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When studying the QFT, one considers the vacuum state when the field is not excited and therefore no particles are present.

Now for the matter fields this makes sense to me.

But what about the radiation field?

Suppose we have an arbitrary small volume of space in the universe without any matter particles inside of it. An empty volume of space.

But can we say that there are not any photons inside this empty spatial volume?

I mean regardless of where we pick the empty volume in the universe there is some radiation coming to that volume from some galaxy source.

Then what is actually the difference between an empty (of matter) space and the vacuum that is talked about in the QFT.

I suppose by QFT vacuum we actually mean even there is no excitation of the electromagnetic field and therefore no photons.

But can we have any volume of space at any time through which a photon doesn't pass?

VVM
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  • The photons are on par with all the other elementary particles in the standard model QFT, so if you understand it for the rest of the fields you should not exclude photons. https://upload.wikimedia.org/wikipedia/commons/thumb/0/00/Standard_Model_of_Elementary_Particles.svg/360px-Standard_Model_of_Elementary_Particles.svg.png – anna v Jan 20 '22 at 14:05
  • I know. But the question is that whether we can have a vacuum at all when photons are everywhere in the universe? Don't we mean by vacuum a space empty of photons as well as other particles? – VVM Jan 20 '22 at 15:00
  • You are assuming a universe full of only photons. Why not assume a universe full of only electrons and positrons? it is all assumptions and the answer is the same – anna v Jan 20 '22 at 16:13
  • I feel like there's a misunderstanding here. I'm not assuming anything. I'm asking when we talk about the vacuum in the universe and the vacuum energy, how can we have an empty volume of space at all, I can see that there are empty volume of matter field in the universe, between stars for example, but even there there should pass some photons and so it cannot be a vacuum! – VVM Jan 20 '22 at 16:29
  • you are thinking empty as in the classical vacuum, not the QFT one, see https://physics.stackexchange.com/questions/146003/are-vacuum-fluctuations-really-happening-all-the-time – anna v Jan 20 '22 at 17:09
  • I know that in the vacuum of the QFT there exists quantum fields. But none of them excited to become a particle like electron or photon. All are virtual particles. But again my question is about a real photon that passes through a quantum vacuum. Because wherever you have your quantum vacuum you will have a real photo passing by from some source. That is confusing to me. – VVM Jan 20 '22 at 17:52

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I think there are actually three concepts of vacuum that are being confused here

  • The "free vacuum" is the one where there are no excitations. That means no matter particles, no photons, it is the 'nothing' state.
  • The "interacting vacuum" is the actual ground state (lowest energy state) of a quantum field theory, and it is (perhaps surprisingly) not the same thing as the free vacuum, colloquially we say there are particle-antiparticles populating the vacuum.
  • This is not standard terminology, but I believe you are also mentioning the "cosmic vacuum", that is to say, what we think of as empty space, if I were to travel to outer space in a rocket. I'm basing this off this quote in your question "there is some radiation coming to that volume from some galaxy source". This 'outer space' is, as you've observed, not really empty at all, in fact the Cosmic Microwave Background photons are flying around in outer space, heating it to a temperature of about 3 Kelvin.

These three vacuums are different. In Quantum Field Theory, most often you will be working with the first two, and not dealing with thermal effects.

QCD_IS_GOOD
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  • Exactly! Now my question is how can we observe and measure interacting vacuum value when we don't have a cosmic vacuum? I think the answer is: because the distance scales that we talk about and calculate in interacting vacuum and vacuum energy in QFT is much much smaller than the distance scales relevant for the cosmic vacuum and the thermal effects energy, right? Actually we subtract the CMB from the energy inside of empty space to obtain experimental data on the value of interacting vacuum energy and compare with the QFT prediction, right? – VVM Jan 21 '22 at 14:37