Vacuum in Quantum Field theory is not empty

[olgranpappy]

Is space similar to an empty set in math ?

No. Space is like $$R^3$$ the set of all ordered triples of real numbers.

 

[Nick666]

And the real numbers corespond to what?

 

[olgranpappy]

points in space.

 

[Nick666]

And the points corespond to ?

 

[meopemuk]

And the points corespond to ?

In my opinion, we need to distinguish two things: "vacuum" and "position space".

Vacuum (or "empty space") is an example of a physical system from which all particles has been removed. It is simply a no-particle physical system. So, vacuum is somewhat analogous to the "empty set"

Position space is a linear 3-dimensional space $R^3$ which is a common set of eigenvalues of three commuting components of the position operator. Points in this space enumerate possible values that can be obtained by measuring the observable called "position". Position-space wavefunctions are defined on this space. This is an abstract space, similar to the momentum space or any other common set of eigenvalues of commuting operators in quantum mechanics.

Eugene.

 

[olgranpappy]

And the points corespond to ?

The ordered triples of real numbers.