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But "symmetry arguments" are usually considered "first principles reason". Of course, if you have a non-static background spacetime, time-translation symmetry is gone, i.e., at least this argument is no reason for unitarity.
How do you know there isn't a time-translation invariant CPTP evolution?vanhees71 said:But "symmetry arguments" are usually considered "first principles reason".
Let me give some context, because it's not really that I disagree in any way.vanhees71 said:This I don't know, but by definition a symmetry is realized in QT as a unitary (or antiunitary) ray representation. Analyzing the Galilei or Poincare groups for Newtonian or special-relativistic dynamics leads to unitary representations for the time translations, and that's why the time evolution of the system is described by a unitary transformation. The assumption of a symmetry is pretty restrictive in this sense.
Agreed, basically students are increasingly asking why can't the total closed system also be described with a CPTP evolution.vanhees71 said:Only the total closed system, particle+heat bath, is described by a unitary time evolution.
@vanhees71: nowhere in my post did I mention time reflection symmetry. A process can be time reversible (i.e. there exists a way to infer the past from the present) without being symmetric under time reversal.vanhees71 said:Time reflection symmetry has nothing to do with the unitary time evolution. In the parts of Nature (i.e., neglecting the weak interaction) it's an additional discrete symmetry, which must necessarily be represented as an anti-unitary transformation since the Hamiltonian must stay bounded from below under time-reversal. Although with the weak interaction the time evolution in Q(F)T is unitary.
The symmetry argument for unitarity of the time evolution is that time-translation invariance as a continuous symmetry must be realized as unitary transformation.
I don't know, where in this paper (no math!) is this important proof. The proof is of course due to Wigner and Bargmann. A very nice treatment is in the old edition in the QT textbook by Gottfried.bhobba said:What is it they said in Blazing Saddles - I like to keep my audience riveted. Lovely thread.
For a textbook reference, see Ballentine, page 64 in my edition, but is likely in the first couple of pages of Chapter 3 in any edition. Here he evokes Wigner's Theorem, which has already been mentioned.
My contribution is for those that may not have heard of it before; here is the statement and proof (as mentioned originally due to Weinberg):
https://arxiv.org/pdf/1603.00353
Thanks
Bill
I guess you wanted to post a different reference. This is the same reference you also posted at the same time in another thread, and is unrelated to unitary evolution.bhobba said:My contribution is for those that may not have heard of it before; here is the statement and proof (as mentioned originally due to Weinberg):
https://arxiv.org/pdf/1603.00353
I only read Ballentine recently thanks to this forum. A really good text, wished I'd had it as an undergraduate. I loved the section on state tomography.bhobba said:For a textbook reference, see Ballentine, page 64 in my edition, but is likely in the first couple of pages of Chapter 3 in any edition. Here he evokes Wigner's Theorem, which has already been mentioned.
Whoops. Sorry guys - fixed now.gentzen said:I guess you wanted to post a different reference. This is the same reference you also posted at the same time in another thread, and is unrelated to unitary evolution.
This book had a strong effect on me.LittleSchwinger said:I only read Ballentine recently thanks to this forum. A really good text, wished I'd had it as an undergraduate. I loved the section on state tomography.
Thanks for that. What a lovely paper. Given the above and your like of Ballentine, I think you might enjoy Talagrand's new book on QFT where he really digs deep into representations of the Poincaré group. He treats even massive Weyl Spinors.bhobba said:Whoops. Sorry guys - fixed now.
Thanks
Bill
LittleSchwinger said:Thanks for that. What a lovely paper. Given the above and your like of Ballentine, I think you might enjoy Talagrand's new book on QFT where he really digs deep into representations of the Poincaré group. He treats even massive Weyl Spinors.
vanhees71 said:But Dirac's book is excellent. What's the problem with it? Von Neumann is of course mathematically rigorous and Dirac is not.
Interesting, can you give a reference with more details?vanhees71 said:Note that, despite for claims often to be read in textbooks, there's no need for parity or time-reversal symmetry for the detailed-balance relations to be valid.
So in classical physics, detailed balance is a consequence of the Liouville theorem, would you agree?vanhees71 said:Landau and Lifshitz vol. X! You find the argument also in my transport manuscript:
https://itp.uni-frankfurt.de/~hees/publ/kolkata.pdf
It has an explicit collapse postulate!vanhees71 said:But Dirac's book is excellent. What's the problem with it?
This also applies to reading your lecture notes and your contributions to PF.. The collapse - not necessarily the von Neumann form but in the general POVM related version - is used informally almost everywhere, namely whenever one argues how a state is prepared.vanhees71 said:physics students also have to learn to "not listen to their words but looking at their deeds" (as Einstein adviced concerning all writings of theoretical physicists).
It does not. And not because Dirac uses the word "principle" instead of "postulate", or the word "jump" instead of "collapse". But this is indeed off-topic.A. Neumaier said:It has an explicit collapse postulate!
You are mistaken. See https://www.physicsforums.com/threads/is-collapse-indispensable.854384/post-5359158physicsworks said:It does not. And not because Dirac uses the word "principle" instead of "postulate", or the word "jump" instead of "collapse".
Again, this is off-topic, but: thank you, I actually have read Dirac, both the original and the first Russian edition edited by Fock. Nowhere in the book did he elevate the notion of throwing out a part of the probability distribution describing a physical system to a grand status of a physical principle (using Dirac's language when writing the book). Therefore, not even esteemed Peres could find (not that he would or should have) even a small section in Dirac's book with the words "jump" and "principle" in its title (Dirac never uses the word "collapse" in his book). However, you will find an entire chapter on "The Principle of the Superposition" and separate sections on "Heisenberg's Principle of Uncertainty" and "The Action Principle".A. Neumaier said:You are mistaken. See https://www.physicsforums.com/threads/is-collapse-indispensable.854384/post-5359158
I have just now re-read the relevant section of Dirac's book (The Principles of Quantum Mechanics, 1982 ed). On p35 he writes:physicsworks said:Again, this is off-topic, but: thank you, I actually have read Dirac, both the original and the first Russian edition edited by Fock. Nowhere in the book did he elevate the notion of throwing out a part of the probability distribution describing a physical system to a grand status of a physical principle (using Dirac's language when writing the book).
This is not exactly the usual collapse-like assumption, but Dirac goes on with: "some of the immediate consequences of the assumptions will be noted ..." (my emboldening). Among these "consequences of the assumptions" is the passage referenced by Peres and Terno, i.e., (p36):Dirac said:We now make some assumptions for the physical interpretation of the theory. If the dynamical system is in an eigenstate of a real dynamical variable ##\xi##, belonging to the eigenvalue ##\xi'##, then a measurement of ##\xi## will certainly give as result the number ##\xi'##. [...]
It's pretty clear that Dirac infers a jump in the state of system (what in modern times would normally be called "collapse") as an "immediate consequence" of his assumption. Sure, it's not in a section title, afaict, but so what?Dirac said:When we measure a real dynamical variable ##\xi##, the disturbance involved in the act of measurement causes a jump in the state of the dynamical system. 'From physical continuity, if we make a second measurement of the same dynamical variable ##\xi## immediately after the first, the result of the second measurement must be the same as
that of the first. Thus after the first measurement has been made, there is no indeterminacy in the result of the second. Hence, after the first measurement has been made, the system is in an eigenstate of the dynamical variable ##\xi##) the eigenvalue it belongs to being equal to the result of the first measurement. This conclusion must still hold if the second measurement is not actually made. In this way we see that a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured, the eigenvalue this eigenstate belongs to being equal to the result of the measurement.