Re: Measurements in GR

On Aug 11, 3:25 am, thomas_larsson...@xxxxxxxxxxx wrote:
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 coordinateshttp://www.arxiv.org/abs/gr-qc/0110003use 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.

That is actually the exact model I had in mind...

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.

That is an exceptionally nice way to think about it -- I wonder why
this view isn't more prevalently known? (I'm only an undergrad, so
I've got a fairly limited view of what the current frontiers are --
mostly from reading papers that I can only half understand and JB's
weekly finds, which are usually a only a little better.)


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.

I've tried reading that paper, and to be honest it is very much beyond
me. My current mathematical level is fairly low -- simple differential
geometry and elementary linear algebra, I'm afraid I'm only a
physicist, and not a maths student. Still, the basic idea I do grasp,
even if I don't even understand the technical issues that you're
trying to solve.

There is one thing that has been bothering me -- Rovelli, in his book
and elsewhere, go to great lengths to create a manifestly covariant
Hamiltonian approach to classical mechanics, and even to quantum
mechanics. The classical particle and field theories are nice and
simple, and the quantum particle theory is pretty straightforward.
However, having never formally been taught QFT, I can't follow all the
technical details of his covariant quantum field theory, so I can't
really make any sensible comments. The puzzling point is that he then
completely ignores all this work, and go on to describe LGQ, in its
3+1 foliated form. Still -- I found the formalism that he used to be
much more understandable, in fact much more so than the Dirac version
of constrained Hamiltonian mechanics with the different classes of
constraints and the sophisticated algebra that then results. I'm going
to try and see if your "jets" can be cast in that language.

Thanks for the pointers, and hopefully you won't mind me stalking your
work from now on ;-)
Gen Zhang

.

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