Essay Abstract

Some theories are declared as fundamental to mathematics or to physics while they are strictly speaking rather based on semi-fundamental constructs, at best. Application of complex Fourier transform (FT) on functions of time f(t) was in the 20th century and is perhaps still considered as a if not the most fundamental mathematical method of physics and technology. Actually, FT is a tool that doesn't immediately fit to measured data of real processes. Fourier assumed f(t) to extend indefinitely to both sides, mathematically speaking from minus infinity to plus infinity. This implied taking a static view of the world. The alternative dynamic view has proved the more appropriate basis: In reality, in contrast to closed models of processes, the future is more or less open to erratic influences and evades therefore complete prediction. Causality means: Only the past is absolutely closed in the sense it cannot be changed. This essay reminds of how a trick adapted the FT on real conditions where future data are not yet available and asks: Is complex FT with analytic continuation indeed a primary and indispensable fundament? There is a surprising but compelling counterargument: Instead of using complex calculus, any analysis of measured data may, in principle, be based on the real-valued cosine transform (CT). Real time audio technology benefits from CT. The missing in CT imaginary part is obviously a redundant copy. CT and FT are equivalent to each other except for an arbitrarily added to the latter point of reference, and subjectively chosen references are definitely less fundamental than non-arbitrary ones. Therefore, some putative pillars of science are suspected to be just semi-fundamental constructs on a shaky basis. Judge yourself.

Author Bio

See http://www.fqxi.org/community/forum/topic/369 . The author would like to appreciate FQXi contests and discussions guiding him in his ongoing critical and self-critical search for correct basics. His last boss had refused to comment on his IEEE paper [4] because he considered the matter as too ("so was von") fundamental.

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Dear Eckard,

THE REFERENCES ARE MISSING FROM YOUR ESSAY!

If I understand your essay correctly, your key point is that mathematics and physics are different. Physics describes the real world, while mathematics provides tools that can quantitatively model physical phenomena. When the physical foundations are unclear, mathematic models are sometimes taken to represent the physical foundations, but this is incorrect.

I agree. I give several examples along these lines in my own essay. For example, I argue that quantum entanglement is a mathematical artifact that first entered quantum theory by way of Pauli's mathematical construction to generate the exclusion principle for electrons. The exclusion principle is true, but can arise from nonlinear mathematics in a way that does not require quantum entanglement.

These issues can go beyond philosophy to have technological implications. For example, quantum computing has recently become a multi-billion-dollar enterprise, and depends completely on quantum entanglement for its success. I predict that this technology will fail, which will likely bring about a fundamental reassessment of quantum foundations, probably within about 5 years.

Best Wishes,

Alan

    Dear Eckard Blumshein,

    A tour de force! Congratulations on an incredibly information-dense essay.

    I appreciate your beginning with Fourier transforms, without which quantum mechanics surely would not exist. You have for several essays focused on cosine transforms providing insight based on your audio work. Your issues concerning t = 0 are subtle. I do agree that physicists tend to stay away from the foundations of mathematics, some actually considering mathematical structure more fundamental than physics.

    You note a truly fundamental assumption besides causality: "There is only one reality." My essay treats the fundamental nature of time essential to reality, which is universal simultaneity.

    You observe that rigorous formalizations are notorious for causing paradoxes. I observe that all special relativity (SR) texts base the derivation of the Lorentz transformation on two inertial frames, seeming to impute that the very existence of the Lorentz transformation implies the existence of two (or more) time dimensions, per Einstein. In An Energy-Based Derivation of Lorentz Transformation in One Inertial Frame I prove that two inertial frames are not required for the existence of the LT. I believe this is both mathematically and physically significant. In the first place it gets rid of the paradoxes associated with Einstein's 'space-time symmetry'-based "gedanken" experiments [based on railway examples not subject to measurement] while retaining the relativistic [energy] particle physics so well-supported by twentieth century physics.

    In a yet-to-be-published a paper I examine Einstein's faulty 'simultaneity detector' based on which he declares "the relativity of simultaneity". Deriving the Lorentz transform in one real world (one inertial frame) argues against multiple time dimensions (and all of the non-intuitive nonsense that depends from this) and leads to the classical understanding of time as universal simultaneity. His denial of this caused Einstein to admit "the now worries him seriously." Universal simultaneity is, of course, now.

