Why do you think that I think that CP symmetry is not broken?
Because you apparently agree that breaking C symmetry would falsify your theory, but you do not understand that breaking CP symmetry has the same effect.
So: I am not clear on where you are getting that from either. I don’t even recall discussing pure C symmetry in this thread.
Your messages so far seem to be concerned with whether C and P flip, and what happens if they don’t.
No. I have assumed that C and P flip. Hence my words: “Start with a left-handed neutrino, flip T under your assumption, end up with a right-handed antineutrino”. A right-handed antineutrino is C and P flipped with respect to a left-handed neutrino. But, because CP is violated, it does not exactly retrace the steps its antiparticle took, unless T symmetry is violated so as to make up for the CP violation.
Right, yes, so CPT all need to flip. I agree with that. You agree with that. Everyone agrees on that. At least that has nothing to do with our issue. The issue is not whether these things all need flipping, but whether they flip themselves automatically when T reverses (like momenta do). So far, you don’t seem to have got as far as that issue—and are assuming that I am making the mistake that you just described. Which is not what is going on here at all.
Since you are asserting that T is a good symmetry, that cannot happen under your theory; consequently your theory is experimentally falsified. That your T flip carries with it the CP flip is not relevant, it has no effect on the argument.
If T flips, and consequently, C and P also flip, then C,P and T have all flipped—in which case we apparently just agreed that evolution proceeds backwards.
Here you can doubt the premise (sure, go ahead), but that’s about the only option for criticism. I don’t see how you can claim that flipping C, P and T does not lead to backwards evolution, having just agreed that it does.
Addendum, let me see if I can phrase this in language you are more likely to understand. Neither C, P or T symmetry hold alone. However, under the hypothesis that reversing T flips C and P, reversing T has the effect of reversing C, P and T, which then makes everything run backwards. That is what I am talking about—using your preferred terminology as best as I can manage.
Hopefully you can imagine why I prefer to describe that in terms of simple T-symmetry. Under the hypothesis, it makes much more sense to describe it that way.
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.
So: I am not clear on where you are getting that from either. I don’t even recall discussing pure C symmetry in this thread.
In your post of 08:35, where you quoted someone saying there was evidence of charge violation, specifically neutrinos and antineutrinos having different masses, and said that if it was so, then CPT violation was broken. This is not actually true, because the P and T symmetries can be broken so as to exactly compensate. In fact this almost exactly happens in the weak force, where the C and P symmetries are separately almost-completely violated, but CP is almost a good symmetry. But all that is a separate point.
Neither C, P or T symmetry hold alone.
Ok, I’m glad we were finally able to agree on this, because that’s what I’ve been saying all along: The laws of physics are not in fact T-symmetric.
Hopefully you can imagine why I prefer to describe that in terms of simple T-symmetry.
No, in fact I can’t. You are confusing separate operators and introducing your own notation, and it has led to comments six deep because you refuse to distinguish T from CPT symmetry. Moreover, it leads to you contradicting yourself: In one paragraph you agree that T is not separately a good symmetry, and then in the next you say that you “prefer to describe [physics] in terms of simple T symmetry”. If the symmetry is one that doesn’t actually hold, then I suggest that it is not simple at all, and certainly not worth introducing nonstandard notation for.
You are confusing separate operators and introducing your own notation, and it has led to comments six deep because you refuse to distinguish T from CPT symmetry. Moreover, it leads to you contradicting yourself: In one paragraph you agree that T is not separately a good symmetry, and then in the next you say that you “prefer to describe [physics] in terms of simple T symmetry”.
Paragraph 1 was me trying to “phrase this in language you are more likely to understand”
Paragraph 2 was me using the language I would normally use.
So: that was not a case of me “contradicting” myself at all.
If you simply reverse T, and the whole universe starts to run backwards, then it makes an awful lot of sense to call the universe “T symmetric”, IMHO, conventional terminology or no. Then it is time to start saying “T”—instead of “CPT”—since the old “T” has turned out to be not a fundamental or interesting concept.
So: I am not clear on where you are getting that from either. I don’t even recall discussing pure C symmetry in this thread.
Right, yes, so CPT all need to flip. I agree with that. You agree with that. Everyone agrees on that. At least that has nothing to do with our issue. The issue is not whether these things all need flipping, but whether they flip themselves automatically when T reverses (like momenta do). So far, you don’t seem to have got as far as that issue—and are assuming that I am making the mistake that you just described. Which is not what is going on here at all.
If T flips, and consequently, C and P also flip, then C,P and T have all flipped—in which case we apparently just agreed that evolution proceeds backwards.
Here you can doubt the premise (sure, go ahead), but that’s about the only option for criticism. I don’t see how you can claim that flipping C, P and T does not lead to backwards evolution, having just agreed that it does.
Addendum, let me see if I can phrase this in language you are more likely to understand. Neither C, P or T symmetry hold alone. However, under the hypothesis that reversing T flips C and P, reversing T has the effect of reversing C, P and T, which then makes everything run backwards. That is what I am talking about—using your preferred terminology as best as I can manage.
Hopefully you can imagine why I prefer to describe that in terms of simple T-symmetry. Under the hypothesis, it makes much more sense to describe it that way.
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.
In your post of 08:35, where you quoted someone saying there was evidence of charge violation, specifically neutrinos and antineutrinos having different masses, and said that if it was so, then CPT violation was broken. This is not actually true, because the P and T symmetries can be broken so as to exactly compensate. In fact this almost exactly happens in the weak force, where the C and P symmetries are separately almost-completely violated, but CP is almost a good symmetry. But all that is a separate point.
Ok, I’m glad we were finally able to agree on this, because that’s what I’ve been saying all along: The laws of physics are not in fact T-symmetric.
No, in fact I can’t. You are confusing separate operators and introducing your own notation, and it has led to comments six deep because you refuse to distinguish T from CPT symmetry. Moreover, it leads to you contradicting yourself: In one paragraph you agree that T is not separately a good symmetry, and then in the next you say that you “prefer to describe [physics] in terms of simple T symmetry”. If the symmetry is one that doesn’t actually hold, then I suggest that it is not simple at all, and certainly not worth introducing nonstandard notation for.
Paragraph 1 was me trying to “phrase this in language you are more likely to understand”
Paragraph 2 was me using the language I would normally use.
So: that was not a case of me “contradicting” myself at all.
If you simply reverse T, and the whole universe starts to run backwards, then it makes an awful lot of sense to call the universe “T symmetric”, IMHO, conventional terminology or no. Then it is time to start saying “T”—instead of “CPT”—since the old “T” has turned out to be not a fundamental or interesting concept.
Anyway, I think a miscommunication.