Abstract: simple considerations of a philosophical, non computational, nature, on Space, Time and the Quantum show that the former two are not basic (and that some apparently most baffling traits of the Quantum are intuitive!). Progress in knowledge of the interdependence of things should not be hampered by traditional prejudices. (Not an easy essay: readers are encouraged to jump around it like kangaroos!)


What is time? Today’s physics does not answer that question, it just computes with the notion as if it were obvious. To find out what time could be, a little bout of metaphysics different from the tentative one in today’s understanding of nature, is needed.

Einstein amplified the notion that the universe is about spacetime (x,t) in a reference frame F. He, and his friends Hilbert and Besso used the mathematical, and physical ideas, created by Riemann (and his Italian successors: Ricci, Levi-Civita, etc.)

"Solitary and Uncomprehended Genius"

Riemann: “Solitary and Uncomprehended Genius” (Poincaré said)

Lorentz discovered one had to assume that (x’,t’) in a moving frame F’ cruising by at a steady speed v is related to (x,t) in frame F according to the Lorentz transformations.

Lorentz got the Nobel Prize, for finding these (thanks to the recommendation of the towering Henri Poincaré); I am not pointing this out to compare the relative merits of celebrities, but to establish the hierarchy of the discoveries they made, and thus the logic therein. (Poincaré’s 1904“Principe de Relativite’” was firmly established before Einstein showed up on the scene, and the latter’s contributions, although enlightening, have been vastly overestimated.)

Not that the initial logic of a discovery always perdures, but sometimes it’s important. The Einstein cult has been obscuring reality; Einstein would have been the first one to decry it (Einstein basically ran away with the idea of Poincaré that the constancy of the speed of light, c, being always observed, was thus a fundamental law of physics, and made it the foundation of what Poincare’ called “Relativite'”).

Only by using the Lorentz transformations are the equations of electrodynamics preserved. In other words: only thus is the speed of light measured to be c in both F, using (x,t) and F’, using (x’,t’).

So what is time t?

According to the scheme in Relativity, it’s simple: given the sanctity of the speed of light, c, and space x, time can be measured by having a photon of light going between two perfect mirrors, and counting the impacts (that’s what is called a light clock; it’s very useful to derive most equations of Relativity).

Indeed space is measured by the time it takes light to go back and forth. This sounds like a circular logic: time is needed to measure space and space is needed, to measure time.

Does that mean one of the two, say, time, is derivative?

I used to think so (propped by the lack of time in Quantum Theory, see below). But, actually, no.

Indeed, time can be localized down to the proton scale.

One can measure time at that scale with how long it takes some elementary particle to decay. Or because to any particle is associated its De Broglie wave, hence a frequency (and that particle can be confined in as small a space as a proton).

Basically time can be measured at a point.

However, space, by definition is… non local (space is always an extent, all the more if time is used to measure it, thanks to c; technically my idea is that space depends upon the holonomy group, time does not; thus Minkowsky’s “spacetime” belongs to the dustbin!).

Thus the conceptual universe in which bask electromagnetism makes it look as if, somehow, time was more fundamental.

The situation is the exact opposite in Quantum Theory. Quantum Theory is full of entangled situations. Measure such a situation somewhere, and it changes all over. “Measure such a situation somewhere, and it changes all over” means that a Quantum Process is all over it. Whatever “it” is. Einstein called that “spooky interaction at a distance”. I call it the QUANTUM INTERACTION.

Einstein tried to escape the spookiness. Instead, I claim it should be embraced. After all, Quantum spookiness makes life possible.

We indeed know now that this spooky Quantum interaction is fundamental to life. It allows life to be more efficient than any understanding from classical mechanics could have it. Vision and the chlorophyll molecule use Quantum spookiness at a distance. This recent discovery did not surprise me at all. I fully expected it, just as I fully expect that consciousness will be revealed to be a Quantum effect (an easy prediction, at this point, in this Quantum universe!)

A computer using the Quantum Theory would be more efficient, for the same reason: the Quantum computer computes all over, in a non local way. (The computers we have now are just sleek electron-using versions of the classical computers the ancient Greeks had, with their little teethed wheels; the Quantum computer is founded on a completely different process.)

This “spooky” non locality has alarmed many a thinker. But notice this simple fact: space itself, even the classical space used in electromagnetism, is non local (as one uses light travel, plus time, to determine space).

So it’s only natural that space in Quantum Theory be non local too.

