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Hello Felix,

I'm just reading your essay. It's exceptionally clear and well-written in addition to being well-reasoned. I believe I agree with your findings essentially and would even want to drive the thinking further. I'll try to write down some of the thoughts that spontaneously occurred as I read the essay.

When you say

"The phenomenon of quantum field theory (QFT) has...

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Hello Felix,

I'm just reading your essay. It's exceptionally clear and well-written in addition to being well-reasoned. I believe I agree with your findings essentially and would even want to drive the thinking further. I'll try to write down some of the thoughts that spontaneously occurred as I read the essay.

When you say

"The phenomenon of quantum field theory (QFT) has no analogs in the history of science. There is no branch of science where so impressive agreements between theory and experiment have been achieved."

It's hard to say how much of that very precise experimental agreement can be credited to QFT. Though the Dirac equation is far from perfect, it's outstanding numerical success for certain calculations seems to be the star performer. Would it be fair to say that it was acquired by QFT rather than having been derived from QFT procedures? The related Dirac Lagrangian is an important part of QFT but we should probably remember that all Lagrangians, specifying path independence, are no longer applicable in a topology that is not simply connected and so have limitations. The quote by Dirac which follows really sets the tone of your later arguments nicely.

This statement you make is critical I believe:

"Then a very important observation is that, from the point of view of the measurability principle, the space has a physical meaning only as a space of events for real particles while if particles are absent, the notion of empty space has no physical meaning. Indeed, there is no way to measure coordinates of a space which exists only in our imagination."

That very much reflects a point I make in my essay that the source-less Maxwell equations (for vacuum) that are used as the foundation on which the Lorentz transformation is built do not apply rigorously to any body with which you are making a measurement on. To perform a measurement you must move a charge and then it becomes necessary to employ the Maxwell equations with sources.

Lorentz, in his book on electrons, specifically states that the Lorentz transformation is proven (valid) only in a vacuum. Voigt states also that his transformation is valid only when the the divergence of all fields is zero. The E and D fields are, in principle, zero only when there are no sources. This presents a real conundrum which is difficult to impossible to resolve within the space-time paradigm.

I'd gladly discuss more details as time permits.

Steve

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Dear Felix,

You present a very interesting and useful point of view. Particularly striking is the lack of necessity for the notion of gravitational interaction between elementary particles. A few questions and remarks:

1. As you point out, the usual approach (e.g. Weinberg) to QFT is “symmetries first,” where the symmetries arise from a “spacetime” background that is taken...

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Dear Felix,

You present a very interesting and useful point of view. Particularly striking is the lack of necessity for the notion of gravitational interaction between elementary particles. A few questions and remarks:

1. As you point out, the usual approach (e.g. Weinberg) to QFT is “symmetries first,” where the symmetries arise from a “spacetime” background that is taken for granted. Your approach seems to be “algebras first,” which eliminates the primary status of spacetime. Now, as you know, Alain Connes and his collaborators working in the field of noncommutative geometry begin with Hilbert spaces and operator algebras too. If it’s possible to do so in a few sentences, could you briefly contrast your approach to theirs?

2. You mention (page 6) that “there is no reason to believe that [Galilei and Poincare symmetries] are exact symmetries of nature,” and I strongly agree with this point. However, I am not sure if you mean that some different symmetries (such as dS or AdS) are “exact symmetries,” or if you mean that the symmetry interpretation of covariance is ultimately only an approximation. For instance, you mention (in regard to GFQT) that “sooner or later quantum theory will be discrete and finite,” and this would seem to definitely rule out Lie group symmetries in the fundamental picture. Do you expect finite symmetry groups in GFQT, or is group symmetry replaced with something else?

3. Following question 2, I will remark that I personally believe the symmetry interpretation of covariance breaks down at the fundamental level, and an alternative interpretation in terms of order theory takes over (if you are interested, you may see my essay On the Foundational Assumptions of Modern Physics for more details on this).

4. As you know, there is a version of QM that appears superficially to be diametrically opposed to your thesis, namely the interpretation “spacetime first,” where I take the terminology from the title of Feynman’s 1948 paper on what is now known as the path integral or sum-over-histories version. Of course, this approach is very general and does not actually require spacetime in the traditional sense; any partially ordered set will do (where the partial order supplants time in defining the action, which is used to weight the various paths.) I am wondering what your general view of this approach is. Do you think it is ultimately wrongheaded, or does it play some role?

5. Following question 4, I will reveal that my favorite approach to quantum gravity is a version of the sum-over-histories method, which I would call “relations first,” or “interactions first.” The partial orders used are causal orders, and Schrodinger equations, operator algebras, etc. emerge via path sums. I know this method is quite different from your approach, but I would still be grateful for any remarks you might have about it. In particular, if you know some good reason why it absolutely won’t work, it would save me a lot of trouble!

Thanks for the great read! Take care,

Ben Dribus

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