"The failure of the Michelson-Morley experiment to detect the motion of the earth through the hypothesised ether led Einstein and others to abandon the ether, and look for a set of mathematical coordinate transformations which allow the speed of light to be the same for all inertial observers."

That was a dishonest step that eventually ruined physics. In 1887 (prior to FitzGerald and Lorentz advancing the ad hoc length contraction hypothesis), the Michelson-Morley experiment unequivocally confirmed the variable speed of light predicted by Newton's emission theory of light and refuted the constant (independent of the speed of the source) speed of light predicted by the immobile ether theory and later adopted by Einstein as his special relativity's second postulate:

Alberto Martinez: "In sum, Einstein rejected the emission hypothesis prior to 1905 not because of any direct empirical evidence against it, but because it seemed to involve too many theoretical and mathematical complications. By contrast, Ritz was impressed by the lack of empirical evidence against the emission hypothesis, and he was not deterred by the mathematical difficulties it involved. It seemed to Ritz far more reasonable to assume, in the interest of the "economy" of scientific concepts, that the speed of light depends on the speed of its source, like any other projectile, rather than to assume or believe, with Einstein, that its speed is independent of the motion of its source even though it is not a wave in a medium; that nothing can go faster than light; that the length and mass of any body varies with its velocity; that there exist no rigid bodies; that duration and simultaneity are relative concepts; that the basic parallelogram law for the addition of velocities is not exactly valid; and so forth. Ritz commented that "it is a curious thing, worthy of remark, that only a few years ago one would have thought it sufficient to refute a theory to show that it entails even one or another of these consequences...."

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."

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."

Relativity and Its Roots, Banesh Hoffmann, p.92: "There are various remarks to be made about this second principle. For instance, if it is so obvious, how could it turn out to be part of a revolution - especially when the first principle is also a natural one? 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. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous."

Pentcho Valev

    Dear Pentcho,

    Thank you for your comments. It was my understanding that many many different experiments, carried out independently and using different set-ups, terrestrial as well as astronomical, rule out the emission theory of light to a very high precision.

    With regards,

    Tejinder

    Dear Tejinder,

    Your statement "many many different experiments (...) rule out the emission theory of light to a very high precision" is unfalsifiable - how can I oppose it? We can only discuss the experiments one by one. I hope you agree now that the Michelson-Morley experiment did confirm the variable speed of light predicted by the emission theory, and refuted the constant (independent of the speed of the light source) speed of light predicted by the ether theory and adopted by Einstein as his second postulate. The Pound-Rebka experiment also confirmed the variable (in a gravitational field) speed of light predicted by Newton's emission theory of light:

    Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

    Pentcho Valev

    Dear Pentcho,

    My understanding is that both emission theory and special relativity are consistent with the Michelson Morley experiment, but the former is refuted by subsequent experiments. From what I know, Einstein himself did consider an emission theory of his own, before discarding it in favour of special relativity. As regards the multitude of experiments that refute emission theory, I myself of course do not have the expertise to judge them one by one; I am satisfied that different experiments were reported and published. I would find it extremely hard to believe that a group of experimentalists have over decades indulged in a conspiracy of sorts to deliberately discredit emission theory. I do understand that there are physicists who continue to support the emission theory and probably that is your stance too. I can only say that I respectfully disagree with this stance.

    I wish to add that I am not an all out pro-establishment theorist! :-) I disagree with the establishment view on quantum theory, and I think the theory needs better understanding. However, until a decisive experiment comes along and shows quantum theory to be approximate, the debate is not going to be settled one way or the other. Same holds for the proposal of dark matter: we cannot be sure of its existence until a candidate is found, and I am sympathetic to alternate explanations such as modified gravity and MOND, even though the establishment is strongly pro-dark matter. Another good example I thnk is cosmological inflation: despite all claims to success it is still a hypothesis. I also feel the pro-establishment community is open to considering concrete alternatives, even if these meet pockets of resistance. Thus I am very reluctant to believe that the emission theory is being deliberately suppressed by vested experimentalists and theorists. On the other hand, we do find a healthy response to concrete proposals to modify special relativity.

