# What sort of experiment would directly test time reversal invariance?

I guess the title says it all: how could/would you experimentally test whether our universe is truly time reversal invariant, without relying on the CPT theorem? What experiments have been proposed to check this? Have any of them been performed?

I know that there are indirect tests of time reversal invariance by observing CP violation, in the decay $K_L \to 2\pi$ for example. Then if you assume that the necessary conditions for CPT symmetry are satisfied in our universe, that means there must be time reversal symmetry violation as well. But I'm curious about ways to test time reversal invariance without relying on CPT.

Basically, how could we distinguish between the standard model, which predicts T violation, and some hypothetical other theory that matches current experimental results as well as the SM, but in which CPT symmetry does not hold?

P.S. This may be more of a research-level question, but I'm hoping it won't be too obscure for this site ;-)

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You should probably say what kind of theory you want to test. Obviously, if you want to test a classical theory, then you just start from final position and revert velocity and see whether you'll return to where you started. In quantum mechanics it's the same. It becomes tricky in QFT I guess (where these direct measurements are unavailable), but you should state that is what you are interested in. –  Marek Dec 6 '10 at 21:26
@Marek: well, I'm not talking about classical mechanics or basic QM, since I'm sure those have been tested to death. I guess what I had in mind is the standard model, and/or other as-yet-unknown theories that may display T symmetry even in the presence of CP violation. I'll see if I can make that a bit clearer in an edit. –  David Z Dec 6 '10 at 22:05
yeah, I realized what you were talking about (and this question is probably intended just for those 10 people that know QFT here anyway :-) ) but wanted you to make it a little clearer. Also, I'd like to know whether you are interested in something concrete, like limitations on T-violations in QED, or something general that applies to any QFT. And now I realize that you might also be more precise about whether you want the test to be actually realizable (now or in foreseeable future), or just conceptual. Sorry, this got a little longer than intended :-) –  Marek Dec 6 '10 at 22:14
@Marek: I think any information about any experiments, realizable or not, which would test time reversal invariance without relying on CPT would be of interest. But I'll continue to edit this question as I think of ways to clarify it. –  David Z Dec 6 '10 at 22:34
@DavidZaslavsky: CPT invariance is a consequence of Lorentz invariance. A theory that preserves T while violating CP would not be Lorentz invariant, and there would be plenty of tests of that. –  Jerry Schirmer Apr 29 '12 at 15:44
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## 3 Answers

At research level, you might be interested in the PDG review on conservation laws: http://pdg.lbl.gov/2009/reviews/rpp2009-rev-conservation-laws.pdf Also, the review about CPT invariance gives information about tests of CPT violation in neutral kaons, but I can apparently only post one hyperlink (reputation too low).

Note that CP violation itself is still an active area of research (particularly at Belle and LHCb), since we don't know definitively how many systems display it and whether there's a deeper explanation for it.

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+1 nice reference! If my upvote isn't enough to let you make multiple hyperlinks, you could just edit in the other URL and I'll edit your post just to turn it into a hyperlink, if you like. –  David Z Dec 8 '10 at 21:12
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There are numerous research groups engaged in a search for an electric dipole moment of the electron, which, if it exists, would violate time-reversal symmetry. You can see this because any dipole moment the electron might have would need to be parallel to the spin (or anti-parallel). When you reverse time, the spin necessarily flips, but the electric dipole moment would not change, so the relative orientation of the two would change. That's the best example of a T-violating phenomenon that I know of.

At the risk of unseemly self-promotion, I wrote an article on edm searches for Physics World last year. You need to register to read the whole thing, but it's free.

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Great article! (I finally got around to reading it just now) –  David Z Dec 10 '10 at 0:18
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The C, P and T symmetries came from the equations due to Schrodinger, Klein-Gordon and Dirac. These partial differential equations depend on time and position. By changing the sign of time and position, these equations remained unchanged, so here is the origin of P and T. The C symmetry resulted originally from Dirac's equation. Since these equations are very good at describing the behaviors of particles, we can safely say that C, P and T came from observations.

After the discovery of the weak interaction, C and P turned out to be violated, and the hope was that their combination CP is still preserved. After the discovery of the violation of CP, the hope moved to CPT. So, the experimental data said that each of C, P, T is respected when no weak interaction takes place, otherwise we should be happy with the combined CPT.

So, I think that the answer is that the experimental data told us that the universe is T-invariant, then when the weak interaction was involved, it told us that CP is violated, and from CPT that T is violated. And CPT is not specific to the standard model, it results from the Lorentz invariance and the fact that the energy is bounded for below.

A presumable CPT violation would imply the violation of the Lorentz invariance (http://en.wikipedia.org/wiki/CPT_symmetry#CPT_violation). So, if an alternative theory wants to distinguish itself by experiment, it should predict violations of the Lorentz symmetry. The theory itself will say the regimes in which this violation occurs (I bet that it will be at the Plank scale!). In this case, probably the Lorentz violation will imply with ease the CPT violation.

I find it very unlikely a violation of the Lorentz invariance, because this principle is (probably) the most ubiquitous principle in Physics, but who knows...

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If space-time is discrete in ultimate analysis, a violation of Lorentz invariance is not unthinkable. But would this also mean a violation of CPT? Probably depends on the kind of theory. –  Raskolnikov Dec 6 '10 at 23:50
This answer explain violations in general but completely ignores what the question is about. It doesn't say anything about the actual direct T-violation. I have a strong feeling I should down-vote this. –  Marek Dec 7 '10 at 0:24
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