# Minimum volume of LQG corresponds to a minimum energy?

• Spinnor
In summary, Loop Quantum Gravity does not have a smallest mass or energy, and it is possible for the smallest quanta of energy, such as radio wave photons, to exist within the LQG spin network. However, Asymptotic Safe QG may be a more promising approach for incorporating matter into quantum gravity, as it is able to incorporate the standard model of particle physics and has recent developments predicting the Higgs mass.
Spinnor
Gold Member
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!

Spinnor said:
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.

marcus said:
...

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?

Spinnor said:
...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.

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## What is the minimum volume of LQG?

The minimum volume of LQG (Loop Quantum Gravity) is the smallest possible volume that can exist in the theory of quantum gravity. It is theorized to be on the order of the Planck length, which is approximately 1.6 x 10^-35 meters.

## What is LQG?

LQG (Loop Quantum Gravity) is a theory of quantum gravity that attempts to reconcile Einstein's theory of general relativity with quantum mechanics. It proposes that space and time are made up of discrete units, or loops, rather than being continuous. It is still a developing theory and has not yet been fully proven.

## How does the minimum volume of LQG correspond to a minimum energy?

The minimum volume of LQG is related to the minimum energy through the Heisenberg uncertainty principle, which states that the product of the uncertainties in position and momentum cannot be smaller than a certain value. In LQG, the smallest possible volume corresponds to the smallest possible volume of space, which in turn corresponds to the minimum energy that can exist in that space.

## Why is the minimum volume of LQG important?

The minimum volume of LQG is important because it is a fundamental concept in the theory of quantum gravity. It helps to explain the discrete nature of space and time and how they are related to energy. It also has implications for understanding the behavior of matter and energy at extremely small scales, such as in the early universe or in black holes.

## Can the minimum volume of LQG be observed or measured?

Currently, the minimum volume of LQG cannot be directly observed or measured due to its extremely small size. However, scientists are working on experiments and observations that may provide evidence for the theory of LQG and its predictions about the minimum volume and energy of space. These include studies of the cosmic microwave background radiation and gravitational waves.

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