Comments on Soul Physics: Two Theorems about Time Reversal

Joseph, The proofs are in the appendix of the pap...

2010-03-05T10:45:39.268-05:00

Joseph,

The proofs are in the appendix of the paper. I'm making this argument in the context of ordinary quantum mechanics, because it's simplest to see how it works there -- but it generalizes naturally to quantum field theory.

Adding interactions isn't a problem -- the antiunitarity of T shouldn't depend on one's Hamiltonian. T is a general transformation of the motions allowed by a theory. So, establishing that T has a certain property for the free-particle case is enough to establish it has the same property in interacting cases as well.

Can you generalize your Theorem 2 if there are int...

2010-03-05T10:38:08.902-05:00

Can you generalize your Theorem 2 if there are interactions?

I looking in your draft, I don't see a rigorous proof of theorem 2. (No rigorous proof for your proposition 1?)

This isn't a complaint, just that if you wrote out the rigorous proof in detail, maybe you will find a way to add various interactions to it where the argument still holds. (Only a guess.)

Good luck with the time issues.

Nice example! I'm still not convinced this is a pr...

2010-03-05T09:00:13.553-05:00

Nice example! I'm still not convinced this is a problem for free motion symmetry though. The natural vacuum state around a Schwarzschild black hole undergoes an irreversible thermal process. But that by itself doesn't violate free motion symmetry. Do we really have a free field in the presence of a black hole? There seem to be two situations, neither of which is a problem for FMS.

(1) Outside event horizon, it's clear that we can have a free quantum field. And in that region, we do expect the equations of motion to have the symmetries of the background spacetime. We even use this fact in the usual derivations of Hawking radiation, when we assume that the equations of motion are "Bogolyubov transformation invariant," whatever they are. Here irreversible processes are not a problem.

(2) Inside the event horizon, it's not so clear that we have a free field. Indeed, one way to put the problem of quantum information loss is that the quantum field seems to interact with the spacetime singularity (or its analogue in quantum gravity) in a way that we don't yet understand. The inverse Bogolyubov transformation doesn't exist here, and time-reversibility may break down -- but should be prepared for this kind of symmetry breaking to occur in the presence of interactions.

so this illustrates my original point that the ide...

2010-03-05T03:08:07.197-05:00

so this illustrates my original point that the idea to 'turn off' all interactions is somewhat ambiguous (and we cannot have direct experience with free particles).

perhaps it can be done in a fully consistent quantum theory of everything (string theory?), but to repeat a previous point, why would one want to do this if we already have the consistent theory with interactions ...

thinking about the q.m. case, i think there is act...

2010-03-05T02:58:51.870-05:00

thinking about the q.m. case, i think there is actually a counterexample here:

first we 'turn off' gravity by setting G=0, which will decouple spacetime geometry from matter. The field equation for the geometry are now Rij = 0 , in other words the geometry is Ricci flat. One solution is the Schwarzschild geometry.

As for the matter we consider a non-interacting quantum field, so we have your 'free particles' case.

But this means you have the situation originally considered by Hawking (non-interacting quantum field on a Schwarzschild geometry). So you will find Hawking radiation and run into the information loss problem. This means that unitarity breaks and your time reversal operator must be problematic.

True, and point taken. But the test particle ideal...

2010-03-04T20:40:54.054-05:00

True, and point taken. But the test particle idealization is just a convenience in general relativity. I could always choose a particular world line in a real evolving matter field -- Geroch showed that such a worldline will be a geodesic, given some reasonable assumptions about the matter field.

>> Just take a 'free particle' to be a test partic...

2010-03-04T18:54:12.488-05:00

>> Just take a 'free particle' to be a test particle

i think you would have to be very careful about what you assume about the test particle (and its mass and the bakground geometry).

Wolfgang: no worries! Here's a bit of a long respo...

2010-03-04T17:10:13.741-05:00

Wolfgang: no worries! Here's a bit of a long response.

Suppose I grant your point, that we could never empirically verify Free Motion Symmetry. We can still have reason to believe it, in the same way that we believe the spacetime manifold is smoothly differentiable -- another empirically unverifiable claim. We accept both principles, because they allow us to construct useful theories and make useful predictions that would otherwise be impossible.

One reason we need Free Motion Symmetry is for the study of whether or not interactions have (or don't have) some symmetry like parity or time reversibility. Without FMS, a parity asymmetry in (say) a W-boson interaction could always be attributed to an asymmetry of the underlying kinematics, and not the interaction itself.

Another reason we need FMS if to apply Wigner's method of deriving quantum numbers. If Wigner hadn't assumed that the amplitudes described by a free quantum system remain fixed under spacetime symmetries, his whole procedure would come undone. But he did assume it, and this procedure (it seems) led to a very fruitful program in the foundations of quantum theory.

Does the principle make sense in GR? I haven't worked this out carefully yet, but I suspect it does. Just take a 'free particle' to be a test particle, and its equations of motion to be the geodesic equations. Then free motion symmetry is a theorem -- it just says that the geodesic equations are covariant under the symmetries (isometries) of the background spacetime.

... Or is my sophistry idle? ;)

By the way, in order to show that this is not idle...

2010-03-04T14:21:59.377-05:00

By the way, in order to show that this is not idle sophistry, consider what you mean with 'free particle' in the context of general relativity.

PS: sorry for posting 3 comments to express one thought...

(by why would you should have been (but why w...

2010-03-04T14:14:25.647-05:00

(by why would you

should have been

(but why would you

But what would be those 'good reasons'? Obviously...

2010-03-04T14:08:49.419-05:00

But what would be those 'good reasons'?

Obviously, we have no experience from/with free particles directly (we can only extrapolate from (weakly) interacting particles).

So I would think you either formulate the principle with interactions and then consider the limit of turning them off (by why would you do that if you already have the principle for the more general case).

Or you have to live with the fact that you are making statements about something which cannot be observed in principle.

That may be true... but why is this a problem? It ...

2010-03-04T12:55:49.147-05:00

That may be true... but why is this a problem? It seems we can still have good reason to believe the Free Motion Symmetry principle.

>> when a system contains only free particles or f...

2010-03-04T05:49:33.656-05:00

>> when a system contains only free particles or fields

One problem with this is that non-interacting
particles and fields cannot be observed.
Strictly speaking you cannot even know if "a system contains only free particles or fields".