 16:55 GMT
In that NY Times article, Einstein is describing how Lorentz explained Michelson-Morley. It really doesn't matter what Einstein's opinion was. If you want to know how we got that explanation, ask Lorentz, not Einstein.

Anonymous replied on Sep. 3, 2012 @ 17:10 GMT
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

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Pentcho Valev replied on Sep. 7, 2012 @ 10:27 GMT
Roger,

What did I tell you? Your wrong statement:

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

catapulted you to the top of the community rating list! Einsteinians are grateful people! Congratulations!

Pentcho Valev pvalev@yahoo.com

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Inger Stjernqvist wrote on Sep. 5, 2012 @ 19:32 GMT
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

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Yuri Danoyan wrote on Sep. 6, 2012 @ 13:27 GMT
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

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Yuri Danoyan replied on Sep. 8, 2012 @ 19:04 GMT
"Plato as the Allegory of the Cave."

Now I realized that Plato guessing holographic nature of the Universe.

Thank you for hint.

Yuri Danoyan

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Stefan Weckbach wrote on Sep. 6, 2012 @ 22:21 GMT
Dear Roger,

you've done a great job in formulating your lines of reasoning in your exciting essay. I will give you a high rating therefore.

Best wishes,

Stefan Weckbach

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Anonymous wrote on Sep. 7, 2012 @ 01:30 GMT
Dear Dr. Schlafly, I enjoyed your very well written essay. This passage especially resonated with me:

"... some people believe that the mathematical possibilities must be the same as the physical possibilities, even if those possibilities cannot be observed."

To me, a good example of this is "negative pressure" as the cause for expansion. IMHO it can live only in math. I agree with you that mathematics in physics has become divorced from the underlying geometry of creation. In my essay I emphasize the role of space as the container for the Universe and bring up its old, forgotten, paradox, "is space empty or solid?" I find it strange that mathematicians are not bothered that space can be both empty (for matter to move through it) and solid (for light to propagate). I offer a geometrical solution to this old paradox of space, in 4 spatial dimensions, which incidentally removes the mystery out of double slit experiments, to which you often refer in your essay. I would very much appreciate your opinion and feedback on my essay.

Thank you and all the best to you!

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M. V. Vasilyeva replied on Sep. 7, 2012 @ 17:10 GMT
oops! I did not realize that I was not logged in. I am one of the authors in this contest, arguing for the reality of a 4th spatial dimension here.

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Anonymous wrote on Sep. 8, 2012 @ 03:10 GMT
Hi Roger,

Yes the mathematical tools we have for modeling physical reality have flaws. It is as if physical reality is playing a game of catch me if you can. It is very good at this game.

Your essay is very readable and points out a fundamental problem with physics.

Don L.

More fuel for your fire: http://digitalwavetheory.com/DWT/5_Math-Physics_Connection.h
tml

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Anonymous wrote on Sep. 8, 2012 @ 14:36 GMT
Dear Roger! Nature Has Faithful Mathematical Representation. Just need to dig deeper into the Ontology. Best Regards!

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Ted Erikson wrote on Sep. 8, 2012 @ 17:13 GMT
RF:

Yours was an interesting and informative essay.. As a newcomer to the FQXi community, I feel few of the "community" grade, or even look at, my essay which approaches the problem very realistically, based on an internal view.. Might you look at it, comment if so inclines, and grade it?

To Seek Unknown Shores

http://fqxi.org/community/forum/topic/1409

Thank you

TE

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Pentcho Valev wrote on Sep. 8, 2012 @ 18:18 GMT
Roger,

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

which catapulted you to the top of the community rating list, is taught by almost all Einsteinians:

http://www.amazon.com/Faster-Than-Speed-Light-S
peculation/dp/0738205257

Faster Than the Speed...

view entire post

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Author Roger Schlafly replied on Sep. 8, 2012 @ 22:36 GMT
My statement is not wrong. The 1801 Young double-slit was the crucial experiment for convincing physicists that light is a wave, and to reject the emission theory. The 1887 Michelson-Morley experiment was crucial for the Lorentz transformations of special relativity. Everyone agrees to this, as far as I know.

Pentcho Valev and Ke Xiao (below) have their own reinterpretations of these experiments. That's great, as this essay contest is a chance to argue that the textbooks are wrong. But even if they are right and the textbooks are wrong, it is still a historical fact that these experiments were crucial experiments for convincing physicists of certain ideas.

Pentcho Valev replied on Sep. 8, 2012 @ 22:59 GMT
Roger,

Since the Michelson-Morley experiment is compatible with Newton's emission theory of light, it by no means showed "that the speed of light was the same in different frames of reference":

http://en.wikipedia.org/wiki/Emission_theory

"Emission theory (also called emitter theory or ballistic theory of light) was a competing theory for the special theory of relativity, explaining the results of the Michelson-Morley experiment. Emission theories obey the principle of relativity by having no preferred frame for light transmission, but say that light is emitted at speed "c" relative to its source instead of applying the invariance postulate. Thus, emitter theory combines electrodynamics and mechanics with a simple Newtonian theory. Although there are still proponents of this theory outside the scientific mainstream, this theory is considered to be conclusively discredited by most scientists. The name most often associated with emission theory is Isaac Newton. In his Corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)."

That is, your statement:

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

is simply wrong.