The “spookiness” is easily understood thus: spacetime physics a la Einstein and company singles out a particular interaction, electromagnetism, and the sanctity of c, to measure the universe with. Why this one, and not another of the fundamental interactions we know?

Quantum Theory (QT) gets out of this would-be choice by choosing none of the traditional forces to measure space with!

As QT has it, as it stands, QT does not need to measure the universe. (I believe it does, using the Quantum Interaction, and I can support that with impossible simultaneous measurements at great distances, but that’s another, more advanced set of considerations.)

Those who think thinking is reduced to computing will object that it is not the same type of non locality (the one I claim to see in classical space and the “spooky” one of Quantum space). Whatever: the non locality in quantum Theory does not depend upon light speed. That’s the important point.

There, the lesson cannot be emphasized enough: on the face of it, the basic set-up of Quantum Theory tells us that light, and, in particular light speed, is NOT fundamental.

This few observations above should they prove to be as deep and correct as I believe they are, show the power of the philosophical method, even in today’s physics. Some will scoff, but not consider carefully all the philosophy behind spacetime a la Einstein.

A warning for those who scoff about the importance of meta-physics: the founding paper of differential geometry in mathematics, and physics, was a lecture by Bernhard Riemann. It’s full of metaphysics and metamathematics, for the best.

The paper had just one equation (and it is a definition!)

That lecture was entitled “Über die Hypothesen welche der Geometrie zu Grunde liegen (“On The Hypotheses Which Underlie Geometry“). (Call these “hypotheses” meta-geometrical, metamathematical, or metaphysical.)

The lecture was published in 1868, two years after his author’s death (and 14 years after he gave it). Riemann’s main idea was to define manifolds and curvature. (Riemannian) manifolds were defined by a metric. Curvature ought to be a tensor, Riemann said, not just a simple number (scalar; as Gaussian curvature).

From top to bottom: positive, negative and no curvature.

From top to bottom: positive, negative and no curvature.

Riemann generalized the notion of curvature to any dimension, thanks to the Riemann Curvature Tensor (the simplified Ricci form of which appears in Einstein’s gravitational field equation).

Here is for some meta-physics; Riemann: “It is quite conceivable that the geometry of space in the very small does not satisfy the axioms of [Euclidean] geometry… The properties which distinguish space from other conceivable triply-extended magnitudes are only to be deduced from experience.

Gauss, Riemann’s teacher, knew this so well that he had tried to measure the curvature of space, if any, using a triangle of tall peaks. Gauss found no curvature, but now we know that gravitation is best described as curved spacetime.

(This lack of Gaussian curvature shows that it’s not because situation is not found under some conditions that it is not there under other conditions; in biology the proof by Medawar that Lamarckism was false, using mice, for which he got the Nobel (being British, ;-)) comes to mind: no Lamarckism in Medawar experiments did not prove that there would be no Lamarckism in other experiments; now four Lamarckist mechanisms are known!)

Twentieth Century physics, in particular the theory of gravitation, exploits the following fact, understood by Riemann as he laid, dying from tuberculosis in Italy. Force is a tautology for geodesics coming closer (or not). Thus curvature is force.

Einstein remarkably said: “Only the genius of Riemann, solitary and uncomprehended, had already won its way by the middle of the last century to a new conception of space, in which space was deprived of its rigidity, and in which its power to take part in physical events was recognized as possible.”

(I find this statement all the more remarkable and prophetic in that it is not in Einstein’s physics, and could not be, but rather in the one I would like to have, where fundamental dynamic processes literally create space…)

The fact that a tautology is at the heart of Einstein’s Theory of Relativity means that it explains nothing much! (Relativity fanatics are going to hate that statement!…although it describes very well what happens to objects evolving in spacetime, especially GPS, let it be said in passing.)

“Only to be deduced from experience”, said mathematician Riemann. What’s the ultimate experience we have? Quantum Theory. And what did we find QT said? You can’t measure with space, you can’t measure with time (although clearly the Quantum depends upon the differential topology of the situation, see the Bohm-Aharanov effect! where, by the way, the space metric is made fun of once again!)

Last splendid idea from Riemann (1854-1866):

“Researches starting from general notions, like the investigation we have just made, can only be useful in preventing this work from being hampered by too narrow views, and progress in knowledge of the interdependence of things from being checked by traditional prejudices.”



