Quantum fluctuations and Inflation

[rodsika]

Wikipedia defines quantum fluctuations as:

"In quantum physics, a quantum fluctuation is the temporary change in the amount of energy in a point in space,[1] arising from Werner Heisenberg's uncertainty principle.

According to one formulation of the principle, energy and time can be related by the relation

delta E delta t ~ h/2pi

That means that conservation of energy can appear to be violated, but only for small times. This allows the creation of particle-antiparticle pairs of virtual particles. The effects of these particles are measurable, for example, in the effective charge of the electron, different from its "naked" charge.

In the modern view, energy is always conserved, but the eigenstates of the Hamiltonian (energy observable) are not the same as (i.e. the Hamiltonian doesn't commute with) the particle number operators.

Quantum fluctuations may have been very important in the origin of the structure of the universe: according to the model of inflation the ones that existed when inflation began were amplified and formed the seed of all current observed structure."Also I read elsewhere"It is primarily the successful prediction of the form of the microwave background fluctuations that has caused inflation to be generally accepted today by most early universe physicists. Since these small inhomogeneities are what later gave rise to galaxies, stars, and us, all of the structure we see in the universe arose because of quantum fluctuations."

Now question:Virtual particles are supposed to be mathematic artifact of perturbation theory as many emphasized here. But how could virtual particles fluctuations got amplifed and and formed the seed of all current observed structure if they were supposed to be just mathematical artifacts without physical contents??!

Hope someone can settle this once and for all.

 

[Bill_K]

As the Wikipedia article says, the Hamiltonian does not commute with the number operator. The difference arises in which boundary conditons you choose to impose. You can solve for a steady state in which the solution is a superposition of states with different particle numbers. You may wish to interpret this by saying that virtual particles are continually being created and destroyed.

Or you can start with an initial state with a definite number of particles present and solve for its time evolution. In this case, since the initial state is not an eigenstate of H, real particles will be created.