    Those are my two cents :-)

    Best regards,

    Tejinder

    4 days later

    Dear Anshu and Tejinder,

    I just red your reply following my very positive appreciation of your essay.

    There is another essay about science and cognition by Vincent Douzal that you should not miss.

    Me too I am not yet convinced by Hameroff and Penrose, I met them sometimes ago at a Tucson conference.

    I am now rating your essay highly. I hope it will not be balanced by a stupid 1 as usual. Myself I already got 1 three times.

    Best,

    Michel

      6 days later

      Tejinder and Anshu,

      Congratulations on a weighty discussion. As a modeller in the urbane, offensive and defensive weapons cost and support, and as a teacher of English, I see human mathematics as building on metaphors, not being an entity itself. My background lends that prejudice.

      You do not burden yourself with this question, but do state your feeling: "tempting but erroneous to conclude that the beautiful math description is resident in the physical world."

      I also believe that Cognition draws on the physical world to invent the stable human language of math. Such modelling has led us to discoveries quantum biology, DNA, and LHC through what I see as the connections of math, mind, and physics.

      Thanks for the opportunity to share your views.

      Jim

        Dear Michel,

        Greetings, and thanks for pointing us to Vincent Douzal's paper, which we read and liked. Indeed there are a few papers in the contest emphasising the importance of cognition in the present context (though perhaps too few!). The research works of Lukaff, Nunez, Dehaene, Hestenes, amongst others, are noteworthy.

        Kind regards,

        Anshu, Tejinder

        Dear Jim.

        Thank you for reading our essay and for your kind comments. Happy to know we are in agreement.

        Best regards,

        Anshu, Tejinder

        Dear Anshu,

        Dear Tejinder,

        You are anti-Platonists (or rather non-Platonists), and I am a Platonist aware of all difficulties this option represents. But similar difficulties do undermine ALL options that could be discussed within the framework of this contest. Personally I see (i) this contest as a philosophical one and (ii) philosophy as the choice to focus on issues that do not allow one single answer. Of course sometime an initially philosophical question finally gets a definitive answer, but in this case it ceases to be a philosophical question. Anyway, regarding foundational research about mathematics and/or links between mathematics and physics, we must "empirically" recognize that for n people debating about, there are at least n + 1 opinions. Under these conditions, the BEST we could do is to try a mutually benefit full constructive dialogue, and this primarily with colleagues defending "opposite standpoints." You agree probably that such a constructive dialogue should be for everyone the main motivation to participate in this contest.

        The calm, circumspect, and courteous background tone of your well written, highly interesting essay expressing a wide deepened culture about history of mathematics and physics make me think that you are seeking in turn dialogue.

        Before going further, I would state - even repeating myself - that it has been an enormous pleasure for me to read your really well written elegant essay with its beautiful symmetry between sections I and II. You are absolutely right to emphasize that mathematics and (the interminable stammering of) physics initially knew essentially separate paths, and that the manifest collusion between physics and (a relatively modest part of) mathematics represents at least at first glance a mystery to elucidate; otherwise the subject of this contest would not have any reason to be proposed.

        Well, and now let us discuss some essential points of your essay, with the sole aim to exchange ideas.