    CS Peirce, as you note, insisted that "axioms are not a priori truths, but synthetic statements." Einstein's two axioms are contradicted by a one-frame derivation of the Lorentz transformation and by local gravity as ether. Again you state (p5) that "unjustified rigor is to blame for [much] nonsense." Einstein's rigorous derivation of LT in two inertial frames is the basis of much nonsense that vanishes when LT is derived in one inertial frame.

    I also like your treatment of symmetry. You say "in reality, symmetries tend to be rarely perfect." Amen. The SU(3) basis of the Standard Model is valid only if masses are equal. In reality the relevant masses differ by two orders of magnitude! Approximate symmetry is all that one finds in the real world.

    I also like:

    "Should we try and alternatively deal with some fundamentals of physics from the perspective of elapsed time-span...". I would apply this to the elapsed time of the cycle of vibration characterizing the energy of the 'clock' mechanism, and the realization that clocks actually measure energy, and only indirectly are measure 'time'. This demolishes Einstein's clock-based derivation of SR, while fully retaining the energy-time basis of relativistic particle physics. Most particle physics occurs in collisions, which obviously occur at one point in time, not in two time dimensions, as per the theology of SR.

    You then note that

    "Time t and circular frequency w constitute a pair of conjugate quantities."

    That is, time and energy! And note that circular frequency is the basis of all clocks.

    In conclusion, you say

    "Let's likewise check the historic line of reasoning behind what led to Einstein's special theory of relativity for possibly not justified analogies and generalizations."

    That, of course, is exactly what my essay does. I believe our conclusions are almost identical.

    Congratulations on a truly magnificent essay.

    Edwin Eugene Klingman

    Dear Alan,

    Thank you very much for your hint. Hopefully it is possible to add the missing references. [4] is my paper "Adaptation of Spectral Analysis to Reality". There is a version M250 available with corrections by Roland Fritzius. For instance I had written "blue-eyed" instead of naive. [3] lists my FQXi essays in chronological order:

    3.1=369, 527, 833, 1364, 1793, 2021, 2342, 3.8=2747. This 9th essay is 3009.

    Being not an expert in the history of quantum mechanics, I didn't yet deal much with Pauli's role. I got aware of some other details: Schrödinger was on vacation only equipped with his lover Itha Jünger and a tiny booklet, and in the 4th communication he explained why he introduced a complex wave function. His picture was not by chance equivalent to that of square matrices with Hermitian symmetry by Heisenberg and Born. What about the latter, I read that he objected to Robertson's metric and called the expansion of space nonsense. Speculating a lot, they all followed the piper (as Weil called him) Hilbert who even denied the arrow of time. Nobody even considered the possibility of half-matrices and unidirectional timespan, respectively.

    You are claiming that there is no Hilbert space. I agree on that it is perhaps questionable as a basis for physics. However I disagree in the sense that even Cantor's naive set theory still exists in textbooks as a mental construct. I meanwhile understand that there are two mutually excluding views in mathematics: A infinity and B infinities.

    What about quantum entanglement and quantum computing, I am cautious with predictions. If I recall correctly, the latter were already announced to function in principle at least two decades ago. Therefore I don't expect a breakthrough of them in the rest of my life.

    Best,

    Eckard

    Eckard,

    I must state that you are consistent. Your last few essays and many of your FQXi forum comments deal with the issue of Cosine Transforms vs Fourier Transforms. The fundamental issue being time symmetry with respect to the present moment.

    My education is lacking with respect to the history of Math and Physics. So I am very appreciative of the many historical references that you make regarding the development of thinking.

    You also take a novel approach to the question of "what is fundamental". You state several things that you believe are NOT fundamental. Therefore, what IS fundamental is contained in whatever remains. That's a nice touch.

    AND you zero in on a possible error that is very fundamental ... How can a theory reject the assumption that there is a medium if that theory is based upon another theory that was derived by using a medium. That's a nice logical paradox.

    All in all, this is a good essay.

    Best Regards and Good Luck,

    Gary Simpson

      Yes Gary Simpson,

      When I responded to all of the various topics of nine FQXi contests as to reveal hidden mistakes in the very foundations of science, in particular of physics and mathematics, my consistent credos were definitely understandable to every open mind and they are most fundamental:

      - In reality, the past is undeniably different from the future. Mirror symmetry up to time reversal belongs to abstract models.

      - Attributing conjectured causality (but not determinism) to nature is the only and therefore an indispensable alternative to mysticism.

      - While there is only one present moment, all other reference points of time are just chosen at will.

