# Vacuum Zero-point Fluctuations

Q:
I was reading Stephen Hawking's Universe in a nutshell reasently and it said that virtual particle pairs were created constantly in vacuum. It said that the ground state fluctuations were negitive if the virtual particle was a fermion and positive if it was a boson and that these should cancle out. 1) But what is meant by negitive energy for fermions? 2) How can energy be negitive? 3)Does this mean that Albert Einstein was wrong and space-time can be curved in the opposite way so that gravity can be repulsive? Much apprechated, Greg
- Greg Cowan (age 13)
Nelson, New Zealand
A:
1. That's a good question, but I don't understand quantum field theory well enough to answer it. If I get some help, this answer will be updated.
2. Even in classical physics, negative energies are common. For example, the gravitational potential energy of two nearby objects is negative, if we start with the standard convention that when the objects are very far apart that energy is zero.
3. Oddly, it's the positive energy density of bosons which creates a repulsive effect in Einstein's General Relativity. (Einstein guessed correctly that some effect like that might exist, but then retracted the guess.) A negative background energy density creates an attractive effect. This is reversed from what you might expect essentially because the vacuum energy is not some fixed amount but rather a fixed density. As space expands or contracts the background energy associated with some particular region changes because the density is fixed and the volume changes. In contrast, most of the energy associated with simple matter is unaffected by the expansion of space, and the resulting gravitational effects are always attractive.

Mike W.

(published on 06/29/2008)

## Follow-Up #1: dark energy

Q:
In the third part of your answer to the last question, you meantioned that as space or 'the universe' expands, the dencity of the vacumme chages. Does this mean that gravity is changing strength? Will the changed density change the liklyhood of a vacumme bubble. Many thanks, Dave
- Dave Williams
NZ
A:
We've touched up our old answer to further emphasize that the dark energy density remains fixed. That means that the gravitational effects from it stay constant. Other types of energy, associated with matter, do not have a fixed density. Therefore their gravitational effects change as the universe expands. As ordinary matter gets more dilute, its effects on the universal expansion become small.

Mike W.

(published on 09/02/2008)

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