Talk:T-symmetry

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Contents 1 Second law of thermodynamics is not related to T-symmety ? 2 2nd law T violation depends on initial condition ? 3 Changed statements considerable 4 Second law of thermodynamics 5 Electric Dipole Moment and Notation

[edit] Second law of thermodynamics is not related to T-symmety ?

You say "All of the accepted laws of physics exhibit T-symmetry", and "the second law of thermodynamics (..) is not related in any obvious way to T-symmetry". That seems odd, and contrary to all sources I can read. When one says "dS/dt > 0", or entropy always increases with time, this is clearly sensitive to the sign of t. Are you saying that the second law of thermodynamics is not a physical law ? Or are you saying that this law is wrong ? Pcarbonn 20:06, 28 May 2004 (UTC)

The CPT theorem applies to the microscopic laws, the ones that apply to individual particles/quantum strings. The second law applies to macroscopic systems, containing enough particles for statistical mechanics to be valid. (A solitary atom doesn't have a temperature.) For the purposes of T-symmetry therefore, the second law doesn't count. Carandol

And when you say that gravity is a contender for T-symmetry violation, this is even stranger. F= G * m * m' / r² = m * m' dr²/dt² remains unchanged if the sign of t is changed. If time was reversed, the earth would turn around the sun in reverse, so the world would not be much different. Of course, a falling stone would not go up after a time reversal, but that is precisely because of the second law of thermodynamics: the heat of the fall cannot be converted back into kinetic energy. Pcarbonn 20:06, 28 May 2004 (UTC)

[edit] 2nd law T violation depends on initial condition ?

You say "2nd law (..) only creates a T-asymmetry if asymmetric initial conditions are imposed". I can see where the point comes from, but I have some doubt on it. This is because an open system (as opposed to a closed system) that receives energy from the outside has a tendency to auto-organise itself (see self-organizing system).

In such a system the direction of energy flux is a time-asymmetry in the boundary conditions. Time-symmetric conditions for a macroscopic system are that it starts in thermodynamic equilibrum with zero fluxes across its boundary.

Temporarily excluding gravity, randomly chosen initial conditions will be thermodynamic equilibrum, since that's the macrostate with by far the most microstates. It's only if you choose the extremely rare initial states out of equilibrum that there's any observable time asymmetry.

Gravity interacts perversely with the second law, even in closed systems. A uniform gas cloud filling a closed universe will collapse, self-organising into many clumps. On the surface this looks like a decrease in entropy, but isn't really. It happens because gravitational potential energy is unbounded below, but once this is taken full account of a randomly chosen initial state is almost certainly at maximum entropy for its energy, and no time asymmetry will be observable. Carandol

Once organised, the 2nd law applies. For example, the solar system was created from a gaz cloud that had no special initial conditions.

Actually, very special. A randomly chosen initial state, with all microstates equally likely, wouldn't be much like a gas cloud. Carandol

And the entropy increase that we observe today is within that solar system. So the entropy that we see increasing is not dependent on particular initial conditions. (This is not fully clear to me though, because the solar system does not seem to be an open system in this explanation) Pcarbonn 06:05, 29 May 2004 (UTC)

Also, a T-symmetry violation must be dependent on initial conditions, by definition (unless the initial and end conditions are identical, and the law describes a cycle that can go only one way; possible, but highly improbable). In other words, if you require that a T-symmetry violation be independent of initial conditions, you will have a hard time finding one ! Pcarbonn 06:28, 29 May 2004 (UTC)

That's just the kind of T-symmetry violation physicists are interested in, and that is required by the CPT theorem. There are apparently processes that only go one way at the microscopic level, for reasons completely unrelated to thermodynamics. Carandol 22:25, 29 May 2004 (UTC)

Thanks for your kind explanations. I understand your definition of time-symetric initial conditions, and agree that the gaz cloud does not fit it. However, if physicists find a new T-symmetry violation, I would think that this law would also be dependent on initial conditions. Maybe you can help me understand this better.

First of all, I think you'll agree that a law is not dependent on initial conditions; it is our possibility to observe it that depends on the existence of adequate initial conditions.

From what you say, I understand that physicists are looking for a law that would say : a system in random state A would naturally go in random state B, without gaining entropy; and that going from B to A would not be possible.

We are talking about a law that applies even when entropy is not a meaningful concept, e.g one or two particle systems. Carandol

Then, we could only accept this law if we could observe state A. So our observation of the law would also be dependent on the initial conditions, just as the second law. The way to characterize the initial condition would be different from the thermodynamic one, but we would probably be able to define the state A or B by some kind of an index similar to, but different from, entropy. If physicists found such a law, it would be a second violation of T-symmetry, but not very different in essence from the second law. Does it make sense ? Pcarbonn 09:02, 30 May 2004 (UTC)

No. Entropy is a macroscopic concept, and the fluctuation theorem does not extend its range that far.

