Talk:T-symmetry/Archive 1

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)

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.

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


 * I added an explanation in the end why the two are unrelated.Dan Gluck 07:45, 24 May 2007 (UTC)

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 backinto kinetic energy. Pcarbonn 20:06, 28 May 2004 (UTC)


 * The problem is with black holes, as expalined in the articleDan Gluck 07:44, 24 May 2007 (UTC)

"Unitary" representations
In the Kramer's theorem section, I found:

Quantum states which give unitary representations of time reversal, ie, have T2=1

But before it's been said (as it should be) that time reversal admits only antiunitary representations. Why is T2=1 a unitary representation? T implies complex conjugation always, and it's representations are antiunitary. The reason for having T-parity in the T2=1 case is not unitarity. Maybe there's a confusion about the fact that unitary representations of abelian operators are one-dimensional, and they are indeed 1D in this case. But I don't think you can say unitary. El perseguidor 20:20, 7 October 2007 (UTC)

Other Macroscopic-Level Examples of T-symmetry?
When I originally heard of time reversal and T-symmetry, I heard about it from my professor when in a lecture about Optical phase conjugation. I wondered why this article didn't talk about other macroscopic examples of the preservation of T-symmetry that don't involve mechanics but electrodynamics and magnetodynamics such as light waves. Has anyone else heard of optical phase conjugation or other non-mechanical macroscopic examples where T-symmetry is preserved?68.155.153.249 (talk) 16:54, 1 January 2009 (UTC)

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)


 * I have some interjections and observations. I have just played the Maxwell's Assentation Induction Game  to find where the Laws and Correlations in the Classical Dynamic systems Plank was looking at appear to be good for the "Chaotically Self Ordering of the Cosmic Gravitational  Laws Impose".  I'd like to site AAAS Science Journal Vol. 331 Pg. 889; Time-Reversed Lasing and Interferometric Control of Absorption, as 'new evidence' and then reassert the  "Maxwell Assertion and Correlation Game".  If a System is forced to become 'Highly Ordered' in favor of a single vector in a T-Symmetry CD-System the 'Delta' of all constants of a gradient in the system will shift towards a normal and prove completely Dynamic, but not natural for our superposition in the time and space system model of our place in the cosmic order of the universe.  I postulate that this could be proven in physical systems by taking the same aforementioned laboratory data and Forcing the silicone echelon to become superconductive and exposed to a magnetic field which forced more vectors into to be time-reverse ordered.  For Example: The same conditions of an MRI.  In this system, Current, Flux, and Lux are all Time Invariant, and the conditions of entropy and PC would shift slightly to the observer perspective from the CD System of measurement.  — Preceding unsigned comment added by ProtoBytes (talk • contribs) 11:24, 24 March 2011 (UTC)

Unclear Sentence
The following sentence is unclear to me.

''Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics. Hence time is said to be non-symmetric, or asymmetric. However, quantum noninvasive measurements are predicted to violate time symmetry, [1] contrary to their classical counterparts, although it has not yet been experimentally confirmed.''

Breaking down the sentence, it contains the following statements:
 * A. T-symmetry can be found only in restricted contexts ("in restricted contexts one may find this symmetry").
 * B. T-symmetry cannot (in general) be found in the observable universe ("the observable universe itself does not show symmetry under time reversal").
 * C. Therefore, it is said that there is no T-symmetry ("Hence time is said to be non-symmetric, or asymmetric", by generalization of B).
 * D. However (?), there are specific violations of T-symmetry in the context of quantum noninvasive measurements ("However, quantum noninvasive measurements are predicted to violate time symmetry").
 * E. The classical counterparts to quantum noninvasive measurements do not violate T-symmetry ("contrary to their classical counterparts").

Since D. begins with an adversative conjunction ("however"), it should oppose what has been stated in C. But in C. it is said that T-symmetry in general does not hold, while in D. it is said that T-symmetry does not hold in the particular case of quantum noninvasive measurements. So D. does not oppose C. and either "however" is confusing or quantum noninvasive measurements do violate T-asymmetry (and not T-symmetry).

