Constantinos

The most balanced view of the role of maths and theory I've read. I loved the essay which was well written and pertinent (and felt honoured by the mention).

In particular;

"A theory is a view. The very word theory in Greek means 'divine view'. Physics without a view is thinking without thought." .. also..;

"Mathematical truths are always conditional. They depend on our presuppositions and our premises."

An important point on which many here agree but so many elsewhere are blind to. And to sum up another much agreed truth;

"Mathematical truths are always conditional. They depend on our presuppositions and our premises."

I tried to find something to challenge but could not. Congratulations on a direct and masterpiece blowing most assumptions about the role of maths to bits.

I do hope you will read and can comprehend the complex logical structure in my own essay, beneath the metaphorical dressing, designed to aid kinetic visualisation. The findings are revolutionary, deriving SR direct from a quantum mechanism, but it seems a little lost to mathematically based thinking so far, and certainly not penetrable by a quick scan over.

The equations at the end notes describe the wavelength Doppler shifting on a progressive acceleration (frame transformation), which produces CSL to all moving observers. The wave-function itself does not change as assumed.

Well done and best of luck.

Peter

    Peter my friend, thanks for the kind words.

    My intent is not to 'blow off' the use of math in Physics. But to raise concerns about the abuse of it. In this regard I am with many others in this contest that feel the same way. But perhaps for different reasons. I truly value mathematics but question some of its applications in Physics. In my view, seeking to know 'what is' the Universe is metaphysics, pure and simple. Whether mathematical or not is besides the point. The Pythagoreans tried to do the same 2500 years ago!

    But I also argue for the proper use of math in Physics. And that is in the application of mathematical truisms to physical measurements. And this I show is possible! Planck's Formula, for example, is actually a mathematical truism, and NOT a Physical Law based on 'energy quanta'.

    The essay, of course, is much more than that! In it you will find some remarkable derivations, including proof of the inconsistency between the CSL Postulate and the Photon Hypothesis. This should be of special interest to you since this confirms that light propagates as a wave and not as a particle-photon.

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    • Post #4

    Constantinos,

    Monte Carlo simulation. Maybe the most brilliant mathematical modeling protocol ever invented in relation to physical science or ever invented, period. As long as you're dealing with bosons and weakly-interacting fermions. But MC can't address strongly-interacting fermions. The modeling of strong fermionic interaction appears to be mathematically and computationally impossible thanks to the minus-sign problem. Jan Zaanen calls this issue "the nightmare of modern physics." Its ramifications are enormous if we're ever to understand how solid matter emerges from quanta. Matthias Troyer and Uwe-Jens Wiese have demonstrated (although not to the satisfaction of everyone ... cf. Konstantin Efetov) that putting these fermions on the lattice for bosonization and MC simulation is NP-hard. Prove Troyer-Wiese wrong and you may have also proven P=NP and earned a million dollars (US) from the Clay Mathematics Institute in addition to whatever the Royal Swedish Academy of Sciences might be willing to give you on behalf of that award fund they oversee.

    Understandably there's a lot of denial and deliberate (if often unconscious) avoidance of knowledge in regard to this issue. You hardly ever hear about it. Many people insist on seeing the sign problem as a technical conumdrum that numerical simulators and/or condensed matter physicists simply need more time, labor and ingenuity to resolve. One metaphysical assumption at work here is that accumulated scientific knowledge can overcome all obstacles placed in the way of science by nature. Maybe, or on the other hand we might be facing a drama worthy of ... well, hey, why not of a Dionysia.

      Dear nmann,

      My only familiarity with the Monte Carlo method from my years of teaching math was its use as a practical (pre-computer) method of calculating definite integrals. I am not at all surprised when any clever math should find its way in Physics. To so model the Universe, however, is a gamble in my view. Or perhaps not! Since such 'cosmic casino' model does not describe 'what is' (what I argue is metaphysical). But makes the point convincingly that 'what is' is as unknowable as 'throwing darts' on a cardboard square. Such randomness can be even considered 'truism'. This fits well with the overarching theme in my essay!