Compare this with the other two symmetries involved. If all photons were left handed that would be a violation of P-symmetry. If positrons and electrons had a different mass that would violate C-symmetry. Neither violation would be due to initial conditions - if something is true for all initial conditions it's not true because of the conditions but because of the fundamental laws.

• For almost all initial conditions, entropy is already a maximum and the second law predicts T-symmetry, with near certainty.

• For all initial conditions, the CPT theorem and observed CP-asymmetry require T-asymmetry.

This is qualitatively different behaviour, stemming from fundamentally different causes.

Therefore, I'd say the only mention of entropy appropriate to this page is a brief note of why it is irrelevant, and that such details as the fluctuation theorem do not belong here. Stick to the core principle, that there is a violation of T-symmetry by the fundamental laws, independent of the initial conditions. Carandol 11:19, 30 May 2004 (UTC)

Thanks again. I have done some more research on the web, and updated the article accordingly, in line with what you say. Indeed, most physicists see a qualitative difference between 2nd law and T-violation (and some disagree). Feel free to correct if you see any mistake ! Pcarbonn 20:33, 30 May 2004 (UTC)

[edit] Changed statements considerable

Pretty much every physical law at the macroscopic level is not T-symmetric. Any description of physics which includes friction or dissipation is not T-symmetric.

Friction etc are just trivial applications of the second law, not coequal in standing with it (as your edits could be read as implying). They can be mentioned as examples of the second law in action, but no great importance should be attached to these trivialities. Carandol

Also changed description

of CPT. Correct me if I am wrong but there is no experimental reason to think that CPT is correct. The reason for believe it is is that it a property of pretty much all of quantum field theorem.

There is very strong experimental evidence that reality is described by quantum fields, and quantum fields without CPT symmetry would have major -and easily observable consequences.

Hence, there is very strong, if indirect, experimental proof that CPT symmetry holds. Carandol

Also I disagree with the gist of the some of what has been argued above. T-symmetry is a mathematical concept. There is no reason I can see to reduce discussion to particle physics.

Roadrunner 05:30, 31 May 2004 (UTC)

Particle physics is the field in which T-symmetry is normally discussed, at least by that name, and all other physics does ultimately reduce to it. That's reason enough for it to provide the overriding concepts in this article.

Move here for discussion. My main problem with this statement is that most physicists don't say this.

It's true, and provably so. What proportion of physicists in the field dispute this (not just say the same thing in superficially different ways)? Carandol 06:06, 31 May 2004 (UTC)

[edit] Second law of thermodynamics

Most physicists say that we observe a constant increase of entropy only because of the initial state of our universe. Other possible states of the universe would actually result in decrease of entropy. To illustrate it simply, if the velocity of all particles was suddenly inverted, the world would go in reverse, and the second law of thermodynamics would not hold anymore (entropy would decrease). A randomly chosen initial state is most probably in thermal equilibrum, with constant entropy and T-symmetry.

Thus, the second law of thermodynamics is "fact-like" instead of "law-like".

Of course, this raises the question of why the universe is one way rather than another. One explanation involves the anthropic principle: if the world were otherwise, we could not observe it.

Roadrunner 05:58, 31 May 2004 (UTC)

Explanation for change.

I think I can think of cases in which T-symmetry is violated, but the second law doesn't appear. Suppose I have a turbulent flow in which there is viscosity which takes energy at large scales and disspates them at lower but still non-molecular scales. There is a broken t-symmetry, but the local entropy of the flow doesn't increase.

Roadrunner 06:07, 31 May 2004 (UTC)

Actually, it does. For a start, viscosity always causes frictional heating. The entropy increase is negligible for incompressible flows, under the Boussineq approximation, but it isn't really zero. Carandol 06:11, 31 May 2004 (UTC)

I'm going to take issue with everything past the first sentence in the paragraph that starts this part of the "talk." I'm not sure what to say about it except that it is incorrect.

[edit] Electric Dipole Moment and Notation

The section on the electric dipole moment is difficult to understand. Why does the permanent electric dipole moment have to be proportional to the expectation value of the current, <Psi|J|Psi>? Or is J really the total angular momentum operator (not that it would make the dipole argument easier to understand)? Perhaps J should be defined again in the section on anti-untiarity.

Second question: Shouldn't the similarity transforms in the section on anti-unitarity really be like TxT^-1, instead of TxT? For P it doesn't matter, of course, but if T^2=-1 is does make a difference.