Finally, E. is opposed to D. ("contrary"), which in turn is opposed to C. ("hovever"). So E. should be consistent with C., that is, T-symmetry does not in general hold in classical mechanics. Is this true? Thank you very much for any clarification. --93.205.120.48 (talk) 11:19, 3 August 2014 (UTC)

I agree this is confusing, it seems there is one simple mistake: 'symmetry' should be 'asymmetry' then it makes sense and seems to be correct.

Propose replacing:

'However, quantum noninvasive measurements are predicted to violate time symmetry, [1] contrary to their classical counterparts, although it has not yet been experimentally confirmed.'

with:

'However, quantum noninvasive measurements are predicted to violate time asymmetry [1] (and are thus T-symmetric) contrary to their classical counterparts, although this has not yet been experimentally confirmed.'

Couple of small changes I believe makes a clearer and nicer sentence. 1.124.49.46 (talk) 03:28, 24 November 2014 (UTC)


 * The point is that the second law of thermodynamics predicts symmetry in equilibirum. The classical noninvasive measurements are still symmetric but quantum do not. Sorry for the confusion. I hope the corrections I just made are OK. Adamb76 (talk) 23:18, 13 January 2015 (UTC)

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Anti-unitary and Negative energy
Most of the anti-unitary section is based on "energy is always positive" but it is generally believe gravitational energy is negative. Ywaz (talk) 12:01, 24 March 2019 (UTC)

Misleading notation for involution vs. matrix vs. operator
This article confuses and mashes together multiple distinct concepts of T symmetry. For example, for spinors the correct equation is


 * $$\mathsf{T} \psi(t,\vec{x}) = T \psi(-t,\vec{x})$$

where $$\mathsf{T}$$ is an involution (mathematics), and $$T$$ is just an ordinary matrix (a 8x8 matrix for Dirac spinors, i.e. a 4x4 matrix with real and complex components, for 8x8 real components; likewise, a 4x4 matrix for Weyl spinors, because the involution $$K: x+iy \mapsto x-iy$$ can be thought of as a 2x2 matrix.) These two "T"'s are not the same "T" ! The way math textbooks, and the better physics textbooks write this is


 * $$\mathsf{T}: \psi(t,\vec{x}) \mapsto \psi^\prime(t,\vec{x}) = T \psi(-t,\vec{x})$$

which has the advantage that you can now plug this into differential equations, and actually solve for $$T$$ to find out what it is. So, for example, instead of asserting that $$T=e^{i\pi J_y}K$$ you can actually derive this. For quantum fields, there is also a third T, written as $$\mathcal{T}$$ which is actually an infinite dimensional operator acting on a Hilbert space! It acts on quantized fields $$\Psi$$ as


 * $$\mathsf{T}: \Psi(t,\vec{x}) \mapsto \Psi^\prime(t,\vec{x}) = \mathcal{T} \Psi(-t,\vec{x}) \mathcal{T}^{-1}$$

By failing to distinguish between these three different "T"'s, it just leaves the uninitiated reader completely confused, and it leaves people like me, who actually knows this stuff, swimming pretty hard to extract any kind of useful information out of this article. 67.198.37.16 (talk) 21:54, 14 December 2020 (UTC)


 * I added the above to the article. 67.198.37.16 (talk) 23:30, 14 December 2020 (UTC)

Update Needed: Experimentally Confirmed
The opening paragraph incorrectly says the quantum theory has not been experimentally confirmed. This just changed. Someone smarter than me needs to update this article to reflect recent experiments that have confirmed it.

Reference: https://scitechdaily.com/exotic-physics-phenomenon-involving-time-reversal-observed-for-first-time/ — Preceding unsigned comment added by 170.218.219.22 (talk) 17:16, 10 September 2019 (UTC)


 * Above is for an experimental observation of a non-Abelian Aharonov–Bohm effect. Not sure what it has to do with T-symmetry, but whatever. 67.198.37.16 (talk) 23:32, 14 December 2020 (UTC)

missing T-symmetry case annotation
In all the physics I ever did, time as a variable was t.

