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A quantum vacuum corresponds to closed loops of particle-antiparticle pairs, in the language of Feynman diagrams. There is no relation between $E$ and $p$ for these particles, i.e., they are not on their mass shell. It is suggested that the QV is insensitive to the direction of time (seen as an irreversable thermodynamic process), but I'm not sure what this means. On top of that it is said that we can't make a mental picture of a QV, and it's purely a mathematical construct (which means we can make a time reversal operation on the QV). But it has to correspond something physical. So suppose we could make a film of the process (which involves time), could we see a difference between the film running forwards or backwards. That is, is the QFT vacuum $T$-invariant?

Qmechanic
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Deschele Schilder
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    This is a perfectly good question and completely clear. I don't understand the down votes or close vote. – N. Virgo May 23 '18 at 13:37
  • possible duplicate of https://physics.stackexchange.com/questions/253540/why-are-there-e-m-vacuüm-fluctuations by OP. – AccidentalFourierTransform May 23 '18 at 14:20
  • Time's arrow only gets defined when thermodynamic (entropy) issues come into play. Since the temperature of the quantum vacuum is 0 both prior to and after the fluctuation, there can be no sensitivity to the direction of time. – Lewis Miller May 23 '18 at 14:27
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    Virtual particles don't "pop" into existence. To exist means to move in time. Virtual particles don't move in time. So reversing time would not change the picture. – safesphere May 23 '18 at 14:46
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    @Nathaniel Because "virtual particles popping in and out of existence" has no basis in actual QFT, it's a crude picture used in pop science. If the question starts from an incorrect premise, it can't be answered. – knzhou May 23 '18 at 14:59
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    Also, OP has about 25 questions about this exact same subject, and the answer to every single one of them is "don't take popsci too literally" or perhaps "read a textbook". – knzhou May 23 '18 at 15:00
  • @knzhou (re: your second comment) fair enough, but (re: your first to last comment) should we not be charitable and interpret the question as "does the vacuum state have an asymmetry with respect to time reversal?" Then it's a technical question that as far as I know has quite an interesting answer to do with CPT symmetry. – N. Virgo May 24 '18 at 01:58
  • (Also I'm pretty sure "particles popping in and out of existence" just means Feynman diagrams.) – N. Virgo May 24 '18 at 02:03
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    @knzhou-I've read Lewis H. Ryder's book on QFT together with a piece of work written by the professor (and many articles on the net after that) for my exam on QFT and strange enough I did well! To say I only read popular science books is simply not true. Who are you to say so? You don't know anything about me! I don't make any difference between so-called experts and laymen. And where are all the questions I asked about this? This is the first time I asked this! – Deschele Schilder May 24 '18 at 07:40
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    @safesphere-So time is standing still in a quantum vacuum? – Deschele Schilder May 24 '18 at 07:48
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    @knzhou- You write: "about 25 questions about exact this object". Be a bit more scientific and check the facts you state! You'll see I've asked questions about virtual particles, but not about "this exact same subject". And certainly not 25! – Deschele Schilder May 24 '18 at 07:55
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    @Nathaniel-You seem to be the only one who understands what I ask! – Deschele Schilder May 24 '18 at 07:57
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    @Nathaniel If you were to answer the question as asked, you would have to make up a story about how virtual particles behave, which would be wrong. If you were to just answer the question you say, you would have to ignore the entire body of the question. – knzhou May 24 '18 at 09:07
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    @descheleschilder You have 25 questions on the behavior of virtual particles. If you read Ryder, that’s great, but surely you noticed that Ryder did not talk about virtual particles in the literal way you do. This picture you are using comes from popsci. – knzhou May 24 '18 at 09:09
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    @descheleschilder I’m not against trying to get intuition for QFT by any means, but if you use virtual particles as your primary tool you’re just digging yourself a deeper hole! – knzhou May 24 '18 at 09:16
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    Agree with Nathaniel in that IMO this question is perfectly clear, and I totally don't get the downvote rage. OP, can you please reformulate it to ask whether the QFT vacuum is T-invariant (or CP-invariant, those are the same according to the CPT theorem)? – Prof. Legolasov May 27 '18 at 22:33
  • @SolenodonParadoxus-I tried to reformulate the question, as you asked. Thanks for the advice! – Deschele Schilder May 30 '18 at 07:30

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A quantum vacuum is an eigenstate of the Hamiltonian, so the energy is certain and the occupation numbers are certain too. "Fluctuations" of some variables (like $x$ and $p$) do not change this fact. So it is a T-invariant state.

Vladimir Kalitvianski
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