Bohm's Hidden Variables HV in orthodox quantum theory are "test particles" in a similar sense to Einstein's GR test particles. The paths of HV are piloted by the quantum potential Q(nonlocal configuration space for entangled systems) without any direct influence of HV back on Q just like geodesic GR test particles are piloted by the local curvature tensor Ruvwl without being included in Tuv(source). The lack of direct back reaction in the quantum case corresponds to Valentini's "sub-quantal thermal equilibrium" with Shimony's "passion at a distance" and the no-cloning a quantum theorem.
"Now, in special relativity we can think of an inertial coordinate system, or
`inertial frame', as being dened by a field of clocks, all at rest relative to each
other. In general relativity this makes no sense, since we can only unambiguously
dene the relative velocity of two clocks if they are at the same location. Thus
the concept of inertial frame, so important in special relativity, is banned from
Baez means Global Inertial Frame (GIF) above. GR replaces GIF with LIF as he points out below.
"If we are willing to put up with limited accuracy, we can still talk about the
relative velocity of two particles in the limit where they are very close, since
curvature eects will then be very small. In this approximate sense, we can talk
about a `local' inertial coordinate system. However, we must remember that
this notion makes perfect sense only in the limit where the region of spacetime
covered by the coordinate system goes to zero in size. ...
Einstein's equation can be expressed as a statement about the relative acceleration
of very close test particles in free fall. Let us clarify these terms a
bit. A `test particle' is an idealized point particle with energy and momentum
so small that its effects on spacetime curvature are negligible." A particle is said
to be in `free fall' when its motion is affected by no forces except gravity. In
general relativity, a test particle in free fall will trace out a `geodesic'. This
means that its velocity vector is parallel transported along the curve it traces
out in spacetime. A geodesic is the closest thing there is to a straight line in
curved spacetime. ...
in general relativity gravity is not really a `force', but just a manifestation
of the curvature of spacetime. ...
To state Einstein's equation in simple English, we need to consider a round ball
of test particles that are all initially at rest relative to each other. As we have
seen, this is a sensible notion only in the limit where the ball is very small. If
we start with such a ball of particles, it will, to second order in time, become
an ellipsoid as time passes. This should not be too surprising, because any
linear transformation applied to a ball gives an ellipsoid, and as the saying goes,
'everything is linear to first order'. Here we get a bit more: the relative velocity
of the particles starts out being zero, so to first order in time the ball does not
change shape at all: the change is a second-order effect.
Let V(t) be the volume of the ball after a proper time t has elapsed, as
measured by the particle at the center of the ball. Then Einstein's equation
V^-1d^2V/dt^2 ~ -(1/2)(Ttt + Txx + Tyy + Tzz)
where these flows are measured at the center of the ball at time zero, using local
inertial coordinates. These flows are the diagonal components of a 4x4 matrix
T called the `stress-energy tensor'."
I add here that for random virtual quanta (zero point vacuum fluctuations) in the isotropic case, Lorentz invariance + equivalence principle demand
w = (Pressure per space dimension)/(energy density) = -1
Ttt = - Txx = - Tyy = - Tzz = - P
Therefore the RHS of (2) reduces to - P
If there are anisotropic Casimir effect boundaries this result will change.
Free virtual bosons have P < 0 causing anti-gravity repulsion dark energy
Free closed virtual fermion loops have P > 0 causing gravity attraction dark matter that mimics w = 0 CDM.