Pentcho Valev pvalev@yahoo.com

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Author Roger Schlafly replied on Sep. 8, 2012 @ 23:24 GMT
The MMX did show that because the emission theory had already been rejected for other reasons. Perhaps you would prefer some qualification on the statement, such as one of these:

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

"The crucial experiment was by Michelson-Morley in 1887, which (combined with prevailing theories of light) showed that the speed of light was the same in different frames of reference."

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

Ke Xiao wrote on Sep. 8, 2012 @ 18:26 GMT
Dear Roger Schlafly,

The double slit need a deep thinking.

Please see my essay: Rethink the double slit experiment"

http://fqxi.org/data/essay-contest-files/Xiao_KeX
iaoFQXi828.pdf

The cross-linked angle established the connection between two slits by the fine structure constant.

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Pentcho Valev wrote on Sep. 9, 2012 @ 04:52 GMT
Roger,

In 1887 Newton's emission theory of light was the only existing theory able to explain the null result of the Michelson-Morley experiment. So your statement:

"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..."."

is both wrong and misleading, which means that you will be one of the winners in this essay contest.

Pentcho Valev pvalev@yahoo.com

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Author Roger Schlafly replied on Sep. 9, 2012 @ 05:14 GMT
Pentcho, you are right that the emission theory was the only known explanation in 1887, but it is a historical fact that Lorentz and others eventually convinced everyone that light was a wave subject to the Lorentz transformation. You can argue for emission theories all you want, but can you find any physicist from a century ago who said that emission theory explains light and Michelson-Morley better than Lorentz?

Pentcho Valev replied on Sep. 9, 2012 @ 08:03 GMT
Walther Ritz was the genius, Lorentz and Einstein were dwarfs compared to him. Clever Einsteinians are often secret Ritzians:

https://webspace.utexas.edu/aam829/1/m/Relativity.h
tml

Alberto Martinez: "Does the speed of light depend on the speed of its source? Before formulating his theory of special relativity, Albert Einstein spent a few years trying to formulate a theory in...

view entire post

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Eckard Blumschein replied on Sep. 9, 2012 @ 15:12 GMT
Pentcho,

While I am waiting for a reply by Roger Schlafly, I would like to tell you that in 2007 I tried to publish a paper "A still valid argument by Ritz". I referred to their agreement to disagree. Ritz rejected Einstein's anticipated future.

Given it was a mistake from the very beginning to expect a non-null result from the MMX then both Einstein and Ritz could not find the correct solution. I was guided by Norbert Feist's experiment when I found a quite logical quantitatively matching explanation for the unexpected null result, see my Fig. 5. Any factual objection?

Eckard

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Eckard Blumschein wrote on Sep. 9, 2012 @ 05:58 GMT
I reiterate my request:

Dear Roger Schlafly,

While your views are often at variance with accepted tenets, they largely agree with my own experience, reasoning, and critical analysis of literature.

Inspired by a stunning result of experiments by Feist, Fig. 5 of my essay offers a plausible explanation of why the MMX failed to measure the aether drift. Pentcho did not yet respond.

I have to credit Paul Marmet for making me aware of the key importance of a possible mistake in Potier's correction to Michelson's original calculation: Most likely, this correction was still not yet correct.

Israel Perez claims to reinstate the preferred frame of reference while maintaining Einstein's SR. How do you judge this claim?

Sincerely,

Eckard

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Rick Lockyer wrote on Sep. 9, 2012 @ 17:24 GMT
Roger,

Rather than “everything is made from math”, most believe everything can be described by math. There is a difference. Physical reality is described by a subset of the totality of mathematics, and the math to reality map is surjective. The real problem is we look back from the physical reality perspective to mathematics that presents many choices, likely some we may not yet understand or possibly even know about at this time.

The reality of this surjection is some mathematical theories may show initial promise, yet not be fundamental enough to enlighten us on what we do not know. This should not be taken as a condemnation of the concept of using mathematics to describe physical reality. Too few mathematical physicists seem to have the flexibility to keep an open mind on other possibilities, like my shameless plug for my essay. Their intuition and physical religion tenants keep them on the path they are on, and really none of us are capable of demonstrating their efforts are for nothing, whether or not we subscribe to the idea reality has a mathematical characterization. You just have a different religion.

Physicists too often rely on mechanical models that set a particular mathematical path that more often than not more true to the model than it is to actual physical reality. It would be much easier to believe physical reality cannot be mechanically modeled than it is that it cannot be mathematically modeled. Multiple times in your essay you seem to dump on mathematics that could be taken as the result of a poor initial mechanical model and the host of assumptions it provides. You throw the baby out with the bath water.

Rick

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Michael Popov wrote on Sep. 10, 2012 @ 11:10 GMT
Roger,

If you agree that human tradition of entangled co-existence of Physics and Mathematics has sufficient foundation and very long history,then problem is not in belief in pure mathematical reality, but in the search of the new ways of Mathematics-Physics optimization.In my essay I considered such problem as poor mathematical foundations of Relativity, connected with Einstein's complex numbers.R.Penrose made attempt to improve Einstein, and( as is known ) his twistor concept became foundation of String physics. Thus, more or less positive improvements in Relativity mathematics can produce new forms of advanced physics also. I await that some sort of refinements of Einstein's interval technique as well as Einstein-Penrose complex numbers can produce new unexpected developments in theoretical physics and cosmology.

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Pentcho Valev wrote on Sep. 10, 2012 @ 13:05 GMT
Roger,

You wrote: "Pentcho, you are right that the emission theory was the only known explanation in 1887, but it is a historical fact that Lorentz and others eventually convinced everyone that light was a wave subject to the Lorentz transformation."

