The issue is not whether these things all need flipping, but whether they flip themselves automatically when T reverses (like momenta do).
T-reversal isn’t a physical process to be performed, it’s a transformation of coordinates, t goes to -t. It “automatically reverses” momenta, because momenta are first derivatives of x with respect to t. It does not include reversal of spatial axes (P), but it includes charge change of particles into antiparticles, by definition.
In our world we may observe a decay of a muon into an electron, a right-handed electron antineutrino and a left-handed muon neutrino. A T-reversed process would include a right-handed electron neutrino, a left-handed muon antineutrino and a positron merging into an antimuon (T includes turning particles into anti-particles, also by definition). But such a process contradicts the experimentally observed fact that right-handed neutrinos and left-handed antineutrinos don’t interact (except gravitationally, if they exist at all). Therefore, T is not a symmetry.
Alternatively, T would be a symmetry iff the equations of motion (or Lagrangian) looked exactly the same (up to a total 4-divergence in case of the Lagrangian) after substituting -t for t. But it does not happen for the Lagrangian of the Standard Model, because T changes the left-handed weak interaction term to a right handed one.
T-reversal isn’t a physical process to be performed, it’s a transformation of coordinates, t goes to -t.
It depends on how you define a “physical process”. Reversing time in a billiard ball machineis a physical process. Perhaps think about that to understand how time reversal could operate physically.
It “automatically reverses” momenta, because momenta are first derivatives of x with respect to t. It does not include reversal of spatial axes (P), but it includes charge change of particles into antiparticles, by definition.
No, it doesn’t—that is simply incorrect. Perhaps read through the section of this, that I quote below—it should explain things:
The implication of CPT symmetry is that a “mirror-image” of our universe — with all objects having their positions reflected by an imaginary plane (corresponding to a parity inversion), all momenta reversed (corresponding to a time inversion) and with all matter replaced by antimatter (corresponding to a charge inversion)— would evolve under exactly our physical laws. The CPT transformation turns our universe into its “mirror image” and vice versa. CPT symmetry is recognized to be a fundamental property of physical laws.
C reversal is described here—and it is not conventionally included in T reversal.
You are right that T doesn’t include particle-antiparticle mixing, of course. My previous comment was confused, I should never comment at 4AM.
But still, the interaction Lagrangian of the Standard model is not invariant with respect to T, since it is invariant with respect to CPT and CP invariance is violated by the CKM matrix.
Edit: ignore the comment, it is wrong.
T-reversal isn’t a physical process to be performed, it’s a transformation of coordinates, t goes to -t. It “automatically reverses” momenta, because momenta are first derivatives of x with respect to t. It does not include reversal of spatial axes (P), but it includes charge change of particles into antiparticles, by definition.
In our world we may observe a decay of a muon into an electron, a right-handed electron antineutrino and a left-handed muon neutrino. A T-reversed process would include a right-handed electron neutrino, a left-handed muon antineutrino and a positron merging into an antimuon (T includes turning particles into anti-particles, also by definition). But such a process contradicts the experimentally observed fact that right-handed neutrinos and left-handed antineutrinos don’t interact (except gravitationally, if they exist at all). Therefore, T is not a symmetry.
Alternatively, T would be a symmetry iff the equations of motion (or Lagrangian) looked exactly the same (up to a total 4-divergence in case of the Lagrangian) after substituting -t for t. But it does not happen for the Lagrangian of the Standard Model, because T changes the left-handed weak interaction term to a right handed one.
It depends on how you define a “physical process”. Reversing time in a billiard ball machine is a physical process. Perhaps think about that to understand how time reversal could operate physically.
No, it doesn’t—that is simply incorrect. Perhaps read through the section of this, that I quote below—it should explain things:
C reversal is described here—and it is not conventionally included in T reversal.
You are right that T doesn’t include particle-antiparticle mixing, of course. My previous comment was confused, I should never comment at 4AM.
But still, the interaction Lagrangian of the Standard model is not invariant with respect to T, since it is invariant with respect to CPT and CP invariance is violated by the CKM matrix.