So one might think that outside of sentence-initial context, it would be written t-symmetry.

But not in this article. A painful search to the bottom found a couple of instances not in sentence-initial context, written with a full T.

This seems to be a problem with Wikipedia everywhere: many ambiguous terms are introduced as the first bold word of the lead, and the reader is left to play ctrl-F whack-a-mole.

I can't myself annotate the lead to the effect that the T in T-symmetry is always written uppercase, because I really don't know that. But it seems to be implied by this article as it stands, and it chances are high that it could be made usefully explicit by someone else. &mdash; MaxEnt 00:26, 4 February 2019 (UTC)


 * The current version of the lede now uses both upper and lower-case T. It is still confusingly written, though, and could be improved. I will try to do that now. 67.198.37.16 (talk) 23:36, 14 December 2020 (UTC)
 * ... Done. 67.198.37.16 (talk) 03:00, 15 December 2020 (UTC)

Amend lead as not true - Now theory, seem true/better
"does not show symmetry under time reversal, primarily due to the second law of thermodynamics." in the lead is not true, from "primarily".

"The Eddington proposal, that the arrow of time is related to entropy increase, has many shortcomings. At its heart, the second law is basically tautological" I've read that paper, not the book Now, or some links I found:

http://news.berkeley.edu/2016/09/20/new-book-links-flow-of-time-with-big-bang/

https://ww2.kqed.org/forum/2016/11/21/physicist-richard-muller-on-the-nature-of-now/ comp.arch (talk) 13:55, 23 January 2017 (UTC)


 * The second law is indeed tautological. This was conclusively proven in the 1960's thru 1990's during the development of chaos theory. But, sorry, linking the flow of time to big bang sounds like bunkum to me. But what do I know. 67.198.37.16 (talk) 03:03, 15 December 2020 (UTC)

Wrong kind of teeter-totter
The image next to the section: Macroscopic phenomena: the second law of thermodynamics has text about 'A toy called the teeter-totter' which links to the see-saw page through a redirect page. That's not what the image is referencing - it's a balancing toy such as this, this, or this. (I'm not sure how to describe the toy other than using links, sorry.) I was a bit confused as it took me a while to realize this and I thought the image was supposed to be a see-saw at first. I'm not really sure how to make this clearer, as teeter-totter is a correct (if old fashioned) way to refer to the balancing toy and I don't know of a better name or a page about this kind of toy on wikipedia. Perhaps someone else knows a page that has these kinds of toys, can re-write the description, or maybe just remove the hyperlink. A better image may help, as well. I also think the [how?] can be removed, as that's how the toy is meant to be used. --Zemaniac (talk) 00:07, 2 September 2016 (UTC)


 * A deeper issue is that I have no clue at all of what the text that goes with that picture is trying to say. It's word-salad to me; I don't understand what it has to do with irreversibility. A much, much better example might be finite-dimensional chaos e.g. the double pendulum. 67.198.37.16 (talk) 03:06, 15 December 2020 (UTC)

crossing the black hole event horizon
I think an object can not cross the event horizon, at least viewed by a distant observer. It can only asymptotically approach it. check this vid: https://www.youtube.com/watch?v=vNaEBbFbvcY — Preceding unsigned comment added by 84.3.64.74 (talk) 07:58, 27 January 2016 (UTC)


 * The distant observer never sees it cross. The object itself, however, crosses and is smushed in finite time. You should try it sometime, its like going over Niagra falls, but without the barrel. 67.198.37.16 (talk) 03:08, 15 December 2020 (UTC)

Deleted paragraph dealing with point space vs function space
Phase space is quantum mechanically required anyway, so this paragraph is irrelevant to the article. It is interesting, but: Dan Gluck (talk) 20:22, 25 December 2020 (UTC)
 * 1) Needs citing
 * 2) Belongs to a different article, e.g. phase space