Silly question about quantum gravity

[paweld]

It is generally belived that there exists fundamental length scale given by the Planck length
at which GR and in particular local Lorentz invariance breaks. But accoring to me
we can define a resonable length scale only if we assume beforehand that Lorentz
invariance is broken. Otherwise how would it be possible to define any spatial
distance scale if all observers were put on equal footing (Lorentz–FitzGerald contraction)?

 

[marcus]

Try this 2002 paper by Rovelli
http://arxiv.org/abs/gr-qc/0205108

 

[tom.stoer]

I don't think that an "emergent" minimal length or "quantized spacetime" necessarily break Lorentz invariance. Quantized angular momentum doesn't break rotational symmetry, either.

 

[qsa]

I don't think that an "emergent" minimal length or "quantized spacetime" necessarily break Lorentz invariance. Quantized angular momentum doesn't break rotational symmetry, either.

would it make a difference if the minimum length was .2 proton size

 

[tom.stoer]

as far as I understand the relevant math - no

 

[czes]

The relation (Planck lengt/Compton wave length) shows the spacetime curvature in General Relativity, gravitational time dilation and relation gravitational/electromagnetic force. The Compton wave length represents a quantum information and Planck length represents length contraction and time dilation of each relation between quantum information. It shows also the Holographic Principle relation.

We may measure the Compton wave length and Planck length is very precisely calculated constant. Only this precise value gives the observed results in General Relativity.

 

[paweld]

After reading the introduction of Rovelli paper I still don't understand intuitivelly why
quantization of area might be compatible with Lorentz invariance (probably it's better
to speak about quantization of area then lenght). Firstly I'm not sure if I properly
grasp the idea of area operator. If this is an observable what element of physical reality
it coresonds to? Can I think of its eigenvector as a (three-dimensional) chunk of space
with well defined area of its (two-dimensional) surfaces? [I imagine a spin
network which this operator acts on as a collection of chunks of space - to do it I
have to beforehand split spacetime into space and time; this split is directly related to
the choice of observer]. If yes let's imagine the following situation: we have two observers.
For each of them the hypersurface of constant time consists of very small
lumps (which cannot be divide any more). The first observer sees the macroscopic
obcject at rest, measures its area and obtains huge number (in comparison to Planck scale).
In the reference frame of the second observer this object move very fast and
the area of its surfaces parallel to the direction of motion is comparable with Planck area.
In order to describe the motion of an object the second observer has to take into
account the quantization of space whilst the first one supposedly hasn't. How to
reconcile this?

From intuitive point of view it would be better if values of some covariant quantities
were quantized (e.g. scalar curvature). Otherwise for me it's difficult to tell in what
regime the quantum effects shuld be taken into account.

 

[tom.stoer]

Have you ever studied canonical quantization of gauge theories?

In a theory with local gauge invariance (QCD with SU(3)) gauge fixing is something like constraining the Hilbert space to the gauge-singlet sector. But in the singlet-sector the gauge trf. acts as the identity. In that sense LQG is locally Lorentz-invariant

Neither GR nor LQG have global Lorentz invariance in general - only in certain sectors / solutions.