Vacuum in Quantum Field theory is not empty

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In Quantum Field Theory (QFT), the vacuum is not truly "empty" but rather a dynamic state with fluctuating energy levels, where particles can emerge through processes like pair production. While some may claim particles are created from "nothing," this is misleading; they arise from energy interactions, not a void. The distinction between "bare" and "physical" particles complicates the understanding of the vacuum, as the former are mathematical constructs that do not represent observable phenomena. The concept of virtual particles, often discussed in QFT, serves as a useful tool in calculations but does not correspond to real, observable entities. Ultimately, the vacuum in QFT is a well-defined state of lowest energy, filled with potential rather than emptiness.
  • #31
Nick666 said:
Is space similar to an empty set in math ?

No. Space is like R^3 the set of all ordered triples of real numbers.
 
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  • #32
And the real numbers corespond to what?
 
  • #33
points in space.
 
  • #34
And the points corespond to ?
 
  • #35
Nick666 said:
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.
 
Last edited:
  • #36
Nick666 said:
And the points corespond to ?

The ordered triples of real numbers.
 

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