      Constantinos

      Dear Constantinos,

      What a wonderful essay! It is also rewarding to see how our theories [divine views] improve from year to year. I very much appreciated your last essay, A World without Quanta?, but I found a few points to disagree with. Like Peter above, I found nothing in your current essay to challenge on first reading. I do tend to see 'action' as fundamental, and continue to find your 'eta' formulation to be quite beautiful. I do agree with your claims concerning math and metaphysics, and wherein we should "put our faith". The world is far too complicated to capture in a mathematical map. The inherently religious effort to do so ("Scholastic Metaphysics") is "cruisin' for a bruisin'" and this particular FQXi essay contest is landing some serious blows.

      Like you I am thankful for Templeton's initial funding and for the hardwork and good will of the FQXi administrators as well as all those who take it seriously and work to present their own thoughts to their fellows. In a world that often gives one a headache, FQXi tends to restore my faith in my fellow man.

      Thanks again for an essay that almost qualifies as 'wise'.

      Edwin Eugene Klingman

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        • Post #7

        Constantino,

        I'm afraid I'm going to have to take you to task on this one. While you put up lots of interesting thoughts, it seems more like notes on a subject, rather than an essay. Given the areas you cover, it would take a good length book to do them all justice, but squeezing them into a ten page essay isn't effective. Possibly you might have focused on clarifying the difference and relationship between mathematical truism and universal law. That would be the kind of single topic more suited to this form and forum.

        Good to see you anyway and don't take this as anything more than comments from a friend.

          Not sure where Monte Carlo came from on this thread, and I had not previously thought of it as "Maybe the most brilliant mathematical modeling protocol ever invented in relation to physical science or ever invented, period" but I do recall falling in love with it when I first discovered it. Like Constantinos, I knew it as a technique for calculating definite integrals, but it is almost infinitely flexible. I once needed to model large polymer molecules adhering to metallic surfaces where the sticking coefficient was unknown. With Monte Carlo methods one can very easily 'shape' the distribution, and it was known that the particles re-evolved with a cosine distribution. This was easy to solve analytically in 2D so I both Monte Carlo modeled the process and also calculated the exact solution and they agreed as closely as I wished (just run longer!) Thus convinced of the validity of the technique I used the Monte Carlo in a 3D configuration (which I could not solve) and got great results to compare with experiment. I suspect there are thousands of unique applications of Monte Carlo to accomplish otherwise almost impossible tasks.

          Edwin Eugene Klingman

          John, thank you for your honest comments. Certainly volumes can be written on any one topic in my essay. But does 'volume' equate with 'clarity'? I tried purposefully to focus each idea, haiku-like, on a metaphor that makes sense. And let the reader fill in instances of its truthfulness.

          As to the "relationship between mathematical truism and universal law" you highlight in your comment. That indeed is the central key idea in my essay. Besides all the other central key ideas! ;) Just to take this point further.

          In my view, the only logical connection between math and physics is the application of mathematical truisms to physical measurements. These are or should be the universal laws of physics. There is no other reason why the Universe should follow mathematical models. Models of 'what is' the Universe are metaphysical, in my view. My objective was to demonstrate in a limited way (commensurate with my knowledge and abilities; others can do much more) this is possible. I show that Newton's Laws of Motion are such mathematical truisms and not physical laws. As is also Planck's formula for blackbody conditions; Boltzmann's Entropy Equation; Schroedinger's equations, and many more. Further, using this formulation, I am able to prove the inconsistency between the CSL Postulate and the Photon Hypothesis.

          In another of your posts under some other forum (I forget where) you raised the relationship between 'time' and 'temperature'. I agree there is indeed such a relationship. This naturally shows up in my results. In fact, I show how 'time' and 'temperature' are reciprocal. The duration of time, for example, for an 'accumulation of energy' equal to h to occur (in ideal blackbody conditions) is given by h / kT. Thus, the higher the temperature, the quicker the accumulation. And visa versa.

          Thanks for all you do. Our discussions are always enriched by your insights.

          Constantinos

          Dear Edwin Klingman,

          Thank you very much for your kind words. I too remember very fondly the exchanges we had in my previous essay and am looking forward to all your great insights and comments on this one.

          You write, "I do tend to see 'action' as fundamental". In my formulation, "action" and "accumulation of energy" are equivalent. Both are expressions of the same primary quantity 'eta'. 'Action' concerns 'momentum' while 'accumulation' concerns energy. While 'momentum' is an 'extension of eta' in space, 'energy' is an 'expansion of eta' in time.

          At the End Notes of my essay I include a mathematical proof of the following proposition: "If the speed of light is constant, then light propagates as a wave". I find this so very relevant and wonder why others do not!

