[jeffreyH (OP)]

In a universe containing only vacuum could different fields still be defined? Could the quantum fluctuations generate such fields?

[jeffreyH (OP)]

While thinking about this one bear in mind that there are vacuum solutions for gravitation.

[saspinski]

There is a reflexion about vaccum solutions and the energy moment tensor in https://arxiv.org/pdf/1605.09236.pdf
The author seems to agree with the Mach idea that we can not speak of a spacetime without its fields. Or that spacetime and fields are the same. But he disagrees that sources requires the energy moment tensor.

I compare the vacuum solutions of GR to the Poisson equation for classical gravity: ∇²Φ = 4πGρ. Out of the Earth for example, ρ=0, so ∇²Φ = ∇.a = 0. But the divergence of acceleration being zero doesn't mean that each of its parcial derivatives are zero.

In the same way, each component of the Ricci tensor is a sum of components of the Riemann tensor. The later can be non zero while the former are zero.

[yor_on]

A vacuum as a geometry?

that's difficult, how should I define a magnitude?

[Bill S]

Are we considering an “absolute” vacuum, or a “quantum-type” vacuum?

If it is the former; where would quantum fluctuations come from?

If the latter; then there must be something filling the “vacuum”, so, I would think, there must be fields already present. 

[petelamana]

Please define the degree of vacuum you are considering.  For example...

A perfect vacuum is defined as a state with no matter particles, and also no photons. This state is impossible to achieve experimentally because it is nearly impossible to remove the matter, and is impossible to eliminate all the photons. Since there is also some energy available, virtual particles can hop into and out of existence.

[jeffreyH (OP)]

It is THE vacuum containing vacuum energy.
https://en.m.wikipedia.org/wiki/Vacuum_energy

[petelamana]

Fascinating.  Thank you jefferyH.  I now have something to study this week.

[Bill S]

It is THE vacuum containing vacuum energy.
https://en.m.wikipedia.org/wiki/Vacuum_energy

That clears "vacuum = nothing" out of the way, so there should be nothing to prevent the "development" of fields associated with any particle that might be present.

Would the fact that they are virtual particles complicate the situation?

[jeffreyH (OP)]

It is THE vacuum containing vacuum energy.
https://en.m.wikipedia.org/wiki/Vacuum_energy

That clears "vacuum = nothing" out of the way, so there should be nothing to prevent the "development" of fields associated with any particle that might be present.

Would the fact that they are virtual particles complicate the situation?

That is a very good question. To which I have no answer.

[geordief]

Do virtual particles require  (exchange? mediate?) energy from the system they are associated with ?

I know little of this.