        You are wondering how are we ever going to be able to scientifically prove Platonism. Here, my position as a Platonist - I expose it at length in my own essay - is clear. Platonism IS metaphysics and still metaphysics and nothing but metaphysics. Yes, but all competing theories of Platonism are as well metaphysical as Platonism they are trying to "refute". If such a refutation was possible, the competing theory in question would transform Platonism in a no longer metaphysical but scientifically refutable approach being effectively refuted, just like it can happen to other entirely scientific approaches. At first sight it seems certainly strange to postulate that "there is a mathematical universe, which we somehow grasp in an extra-sensory manner". But in my own essay, I quote a reference text of R. Carnap where this categorical anti-metaphysical main representative of logical positivism relegates material realism to metaphysics, making no difference with other ontological theories like idealism. Of course, we receive information on material reality by our sensory channels before cognition processes this information. But it seems to me that the problem is just THERE: To evaluate (i) objectively and (ii) non-metaphysically the degree of adequation between the image we have of reality following its cognitive processing and reality "as such" (??), we should transmute us in pure immaterial spirits able to go out/beyond of our cognition. The fact that all our information about material reality run through our sensory channels, whereas there is nothing equivalent concerning our access to an immaterial mathematical world being objectively given, this only fact does not refute Platonism. First, nothing allows us to predict that humans will "never" discover brain channels able to receiving directly immaterial information. At present we do not know anything about that issue - at least to my knowledge - but anyway, scientists who by definition do not have the vocation to utter metaphysical and /or arbitrary propositions should not play the prophets of what "will or will not be discovered." I would add that the (too) famous "Benacerraf argument against Platonism" - "we have good knowledge about cognition dedicated to the empirical reality, whereas there is no equivalent for an immaterial world" - has not at all "definitely refuted Platonism." Some authors like Penelope Maddy even do not think that Benacerraf would advance an anti-Platonist evidence. Anyway, discussions about "Benacerraf's argument" are continuing for 43 years, and nobody sees the end.

        On the other hand, the material reality which exists - let us admit that it exists - could also not exist. A scientific is generally not interested in the issue "why exist the material reality, instead of not existing." Well, but this issue equivalent to this other: "why should an immaterial objective mathematical world NOT exist instead of existing?" Everywhere we encounter metaphysics, much more metaphysics then we would admit it spontaneously. In other terms: If we deny the existence of material world, we must assume an infinite number of epistemological problems. But we must also ask - without any a priori - if it is not the same for Platonism, and more specifically, if the denial of Platonism does not cause in turn a jolly good number of epistemological problems regarding for example the links between mathematics and physics. In my own essay, I try to raise such problems, leaving it to the reader to appreciate these problems in her/his personal manner.

        In your essay you say that "in their work physicists and mathematicians generally prefer to ignore or 'forget' the brain (...)." Personally, I don't think (i) that it is a question of ignoring or forgetting and (ii) that this point is not a detail. Let me use a metaphor. Imagine you are resolving a mathematical or physical problem, using a computer to facilitate your task. Doing this, you don't "ignore or forget" your computer and its internal functioning. But in this context, the computer is accessory. Perhaps and even probably it is an unavoidable mediator between your work and the given object of your work, may it be mathematics or physical reality. This certainly does not hinder you to be interested about hardware oriented computer science computer science. However, making mathematics or physics as such, you tacitly are bracketing all issues related to computer science or hardware. Now it is clear that your computer and more generally each information processing system must be equipped so that it can carry out its task. Hence the system is supposed to share the logic (and other factors) of (i) the task to be effectuated and (ii) the object that this task concerns. But this does not necessarily mean that information treating system "GENERATE" or "CREATE" the object of its task. Moreover, in the case of a computer or other artificial information processing systems, we can KNOW that the system does not "generate" or "create" the object of its task, since we are outside the circuit linking the system to the object of its task. But it is not the same for our brains, or, more generally, for our cognition.

        Of course, to be able to make mathematics or physics, our brains must be equipped for. Concerning mathematics, it is often said that elementary mathematical structures, principally counting, are innate and do pre-exist in infants to all effectively effectuated operations. Given the complexity of the issue, I am not sure that this point can be categorically asserted, but it is not so important. Not only it is obvious that our brains are disposed for mathematics - otherwise there would be no mathematics, at least no mathematics effectively written on paper - but we can still do some interesting overlaps between the theories of "constructivist" philosophy (Brouwer, Heything ea) reducing any form of mathematics effectively constructable to "intuition of counting", and, on the other hand, modern computational mathematics. Regarding physical reality (in a very vast sense), it is in turn clear that our cognition is able not only to register it, but also to investigate it. Otherwise there would be neither physics, nor other sciences.

        But now complications arise.