          Constantinos

          Dear Constantinos,

          What a wonderfull and comprehensive essay ! I was honoured to be quoted by you.

          Indeed "reality" cannot wholly be described wwith mathematics, mathematics is a good tool, but every tool is not apt for the whole oeuvre. I am glad that you also treat "metaphysics" , you will see that the "public rating" will flow from high to low, I think that our opinions do not ask for medium opinions. In the last posts that I received the question was asked about the "theological consequences" of the thread, I gave an answer which states that we all are searching and that it will never be possible to give "proof" of GOD. GOD is not a physical problem that can be solved, God is state of mind.

          Good luck in the contest.

          Wilhelmus

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          • Post #12

          Constantios,

          I understand you were drawing a web of connections, but they tended to obscure the central focus somewhat. I think the existence of this contest and its question is a small breach in the wall of status quo physics, or should I say, static physics, since I'm on Heraclitus' side of the issue. So I'm trying to make sure there is as much pressure being applied as possible.

          I think that the search for the Higgs proving to be a climb up a lonely mountain and not a stairway to heaven of ever more exotic particles, will prove to be the apogee of the current model, because future generations of theoretical physicists have no options to work on, other than examining the many loose ends left patched over, or unanswered in the present situation.

          There are a few truly preposterous entries in this contest, by well respected professionals, which I will leave un-named, that make claims which would make multiworlds and inflation seem almost reasonable. If they think future physicists will follow them further down that path, they would seem to have little knowledge of the more introspective and less sheep like qualities of human nature.

          As for truism, vs. laws, I'm more and more of the opinion that it is all truisms and there is no platonic realm of universal law. If we have no matter, energy, shape, form, structure, then there are also no defining principles. If we start with nothing, then nothing necessarily has no boundaries or action. Therefore nothing would seem to be infinite and inertial. It would seem nothing is empty space. Then we add action, which would mean the need for opposites, since one defines the other. Then we get multiplicity and interaction. Each layer of emergence creates the properties that define it. So what do the Platoists look at, when they seek those universal laws? Basic concepts and shapes; points, lines, planes, volume, triangles, circles, causality, reactiveness, etc. Basically they point to the initial levels of emergence and their properties. Then they do away with the nothing of space and call it an ether. Now they are trying to do away with the physical and say it is all just a platonic realm of math and information.

          Just thinking out loud. Good to see you and keep hammering away.

          Dear Wilhelmus,

          Too often when we speak of God we are understood through the misconceptions of others. As these are attributed to us. I try to avoid such discussions all together. I am perfectly comfortable with the notion that God exists or God does not exist! Or even God may in the future exist. Or had existed at one time.

          But I am convinced (and have good reasons to be convinced as per my essay) any description of 'what is' the Universe is metaphysical. Whether mathematical or not! And any such metaphysical description will ultimately fail. Just as it has in the past. And it will fail because the Metaphysics stretches the limits of the sensible. And so it is no longer believed. I believe we are near that point now with Modern Physics.

          But in my essay I also argue Physics can be based on mathematical 'truisms' applied to measurements. Though we cannot know 'what is', we certainly know our measurements of 'what is'. And though there is no logical basis that the Universe follows mathematical 'models', there is logical certainty applying mathematical 'truisms' to measurements.

          Thank you for your good wishes ...

          Constantinos

            John you write,

            " I'm more and more of the opinion that it is all truisms and there is no ... universal law".

            I completely agree with that! Sorry this was obscured in my essay.

            Constantinos

            Hello Constantinos,

            I couldn't resist reading, and found myself at the end before stopping. A masterful exposition of how deeply entrenched Physics is in Metaphysics, yet in denial about this fact. I might go even further. I find a lot to agree with, as you would know from my own essay on "Cherished Assumptions and the Progress of Physics," but I find also myself living outside of the box you have so cleverly designed.

            I think a lot of lies can get told with Math, because it is a language and people forget Korzybski's dictum "The word is not the thing, and the map is not the territory." I point out in my essay from 2 yrs. ago that we should add "The equation is not the Physics it represents." And I elaborate on the problems of applying linear Math models in a largely non-linear world, this year.

            A lot of people forget that the Math is meant to model Physics, and is often imperfect in that role, acting as though the Math is creating the Physics instead - and this is usually false. However; there is a need to acknowledge that sometimes the rule we observe through physical measurement actually does arise from mathematical or geometrical rules at work, that dictate the relationship between physical objects and forces.

