Quarker said:
In a double-slit experiment, an EM wave is said to travel all paths to the screen
No. If you're using QM--and really the path integral version of QM--in this way, you're not talking about EM waves any more. You're talking about quantum objects. An "EM wave" is a classical concept.
Quarker said:
even though only one path will appear at measurement.
No, this is not correct. If you are running the experiment with a normal light source of normal intensity, an interference pattern will appear on the detector screen. That pattern is produced by many "paths".
If you run the experiment with the light source at sufficiently low intensity, you will see individual dots appear on the screen, one at a time, and over time, the impact points of those dots will build up the interference pattern. But any individual dot on the screen tells you nothing about any "path". All it tells you is the location of the dot on the screen.
Quarker said:
Do any of those paths include the possibility of the EM wave traveling backwards in time?
So far we've been talking about non-relativistic QM, where there is no such thing. For the double slit experiment, this works fine--you can just look at the spatial paths from the source to the detector and assume that everything moves forward in time.
You could analyze the experiment using QFT, in which, at least on one viewpoint, there are nonzero amplitudes for paths (in
spacetime, not space) that are spacelike. But even QFT does not predict that you'll ever see, for example, a dot on the screen at a time that would imply that something traveled faster than light from the light source to the screen.
Quarker said:
Or does “all” paths mean only those paths allowed by physical laws?
It depends on what particular approximation to "physical laws" you're using. See above.