1
$\begingroup$

I'm puzzled by this statement by Dieter Zeh: "Various types of quantum fluctuations (in particular vacuum fluctuations, often visualized in terms of 'virtual particles') are used to describe genuine quantum properties, such as the minimal curvature of the wave function or a certain entanglement that exists in the static ground states of interacting quantum fields (their physical vacua)." (Quoted in Quantum discreteness is an illusion, 2008 p.18).

And I can assure you that this thesis is to be found everywhere in his writings. Vacuum fluctuations represent static quantum correlations (=entanglement) in the Schrödinger picture. Could you help me interpret this statement (about which, alas, it doesn't say much more, at least as far as I know)? I'm struggling to see what an entanglement between the respective voids of two fields could mean. Nor do I know whether this thesis is particularly heterodox.

Improve this question
$\endgroup$
2
  • 3
    $\begingroup$ "Vacuum fluctuations" always seemed more like a poorly conceived mental model than a real physical effect to me. I certainly don't know how to measure them with an experimental method. I also don't know why they are supposed to be linked to entanglement. What is "the ground state of the physical vacuum is entangled" supposed to mean? Entangled with what? Itself? That's contrary to the usual statements about the locality of quantum fields, isn't it? Do you have an example from the literature? $\endgroup$
    – FlatterMann
    Commented Jul 4 at 13:44
  • 1
    $\begingroup$ No idea. It's simply a thesis I've read in Zeh's paper : Entanglement exists in the static ground state of relativistic QFT , where it is often (erroneously, according to Zeh) regarded as vacuum fluctuations in terms of " virtual " particles. As far as I understand, then, it would be an entanglement between two (ground states of two) fields. $\endgroup$
    – Husserliana
    Commented Jul 4 at 13:59

1 Answer 1

Reset to default
6
$\begingroup$

By some measures the vacuum state is highly entangled as described by a result in quantum field theory called the Reeh-Schlieder theorem. See Section V of a review of "Quantum Information and Relativity Theory" in Reviews of Modern Physics in 2004 by Peres and Terno:

It asserts that there are local operators $Q \in A(O)$ which, applied to the vacuum, produce a state which is arbitrarily close to any arbitrary $|\gamma\rangle$ (the vacuum state can be replaced by any state of finite energy). Thus in principle any entangled state can be arbitrarily closely approximated by suitable local operations on any other state.

The idea that the vacuum is highly entangled is entirely compatible with the locality of QFT since locality states that the observables of spacelike separated systems commute with one another and in general the observables of two different systems, including two entangled systems, commute with one another. For more discussion of some of the issues raised by the Reeh-Schlieder theorem see this paper, especially Section 5:

https://arxiv.org/abs/quant-ph/0112148

Improve this answer
$\endgroup$
4
  • $\begingroup$ Do we have a physical interpretation for this result? How do I even measure the vacuum ground state? It doesn't produce any quanta of energy that I can conceivably measure. To put it mildly... the physical vacuum doesn't glow and it's generally unobservable. What does it mean that something unobservable is entangled in physical terms? That an excited state is necessarily entangled with some other part of the physical vacuum seems obvious, but we don't even need QFT for that. It follows directly from conservation laws, does it not? $\endgroup$
    – FlatterMann
    Commented Jul 4 at 20:46
  • $\begingroup$ There have been some proposals for observing the Unruh effect: arxiv.org/abs/1003.0720 arxiv.org/abs/2007.09523 but not every implication of a theory is going to experimentally testable. $\endgroup$
    – alanf
    Commented Jul 4 at 21:32
  • $\begingroup$ Thanks. I will read that paper and try to understand the implications. With regards of the experimental testability... there are obviously things in the theory that are mathematical "artifacts". Coordinate system independence is one of the examples that come to mind, or the additive constant in a potential. Shall we treat this result in the same light? $\endgroup$
    – FlatterMann
    Commented Jul 4 at 22:04
  • $\begingroup$ I doubt it's a mathematical artefact because it is in principle detectable and there are theoretical reasons to think it's a real effect. $\endgroup$
    – alanf
    Commented Jul 5 at 8:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.