The object is to show that, in a non-simply-connected spacetime, a physical effect can depend on the potentials, and not just the fields.
Mathematically, the field is the curvature of a differential geometry connection, and a connection is the infinitesimal relation between nearby points. The physics depends on the connection, and not just the curvature.
This is portrayed as a great paradox, with physicists being split on how to explain it. Some resort to nonlocal nonsense.
Bohm himself was a Communist, as the video explains, and he had weird beliefs.
There are indeed a lot of papers on this subject, but it is all long-settled. Eg, see this paper claiming Impossibility of Gauge-Invariant Explanations of the Aharonov–Bohm Effect. I do not get what this paper is saying, as all the observables are gauge-invariant.
Lenny Susskind's AI impostor explains it somewhat in this video. These AI videos are amazingly good. I wonder what the real Susskind thinks about fake videos being better that his real lectures.
The point here is that curvature is a measure of something being curved. It should not be surprising or paradoxical that the something has physical significance.
The argument is given that the potential cannot be real, if two different potentials give the same fields.
The examples are not really two different potentials. The two potentials correspond to the same connection. The connection is what is real.
Besides, there are lots of physical variables that depend on choices. Measuring height depends on choice of coordinates. Measuring momentum depends on a reference frame. Wave functions depend on a choice of phase factor.
This comment has been removed by the author.
ReplyDeleteWell, on second thoughts, my above comment hasn't come out right --- its phrasing. So, I am deleting it. But yes, as I said in it, I will write something about this issue of potentials and fields (as it appears from viewpoints of both ED and QM), at my blog. Not all aspects, but many of the most important ones. I will also try to cover a bit about the AB effect. (It won't be possible to address all the points physicists and mathematicians have said about it --- they both have both hyped and anti-hyped this issue far too much. But I will try to cover the main essentials of the scenario itself.)
ReplyDeleteBest,
--Ajit
Dear Roger,
ReplyDeleteWell, on the third thoughts:
ping: https://philsci-archive.pitt.edu/: Name or service not known
Also ditto for the other papers you mentioned in the recent past.
Just to let you know, after days or so... .
Best,
--Ajit