      - Mathematics is a tool that requires to not blindly "shut up and calculate" but to be aware how it works and how it relates to reality.

      - Having dealt for decades with complex calculus including Fourier transform, I feel competent enough in this area.

      - In case of denied inconsistencies, something might be fundamentally wrong, no matter how experimentally confirmed it seems to be.

      Initially, I did not yet see much how inconsistencies in mathematics and physics depend on each other.

      Regards,

      Eckard

      Dear Eckard Blumschein,

      I have concluded from my deep research that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

      Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

        Joe Fisher,

        My last boss, an Egyptian muslim, in contrast to octonionist Gary Simpson, understood my "consistent" criticism as a sort of fundamentalism in science.

        Gary ignored my uncommon view that already descriptions of physical reality in complex domain tend just add redundant abundance. Nonetheless he demonstrated his ability to look for utterances of mine with which he agreed.

        You seem to intend telling me something that is at least not obviously related to a single one out of my nine FQXi essays.

        Since you are again and again referring to the structure of universe, I hope you can provide answers to my questions why did Max Born suspect Robertson's expanding universe to be "rubbish" and why I as a layman cannot find a discussion among experts on this issue.

        Eckard Blumschein

        Eckard Blumschein,

        In qualifying the aim of the 'What is Fundamental?' essay contest, Dr. Brendan Foster, the FQXi.org Science Projects Consultant wrote: "We invite interesting and compelling explorations, from detailed worked examples through thoughtful rumination, of the different levels at which nature can be described, and the relations between them.

        Real Nature has never had any finite abstract levels.

        Your essay was replete with finite abstract speculation. I do not know why Max Born only suspected that Robertson's expanding universe was a load of "rubbish.". I do know for certain that all speculation about any finite abstract expanding universe am utter codswallop because

        I have concluded from my deep research that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

        Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

        Dear Eckard,

        An interesting essay...

        I noticed your discussion about the meaning of complex numbers and I have found in the analysis in my paper on the electron/positron wave functions (located here: http://vixra.org/pdf/1507.0054v6.pdf , in regards to the Schrodinger equation) the following (quoted from my comment on another essay):

        "The reason that the vectors are complex, is that the Schrodinger equation requires them to be, as it relates two vector quantities with a complex 'i' in the equation. The reason for that is that the two quantities are orthogonal - multiplying any complex vector by 'i' has the effect of rotating it 90 degrees around the origin in complex space. The vectors are actually real, but the Schrodinger equation uses this mathematical 'trick' to express orthogonality in a concise way."

        Hope this helps...

        Regards,

        Declan Traill

          Hi Eckhard,

          First of all I like very much your contribution especially the first part.

          However;

          You say : "Only the past is absolutely closed in the sense it cannot be changed.". I advise you to read the "Wheelers Gedanken Experiment"(1978).

          Alan Aspect and colleagues at the Institut d'Optique, Ecole Nationale Superieure de Cachan and the National Centre for Scientific Research, all in France ,actually performed this delayed choice experiment in 2007 with single photons.(Wheelers delayed-choice Gedanken Experiment with a single atom) click here to read it They used beam-splitters instead of slits. By removing or inserting a second beam-splitter randomly they could either recombine the two paths or leave them separate. It became impossible for an observer to know which path a photon had taken. They showed that if the second beam-splitter was inserted, even AFTER the photon would have passed the first one, the interference pattern was created ! This implicates that an articles wave or particle nature is most likely undefined until a measurement is made. It also gives an indication of "Backwards Causation" : the particle must have somehow information from the future, which could mean that this involves sending a message faster than light....THE FUTURE IS ACTING ON THE PAST.

          I hope that you also willhave the time to read my essay Foundational Quantum Reality Loops wher I give in my model an explanation of this phenomenon.

          Good luck and best regards

          Wilhelmus de Wilde

            Dear Declan,

            Just interesting? I hope we may support each other. Yes, use of complex plane or equivalent square matrices is just a trick to express orthogonality in an elegant way. Because I was a teacher of fundamentals of EE, my recent essay gave another example: R and omega L. This means, Pauli was not correct when he declared QM the first disciplin in which i is absolutely indispensable.

            What about the claimed fundamental difference between QM and classical physics, I guess we may agree.

            When my last boss called my ideas "sowas von" fundamental he understood that they were just seemingly marginal. Indeed, my reasoning has been forcing me to question some pillars of not just modern physics but also of mathematics.