Something similar happened in Orwell's Oceania:

http://www.liferesearchuniversal.com/1984-7

George Orwell: "In the end the Party would announce that two and two made five, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality, was tacitly denied by their philosophy. The heresy of heresies was common sense. And what was terrifying was not that they would kill you for thinking otherwise, but that they might be right. For, after all, how do we know that two and two make four? Or that the force of gravity works? Or that the past is unchangeable? If both the past and the external world exist only in the mind, and if the mind itself is controllable what then?"

Pentcho Valev

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Pentcho Valev replied on Sep. 17, 2012 @ 21:56 GMT
Yes "Lorentz and others" did manage to convince everyone that the Michelson-Morley experiment had proved constancy of the speed of light when in fact it had proved variation à la Newton, and that was a tremendously difficult task. The success was so great because relativists were very diligent and constantly exercised themselves in crimestop:

George Orwell: "He set to work to exercise himself in crimestop. He presented himself with propositions - "the Party says the earth is flat", "the party says that ice is heavier than water" - and trained himself in not seeing or not understanding the arguments that contradicted them. It was not easy. It needed great powers of reasoning and improvisation. The arithmetical problems raised, for instance, by such a statement as "two and two make five" were beyond his intellectual grasp. It needed also a sort of athleticism of mind, an ability at one moment to make the most delicate use of logic and at the next to be unconscious of the crudest logical errors. Stupidity was as necessary as intelligence, and as difficult to attain."

Pentcho Valev

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Saibal Mitra wrote on Sep. 10, 2012 @ 16:17 GMT
Roger,

While I accept most of what you write, I still come down to rejecting the existence of a physical world in favor of only a mathematical multiverse. I explain this in my essay.

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Author Roger Schlafly replied on Sep. 10, 2012 @ 17:50 GMT
I don't know why your essay says "without postulates". You have the biggest postulate of them all -- that there is no physical world and we all live in a big mathematical formula like Tegmark's universe.

Saibal Mitra replied on Sep. 10, 2012 @ 23:16 GMT
It is "without postulates" because (at least in principle) everything should be derived from pure math only. If you assume a physical world then you may have psotulates that can be explained in terms of deeper principles, but there has to be some ultimate set of postulates that are beyond explanation. Everything is then (in principle) explained from thosse fundamental postulates. But if there is no physical world, then there can be no fundamental postulates.

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Yuri Danoyan replied on Sep. 12, 2012 @ 21:40 GMT
Roger

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

Tegmark's universe not his property

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Lawrence B Crowell wrote on Sep. 11, 2012 @ 17:01 GMT
Roger,

I just read your paper. It took me a while to get to this. I am also not entirely sure what I think of it. I will be honest and say I don’t hold fast to any particular metaphysics or philosophy of science/physics and so forth. I see these at best as hats to be worn at different times.

The relationship between mathematics and physics or science in general will probably never be understood. It is hard to imagine how a mathematical system can function with some concept of ontology, and conversely I am not sure how any theory of science can ever provide empirical content for mathematics. The distant prospect for that might be neurophysiology in the future with some scientific or testable theory of consciousness. For now I am not holding my breath on that.

It is interesting how mathematics used in one particular model system can appear in some other model. Isospin is formally much the same as the old nuclear model, and the AdS/CFT correspondence for quantum gravity, strings and M-theory has appeared in some form with London equations for superconductors. It is then most likely wrong to say that mathematics has nothing to do with physics, and that all of our use of mathematics in physical theory is either some accident or illusion. I also think it is likely the opposite is false as well where people say the physical world is mathematics.

In Penrose’s book “Road to Reality” he starts out with a rather speculative idea of Matter, Mind and Mathematics in a triality system. This is similar to Plato’s idea of physical and perfect forms that are “bridged” by mind, expanded on by Plotius, and frankly the opening of the Gospel of John is basically this same idea. However, this all looks like indemonstrable metaphysics.

Cheers LC

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Lawrence B Crowell replied on Sep. 11, 2012 @ 17:06 GMT
The spelling Plotius should be Plotinus.

LC

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Yuri Danoyan replied on Sep. 12, 2012 @ 02:31 GMT
Lawrence

Arnold was great mathematician,not metaphysics

but is favour observation was trinity

http://www.neverendingbooks.org/index.php/arnolds-tri
nities-version-20.html

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Pentcho Valev wrote on Sep. 12, 2012 @ 20:58 GMT
Roger,

"...the emission theory was the only known explanation [of the null result of the Michelson-Morley experiment] in 1887..."

is extremely important, although its effect will not be felt immediately. Divine Albert's days are numbered - high-ranking Einsteinians are leaving the sinking ship.

Pentcho Valev

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Constantinos Ragazas wrote on Sep. 12, 2012 @ 22:12 GMT
Hello Roger,

You have raised a most relevant question regarding Math and Physics. I have often puzzled why math should be reflected in our measurements of Nature. And have come to the same conclusion as you, I think. This is a 'metaphysical belief' physicists make. I have referenced your essay in my own, “The Metaphysics of Physics”. And further made the argument this belief is only logical if the Laws of Physics are in fact mathematical tautologies. I have shown this to be true, for example, for Planck's Formula of blackbody radiation. This Formula I show is a mathematical truism and not a physical law depending on the existence of 'energy quanta' (see End Note I of my essay).

