If you read Einstein’s 1917 paper on Blackbody radiation: “Zur Quantentheorie der Strahlung”

Einstein stresses the fact that an important difference between classical radiation and quantums of light is that a quantum of light is always pointed exactly in one direction.

This distinction doesn’t exist any more since Wheeler-Feynman Electrodynamics.

I am not very familiar with Neutral Differential Delay Equations, but I was very impressed by the work by Jaime de Luca calculating radiation-free solutions to the twobody and double slit problem.

https://scholar.google.at/citations?hl=en&user=PoyxoUoAAAAJ&view_op=list_works&sortby=pubdate

]]>It looks like that file, which someone had on Google Drive, is gone. The paper is this:

• C. J. Eliezer, The hydrogen atom and the classical theory of radiation, *Proc. Camb. Phil. Soc.* **39** (1943), 173–180.

but it’s not free from the journal, unfortunately!

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Yes, it’s great! I think I gave enough information to reconstruct it, but it’s a lot easier to read his papers, and even that isn’t *extremely* easy. These are the best:

• J. Kijowski, Electrodynamics of moving particles,

*Gen. Rel. Grav.* **26** (1994), 167–201. Also available at http://www.cft.edu.pl/~kijowski/Odbitki-prac/GRG-NEW.pdf.

• J. Kijowski, On electrodynamical self-interaction,

*Acta Physica Polonica A* **85** (1994), 771–787.

http://www.cft.edu.pl/~kijowski/Odbitki-prac/BIRULA.pdf.

Thanks for catching that! It was due to a flaw in my algorithm for converting ‘ordinary’ LaTeX to WordPress LaTeX. Fixed!

]]>Thanks—fixed!

]]>Peter Morgan wrote:

do there have to be points?

Maybe not! Try to develop physics without them and get back to me!

The real issue is not so much the points *per se*, as the tendency for answers to interesting physics questions to be infinite or undefined. There are purely formal ways to avoid mentioning points just be rephrasing everything, but the ways that I know don’t eliminate these problems.

The points in probability theory are points in a purely formal space of “outcomes”, called the sample space. It’s a measure space. The individual points in here don’t matter if they have measure zero. As my advisor Irving Segal emphasized, we can avoid talking about these points using algebraic integration theory. But he proved this formalism is equivalent, in a certain sense, to the usual one.

The points I’m talking about here are points in spacetime, which is something like a Lorentzian manifold.

Ultimately, when we take quantum gravity into account, it seems highly unlikely to me that spacetime will be modeled as a Lorentzian manifold. However, despite dozens of different proposals, nobody really understands quantum gravity yet.

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