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) 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.

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... so as you can see, the Heisenberg uncertainty principle actually says alot about something being made from nothing.

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