            Best hopes,

            Eckard

            Dear Wilhelmus de Wilde,

            I consider Fig. 1 in your essay a good illustration that supports my opinion that Parmenides was wrong.

            What about Wheeler and his "gedanken", I wrote an essay "Shannon's view on Wheeler's credo. I learned from Nimtz hype and from the many failed mathematicians who attacked G. Cantor's diagonal argument that it is better to look for the most fundamental mistakes than to struggle with illusionists.

            While I am familiar with back propagation in neural networks, I wonder if Wheeler's construct of back causation is something new and trustworthy. The word for sunday in Russian language is voskrecenie (resurrection). I rather trust in a causality that doesn't loop within a logical circle.

            Since I admire how Klingman manages to grasp and acknowledge many valuable ideas in nearly any essay, I was curious how he could enlighten me in case of yours.

            Could you please tell me by whom and when the expression Planck area was first used? Why didn't you refer to https://en.wiktionary.org/wiki/Planck_area ? Should I take the time and read your earlier essays?

            Curious,

            Eckard Blumschein

            Dear Eckhard,

            I hope this will answer your questions on my thread:

            Wheelers Gedanken experiment is not at all a "new" idea, he proposed it already in 1978. Only in 2007 and 2015 I gave you the link to the paper in my earlier post to you) it was proven. So it seams that our "reality" is far more "strange" as we like to admit. On page 5 of my essay you will find the explanation I gave using the model of FQRL. The causality you favour is still in action , it is just one of the four loops of reality mereging from Total Simultaneity (Planck Area ?).

            The "official" meaning of a Planck Area is the square of the Planck Length, its symbol in physics is Ap. I have to agree with you that the word AREA is not a good one as I mention it also in my essay on page 4 (3.1).

            In my earlier essay The Purpose of Life on illustratio 2 (page 6) and 3(page 7) I gave an idea of the boarder between "REALITY" and the "dimension" it emerged from. The AREA is NOT an Area, and I am thinking about a new term, so thank you for pointing it out to me...

            The Euclidean Point of Reality is an emergent phenomenon (illusion). An Eternal Probability is again beyond this illusionary reality. Probabilities are also available in our Reality, and it depends on which Loop we are choosing (free will) on which probability we will make a memory. All probabilities in our specific reality represent ALL Reality Loops that can emerge from Total Simultaneity. 5 I think I will fall back on this first description of the "area wherfrom realities are emerging.

            I studied Architecture in DElft (title in 1988), which is far from Physics but encourages creative thinking.....When I was 8 years I wanted to go study physics and Einstein was my favorite scientist, till my 12th I added the then available quantum physics as a hobby...and then...my hormons started to win the war and I decided to take a CREATVE art direction : Architecture in DElft. But in the meantime Physics were still my hobby, later on accompanied with ¨Filosophy". I am living since 20 years on a farm far from society in France happily with my wife Corrie.

            So now you know me (a little).

            Best regards

            Wilhelmus

            Dear Wilhelmus,

            Since you revealed being just a hobby physicist without a profound mathematical training similar to what my EE students learned, I should tell you what a non-causal blackbox is, e.g. a non-causal filter or a usual spectrogram. A blackbox has an input and an output. Imagine for instance a mouse running in and coming out of it. Common sense tells you that the mouse must first run into it before it may come out of it. EEs don't bother much that complex theory yields the strange result that the mouse or an electric impulse can come out before running in. This has definitely nothing to do with quantum weirdness.

            Your opinion arose perhaps from reading most exciting papers. Accordingly you did not understand what I meant with resurrection (of Christ). Already Ben Akiba meant: anything repeates itself as do day and night, etc.

            What I called an EUCLIDEAN point is defined as something that has no parts. Being an ideal abstract notion, it cannot emerge in reality.

            I cannot rememer having read your essay The Purpose of Life. Already the title might have deterred me because there is no evident purpose of life. When I agree with Kadin that menkind as a whole has to limit its number of people and consumptive deterioration of earth, I see this responsibility from the perspective of all of us.

            Regards,

            Eckard

            Eckard,

            It is interesting reading through the various entries and seeing some congruence, especially among the stalwarts, as to a consensus about particular problems in physics, with the issue of time becoming paramount. It would be nice to see some of the more knowledgable members build a well stated argument that might, with the help of FQXI, get some broader attention. I, for one would certainly be cheering it on from the outside.