Through mathematical derivations referenced in my essay I have shown that energy propagates continuously as a wave while it manifests discretely in interactions. And that before manifestation there is 'accumulation of energy'. Such 'loading theory' has also been demonstrated experimentally by Eric Reiter in his essay, ”A Challenge to Quantized Absorption by Experiment and Theory”. I think you will find these essays well worth reading and rating.

All the best,

Constantinos

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Author Roger Schlafly wrote on Sep. 12, 2012 @ 22:14 GMT
I defend my essay on my blog, with postings on Limits of math and A photon is not a math object. Bob Jones has posted some disagreements with me, and I think he gives a good presentation of a mainstream physicist view.

Yuri Danoyan wrote on Sep. 13, 2012 @ 01:01 GMT
Roger,

I send to your blog some suggestion.

My nick name is gorgios

Can you answer to me for convinient reason here?

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Avtar Singh wrote on Sep. 14, 2012 @ 15:42 GMT
Dear Roger:

I enjoyed reading your well-written and intuitive essay describing the weaknesses of mathematics in representing the Natural physical reality.

My paper -“ From Absurd to Elegant Universe” strongly vindicates the following conclusions of your paper especially related to the QM paradoxes -

“….A faithful representation of the elementary particles (quarks,...

view entire post

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Eckard Blumschein wrote on Sep. 14, 2012 @ 22:17 GMT
Dear Roger Schlafly,

May I remind you again of my humble request for a comment? Meanwhile I am sure; my Fig. 5 illustrates that the basis for what led to Einstein's SR was an obvious mistake.

I criticized Hilbert mainly because he agreed with Einstein do deny the separation between past and future, and I share Alan Kadin's doubt that Hilbert space is adequate. Do you object?

Sincerely,

Eckard

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Author Roger Schlafly replied on Sep. 14, 2012 @ 22:42 GMT
I do not know anything about Feist's experiment. Much of modern physics depends on Lorentz's analysis of Michelson-Morley, and of the resulting special relativity. I do not know what it would mean for relativity to be wrong. Likewise with Hilbert space.

Eckard Blumschein replied on Sep. 15, 2012 @ 22:14 GMT
Dear Roger Schlafly,

Feist's relevant measurements are clearly shown in Fig. 7 of the paper I quoted. I quoted Bruhn in order to show how brutally Feist was declared a crank without any attempt to understand his ingenious, carful, and quantitatively convincing measurements. Not even Feist himself gave an acceptable explanation. Having now understood Feist's measurement, I feel ashamed why I did not earlier see that Michelson's reasoning was flawed. Being not the first one who found out that the MMX is inconclusive, I am hoping that my Fig. 5 makes it obvious.

What will it mean for Einstein's relativity to be wrong? Shouldn't it cause you to rethink the chapter "Lessons from relativity" of your essay? In DarkBuzz 2011 you wrote "How Einstein Ruined Physics". Michelson did not like Einstein's relativity while you derived lessons from it. Incidentally, some words in DarkBuzz are almost unreadable for my old eyes.

Maintaining my restricted support for your opinion that mathematical models just tend to approximate the reality I suggest discussing some details at 1364.

Sincerely,

Eckard

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Author Roger Schlafly replied on Sep. 15, 2012 @ 22:48 GMT
It would be exciting if someone devises an experiment that proved relativity wrong. The Faster-than-light neutrino anomaly sure got plenty of attention. But I am not sure it would have anything to do with my essay. We still learned lessons from relativity, even if the theory has to be modified someday.

Viraj Fernando wrote on Sep. 16, 2012 @ 04:55 GMT
Roger,

I posted a response just now to your last message. Unfortunately the system has put it in the hidden mode. Pls click "show hidden" to see it.

Viraj

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Pentcho Valev wrote on Sep. 16, 2012 @ 15:26 GMT
Roger,

You wrote: "...how do you explain all the experiments that have confirmed relativity?"

At least the Adams-Eddington 1925 glorious confirmation of "Einstein redshift" is easy to explain, Roger. One word is enough: FRAUD.

Open Questions Regarding the 1925 Measurement of the Gravitational Redshift of Sirius B, Jay B. Holberg Univ. of Arizona: "In January 1924 Arthur...

view entire post

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Author Roger Schlafly replied on Sep. 16, 2012 @ 15:45 GMT
My essay is not about the evidence for and against relativity. I do not doubt that some people have been misled by bad experiments, but that is off-topic. There are many other experiments.

Eckard Blumschein replied on Sep. 16, 2012 @ 21:10 GMT
Dear Roger Schlafly,

Wouldn't providing any evidence be OK because wrong evidence can be refuted? The welcome rather than suicidal argument "there are many other experiments" indicates either blind or pretended trust in the a mandatory belief. You were courageous enough as to write "Einstein Ruined Physics". Isn't such utterance premature without the clarification that Einstein's main theory is wrong? If you yourself were mislead by a bad experiment, is this off-topic?

Didn't you call Einstein overestimated? Even if Einstein's relativity is wrong I will not primarily blame himself for that. Einstein was fostered by Max Planck, and his ideas on relativity were not much different from those by Lorentz and Poincaré, and they altogether were misled by Michelson's experiment.

Since you have a PhD in mathematics, I would appreciate your opinion at least concerning my Figs. 1 to 4. You wrote "some irrational numbers are so complicated that no computer can generate their decimal expansion". Can you please exemplify this?

