# Quantum vacuum nothing or sea of energy

1. Nov 7, 2012

### osman ibn ali

I always thought that the quantum vacuum was absolutely nothing. But I have heard that the quantum vacuum is not nothing and contains energy although it is the lowest state of energy. I am not talking about the fluctuations rather I am talking about the vacuum itself. Also do quantum fluctuations have causes or do we adopt an in deterministic interpretation??

2. Nov 8, 2012

### Sonderval

The vacuum in QFT is a superposition of different field configurations. You can compare it to the ground state of a harmonic oscillatorin the following way:
Consider one fourier component phi(k) only.
phi(k) is the classical amplitude of the field. It corresponds to the x-coordinate in teh ground state of the H.O.
In the H.O. ground state, the x component has a probability distribution that looks like a Gaussian function - there is a prob. to find the particle at position x given by this distribution.
The same holds for the field amplitude: There is a gaussian distribution to measure any field amplitude, centered at an amplitude of zero and falling off to larger values.
Similar to the zero-point energy in the H.O., this non-vanishing of the probability for an amplitude that is not zero gives you a zero-point energy.
For the full vacuum, you have to consider all possible k-values, this is why you get very large (unphysical) values for the zero-point energy.

Quantum fluctuations are a slightly different thing - in a free field theory, there are no fluctuations (there can't be because the vacuum is Lorentz invariant, so there is no reason for a fluctuation to be "here" and not "there"). In an interacting theory, you can imagine that the interaction "measures" the field amplitude and thus "realises" a fluctuation; exactly in the same way as you could measure the particle in the H.O, ground state and realise a non-zero position. Similar to the measurement problem, there is no way to determine the actual outcome of such a "field measurement".