            That is; it is not so clear cut, and it works both ways. I have 25 years of accumulated evidence I would need ignore, to feel otherwise. Sometimes, things believed to be objects of pure Math exert an inexorable pull on reality. I'll comment more later, and make some mention too of objections to the concept of the unknowable - as though it was an absolute. It is not.

            All the Best,

            Jonathan

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              • Post #16

              I can understand why you need to lay considerable groundwork for that. Even many who do think physics is off on the wrong track are not willing to go that far, for rather deep reasons. Not too many people want to face the void. Personally it just gives me vertigo when I try, so I just hold onto the daily life business and don't push it any further than necessary. Of course, the mess the world is in, is making facing up to a lot of things necessary.

              Hi Constantinos,

              You said, "The failing of physics is in not providing us with a physical view that makes sense".

              I couldn't agree more!

                Dear Constantinos,

                A measurement is an "observation", and as I wrote in "THE CONSCIOUSNESS CONNECTION" the result of an obsevation is the origin of "awareness", which in fact is the CAUSE, our consciousness "creates" these outcomes in the for us causal beings not yet existing future.(by the collapse of the alpha-probability to a historical fact in the bète time line, which is an entanglement of the alpha-probability).

                So aren't we influencing ALL of our experiments,

                and indeed all our "isms" as you point it out.

                the extraterrestial

                Wilhelmus

                John,

                In my essay I tried to strip away all the arguments often presented to draw distinctions between Physics and Metaphysics. And to argue any modeling of 'what is' is metaphysical. Whether it is mathematical or not. Among the layers of defenses physicists put up against this recognition are: 1) the use of math in Physics to draw logical deductions. 2) the use of experiments to falsify hypotheses 3) the predictability their calculations allow for their experimental outcomes. I had another in that list which I had to cut out because of length restrictions. 4) the great advances mankind made through science.

                I hope my arguments are clear and convincing on the first three in the essay. As to the fourth, all I can say briefly is that technology and engineering and experimentalists and entrepreneurs should likely take the greatest credit for that advancement. Interestingly, these are the very people that have voiced the same concerns on Modern Physics as we have been debating in these blogs for years.

                Why is such striping away of the knee-jerk defenses physicists put up necessary? Because this is their greatest obstacle in 'making sense' of what they know! They are so intelligent and intellectually gifted. But often intelligent people are the most difficult to convince. Try arguing with an intelligent spouse!

                Constantinos

                Dear Constantinos,

                You´ve written

                ''Our understading of the universe is deeply rooted in the views we have.

                If we believe in atoms, our explanations of what happened will be in terms of atoms (...) In all cases, our explanation will only be a description of 'what happened'. Using words and ideas drawn from our beliefs.''

                This is something often overlooked by professional physicists. The ''words drawn from our beliefs'' are something created at the very start of physical theories, and physics deals much more with the manipulation of these words then with questioning their appropriateness. For instance, dynamics is about the motion of objects in space and time, but the concepts of object, space and time themselves are rarely questioned. But different ''first conceptions'' (which are different metaphysical positions), for instance about space, motion and time, may lead to different and testable physics. In this point I agree with you that physics is not immune to metaphysics. I develop this thought in my essay Absolute or Relative Motion...Or Something Else? which you might find interesting, and show how metaphysical ''first conceptions'' may lead to new physics.

                However, the metaphysical question of what the universe is seems to have no definite awnser, and I´m not even sure if it makes sense. Thousand of years of unresolved metaphysical disputes seems to confirm my hypothesis.

                I feel that all we can do is take a particular metaphysical position, develop a physical theory upon it and check it with experiments.

                Best regards, Daniel

                  Dear Wihelmus,

                  Our 'measurements' indeed are 'observations'. As are our 'understandings' measurements! In all such interactions the 'subject' and the 'object' are in 'local equilibrium of self-recognition'. We indeed influence our experiments. But not in a 'spooky way'. But because everything that comes to be known to us gets filtered through our minds.

                  I am not at this time puzzling over Consciousness in Physics. Quite the opposite, actually. I am arguing that in order to avoid all such metaphysical questions, Physics should be based on 'measurements' and mathematical truisms (not models) applied to measurements. And this I show is possible.

                  Constantinos