Guys,
Let me ask you the silliest question of the year. I am looking at the Maxwell equations in their standard form. No 4-dim potential A, no Faraday tensor F, no mentioning of special relativity - just the standard form from a college-level textbook.
I know that the eqns are NOT form-invariant under the pure Galilean transformation (addition of a constant velocity). That's fine.
Now, how about the other subgroups of the full Galilean group?
That the equations are form-invariant under time-independent spatial rotations, spatial translations and time dilations is most obvious.
Form-invariance under inversion of the spatial axes will also become clear if we agree that B is not a vector but a pseudo-vector.
What remains is the inversion of time. From looking at the equations with curl E and curl B, I see two options:
1. One would be to agree that B changes its direction to opposite under a time inversion. This option is not easy to justify, because B = curl A is not expected to "feel" a time reversal.
2. Another option would be to agree that an inversion of time yields a simultaneous change of the sign of charge and of the E field. My guess is that this option is right and that this has something to do with the CPT business.
How would a physicist of the late XIX century resolve this issue, a guy who knew nothing about special relativity or CPT, and who operated with only elementary concepts?
Many thanks!!
Michael
Let me ask you the silliest question of the year. I am looking at the Maxwell equations in their standard form. No 4-dim potential A, no Faraday tensor F, no mentioning of special relativity - just the standard form from a college-level textbook.
I know that the eqns are NOT form-invariant under the pure Galilean transformation (addition of a constant velocity). That's fine.
Now, how about the other subgroups of the full Galilean group?
That the equations are form-invariant under time-independent spatial rotations, spatial translations and time dilations is most obvious.
Form-invariance under inversion of the spatial axes will also become clear if we agree that B is not a vector but a pseudo-vector.
What remains is the inversion of time. From looking at the equations with curl E and curl B, I see two options:
1. One would be to agree that B changes its direction to opposite under a time inversion. This option is not easy to justify, because B = curl A is not expected to "feel" a time reversal.
2. Another option would be to agree that an inversion of time yields a simultaneous change of the sign of charge and of the E field. My guess is that this option is right and that this has something to do with the CPT business.
How would a physicist of the late XIX century resolve this issue, a guy who knew nothing about special relativity or CPT, and who operated with only elementary concepts?
Many thanks!!
Michael
