Minimum volume of LQG corresponds to a minimum energy?

[Spinnor]

Mass and energy curve spacetime, lots of concentrated mass, lots of curvature. Does the quantized volume of Loop Quantum Gravity correspond to a minimum quantum of energy? If so how does that minimum energy compare to the energy of a individual photon from say a radio station broadcast? It seems the energy of such a photon can't curve spacetime much at all but must do so a little?

Thanks for straightening me out!

 

[marcus]

Does the quantized volume of Loop Quantum Gravity correspond to a minimum quantum of energy? ...

No, volume doesn't correspond directly to energy. As you indicate, because in Loop Quantum Gravity the area and volume operators have discrete spectra, there is a smallest nonzero area you can get as the outcome of measuring an area. And a smallest nonzero volume that can result from measuring a volume.

But that doesn't translate into a smallest non-zero energy.

Mass and energy curve spacetime, lots of concentrated mass, lots of curvature.

That's certainly correct and since you bring up the idea of curvature there is a reciprocal relationship between area and curvature.

Curvature is measured in various ways. You may be familiar with "radius of curvature" idea and the idea that the curvature of a path can be measured by reciprocal length. Slight curvature corresponds to a small reciprocal length----a large turning radius.
Large curvature corresponds to a big reciprocal length----a tiny turning radius.

More commonly the unit of curvature is the reciprocal of an area. The fact that the LQG area operator has a smallest positive eigenvalue corresponds to the curvature operator being bounded.
To oversimplify, Loop geometry can't get curved past a point because then the "turning radius" would get too small and go below the measurable limit.

I have to go. Maybe we can discuss this more later.

 

[Spinnor]

...

Marcus, thanks for the help!

If and when you have time, ..., does Loop Quantum Gravity have a smallest mass or energy? I just wonder if the smallest quantums of energy like radio wave photons can happily live in LQG? Is there room for the really small in LQG?

Thanks again for your help!

 

[marcus]

...does Loop Quantum Gravity have a smallest mass or energy? I just wonder if the smallest quantums of energy like radio wave photons can happily live in LQG?...

No, LQG does not have a smallest mass or energy.
The answer to the other question is twofold. There is nothing that in principle prevents all kinds of matter, including the smallest quanta of energy, from living happily on the LQG spin network. The spin network represents a quantum state of geometry. And it can carry extra information, e.g about matter fields, besides purely geometric information---by putting additional labels on the graph. But so far most of the LQG papers have included only very rudimentary kinds of matter in the picture, or no matter at all.

Right now it looks to me as if an alternative approach called Asymptotic Safe QG is entering a phase of very rapid growth precisely because of the issue you raise. AsymSafe quantum gravity is all set up to incorporate the standard model of particle physics. So it is ahead of the game when it comes to including matter. It looks as if it might be able to join matter with gravity as per General Relativity---and have a functioning predictive theory of geometry+matter which is good up to Planck scale energies (possibly beyond that).

If your interest extends to other approaches besides LQG, we have 3 threads now about different aspects of recent AsymSafe research. One about Steven Weinberg's recent paper using it to explain inflation. One called "Grav.+GUT" about the work of Robert Percacci----a leader in combining that type of QG with matter (he is a particle physicist.) And one about work of Wetterich and Shaposhnikov, which among other things predicts a value for the Higgs mass. These are all new AsymSafe results that have come out in the past month or so. It's a good thing to watch.