I got this at
http://zebu.uoregon.edu/~imamura/209/apr14/virtual.html
Can anyone see how he/she justifies the comment at the bottom?
Virtual Particles
The vacuum is seething with activity. Particles continuously come into existence and go out of existence all of the time. This property follows directly from the quantum nature of the sub-atomic world. To see this, recall the Heisenberg Uncertainty Principle (HUP). In the formulation that I have talked about in this class, the uncertainty in the position of a particle and the uncertainty of the momentum of a particle were related. There are also other (equivalent) ways to state the Heisenberg Uncertainty Principle. One such formulation uses the energy of a particle and the time at which the energy is measured. In this case, we have that
d(energy) x d(time of measurement) is greater than (h/2pi)
So, this says that if I measure the energy of a particle to very high precision, then there is a huge uncertainty in when it could have this energy!
Now let's look at the vacuum. Suppose that there is nothing in the vacuum (no matter or radiation at all), according to the HUP there is an uncertainty in the amount of energy which can be contained in the vacuum. On average, the energy is constant, however, there is always a slight uncertainty in the energy, dE. This small uncertainty allows a nonzero energy to exist for short intervals of time defined by
dT = (h/2pi) / dE
Small uncertainties in energy can actually live for very long times. Because of the equivalence between matter and energy, these small energy fluctuations can produce matter (particles) which exists for a short time and then disappears.
The particles produced in this manner are not arbitary. What happens is that pairs of particles are produced -- a particle and its anti-particle twin are produced. This allows certain properties of the Universe to be preserved. Also, an interesting note is that the particles cannot be measured directly (hence the name virtual pairs) and so no physical laws such as the conservation of energy are seen to be violated!
Consider a proton and the anti-proton. They have masses of 1.7 x 10**(-24) grams and so, if a virtual pair is created,
dE = (2m[proton]) c**2 = 3 x 10**(-3) ergs
===>dT ~ lifetime ~ 10**(-27) / dE ~ 3 x 10**(-25) seconds!!!!
So a proton/anti-proton pair will pop into and go out of existence in the background after less than 10**(-25) seconds.
Pair Production
The existence of virtual pairs helps to explain a process known as pair production. The background is always seething with these pairs of particles. However, in order not to violate physical laws, the pairs always return back to the vacuum before they are observed directly.
However, these virtual pairs can become real particles. It is found that when there are very high energy photons, that the energy of the photons can be channeled into the virtual pairs and the virtual particles can become real. This process is known as pair production. The collision and subsequent disappearance of a particle/anti-particle pair is known as annihilation. What this means is that if there is a large supply of high energy photons then particles can be created.
How energetic do the photons have to be?
Consider proton/anti-proton pairs. Recall that the energy of such a virtual pair is 3 x 10**(-3) ergs
To make the discussion more concrete, let's talk in terms of temperatures. Since the temperature of a gas is a measure of the average kinetic energy of the particles, we have that 1.5 k T ~ energy or
T ~(2m(proton)c**2) / (1.5 k) ~ 10**13 Kelvin
So, the gas needs to be hotter than 10 trillion Kelvin in order to make proton/anti-proton pairs.
Particle Rest Energy (MeV) Threshold (Kelvin)
neutrinos ? ?
electrons 0.511 6 x 10**9
muons 105.7 1.2 x 10**12
protons 938.3 1.1 x 10**13
neutrons 939.6 1.1 x 10**13
Comment--note that matter and anti-matter particles seem like that they should be produced in equal amounts. In the Universe, for every billion anti-matter particles produced, there seems to have been one billion and one matter particles produced. Hmmmm.