Sincerely,

Eckard

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Author Roger Schlafly replied on Sep. 16, 2012 @ 21:26 GMT
There are uncountably many irrational numbers, but only countably many computer programs. Therefore most irrationals cannot be generated by computer programs.

I do not get your point about relativity. But if you have some evidence that relativity is wrong, then please go ahead and publish it.

Donatello Dolce wrote on Sep. 16, 2012 @ 22:03 GMT
Dear Roger,

I do not agree with the thesis of your essay. Deny the possibility of a mathematical description of reality is deny the possibility to find general objective rules to describe nature. This would be the end of natural philosophy and science of Pythagoras and Galileo. This means to give up with the effort to understand nature. It is reductive to say that the scientific method is...

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Anonymous wrote on Sep. 16, 2012 @ 22:22 GMT
Why believe old dead guys like Pythagoras and Galileo when we have so much more knowledge than they did? Yes, geometry has done wonders in the past, but we should at least consider the possibility that it will not solve everything.

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Viraj Fernando wrote on Sep. 18, 2012 @ 11:08 GMT
Dear Roger,

You have posed 3 questions to me. Pending providing detailed answers to all in a later post, I will take up the 3rd question for now.

“If so (i.e. if Lorentz transformation is wrong), how do you explain all the experiments that have confirmed relativity?”

I suppose what you mean is: “how do you explain all the experiments that have confirmed...

view entire post

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Yuri Danoyan wrote on Sep. 18, 2012 @ 14:32 GMT
Are you not agree with Eugine Wigner?

http://web.njit.edu/~akansu/PAPERS/The%20Unreasonable
%20Effectiveness%20of%20Mathematics%20%28EP%20Wigner%29.pdf

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Author Roger Schlafly replied on Sep. 18, 2012 @ 18:41 GMT
Wigner gives examples of mathematical formulas being used to make predictions that agreed with experiment. I have no quarrel with that.

Hoang cao Hai wrote on Sep. 19, 2012 @ 15:00 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.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

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

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Yuri Danoyan wrote on Sep. 22, 2012 @ 14:14 GMT
Roger Schlafly wrote:

"Quantum mechanics is the first theory to truly take the cave allegory seriously. It has a theory for how observations correspond to projections, without ever trying to explain what is outside the cave."

It seems to me holographic universe real confirmation of Plato cave.

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Author Roger Schlafly replied on Sep. 22, 2012 @ 23:24 GMT
Yes, if there were any evidence for a holographic universe.

Yuri Danoyan replied on Sep. 29, 2012 @ 17:19 GMT
Roger,

What is your prognosis about Craig Hogan Holometer experiment?

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Jerzy Krol wrote on Sep. 23, 2012 @ 10:04 GMT
Dear Roger,

Nice essay but I have some remarks: the problem of faithful represantation of nature in math would be well-defined under the supposition that mathematics itself is unchanged and fixed. In fact, the development of theories of physics makes the mathematics is developing and changing. Also mathematics itself changes and evolves. If we assume that mathematics is constant and corresponds to fixed understanding, even describing mathematics by mathematics would not give coherent picture and it seems that it would not exist a faithful represantation of mathematics in mathematics. Let me mention model theory which allows for changing reals or naturals as different models. When facing such change from the point of view of 'older' mathematics it is an absurd. Another example is 2-valued logic. Intuitionistic set theory, or some other logics, might be seen as an absurdity from the point of view of Aristotle logic. Another example - non-Euclidean geometries - from the point of view of 5-th Euclid axiom these are absurdities. However, they appeared subsequently to be physically valid. Similarily intuitionistic logic etc., etc.... So, the problems with finding best mathematical representation for physical world is also the problem with developing suitable mathematics. Certainly, this still be a represantation or model rather than a nature itsel. As so, this representation differs from the physical reality. Obviously, one can represent nature by other means, like art works, but this suffers from the individuality and leads to difficulty with representing repetitive results.

In my essay I deal with such changing mathematical perspective as suitable to physics: What if Natural Numbers Are Not Constant? http://fqxi.org/community/forum/topic/1443

Regards,

Jerzy

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Author Roger Schlafly wrote on Sep. 23, 2012 @ 17:40 GMT
Mathematics is defined by what is provable in ZFC set theory. Non-euclidean geometry, nonstandard reals, etc. are all definable in ZFC. Yes, there are other logics, such as intuitionist logic, but it is going to be a whole lot harder to find some representation of nature in intuitionist logic.

Jerzy Krol replied on Sep. 23, 2012 @ 21:19 GMT
In fact, it is not so -

1. only 1-st order properties are expressible and provable in ZFC. Topology, smoothness etc. require higher (2nd) order languages. Also, Paul Benioff showed in 1976 that the mathematics of ZFC is not powerful enough for a formalism of quantum mechanics.

2. intuitionistic logic is 'wider' (or weaker) than the classical, so it can interpret (in the limit) the same what classical logic can do.

3. however, the above two points are merely illustrations for the main point of my previous post which you did not adress at all.

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Author Roger Schlafly replied on Sep. 23, 2012 @ 22:59 GMT
Topology and smoothness can all be analyzed in first order logic (ZFC). No, 2nd order languages are not necessary. I am not familiar with that Benioff paper. Do you have a link?

Author Roger Schlafly replied on Sep. 24, 2012 @ 04:04 GMT
I found this 1976 Benioff abstract and this. He seems to have tried to show that the choice of ZFC model can have some physical significance. I am not sure this has much relevance to our discussion here.

