Dear Ben,

I read your essay. Your field being mathematics, as I expected, your remedy is also mathematical.In your comment about my essay, you mentioned about mathematical convenience. I agree. But convenience is more related to practical work than theory. Mathematical convenience may lead to (has already led to many) technology. The foundational question is more of theoretical nature, the question what matter actually is.

Let us suppose a lump of matter (whatever it may be) devoid of any motion. It will remain the same even after billions of years. So it is motion that causes changes. Motion is a space- time relation that can be mathematically stated, and any change can be mathematically interpreted. That is the role of mathematics.The cause- effect explanations based on mathematics need not necceesarily help us understand what that lump we call matter is. For that we require some physical assumptions about matter.

I have some assumptions about matter, and I think that it agrees with all observations, though it disagrres with the existing cause- effect explanations. However, there may be loop holes in that. So what I suggest is that the main stream scientists propose some physical assumptions about matter and verify whether these agrees with all the recorded observations.

Your suggestions regarding new mathematical approach and new experiments may sometimes lead to new technologies. The experiments can provide proof to the theory. But before that, you have to decide what physical assumption regarding matter is to be proved.

    Dear Jose,

    Thanks for the remarks. I agree that reducing physics to mathematical concepts is not necessarily very satisfying; the question of what makes the real world "real," rather than another of the myriad mathematical possibilities, has plagued scientists and philosophers for as long as there have been scientists and philosophers.

    However, I don't think that causality is a mathematical concept. Nothing causes two plus two to equal four, it just does. While you can describe a network of cause-and-effect relationships mathematically, there is nothing intrinsic to the resulting mathematical structure that identifies it as cause and effect; this is a physical interpretation.

    The point I was trying to make about "mathematical convenience" is that it can lead you to get the wrong answer. Choosing to describe physics in terms of mathematical objects whose theory is well-developed and easy to work with shifts the focus from what the physical universe really is like to what we wish it were like for the purpose of calculating things.

    I agree that ideas leading to technology don't necessarily lead to illumination. However, one could hope for both! Take care,

    Ben

    Dear Benjamin,

    I am going through your essay, but I have not yet finished. (It is interesting that there is no one formula in the body of essay, but it is very demanding mathematically. :) )

    It is interesting that you "reject the symmetry interpretation of covariance", You reject "space time is a manifold", and you have similar ideas. Can you, please, attach your ideas with my interpretation of special relativity, that space-time does not exist in empty space, although space-time of Minkowski means space-time coordinates in empty or non-empty space? I need still some time to understand your ideas, so I please you for help.

    You wrote that matter-antimatter asymmetry might indicate a problem with QFT. It is an interesting idea, and it is linked with the last paragraph in this post.

    It is interesting that such basic idea, as that of Weizsacker one why three dimensions exist, was not presented to me in University. I suppose that others also mainly have not hear this in University courses. I ask why they hide such interesting idea.

    You asked, why my theory is against Higgs boson. I defined that Black holes exist whose are superpositions of Planck's mass and mass zero. They are not against uncertainty principle (UP), I suppose. Their mass can be equal or smaller than masses of elementary particles. (So they can be elementary particles) So their masses are defined, so they need creation of mass by Higgs boson. If CERN will show that 125 GeV particle creates masses of particles, my theory will be rejected, probably. Besides, if my superposition is against UP, my theory will also be rejected. But, who know. (But my rejected theory will be more successful that superstrings, which cannot be tested. :) )

    You said "proof is lacking antimatter interacts in the same way as ordinary matter gravitationally". It seems to me, that you are wrong. Feynman wrote about this in, it seems to me, in "QED: the strange theory of light and matter".

    Other my important idea in the essay is that wave functions are less fundamental than UP. Thus, in curved space, UP is changed, but definition of wave functions is also changed. And this fact has consequences as I wrote. This Idea is not forbidden by Higgs boson. (I regret that I had not enough time to study Higgs mechanism.)

    Best regards

    Janko Kokosar

    Hello John,

    I didn't think or say that you're out to lunch, and I'm sorry you felt that way. If I wasn't in England, I'd like to take you out to lunch to make up for it. I'm sure we'd talk about time, and there might be less misunderstanding that way. I just tried to focus on an idea of yours, and felt I'd shown it to be wrong, and it seemed you kept changing the subject. But if it seemed different to you, then I'm sorry.

    Best wishes, Jonathan

    Jonathan,

    If I am wrong, then I am out to lunch, given that I don't see it.

    Chris Kennedy has an interesting essay on the evolving interpretations of the various thought experiments associated with relativity. I just don't see how insistence on one of them disproves time is an effect of action.

    Dear Janko,

    Thanks for the comments. Regarding your interpretation of special relativity, I agree with your conclusion that "spacetime" does not exist in the absence of "matter-energy," and my approach says the same thing, but in my approach this is a direct consequence of a hypothesis about what "spacetime" and "matter-energy" really are at the fundamental scale (the causal-metric hypothesis), not deduced from an argument on the basis of an existing theory (such as your argument involving the trolley and the rocket in special relativity). Arguments like yours are encouraging for such a hypothesis because they reach downward from existing theory toward a more fundamental theory, while my ideas are trying to reach upward to recover existing theory in some approximation.