Patrice Ayme

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  1. Paul Handover Says:

    I can’t match your essay with an equally profound comment; can’t even come close! So will lower the tone by saying ….. golly, can’t even think of cheap saying! 😉


    • Patrice Ayme Says:

      Dear Paul: Well, take your time! :-)! I am pretty sure that most theoretical physicists would understand not the big ideas in the essay.This is actually extremely original research. I have been thinking of these issues for decades. And I have noticed a few points that have not been pointed at before.

      As I am a research mathematician, I could have used bigger words. I use the fact that physical space depends upon the holonomy group, whereas time is pointwise. This is a big time remark. Funny it was not done before.

      But there are precedents for pretty obvious stuff not being noticed: none of the geniuses who founded Quantum Mechanics, either of first generation (Einstein, Bohr, etc.) or second generation (De Broglie, Heisenberg, Schrodinger, Dirac, Born, Pauli, etc.), nor the founders of Quantum Electrodynamics (Dirac again, Schwinger, Feynman, Yukawa, Dyson, etc.) noticed than in the De Broglie(“-Schrodinger”) equation the POTENTIAL was on the right hand side.

      Noticing this allowed Bohm and Aharanov to predict their effect, which was noticed instaneously…

      But I have nothing instantaneous to roll out…


      • Paul Handover Says:

        Gracious, would love a few hours in your company – ever in the vicinity of SW Oregon? (And I mean that seriously!)

        Of course, granted that Jean and I could offer you the space and time! 😉


        • Patrice Ayme Says:

          Thanks Paul, I very much appreciate, and feel honored. It would come to my mind if I headed towards Mt. Shasta. Yet I am a full parody of the hyper intellectualized hermit. Otherwise I could not write as I do (let alone think). Getting me out of my ivory tower seems related to the virtual processes of Quantum Physics…


  2. de Foucaud Paul Says:

    sorry to answer in french !
    Ce passionnant sujet, de mon humble point de vue, aurait mérité une approche de synthèse s’agissant des “considérations philosophiques simples” évoquées au début de cet essai.
    “Amen” semble alors en être un grand raccouri si elle en est une, de votre point devue.
    “Ainsi soit il” et poursuivons un peu :
    Nos récentes connaissances sur l’univers montrent notre vision rapprochée du Big Bang à sa naissance, jusqu’à un instant où la physique Quantique (Plank) ne s’applique plus.
    En d’autres termes simples : un début d’espace oú il n’est plus possible de définir une unité de distance donc ensuite celle d’une vitesse, position, accélération etc.
    Ceci amène alors naturellement à considérer qu’à la naissance de l’univers, les 4 forces fondamentales de la physique connues à ce jour (gravitationnelle, électromagnétique ou FEM, énergie atomique faible et forte)
    ne pourraient n’être qu’une seule force encore considérée comme unifiée.
    Philosophiquement, ceci nous conduit naturellement à concevoir un univers sans dimension (celui de lhommo sapiens)
    Ainsi, en regardant de plus près ce nouveau point de vue, la physique et les mathématiques fusionnent pour donner une constante sans dimension de l’univers au Big Bang : 1/137.0…
    Nombre sans lequel notre Univers ne pourrait exister et permettre la vie.
    Ce nombre ainsi déterminé par d’éminents scientifiques pose à lui seul la question de son inventeur !


    • Patrice Ayme Says:

      Cher Paul: The Big Bang is a very complex theory that crucially depends upon a number of bold interpretations and hazardous hypotheses (for example the “INFLATON” field, never observed). The probability that the BB, as considered today, turns out to be true, seems extremely low to me.


      • de Foucaud Paul Says:

        as a generalist  within all  areas of science known on  theese times  inbound to become à fighter pilot during a  long time and still surviving now.
        So, my experise seems  different from  yours, might be complementary.
        At speed in the air at M2+ is no a question to go faster for
        human beeing thoughts.
        Then, when  not to have the idea to go the limits ?
        Iinvolved in front of death, time is looking as contracting, why ?
        Pure conciousness is on this crucial time , why ?
        Then, I would  be happy to get from you  a synthesis of your essay about  “philiosphical  considération…”
         what are they ?

        PS : be cool with theese anglosaxon sentences, I made them with my best.


        • Patrice Ayme Says:

          Cher Paul: Mon francais est encore meilleur que mon anglais, donc vous pouvez ecrire vos commentaires en francais.

