Re: Measurements in GR

On 10 Aug, 00:58, Gen Zhang <genn...@xxxxxxxxx> wrote:

Now, classically in GR we care about the metric, and measurements of
said metric is thus our primary concern. I believe it's a known
problem that actually we can't always measure the metric in vacuum --
we need to introduce some matter, at which point things usually become
frighteningly simple (at least conceptually, numerically it's usually
a complete pain).

I think that Rovelli's GPS coordinates
http://www.arxiv.org/abs/gr-qc/0110003 use a minimal amout matter:
four GPS satellites, modelled as particles. An observer can
measure the four components of the spacetime location of an event
by reading his GPS receiver, so these are gauge-invariant, physical
coordinates.

So obviously, we wonder about the quantum case. Most quantum efforts
have been focused on matter-free situations, as there are technical
advantages to do so. However, some of the quantum measurements leave
me a little uncertain.

Any physical experiment is an interaction between a detector and a
system, and the outcome of the experiment depends on the physical
properties of both. We typically want to eliminate the detector
dependence from the results as far as possible, but not further than
that. I claim that in the presence of gravity, one detector
property can not be eliminated: its mass M.

Starting from the more fundamental detector-system physics, we could
eliminate M by going to one of two limits: M -> 0 or M -> infinity.
If M -> 0, we have no clue about the future location of the
experiment: the commutator between the detector's position and
velocity is proportional to hbar/M. If M -> infinity, the detector
will interact strongly with gravity and collapse into a black hole.
Neither alternative is realistic, and a theory of quantum gravity
must therefore depend on the observer's mass.

However, if we ignore gravity, we can set M = infinity. The detector
will then just sit still and detect, and we can forget about it.
This limit should be described by QCD. OTOH, if we put hbar = 0 and
then let M -> 0, the detector will be a test particle which moves
along classical geodesics without disturbing the gravitation field;
this is GR.

From this perspective, it is obvious why QFT and GR are
incompatible; they correspond to different limits for the
detector's mass. Moreover, any theory which does not explicitly
introduce the detector's mass, be it a theory of fields, particles,
strings, branes, loops or whatnot, can not be the correct theory of
quantum gravity.


So the question: does anyone know of the any work, where matter is
explicitly used to measure gravity, on the Planck scale?


I'm working on a formulation of QFT where the degrees of freedom
are the physical ones measured by a real, local detector: the
detector's worldline (measured e.g. by GPS coordinates) and the
values of the fields and its mixed partial derivatives inside the
detector (i.e. on its worldline). The detector is material in the
sense that its mass enters its equations of motion. Earlier
attempts in this direction can be found in the arxiv, e.g.
http://www.arxiv.org/abs/hep-th/0701164, but unfortunately the
formalism was then very cumbersome.

.

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