    The strong form of the causal metric hypothesis treats what we call "spacetime" and "matter-energy" as manifestations of causal structure. Neither has an independent meaning at the fundamental scale; they emerge together. Other "causal theories" (such as causal set theory and causal dynamical triangulations) sometimes impose "matter fields" on causal structure, essentially by adding "weights" to the edges or vertices of a causal graph (the weights might be numbers or various types of mathematical objects such as spinors or elements of SU(2)). There might be some use in trying this, but I would prefer to try to use only the graph-theoretic structure.

    This might seem to contain too little information to describe things like particles in the standard model, but I think there might be enough information present after all. Metric recovery theorems show that causal structure can give a metric up to a conformal factor, and this can be supplied by appropriate volume information, which can also be associated with the causal graph by an appropriate rule (Sorkin uses the simplest possible rule: a constant discrete metric in his "order plus number equals geometry" motto in causal set theory).

    Many of the properties of the particles of standard model come from the representation theory of the Poincare group of symmetries of Minkowski spacetime, so already there is enough information in causal graphs to recover these properties. But there is more information: not only are other metrics recoverable as well, but the microstructure contains local information which has not yet been used. Also, the causal graphs I use are more general than causal sets; for instance, a given causal set corresponds to an entire equivalence class of "degenerate" non-transitive causal graphs, each of which specify information that is lost when taking the transitive closure.

    At the most naive intuitive level, the reason why no spacetime exists in the absence of energy is because energy involves causal relations; i.e., "things are happening" in an energetic system. As the energy goes to zero, all interactions (relations) cease; there is no causal structure because "nothing is being caused." Hence, there is no emergent geometry and no spacetime.

    Bear in mind, though, that all this is based on the hypothesis that spacetime is only a way of talking about causal structure. If this hypothesis is wrong (e.g. if there is a "background manifold") then this whole idea falls through. Take care,

    Ben

    Dear Janko,

    By the way, regarding the gravitational behavior of antimatter, a lot of money is currently being spent to test this experimentally. Here is one of many popular news articles; the paper itself is behind a pay wall.

    If this has already been proven, then a lot of people should be fired for wasting money!

    By the way, I would personally be shocked if antimatter had antigravitational properties, but some people still hold out hope that "gravitational segregation" may account for local absence of antimatter. In any case, I think it should be conclusively tested. Take care,

    Ben

    Benjamin,

    Like Julian Barbour, you create theories in which the "old" concepts cannot be found at all. This is a winning strategy in contests like this one but detrimental for science.

    Earlier you wrote: "Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales. (...) You'll have to remember that my background is mostly mathematical, and therefore I'm inclined to consider the possibility of things that most physicists "know" are wrong. This might be useful in some cases; in others it only reflects my own ignorance."

    Pentcho Valev

      Dear Pentcho,

      Thanks for the feedback. Causality is a rather "old" concept, at least according to Aristotle. In any case, to paraphrase an "old" proverb, "mathematics is a good servant but a bad master." Regarding the "bad master" part of this phrase, you might have noticed that I've repeatedly expressed the opinion that physical theories should not substitute convenient or "elegant" mathematical constructs (such as manifolds over the continuum) for clear, motivating physical principles. Hence, my own ideas are based on the simplest physical principles you can imagine: order, cause, and effect. However, regarding the "good servant" part, one cannot afford to do without the mathematical tools necessary to implement these simple principles. The physics comes first; the mathematics must be whatever is required to get the job done. Nature demands no less. Take care,

      Ben

      Jonathan,

      As per my entry, that is my subject.

      To clarify the point regarding the initial twin thought experiment, if time is a vector from past to future, one would assume the twin in the faster frame would travel into the future quicker, but the opposite is true, she moves into the past quicker. When her twin returns from the trip, in the slowed frame, she is dead and with every passing day, her live recedes further into the past. That is because she ages quicker and that is comparable to a faster metabolic rate, which was where we first diverged in our view of the discussion. It was you who transferred the topic to two observers passing each other.

      Dear Benjamin

      I see that we both intuitively believe that space-time is background free. You also understand my conclusion about my derivation of special relativity, a referee only wrote that Minkowski spacetime is so defined that time flows also in empty space. :) He also claimed many time repeated words that "derivation with relativistic mass does not give anything new". (I admit that this version needs some corrections about Duff's claims.) I hope that someone will generalize my derivation into general relativity, that influence of diffeomorphism will be easier explained.

      I agree with Machian rule, which is in one version advocated by Barbour. I think that causal relations are based on Machian rule. If we said that spin of universe is zero, then Newton's bucket do not contradict with Mach. Do you agree?