          I answer in English for the general audience (but I know several languages beyond). One reason why time slows down with death approaching is that the processing can get very intense. I got nearly killed a few times, and each time I have noticed that seconds felt like minutes. One reason is that the brain is hyper mobilized and hyper concentrated, so a tremendous quantity of processing occurs. Not necessarily to be remembered fondly later… (So it’s a cause of post=traumatic stress…)

          I think the essay will be indeed, as you suggest, profit from having a crisper, more compact version. Maybe I do that, but no time now. Another solution is re-read it and ask for the elucidation of particular detail(s).


          • de Foucaud Paul Says:

            Thank’s Patrice for this comment.
            I am reading and reading again this essay to be abble to find ” la substantifique moelle”.
            I will tell you what is my is my understanding en français if too much difficult otherwise.


      • EugenR Says:

        Dear Patrice, i come back again to cosmology.
        I just read in New scientist there are some doubts about the inflation theory of the Big Bang. Viz;

        Does it not open the question to an alternative creation theory? Like the big spin, i exposed here in your blog farther on?


        • Patrice Ayme Says:

          Dear Eugen; Big Bang cosmology is OBVIOUSLY wrong.


          Because it depends upon Cosmological Inflation. That, in turn, has at least three drawbacks:
          1) It depends upon the unobserved INFLATION field and its unobserved INFLATON.

          2) It violates energy conservation.

          3) It creates universes everywhere, all over.

          BTW, the universe, as observed, is not symmetric, another problem for the BB…

          I have my own theory, and fully expect the universe to be at least 100 billion years old…

          What was the essence of the “big spin” already?

          Thx for attracting my attention to the article you linked, I will get there ASAP (probably not today!) I love cosmology.


  3. EugenR Says:

    Dear Patrice, You just exposed yourself as a mathematician and i would like to expose to you a naive idea (maybe very childish, since it is not my field of expertise), but i will allow myself to play a child with an idea of alternative theory of creation to big bang. I don’t have the mathematical tools to check what it actually means, and maybe you can easily turn the idea into rubbish.

    So here is my hypotheses. Is it possible that the Universe itself is spinning and creating an immense eccentric force that causes acceleration of the Universe’s expansion? Is it possible that the dark energy is nothing else but this centrifugal force? Maybe also the big bang was not so much a big bang but an enormous spin? If everything else is spinning why “ausgerechnet”, the Universe is not?

    Since the universe is expanding in all directions evenly, to prevent its expansion in one particular axis, it should be an big number of AXIS spin? It is hard to imagine but mathematically it could work. Of course the spin at the beginning has to be of something bigger than zero, and the number of spin axes has to be smaller than infinitive number. Otherwise, as i can understand couldn’t be the asymmetry between the matter and antimatter, that is essential to the creation. By the way, this could probably explain this asymmetry.

    I wonder if the universe spins in velocity of speed of light, what size the first dot of creation should be before it starts to spin and how many axes of spin we need to create enough angular momentum to support the existing expansion rate of the universe at speed of light. Maybe it would even explain the phenomena of increasing acceleration rate of Universe expansion by increased speed of spin.
    The limit of speed of light, would be probably caused by the speed of spin. Is it possible that if the spin velocity increases the speed of light increases too or the time shortens?

    As to my idea, this spin energy is the energy of creation, translated to energy (spin or spring vibration or any other movement) we can observe in the Universe.


    • Patrice Ayme Says:

      Dear Eugen: Most pure research mathematicians know no physics (that’s often how they define purity…). However, I am a mathematical physicist, so I am in my element.

      The Big Bang always depended upon enormous accelerating expansion (“cosmological INFLATION”). Now it has gotten worse, because it looks as if the expansion were accelerating. Inflation precludes expansion from angular momentum, as you suggest (although you get a prize for innovation: I have heard a lot, but never that particular one!).

      Rotating Black Holes do behave differently from static ones, so your idea is not crazy.

      The BB is a theory of expanding SPACEtime. Not just a theory of flung out matter, expanding. Although matter within space cannot go at more than c within a delimited neighborhood inside a local reference frame, SPACEtime is not so limited.

