# Quantum vacuum fluctuations

1. Jan 27, 2008

### bennington

Hello, I was wondering something about the quantum field theory. Do vacuum fluctuations (the ones that create virtual-antiparticle pairs) come from nothing? I have heard three different responses to these. The first is that they do come from nothing, the second is that come from zero-point vacuum energy, and the third is that they come from excess energy in the vacuum. The reason for my misunderstanding comes froma quote from Paul Davies:

“The processes described here do not represent the creation of matter out of nothing, but the conversion of pre-existing energy into material form.”

If one is true, then thermodynamics are violated. If two is true, then is the vacuum energy not really zero-point energy?

Thanks

2. Jan 28, 2008

### CompuChip

Welcome to PF bennington.

I look at this using the picture of the Dirac sea, which fills all the negative energy states, for the vacuum. By adding a certain amount of energy a particle from this sea can be excited to positive energy -- this gives for example an electron while the negative-energy hole that is left is called a positron. Eventually the particle will fall back to its original state, annihilating the electron/positron pair. In principle, this violates energy conservation, though it is actually allowed for short enough times by the uncertainty principle (lifetime of the excitation and the energy needed for it are inversely proportional by $\Delta E \Delta \tau \ge$ some lower bound ($\hbar/2$)).

I'm not sure what is meant by "zero-point energy", isn't that just precisely the energy involved in these kind of fluctuations? So saying the energy comes from zero-point energy sounds tautological then.

You might want to read up on tunneling, which is a similar effect (particles getting to classically "prohibited" states).

3. Jan 28, 2008

### bennington

So, in a way, they do partially come from nothing, right? I'm not so sure about Wikipedia (although I'm sure many members here edit it). Their article on pair production seemed to confuse me even more.

So they're stating that pair production cannot occur without a nucleus (is this right?) But then they say:

By this reasoning, would conservation of angular momentum be violated?

Concerning virtual particles...

How is this possible without any nuclei present to account for angular momentum? I am sorry if these questions seem stupid, but this is simply because I have not yet taken a formal high school physics course yet. Thank you for taking the time to answer these dumb questions.

4. Jan 29, 2008

### CompuChip

If you want, they come from nothing. As I view it, energy (perhaps coming from thermal fluctuations) can be used to temporarily create a particle pair (remember, energy = mass), though conservation of energy and the uncertainty principle require it to be annihilated after a short time again.

I don't really know what is meant here. Is the word "nucleus" used in the same meaning as, for example, a saturated gas only condensing around a "nucleus" (impurity)? I'm not sure that'd be necessary...

Not as far as I can see (maybe the particles aren't rotating at all?). But perhaps there is an uncertainty relation for angular momentum as well (like for position and momentum; or energy and life time). Again, I haven't really read the Wikipedia page (and it may just be wrong, after all it isn't always a reliable source), but I don't immediately see the point of a nucleus and angular momentum... in general I'd say it's possible for one of the virtual particles to have the property, as long as the other one has the opposite property (e.g. angular momenta L and -L, spin up and down, momentum p and -p, etc).

I haven't taken such a course either (and I am far from expert on this area, as well). Anyway, there are no stupid questions (just stupid answers, so watch out, I might have given you some ). We all have to learn some time, and no better way to learn than by asking someone who knows (or at least, in my case, knows a little or pretends to know a little)