Member Hector Zenil wrote on Sep. 23, 2012 @ 21:51 GMT
Dear Roger,

Interesting thoughts. If not mathematical, what is the alternative for a working assumption in science? The positivist view doesn't tell me much about the impact of adopting a non-mathematical position (by the way, paradoxically I think the positivist view in philosophy is your opposite view). It seems that assuming a non-mathematical position would lead to either inoperativeness or would have no impact in the practice of science.

On the other hand, quoting you "It seems unlikely that mathematical structures would be suitable for a true physical reality." I wonder if you wouldn't buy it if "mathematical structures" are replaced by "computer programs". I guess, however, that you see computer programs as mathematical structures. I don't, I think they are fundamentally different, the latter come with their implementation, the former don't, hence it may be easier to accept that something is a computer program rather than a mathematical structure even when a computer program can be mathematically described (and that is the difference, one is a description the other is a prescription).

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Author Roger Schlafly replied on Sep. 23, 2012 @ 22:02 GMT
Yes, computer programs are mathematical structures. If they can be programmed on a Turing machine, then they are reducible to pure math.

Mathematics is tremendously useful for doing science. No one can deny that. But my working assumption is that physics and math are two different things.

Hoang cao Hai wrote on Sep. 24, 2012 @ 02:49 GMT
Nothing more accurate!

Mathematics is just a tool to do the job is directed by the thinking of intellectual.

It only accepted to manifest when a result of the thinking of intellectual was accepted.

Correct is we are doing the opposite: hurry to accepted it (turn it into a basic law in constitution - unwritten - of Science), while there is still a mountain of questions but it does not have the solution response - on over century.

If acceptance to used a tool (as Mathematics) is the mainstream of our Science,certainly is our intellectual achievements will be determined by turning the roulette or will is the series products of an automated production line.

Too incredibly bizarre, when we set up the equation or formula to calculate in order to determine what we imagined, but can not the specific and detailed definitions for them, even when it is incongruous with the reality of nature.

E = m.c2 can calculate the energy of a potato or a loaf of bread?

You have written an "ultimatum" on behalf of all those who recognize that there are a lot of "assuming our basic foundation is wrong" and Mathematical was to "squared" for this the wrong.

I will sign in this "ultimatum" by "10" for your essay.

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Viraj Fernando wrote on Sep. 24, 2012 @ 14:24 GMT
Dear Roger,

(You posed questions to me. I am drawing your attention to the answer I gave)

You have posed 3 questions to me. Pending providing detailed answers to all in a later post, I will take up the 3rd question for now.

“If so (i.e. if Lorentz transformation is wrong), how do you explain all the experiments that have confirmed relativity?”

I...

view entire post

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Author Roger Schlafly replied on Sep. 24, 2012 @ 15:17 GMT
Viraj, please do not post the same thing over and over again. You do not even answer my questions. Your comments have very little to do with my essay.

Jerzy Krol wrote on Sep. 24, 2012 @ 19:00 GMT
Please, find my new post at hidden area of our discussion.

Thanks,

Jerzy

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Viraj Fernando wrote on Sep. 25, 2012 @ 14:48 GMT
Roger,

You wrote "Viraj, please do not post the same thing over and over again. You do not even answer my questions. Your comments have very little to do with my essay".

You say that I DO NOT EVEN ANSWER YOUR QUESTIONS. What a blatant lie!!!.

Have a look at my post to you. I start by saying, “You have posed 3 questions to me. Pending providing detailed answers to all in a later post, I will take up the 3rd question for now”.

I request you to kindly respond to my reply, without trying to EVADE by making false allegations that I "do not even answer your questions".

Once your respond to my reply I will address the other two questions.

Best regards,

Viraj

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Author Roger Schlafly replied on Sep. 25, 2012 @ 15:19 GMT
Viraj, you did not answer my questions. If you think that relativity is wrong, go ahead and post your evidence and reasoning in your essay and your forum. We will all be excited if you show that relativity is wrong. But the issue has very little to do with my essay.

Viraj Fernando replied on Sep. 25, 2012 @ 19:51 GMT
Roger,

You wrote: "you did not answer my questionS" (in plural to cover your lie). I answered one, and expected your response to answer the other two as stated. Since you make the allegation that I did not answer your questionS (in plural), I will answer the remaining two as well.

Best regards,

Viraj

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Steve Dufourny Jedi wrote on Sep. 25, 2012 @ 15:47 GMT
well well well,

I am begining to understand.

This institute has the name FOUNDAMENTAL .and you Mr Tegmark you say that the uniqueness is not essential. the multiverses are not rational Mr Tegamrk.and your responsability is to be rational for the well of this institute.If you have a lack of ideas, so insert the multispheres !!! It is what the probelm, you fear for your place or what...

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Michael A.Popov wrote on Sep. 29, 2012 @ 13:09 GMT
Roger,

I suppose you agree that Physics is Experimental Science, correspondingly, if "The faithful mathematical representation hypothesis is such an

assumption, and it might be completely wrong", then as physicist you must have experiments in order to prove it.

Let us consider thought experiment. Following your ( very popular ) opinion, because Nature has no the faithful mathematical representation, then such sort of mathematical claim as " Nature uses equation of the type x^2+y^2=z^2 but Nature cannot use equation of the type x^3+y^3=z^3 " is wrong.

