Can LQG Explain the EPR Paradox and Instantaneous Action at a Distance?

[Rothiemurchus]

In LQG the minimum time is 10^-43 seconds.
So how can there be instantaneous action at a distance in LQG between entangled photon pairs?
Also, a particle traveling through quantized space would jump from one
position to the next and miss some space in between.The standard quantum mechanical wavefunction would have gaps along its length where the probability of finding a particle is zero, in a plot of psi against position.These points of zero probability would put a particle in a box with walls of infinite potential from which the particle should not be able to escape,and therefore the particle should not be able to move from one position to another.

 

[marcus]

Also, a particle traveling through quantized space would jump from one
position to the next and miss some space in between.

I was told the positions overlap and so there can be no gap between one position and its neighbor Why not?

but seriously Rothie. if there is no space
exept for the discrete set of locations, then how can it "miss some space in between"?

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Actually you seem to be imagining what you call "quantized space"
in a way that is quite different from the way space is modeled in LQG.
In LQG it is a continuum----a differentiable manifold---just like what is used in the 1915 theory of General Relativity. In LQG there are quantum OPERATORS representing measurments of area and volume, and these have discrete spectra----the range of outcomes of geometrical measurments is discrete just like the range of energy levels of one hydrogen atom is discrete.
But the continuum in which the regions live which you measure the area or volume of---this is the basic continuum we are used to.

It is the geometric excitations of the continuum which are quantized---and which coincide with the quantum states of the gravitational field.
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Rothie, please do not confuse LQG with some of the other theories which
represent space by a discrete set of points, or by a lattice, or by a collection of little cells (like cubes or tetrahedra)----there ARE quantum gravity theories in which space really is discrete in some simple straightforward way! they are different from LQG but personally
I think they are fine too! They really can be OK without stuff falling thru the cracks! Waves can propagate fine in honeycomblike cellular complexes and in lattices. Indeed a lot of QFT (quantum field theory) is done, at a practical level, on lattices---and they have waves up the wazoo.

So discrete models are alive and well---no fear---tho LQG is maybe not the perfect example of a discrete theory because it is based on a conventional continuum, just one whose geometric features are quantized.

[edit: corrected spelling of "quantized"]

 

[Rothiemurchus]

Marcus:
It is the geometric excitations of the continuum which are quatized---and which coincide with the quantum states of the gravitational field.

Rothie M:
Generally speaking, in physics,quantization happens to entities that
exist in space.Doesn't this imply that to quantize 3D space we must
use the idea that 3D space can exist in other space dimensions?

 

[selfAdjoint]

Marcus:
It is the geometric excitations of the continuum which are quatized---and which coincide with the quantum states of the gravitational field.

Rothie M:
Generally speaking, in physics,quantization happens to entities that
exist in space.Doesn't this imply that to quantize 3D space we must
use the idea that 3D space can exist in other space dimensions?

No it is not excitations of a continuum. Quanta of area and volume exist apart from any underlying manifold. The manifold is just a part of the classical theory before it is quantized.

You can't apply naive intuitions from standard QM to the quantization of gravity; LQG is quantized in a different way. Now that way may or may not be valid as given to us today (see Urs' posts), but it is not subject to simple comparisons to QM.