What is the origin of vacuum fluctuations in quantum field theory?

[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

 

[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).

 

[bennington]

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).

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 http://en.wikipedia.org/wiki/Pair_production" seemed to confuse me even more.

Since the momentum of the initial photon must be absorbed by something, pair production cannot occur in empty space out of a single photon; the nucleus is needed to conserve both momentum and energy.

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

In semiclassical general relativity, pair production is also invoked to explain the Hawking radiation effect. According to quantum mechanics, at short scales short-lived particle-pairs are constantly appearing and disappearing (see quantum foam); in a region of strong gravitational tidal forces, the two particles in a pair may sometimes be wrenched apart before they have a chance to mutually annihilate. When this happens in the region around a black hole, one particle may escape, with its antiparticle being captured by the hole.

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

Concerning http://en.wikipedia.org/wiki/Virtual_particle#Pair_production"...

In order to conserve the total fermion number of the universe, a fermion cannot be created without also creating its antiparticle; thus many physical processes lead to pair creation. The need for the normal ordering of particle fields in the vacuum can be interpreted by the idea that a pair of virtual particles may briefly "pop into existence", and then annihilate each other a short while later.

Thus, virtual particles are often popularly described as coming in pairs, a particle and antiparticle, which can be of any kind. These pairs exist for an extremely short time, and mutually annihilate in short order. In some cases, however, it is possible to boost the pair apart using external energy so that they avoid annihilation and become real particles.

This may occur in one of two ways. In an accelerating frame of reference, the virtual particles may appear to be real to the accelerating observer; this is known as the Unruh effect. In short, the vacuum of a stationary frame appears, to the accelerated observer, to be a warm gas of real particles in thermodynamic equilibrium. The Unruh effect is a toy model for understanding Hawking radiation, the process by which black holes evaporate.

Another example is pair production in very strong electric fields, sometimes called vacuum decay. If, for example, a pair of atomic nuclei are merged together to very briefly form a nucleus with a charge greater than about 140, (that is, larger than about the inverse of the fine structure constant), the strength of the electric field will be such that it will be energetically favorable to create positron-electron pairs out of the vacuum or Dirac sea, with the electron attracted to the nucleus to annihilate the positive charge. This pair-creation amplitude was first calculated by Julian Schwinger in 1951.

The restriction to particle-antiparticle pairs is actually only necessary if the particles in question carry a conserved quantity, such as electric charge, which is not present in the initial or final state. Otherwise, other situations can arise. For instance, the beta decay of a neutron can happen through the emission of a single virtual, negatively charged W particle that almost immediately decays into a real electron and antineutrino; the neutron turns into a proton when it emits the W particle. The evaporation of a black hole is a process dominated by photons, which are their own antiparticles and are uncharged.

It is sometimes suggested that pair production can be used to explain the origin of matter in the universe. In models of the Big Bang, it is suggested that vacuum fluctuations, or virtual particles, briefly appear. Then, due to effects such as CP-violation, an imbalance between the number of virtual particles and antiparticles is created, leaving a surfeit of particles, thus accounting for the visible matter in the universe.

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.

 

[CompuChip]

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 http://en.wikipedia.org/wiki/Pair_production" seemed to confuse me even more.

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.

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

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...

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

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 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.

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)