Please, can you test it, may be you can find counter-example (for Fermat theorem ) in Nature which you know better?

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Author Roger Schlafly wrote on Sep. 29, 2012 @ 16:51 GMT
I don't know how to experimentally prove that nature has no faithful mathematical representation. If two formulas make different predictions, then an experiment could show that one is right and one is wrong. But even if both are wrong, there could be a third formula that is exact.

The best experimental evidence comes from quantum mechanics, and the failure of hidden variable models. False intuition about mathematical representations had led people to propose hidden variable models, but these have all been disproved by experiment.

Frank Martin DiMeglio wrote on Sep. 29, 2012 @ 17:07 GMT
Roger, here is fundamental proof of the limits of mathematics, including why mathematics will never fundamentally and generally unify or describe physics.

Ultimate unification in physics combines, balances, and includes opposites. MATHEMATICS CANNOT COMBINE, BALANCE, AND INCLUDE OPPOSITES.

In keeping with the above, fundamental gravitational and inertial equivalency and balancing (both at half strength force) fundamentally proves and demonstrates F=ma. A MOST IMPORTANT POINT -- DO YOU AGREE? (As acceleration is fundamentally balanced and averaged as well.)

Accordingly (and most importantly), there are serious, FUNDAMENTAL, and ultimate limits to physical understanding, physical prediction, and physical description (including mathematical). Do you agree?

My essay touches on all of this. Can you review and rate my essay?

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qsa wrote on Sep. 29, 2012 @ 23:03 GMT
Dear Roger,

I think you will have a second thought about your theory if you ever consider my idea. "Quantum Statistical Automata"

Fundamental Theory of Reality,"Reality is nothing but a mathematical structure, literally".

1. How I arrived at the idea.

2. Basic results that shows how QM arises, written in BASIC program.

3. Description of two particles interacting and explaining the program in C++.

4. Showing the results for Bohr atom hydrogen 1s simulation.

5. 1/r law and the running phase

6. The amazing formulas deduced from the system.

7. How spin arises from 2D simulation.

8. The appearance of the mass of the electron through simulation.

9. How gravity arises.(basic simulations not shown yet)

There are many other results not shown.

This idea might answer some of your concerns and it might point to the solution of others.

attachments: newqsa.pdf

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Michael A.Popov wrote on Oct. 1, 2012 @ 12:23 GMT
Roger,

In your answer is containing some incorrectness,sorry :

If Nature has lovely mathematical representations,for example, Nature likes Fermat theorem, then such consequence of Fermat theorem as an impossibility of x^3+y^3=z^3 must be naturally accepted in any human logical system of axioms, hence, it is sufficient to find MERELY physical or mathematical counter-example in order to destroy all modern Number theory of believers in "pure mathematical reality ".Thus, philosophical principle :

"If two formulas make different predictions, then an experiment could show that one is right and one is wrong. But even if both are wrong, there could be a third formula that is exact " cannot be applied in this case.

2 You ,unfortunately, wrongly suggest that " The best experimental evidence comes from quantum mechanics, and the failure of hidden variable models. False intuition about mathematical representations had led people to propose hidden variable models, but these have all been disproved by experiment."

In famous article by J.Bell " on measurements " Bell showed that so-called "hidden variables" are not classical integers of classical number theory, but just classical physics variables.As is known,Bell inequality is connected with an existence of complex numbers in Nature and his four Bell's states are solutions of eqation of the type z^2 = x + yi...

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Author Roger Schlafly replied on Oct. 1, 2012 @ 15:46 GMT
Bell showed that certain plausible hidden variable theories could be experimentally tested. All such experiments have disproved the hidden variable theories. See Bell test experiments.

Joy Christian replied on Oct. 1, 2012 @ 16:11 GMT
"All such experiments have disproved the hidden variable theories."

And I have disproved Bell's claim that "no physical theory which is realistic as well as local [in the senses specified by EPR and Bell] can reproduce all of the statistical predictions of quantum mechanics."

Your assertion is based on a prevalent but unjustified belief system, not on a rational and unbiased scientific investigation.

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Author Roger Schlafly replied on Oct. 1, 2012 @ 17:13 GMT
Joy Christian, your so-called disproof has been rebutted by Moldoveanu, Gill, and Grangier.

Yuri Danoyan wrote on Oct. 1, 2012 @ 16:09 GMT
http://arxiv.org/pdf/0805.4057v1.pdf

http://arxiv.org/pdf/mat
h/0703427v1.pdf

Two interesting articles Yuri Manin

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Yuri Danoyan wrote on Oct. 1, 2012 @ 16:16 GMT
Relation between physics and mathematics by Yuri Manin

http://www.ams.org/notices/200910/rtx091001268p.pdf

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Yuri Danoyan wrote on Oct. 1, 2012 @ 16:29 GMT
Sorry Roger

But Yuri Manin very smart person

Interrelations between

Mathematics and Physics

Yu. I. Manin

http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_
3_157-168.pdf

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Author Roger Schlafly replied on Oct. 1, 2012 @ 17:28 GMT
Yes, Manin is a smart guy with many interesting things to say. Did you see anything to lead you to believe that he would agree or disagree with my essay?

Frank Martin DiMeglio wrote on Oct. 1, 2012 @ 18:08 GMT
Roger. Your reply to my prior post please. Also, the objective is to have a seamless and undivided whole, as ultimate unification in physics combines, balances, and includes opposites. MATHEMATICS CANNOT COMBINE, BALANCE, AND INCLUDE OPPOSITES.

