On the Foundational Assumptions of Modern Physics by Benjamin F. Dribus

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

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

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

Dear Sergey,

250 is quite impressive; I have not managed to understand that many so far. At this rate, you will have read every entry in the contest within another week or so. I appreciate the rating. Take care,

Ben

Dear Michael,

Thanks for the feedback! The complex numbers are undoubtedly the workhorse of much of modern physics, and avoiding them, if it's even possible to do so, will certainly require a great deal of work to achieve the same explanatory power, let alone surpass it. You might ask, "why, then, abstain from the complex numbers at all, if they are so useful?" The important word here is "useful." Many of the properties that characterize the real number continuum, and by extension the complex numbers, are mathematically "useful" without having any clear physical meaning. Even if there were not physical reasons to doubt that spacetime is infinitely divisible (of which there are many), properties like the least upper bound property of the real numbers would never be directly relevant to physics. Even worse, paradoxes like the Banach-Tarski paradox (you can pull apart a solid sphere into nonmeasurable sets and reassemble them into two spheres identical to the original sphere) show that the real and complex numbers have properties that are not only physically irrelevant, but also physically absurd.

But I am not sure if this answers your question? (I suspect it doesn't!) In any case, I see that you have an essay here about an interesting subject, so I will read what you wrote before making any further remarks. Take care,

Ben

Dear Pentcho,

I have heard of a certain company that offers to name distant celestial objects after its clients in exchange for a fee. Calling the causal relations of the universe "mine" would be an even more absurd presumption of ownership.

I'm afraid that suggesting that causal relations are superfluous because spacetime is a large-scale manifestation of them is like suggesting that the pixels on your screen are superfluous because they form a picture. Try doing without them!

Regarding the constancy of the speed of light, "speed" means "change in distance per unit time." Distance and time are both metric concepts. When one begins with something other than a metric, "speed" must be viewed as a secondary, rather than a primary, concept. No assumption must be made about it whatsoever. Take care,

Ben

Dear Michael,

I realize after reading your essay that my answer to you above was mostly irrelevant. Hence, I have left some additional remarks on your thread. Take care,

Ben