      The weakness of the BB is that, although a plausible theory, it supposes lots of things on the way, and one gets very different theories by supposing less outrageous hypotheses…


      • EugenR Says:

        Your answer is very encouraging. So let me develop a bit the idea of the Big Spin.
        I see in the model several variables that can be played with;

        1. The speed of spin, which can be at speed of light, below, but maybe even above, since it is beyond the observed universe. Eventually speed of spin can even accelerate, and this would explain the speeding up of the rate of the universe expansion.
        2. The size of the dot that had to spin before it inflated. Intuitively seems to me it has to be bigger then 0, otherwise what would spin? What about one Planck’s constant size? would it be sufficient? If yes, maybe this could somehow connect the Big Spin to the quantum theory, i am not sure i can figure out how. But this is just an idea.
        3. The number of axises the dot spins. It cant be infinitive, because it would need infinitive energy, and the Universe energy seems to be finite.
        4. And then you have the time and speed of light that is the other side of the same coin. Was the time same at the beginning of time as now, and with it the speed of light?

        If you start with constant spin speed at existing speed of light, and constant dot size to spin of Planck constant, it shouldn’t be hard to calculate the number of axises you need to create all the energy you have in the observed universe. Would its angular momentum be enough to create an all direction expanding universe? If yes, wouldn’t it be a finding with certain value?


        • Patrice Ayme Says:

          Dear Eugen: Your model would fit a linear “Hubble” expansion law. Unfortunately, as I said, the usual BB model has an enormous inflation, to start with, and now apparently we observe an accelerating inflation.

          Another problem is that in a rotation appears a so called “Coriolis force”. On Earth, it causes “Trade Winds”. In space, it would cause something similar, on a larger scale, a systematic Coriolis deviation. an anisotropy of the universe. To my knowledge that has not been observed (although some other features seem present, of unknown origin). it would in particular affect cosmological photons (redder in one direction than in another).

          Still another problem would be that the tremendous acceleration necessary initially would prevent the gathering of matter long present, and observed, as gravity would be nothing relative to that acceleration.

          The usual Big Bang is in part here to convince the public that the “Standard Model” is of some use (that’s my cynical view of it). Although, personally, I think it’s interesting by itself. It’s true it provides a neat explanation of the 3K cosmological background radiation…


  4. Pretentious chat of neophytes about physics | EugenR Lowy עוגן רודן Says:

    […] Ayme Says: August 11, 2013 at 9:14 pm | […]


  5. Lorentz and Einstein | cartesian product Says:

    […] Quantum Trumps Spacetime (patriceayme.wordpress.com) […]


  6. Non-Conservation Of Energy & Multiverse Madness | Patrice Ayme's Thoughts Says:

    […] It just means one has to go back to Riemann’s intuition of the 1860s, and reconsider it carefully. Riemann tried to reduce force to geodesic separation. I would suggest to reduce energy to a function related to geodesics density. As geodesics separate, energy is put in the system. With this notion, the fact that it costs nothing to create a universe disappear. https://patriceayme.wordpress.com/2013/08/08/quantum-trumps-spacetime/ […]


  7. Not An Infinity Of Angels on Pinheads | Patrice Ayme's Thoughts Says:

    […] “map” and “territory”. But I am a differential geometer, and the essential idea there, from the genius B. Riemann, is that maps allow to define […]


  8. Patrice Ayme Says:

    [Sent to Scandinavian education journal suggesting to teach “Einstein’s theory, 2018.]

    The idea that forces can be modelled by changing the distances between geodesics (that is the curvature) was introduced by Bernhard Riemann in 1868. Riemann introduced in the same doctoral lecture the notion of multidimensional manifolds (like the 4 dimensional space-time used in GR), and curvature.

    A warning for those who scoff about the importance of meta-physics: the founding paper of differential geometry in mathematics, and physics, was a lecture by Bernhard Riemann. It’s full of metaphysics and metamathematics, for the best. The paper had just one equation (and it is a definition!)

    Lorentz and Henri Poincaré later established the Theory of Relativity, including E = mcc. Henri Poincaré published gravitational waves according to Relativity on July 5, 1905 (Laplace had done so for his theory of gravitation, a century earlier). Einstein was important, but not as important as the preceding scientists. Attributing everything to Einstein violates logics, science and history, while cultivating childish celebritism, a form of personality cult.


  9. Momentum, Force, Inertia, Middle Ages, Buridan | Patrice Ayme's Thoughts Says:

    […] is incredibly modern (the idea is found in Riemann ~ 1860 CE, as I explained within the text of “Quantum Trumps Spacetime”). This was all in Buridan’s work, in the Fourteenth Century (14C).  Jean Buridan postulated the […]


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