Time is ultimately dependent upon the integrated and interactive extensiveness of being, thought, and experience (and space). Time requires gravity. In the absence of gravity, we are literally out of touch with reality. Another physical fact that mathematics fails at.

The key here is to describe thought [fundamentally and generally] in conjunction with/relation to physics, force/energy, and sensory experience (in general). My essay does this. Mathematics cannot do this.

The reductionist and mathematical approaches are ultimately doomed in conjunction with the following:

The self represents, forms, and experiences a comprehensive approximation of experience in general by combining conscious and unconscious experience. (A great fact of physics too.)

Can you review and rate my essay please Roger?

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Yuri Danoyan wrote on Oct. 1, 2012 @ 18:38 GMT
1.I agree with Manin that physicists more inquisitive to mathematics than mahematicians to physics.

2. I agree with Wittgenstein:

6.21 Mathematical propositions express no thoughts.

6.211 In life it is never a mathematical proposition which we need,

but we use mathematical propositions only in order to infer

from propositions which do not belong to mathematics to others

which equally do not belong to mathematics.

(In philosophy the question “Why do we really use that word,

that proposition?” constantly leads to valuable results.)

6.22 The logic of the world which the propositions of logic show in

tautologies, mathematics shows in equations.

6.23 If two expressions are connected by the sign of equality, this

means that they can be substituted for one another. But

whether this is the case must show itself in the two expressions

themselves.

It characterizes the logical form of two expressions, that they

can be substituted for one another.

6.234 Mathematics is a method of logic.

6.2341 The essential of mathematical method is working with equations.

On this method depends the fact that every proposition

of mathematics must be self-intelligible.

6.24 The method by which mathematics arrives at its equations is

the method of substitution.

For equations express the substitutability of two expressions,

and we proceed from a number of equations to new equations,

replacing expressions by others in accordance with the equations

3.Roger, i am agree with you naturally.

Please don't forget please impartially evaluate my essay

Sincerely

Yuri

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Yuri Danoyan replied on Oct. 7, 2012 @ 04:40 GMT
How are you Roger?

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Michael A.Popov wrote on Oct. 2, 2012 @ 11:59 GMT
Roger,

Sorry, some refinements :

Physically speaking,John Bell showed that it was indeed possible to realize the EPR-experiment, when the two particles are emitted with definite spin directions, which are locally fixed at the decay. These directions, according to Bell,however, might be unknown to the experimentalist. He then showed that if we measure the spin of particle 1(natural number,sorry)along one direction, and the spin of particle 2 along another direction, the results will be correlated. For instance, if we measure the spin of both particles along the same direction, particle 2 will always have the spin down when particle 1 has the spin up.

Thus, they are correlated (or rather, anti-correlated).But if the spins are measured along different directions, the correlation will decrease.(Since Bell's discovery, a number of experimental tests have been performed successfully [by J Clauser and S Freedman (1972), A Aspect, J. Dalibard, and G Roger (1982), and G Weihs, Ch Simon, T Jennewein, H Weinfurter, and A Zeilinger (1998)],etc )...

Mathematically speaking, however, Bell' Nature has faithful mathematical representations in the form of complex numbers which can exist only in Hilbert complex vector space. Thus, iff somebody has alternative more advanced mathematics as well as he knows better Nature's own mathematical taste,it is naturally to ask to prove such sort of claim.Technically and experimentally.

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 09:42 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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Lorraine Ford wrote on Oct. 5, 2012 @ 12:39 GMT
Roger,

I really like your essay even though I don't necessarily agree with all you say. To me, these are the important and interesting issues: what reality do the mathematical equations of physics represent; and what reality do the numbers found in nature represent.

Cheers,

Lorraine

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Concerned Public wrote on Oct. 6, 2012 @ 08:19 GMT
Sergey G Fedosin is bombing entrants' boards with the same "Why your rating has dropped" message. They are all dated Oct. 4... same message.

WTH? I've seen one fine essay drop 89 (eighty-nine) positions, in "Community Rating" in the past 24 hours, and “Sergey’s note” came BEFORE it plummeted. Hmm.

The vote/scaling of this contest is quite nebulous.

"Hackers Rule!", I suppose!

Well??? What else is one to think? The General Public is... Watching…

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Zbigniew Modrzejewski wrote on Nov. 19, 2012 @ 20:39 GMT
Roger,

It is important that your conclusion, Nature Has No Faithful Mathematical Representation, comes from a matematician.

My intuition had always told me that Reality (Nature) is not limited to being mathematical. It is beyond being either digital or analog.

It is neither digital nor analog. "digital" and "analog" we just project with our limited minds onto reality, as our "perception". We mentally project our mental limitations onto reality we experience. See: the problem of perception, in philosophy.

Instead of mathematics, New Physics should start using empirical testing of consciousness. Instead of mathematical quantities, New Physics should concentrate on qualities of mental experience.

Hope you will win one of the prizes.

Zbiggy www.worldsci.org/people/Zbigniew_Modrzejewski

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Author Roger Schlafly wrote on Nov. 19, 2012 @ 22:31 GMT
Thanks. Well put.

Zbigniew Modrzejewski wrote on Nov. 20, 2012 @ 23:15 GMT
Thank you, Roger.

And I forgot to add.

Yes! I agree with you. You are so right --

Einstein Ruined Physics:

http://darkbuzz.com/herp/index.htm

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