            Reading through your essay, I was curious if you know of Carver Meade? Here is an interview he gave a couple decades ago, that was formative in my thinking;

            http://worrydream.com/refs/Mead%20-%20American%20Spectator%20Interview.html

            I thought you would find the following quote similar to your own view;

            "That has hung people up ever since the time of Clerk Maxwell, and it's the missing piece of intuition that we need to develop in young people. The electron isn't the disturbance of something else. It is its own thing. The electron is the thing that's wiggling, and the wave is the electron. It is its own medium. You don't need something for it to be in, because if you did it would be buffeted about and all messed up. So the only pure way to have a wave is for it to be its own medium. The electron isn't something that has a fixed physical shape. Waves propagate outwards, and they can be large or small. That's what waves do.

            So how big is an electron?

            It expands to fit the container it's in. That may be a positive charge that's attracting it--a hydrogen atom--or the walls of a conductor. A piece of wire is a container for electrons. They simply fill out the piece of wire. That's what all waves do. If you try to gather them into a smaller space, the energy level goes up. That's what these Copenhagen guys call the Heisenberg uncertainty principle. But there's nothing uncertain about it. It's just a property of waves. Confine them, and you have more wavelengths in a given space, and that means a higher frequency and higher energy. But a quantum wave also tends to go to the state of lowest energy, so it will expand as long as you let it. You can make an electron that's ten feet across, there's no problem with that. It's its own medium, right? And it gets to be less and less dense as you let it expand. People regularly do experiments with neutrons that are a foot across.

            A ten-foot electron! Amazing.

            It could be a mile. The electrons in my superconducting magnet are that long.

            A mile-long electron! That alters our picture of the world--most people's minds think about atoms as tiny solar systems.

            Right, that's what I was brought up on--this little grain of something. Now it's true that if you take a proton and you put it together with an electron, you get something that we call a hydrogen atom. But what that is, in fact, is a self-consistent solution of the two waves interacting with each other. They want to be close together because one's positive and the other is negative, and when they get closer that makes the energy lower. But if they get too close they wiggle too much and that makes the energy higher. So there's a place where they are just right, and that's what determines the size of the hydrogen atom. And that optimum is a self-consistent solution of the Schrodinger equation."

            Good luck,

            John

              Thank you John, for reminding me of Carver Mead. He is renowned for utterly creative ideas and their successful applications in technology. I admire him who was "merely" trained as an EE, as was I too.

              I feel, as didn't Mead, engineers must not fear restricted by putatively fundamental laws. This is my only criticism of Klingman's otherwise flawless attitude. Klingman frankly uttered that it is "verboten" (he didn't write forbidden or taboo) to criticize Einstein and Feynman although he himself dared deriving gamma without following Einstein and using two different frames of reference.

              Being not in position to read all essays, I wonder if two issues are already sufficiently put in the due focus:

              - the role of reference points (in particular with respect to Michelson's 1923 experiment)

              - the role of action (I am only aware of one belonging essay by Andrew).

              Yes, being equipped with flexible thinking due to my training as an engineer and teacher, I don't shy back from declaring Maxwell's use of the old aether analogy just an although reasonable guess. However, I abstain from claiming that my tentative suggestion of the possibility of an alternative interpretation is more than a guess of mine. While calling propagating em waves their own medium sounds nice, this metaphor might be unnecessary.

              We don't need imagining someone like donar with a hammer if we don't yet have another lazy explanation.

              Kind regards,

              Eckard

              Eckard,

              Edwin has a point that the Institution has Einstein and various others on pedestals, but the field is currently taking various assumptions beyond the point of reductio ad absurdum. It is a bubble. Future generations of physical theorists are not going to spend their careers chasing down untestable and chaotic ideas, just because this generation has committed their careers to doing so.

              There should be some communal effort among dissidents to point this out, sort through the more compelling concepts and present the most evident in a way that at least puts down a marker. Probably a presentist argument for time would be close to the top of the list. Certainly FQXi has been laying some groundwork for this for years, but nothing has congealed beyond the forum stage.

              So the question would be as to how to push it to the next level? Safe to say, the various people who come to mind, you, Edwin, Peter Jackson, Georgina Woodward, are independent minded, but what can pull a team together is not just cooperation, but the existence of an overarching goal and that is becoming very evident.

              While this is just percolating in my thoughts and I don't have the professional authority to be officially included, I am going to try pushing toward that goal. Possibly someone from FQXi might be interested to help, possibly Zeeya Merali