        To respond - in cognitive terms - to the following issue "How to explain that (a part of) physical phenomena correspond to (a part of) mathematics being (at least potentially) pre-programmed in / by the human brain?", we need very heavy hypotheses. In a cognitive perspective, if we assume that mathematics is at least potentially rooted in the brain, we must also assume that our brains organize the physical reality in the way that it aligns with given part of mathematics. This lead to a kind of Kantian or neo-Kantian philosophy which inevitably will be the subject of endless controversies. But regardless the option we would adopt in this area, the fundamental problem remains the same: unlike the information processing system mentioned above, where humans being outside the circuit linking the system to the reality can compare the treated information to its original, human cognition CAN NOT "get out from itself" in order to check the degree of adequacy between the reality as such and the reality as it is conditioned by cognition. In other terms, there is CIRCULARITY, and each tentative to break an objectively given circularity leads to metaphysics.

        Nevertheless it is not a deadlock, but the solution can not be classical.

        The position I defend in my own essay is the following: (i) All foundational approaches concerning mathematics and/or links between mathematics and physics are ultimately metaphysical. (ii) Platonism belongs to metaphysics as well as anti-Platonism, whatever it would be. (iii) Even cognitive approaches ultimately DO NOT escape to metaphysics: all investigations of human cognition are conditioned by human cognition. To appreciate this latter "objectively", human cognitive scientists should be able to get out from their cognition, to go "beyond" of all links between cognition and its objects, and this remains a genuine metaphysical idea. (iv) All we can do is to compare several competing metaphysical theories under EPISTEMOLOGICAL criteria such as simplicity in the logical sense of this term, complexity of primary and secondary hypotheses, internal consistency, consistency on the level of consequences and so on. On these bases, I try to show that a necessarily metaphysical Platonism is more plausible than its (also necessarily metaphysical) competing theories. Further details are in my own essay. Here, I try to summarize it as follows: Platonism is based on assumptions neither provable nor refutable. But it's the same for anti-Platonism. On the other hand, anti-Platonism must additionally assume some forms of circularity that Platonism can - at least in purely logical terms - avoid.

        I would be glad to know your counter-propositions about my vision I tried to summarize here above and also to know the criticism that you would not fail to address to my own contribution. It would be precious to of further reformulations on the foundations of a broader vision. Ultimately, this the raison d'être of the present contest.

        With best regards

        Peter

          I did enjoy reading this essay which covers a wide ranging scope of topics in Mathematics, Physics and Cognitive Science.

          I also enjoyed reading your technical end notes on Quantum Theory and completely agree with your assessment that quantum theory might be incomplete. I think you will enjoy reading my essay: 'solving the mystery' which addresses the four oddities that you mention in your essay. The problem is treated from a different conceptual viewpoint (the spacetime wave theory).

          Best wishes

          Richard Lewis

            Dear Peter,

            Many thanks for your kind remarks, and your detailed and incisive comments. We will respond after understanding them carefully and reading your essay, by later next week.

            Kind regards,

            Anshu, Tejinder

            Many thanks Richard, for your kind comments. We are looking forward to reading your essay and hope to respond in a week or so.

            Kind regards,

            Anshu, Tejinder

            Dear Anshu & Tejinder,

            I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

            I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

            All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

            Joe Fisher

            8 days later

            Anshu and Tejinder,

            Time grows short and I am revisiting essays I have read to determine if I've rated them. Yours I did on 3/28.

            I would like to see your thoughts on mine.

            Jim

            Anshu and Tejinder,

            "And Jim we do not seem to find in your essay an explanation for the central question as to why mathematics is so successfully employed in physics. Wonder what your thoughts on this are."

            First there was the equation on page 3 that represent P, M, and B (physics, math and the human brain), showing their integral interconnection. I provide examples on page 3 & 5 in "Math's Applications" and "Math's Quantum Modeling" section on how math's use in modeling and algorithms, including lines of programming code containing the algorithms that mathematically tie physics concepts together with the LHC, DNA and quantum biology studies and successes.

            My conclusion on page 7 shows how these connections of the brain, math and physics are vital in the stellar progress we've had in all physics but especially in those areas I cite.

            Thank you both for reading my essay.

