Chen, Lu and Read, James (2023) Is the metric signature really electromagnetic in origin?The paper is interesting, but the 4-metric signature +++- is mainly a consequence of causality, be it electromagnetic or anything else.
Causality requires that events only affect nearby events. If spacetime were Euclidean, with metric signature ++++, then an event could be close to an event outside its light cone. Affecting that nearby event would mean going faster than light. Action at a distance.
Electromagnetic effects do not go faster than light. You need the non-euclidean geometry of a +++- signature metric. Once you accept all that, Maxwell's electromagnetism is one of the simplest possible field theories, compatible with the geometry.
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ReplyDeleteDear Roger,
ReplyDelete1. Rapidly browsed through the cited paper, thinking that they might have settled, once and for all, the West Coast vs. the East Coast issue. No such luck!
2. About violation of causality, i.e., IAD (instantaneous action-at-a-distance):
Prof. Andreas Weiler in his notes ``Relativity, Particles, and Fields,'' first says (on p. 13):
``We find a small, exponentially suppressed amplitude but still non-zero outside the light-cone, *causality is still violated*.'' [emphasis original]
One paragraph later, he then says:
``Quantum field theory finds a miraculous solution to the causality problem: the propagation across a space-like interval is indistinguishable from the propagation of an anti-particle in the opposite direction. We will find that the amplitudes for particle and anti-particle propagation exactly cancel outside the light-cone --- causality is preserved!''
Other people too say that there is no IAD in a (relativistic) QFT.
If the essence of their argument is captured by the above explanation, then I would say that it's not so water-tight an argument. QFT hasn't solved the measurement problem, has it?
My ontological-conceptual argument (translatable in mathematical terms) suggests that a degree of IAD (more than the exponentially suppressed) is possible. One of the main reasons: Evolution must be unitary. [Other reasons require too long a context building.]
When it comes to *relativistic* QFT, people mostly work with Lagrangians, and in that approach, unitarity is not obvious. You need the Hamiltonian approach to see it. That may be another basic issue here.
The URL for Weiler's notes:
http://users.ph.tum.de/aweiler/lectures/rpf_weiler_3-8-17.pdf
[ I got to know about these notes starting from the first answer at:
https://www.quora.com/Whats-the-best-resource-to-learn-canonical-quantization-for-someone-who-learned-the-path-integral-formalism-first-Peskin-and-Schroeder ]
Best,
--Ajit