Is space curved in QFT?

[geordief]

Hope the question makes sense as I am only just (well, hopefully) beginning to get the beginnings of  a feel for the subject.

Some objects in QFT have mass (protons,I am thinking )  so do they cause curvature  and does this affect any calculations? 

 

Would /could EM fields be intrinsically (or extrinsically?) curved?

[joigus]

In principle it is quite possible to formulate EM or other quantum fields on a curved background.

The problem, generally outlined, is that curvature tells you about where the particle is and in what direction it's moving. So it's not possible to be entirely consistent with the physics we know. You are finally led to admit that the metric must be subject to the uncertainty principle too, and thereby satisfy quantum commutation rules, and so on. Otherwise, you could in pple. circumvent HUP by measuring gravitational fields.

I think the argument was developed by Feynman in his famous Lectures on Gravitation. Maybe later I can give you a more precise citation.

[geordief]

11 minutes ago, joigus said:

In principle it is quite possible to formulate EM or other quantum fields on a curved background.

The problem, generally outlined, is that curvature tells you about where the particle is and in what direction it's moving. So it's not possible to be entirely consistent with the physics we know. You are finally led to admit that the metric must be subject to the uncertainty principle too, and thereby satisfy quantum commutation rules, and so on. Otherwise, you could in pple. circumvent HUP by measuring gravitational fields.

I think the argument was developed by Feynman in his famous Lectures on Gravitation. Maybe later I can give you a more precise citation.

I was only half thinking of that (the curved background)

 

I had more  in mind whether the fields themselves  might create their own curvature.

 

But are they massless by definition or does the fact that massive objects have their fields mean that those fields contribute to spacetime curvature?

 Were you saying that spacetime curvature is a classic model and so fundamentally inconsistent with any Quantum model to this point?

Edited December 15, 2020 by geordief

[MigL]

Keeping in mind that 'curvature' is apparent in the geometric model, but not necessarily in reality …
It is possible to include Electromagnetism in a 5 dimensional extension of GR, and was first done by Theodore Kaluza and Oskar Klein ( see Kaluza-Klein theory ) in a manner that produces standard GR and Maxwell's equations for the EM field.

However, as Joigus points out, This remains a strictly classical theory, and does not take the HUP into consideration.
So unless you can figure out a way to make the metric 'fuzzy' ( as the HUP does with observables like position and momentum ), this does not yield a good model at quantum scales.

If, on the other hand, you mean do the fields produce 'curvature', of course, the answer is yes.
Any field has an energy density, and this necessarily implies space-time curvature due to that energy density.
( fields are mathematical constructs, and so is their energy density distribution, leading to a mathematical curvature, which seems to describe reality quite accurately, as per the first line of this post ).

[Markus Hanke]

20 hours ago, geordief said:

I had more  in mind whether the fields themselves  might create their own curvature.

 

It’s complicated, because quantum fields are operator-valued (i.e. they assign mathematical operators to every point in spacetime), so attempting to attribute mass or energy to the fields themselves is not especially meaningful. However, the states they describe - most notably the vacuum states - can most definitely have non-zero energy-momentum expectation values, which would form a source of spacetime curvature. 

In “standard” quantum field theory (as utilised e.g. in the Standard Model of Particle Physics) a flat Minkowski spacetime background is assumed, so in other words we choose to neglect both pre-existing background curvature, as well as the gravitational effect of the field states themselves. Joigus has already explained one important reason; another reason of course is that QFT in curved spacetime is mathematically very challenging, so it would be very hard to work with such models for everyday problems.