Calculating the gravity field of a quantum state.

[r***@gmail.com]

How do you calculate the gravity field of a single photon and what are the criteria?

There *is* one answer that is published, but I'm going to skip it and try to start from first principles.

This is what I resolved:
* the field should be treated as a quantum field on a classical curved background,
* the curved classical background should be that which *already* includes the gravity of the quantum state,
* the stress tensor to be used in Einstein's equation is the vacuum
expectation value, where "vacuum" means "zero field, in that classical curved background".
* the classical background is a solution to Einstein's equation with that stress tensor.

So, there's an iterative process that goes like this:
* set the metric g = eta, the Minkowski metric;
* repeat {
* let Omega_g := |g><g| be the vacuum state for that classical background;
* let psi_g be the 1-photon state psi over the state space spanned by Omega_g;
* let T-hat_g be the quantized stress tensor for the state psi_g;
* let T_g := Tr(Omega_g T-hat_g) = <g| T-hat_g |g> be the corresponding classicalized stress tensor;
* update g by solving Einstein's equations G(g) = kappa T_g for g;
* } until (g converges);

This is *not* merely the "RHS = vev" prescription, because the first "v" in "vev" is now g-dependent.

This is *not* a perturbation expansion of a quantum state, because the state space itself is being updated.
Any two quantum state spaces that disagree on which motions are inertial lie in inequivalent state space sectors.

So it's actually shifting the state space across a sequence of
inequivalent state spaces to converge onto the state space which
corresponds to the gravity field of the quantum state.

The quantum state psi_g is simply carried along for the ride and remains
the same - as a function of g; it is only g that is being updated.

[Sylvia Else]

[Moderator's note: My apologies for having overlooked this submission a
few weeks ago. -P.H.]

Post by r***@gmail.com
How do you calculate the gravity field of a single photon and what are the criteria?

You can't. We don't have a theory that lets you do that, and nor do we
have experimental results that would allow the construction or
verification of a theory. At the moment, anything that purports to be
such a theory is nothing more than speculation.

Sylvia.