# Virtual particle content of the vacuum state....

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asimov42
TL;DR Summary
Throw in an electron and what happens?
Hi all,

One more virtual particle question (sorry all!): for individuals who would take virtual particles as being 'real' (but unobservable), what is their understanding then of the content of the vacuum?

For example, if I place a electron all by itself in the vacuum (thus making it no longer a vacuum, I realize), is there some non-zero probability that the electron does not interact with a virtual particle at every instant in time? That is, if the vacuum contains an infinite number of virtual electron-positron pairs, for example, what happens?

I realize the above question may not be well-posed (I'm just trying to get a sense the implications - but would agree with @A. Neumaier about the existence of virtual particles ... although some do not).

## Answers and Replies

is there some non-zero probability that the electron does not interact with a virtual particle
Quantum field theory does not allow one to compute such a probability, not even in principle. This shows that the question is meaningless.

mattt, Demystifier and vanhees71
asimov42
Ah - I should have guessed - is this simply due to lack of state?

Mentor
if the vacuum contains an infinite number of virtual electron-positron pairs, for example, what happens?

Try forgetting about virtual particles for a moment and ask yourself: if there was just a single electron, all alone in what otherwise is a vacuum, what could happen?

From the standpoint of QED, the answer is, only one thing can happen: the electron can just continue to be an electron. In terms of Feynman diagrams, there is only one kind of diagram that can apply to this state: one electron line goes in, and one electron line comes out. So the probability of that happening is one. And without virtual particles, there is only one diagram of this kind: the one with just one electron line and nothing else. So the probability of just this diagram alone is one.

Now put the virtual particles back in: what changes? The answer is, nothing. Yes, the mathematical model including virtual particles will now give you an infinite number of diagrams that satisfy the condition of having one electron line going in and one electron line coming out: but the amplitudes for all of those diagrams except for the zero-order one--the one that just has one electron line and nothing else--must cancel out, since the total probability still has to be one, and the probability with just that single diagram (the one with just one electron line and nothing else) is one. So virtual particles add nothing at all to the analysis. You can ignore them completely and still get the right answer.

mattt, vanhees71, asimov42 and 1 other person
Staff Emeritus
Let me expand on Peter:

A physical electron has no interaction with the physical vacuum.
Questions about how a non-physical electron would interact with a non-physical vacuum are, practically by definition, not something physics can address.

mattt and vanhees71
Mentor
Let me expand on Peter

"Expand on" meaning "restate much more briefly"...

vanhees71 and Vanadium 50
Staff Emeritus
A contronym, like "dust" or "cleave".

asimov42
A physical electron has no interaction with the physical vacuum.
Questions about how a non-physical electron would interact with a non-physical vacuum are, practically by definition, not something physics can address.

Thanks @Vanadium 50 and @PeterDonis - always very helpful. @Vanadium 50 could you comment in a bit more detail on the physical electron and physical vacuum and the lack of interaction? I realize nothing should be 'popping' in and out of anywhere - just want to make sure I'm clear on the meaning of 'physical'.

Mentor
could you comment in a bit more detail on the physical electron and physical vacuum and the lack of interaction?

That would be my post that @Vanadium 50 "expanded" on. The "physical electron" is just the electron that has nothing else to interact with; the "physical vacuum" is the nothing else.

Vanadium 50 and vanhees71