            Jim

            Dear Peter,

            After leaving a post on your essay, we returned again to your comments above and re-read them...you undoubtedly express your stance very clearly - namely that using cognition to understand cognition is also metaphysics. We respectfully tend to disagree, and made some remarks to this effect on your page and perhaps one could avoid repeating them here. Principally we are saying that in considering a cognitive basis for the physics-maths connection there is at least hope for making a scientific model. As opposed to when one half, the mathematical half, is an immaterial reality - at least for now, until and unless, as you say, brains develop channels to communicate directly with such mathematical reality.

            One further remark ... if we ask why does the world NOT exist rather than existing, we feel one day physics will give us an answer to that. Thus instead of relegating this question to a metaphysical realm, we want to think of it as a currently unsolved problem in physics.

            Your criticism of the cognitive approach as being metaphysical is incisive and very clear, and trying to defend it has helped us understand our position better. We appreciate the dialogue you have initiated and will be happy to carry it further. Thank you.

            Best regards,

            Anshu, Tejinder

            Dear Anshu and Tejinder,

            I will start off with what will appear to be irrelevant observations (at least irrelevant to the shared subject matter).

            Your writing style reflects a commitment to writing "flawlessly." I don't correct grammar or spelling of people who are committed to their thought, and let their writing be as it may.

            In future issues of your essay (or parts thereof), you may want to correct a typo now found on page 3, 4th line from the bottom: you will want to replace "word" with "world."

            On page 8, about ¼ of the page down, you will find "Riemannean," which is usually spelled as "Riemannian." I think your choice of spelling was influenced by the spelling of a word that preceded it (Euclidean).

            To most people such details will seem inconsequential, but they help me understand the thinking of the writers. Your essay appears to be edited by someone (and it could be one of you two, or both) educated in the U.K., and subsequently influenced by reading a lot of US texts.

            Your essay says very reasonable things. My favorite observation is this one: "Force, for instance, could be metaphorically related to the primordial human perception of the muscular exertion in throwing a stone at a prey or a threat." You are right. That is precisely where our concept of force came from. As people tried to push or lift bigger and bigger rocks, they realized that the required effort increased with the size of the rock, along with a corresponding increase in "pain" felt in the muscles. They called it "force." Obviously then, you must believe that there isn't any such thing as force out there, but F is a convenient "shorthand" (abstraction) for various things ("m x a" being one of them).

            After this, there is no need to go into further details. The above paragraph "captures" the essence of your message.

            And please do not go to my essay page (and don't feel obligated to read or rate it). It will feel too "mercenary" if you do that.

            En

            P.S. Your essay deserves a high rating.

              Dear En,

              Thank you for your candid remarks, and for pointing out the typos. We regret these errors and will correct them in a subsequent version. [We edited the essay together; and you are absolutely right - we were educated in India, with the medium of instruction being English (which is essentially British English), and then of course followed by lot of US texts in higher education! How you figure out something like that is beyond us :-)].

              We are glad that we agree on the primitive origin of the force concept, and indeed we appreciate your remark that this captures the essence of our stance.

              Kind regards,

              Anshu, Tejinder

              Dear Anshu and Tejinder,

              I have read your reply, and can now see that I did a terrible job of promoting your essay.

              It was not my intention to make any subsequent readers think (and hopefully they will not) that your essay's message could be abridged to something like what my (the relevant) paragraph says.

              On the contrary. Your essay offers interesting and valuable insights, and yes, there is a 'need to go into further details.' Much is to be gained from reading every line of your essay, and consider the thoughts "contained" therein.

              You were too polite in saying "...indeed we appreciate your remark that this captures the essence of our stance." A less "polished" Westerner might have told me to go take a hike.

              There is one question that you may still want to consider (and answer it to yourselves, or in a comment). It concerns this quote taken from page 1 of your essay: "Physics, on the other hand, is an experimental science (hence dependent on technology) of the world we observe, where experiments couple with great leaps of conceptual unification. The mathematics used in physics comes in only at a later stage, when we seek a precise language to describe the observed physical phenomena."

              The question that I had in mind is this. When you talk about physics in the quoted segment, are you thinking about physics as it is actually practiced, or as an idealized discipline ("that's what physics ought to be")? I am only asking whether you would like to make this distinction explicit.

              I enjoyed your essay. It keeps the reader keen to learn more from each new observation you make.

              En