      You write that you hope that your theory will give SR and GR at large scales. It seems to me that such theories need be so clear, that we will see this without long calculations. But, who knows. Thus, for instance, I more like Weizsacker explanation of 3D than with triangulation of Loll. Maybe the theory still needs clarification about foundations, and then quantum graphity will be easier.

      I you can see I avoided causal metrics to give masses to Planckian black holes, but it will be necessary some day.

      Probably we disagree about consciousness. It seems to me that the money which enables Higgs boson, will enable also physical explanation of consciousness. Then we will see, how it is important for physics.

      Those are some my disagreements, but because of your right intuition (I hope) and because of your big mathematical knowledge I give you 10.

      Best regards Janko Kokosar

      p.s.

      I wrote the wrong book of Feynman. Feynman has a Lecture book on gravity available. Here I found his explanation why gravity of anti-particles is not negative. I do not remember it precisely, but it is worth to read it.

      Any theory dealing with (or rejecting) spacetime should be able to provide an EXPLICIT DERIVATION of the constancy/inconstancy of the speed of light, or at least advance either the constancy or the inconstancy as an assumption and then derive conclusions from it. I am afraid your confession:

      "Regarding the constancy of the speed of light, my guess would be that a concept like this only makes sense at sufficiently large scales. (...) You'll have to remember that my background is mostly mathematical, and therefore I'm inclined to consider the possibility of things that most physicists "know" are wrong. This might be useful in some cases; in others it only reflects my own ignorance."

      ...shows that your approach is incommensurable with the speed of light problem. So is Julian Barbour's Shape Dynamics.

      Pentcho Valev

      Benjamin,

      If "The central new principle I propose is the causal metric hypothesis, which states that the metric properties of classical spacetime, up to overall scale, arise from a binary relation, which I will call a causal relation, on a set, which I will call a universe... Mathematical tools necessary to implement these ideas include a synthesis of multicategory theory and categorification in abstract algebra, involving interchangeability of objects, morphisms, elements, and relations; a version of graph 11 dynamics more sophisticated than versions involving uniform probabilities;and the theory of noncommutative algebras over sets with partially defined operations"

      Then your attempt to introduce Some sort of Set-theoretical /Category-theoretical Evolution of Minkowsky spacetime Without Complex Numbers can faced with unavoidable necessary of destruction of some advanced areas of established mathematics and quantum physics... I know you understand it, but pure mathematical doubts on Minkowsky-Einstein complex( number) theory of time can suggest more elegant way to prove some your intuitions...?

        Dear Pentcho,

        Well, you will have to give me time (no pun intended). I have never represented the ideas I discuss in my essay as a complete "theory." The causal-metric hypothesis is just that, a hypothesis, and the ideas so far I term an "approach." A physical theory must eventually make predictions and connect with known physics, or it is not worth the paper it is written on. However, this takes time. I have been thinking about this for three years. Your criticism might be perfectly valid if 1000 people had been thinking about it for 30.

        You seem delighted with my admission of possible ignorance, so I have given you an even better quote above: "A physical theory must eventually make predictions and connect with known physics, or it is not worth the paper it is written on." Feel free to repost it as many times as you wish. No one knows very much about physics compared to what there is to know.

        The problem we were asked to address was "which of our basic physical assumptions are wrong?" It was not, "analyze the implications of the Michelson-Morley experiment." I will opt to interpret your interest in the foundations of relativity in a positive light, as a reflection of your zeal for the integrity of natural philosophy. But please bear in mind that it is counterproductive for everyone to be forced to work on the same problem. Cause and effect is more fundamental than the speed of light, or any speed for that matter, yet I don't insist that you make any definitive statement about causality. Feel free to work on any problem you wish, and please suffer me to do the same. Take care,

        Ben

        Dear Janko,

        Thanks for the feedback. I will see if I can find what Feynman said about this... I always appreciate his point of view.

        Regarding Machian ideas and shape dynamics, a number of us (me, Lawrence Crowell, Sean Gryb, Flavio Mercati, Daniel Alves) have been discussing the possibility of a duality or complementarity between causal theory and shape dynamics. Shape dynamics derives an arrow of time essentially from an asymmetry in configuration space, whereas I take it to be fundamental, but these two ideas need not necessarily contradict each other. Part of that discussion is on my thread, and part of it is scattered about on the other threads.

        Regarding the recovery of relativity, many the ideas specific to relativity (as opposed to Newtonian mechanics) are clear in causal theory; in fact, causal theory is more a generalization of relativity than anything else, since it is in relativity that the primacy of the causal structure and the ideal of background independence are clearly embodied. The technical difficulty comes in recovering manifold structure, and the point of view is that this is really unnecessary to all the important physical ideas of relativity. This will take work, because these ideas are currently expressed in geometric language. If Riemann had been around to advise Einstein rather than Minkowski and his friends, he might have showed him that there are many possible formalisms for expressing his physical ideas that don't involve continuum manifolds.

        I don't know enough about consciousness to agree or disagree with anyone about it, though I think it can't be deterministic. I like to read about it, though! Also, I appreciate the rating! Take care,

        Ben