# Loop Quantum Gravity

marcus
Gold Member
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lets put c and hbar in explicitly and see what the planck units
actually are in (1+2)D

thing to notice is that in 4D we have
$$GM^2 = \hbar c$$
because GM^2 has to equal the unit force x area (inverse sq. law)
and that equation defines the pl. mass in 4D

but in 3D GM^2 will equal the unit force x distance!
and that is the unit energy in the system: Mc^2, so we have instead

$$GM^2 = M c^2$$ which solves to

$$M = \frac{c^2}{G}$$

After that, easy, unit energy is
$$E = \frac{c^4}{G}$$

and unit freq is
$$\omega = \frac{c^4}{G\hbar}$$

That makes unit time
$$T = \frac{G\hbar}{c^4}$$

and unit distance
$$L = \frac{G\hbar}{c^3}$$

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I was meaning to elaborate on the reasons why the ES-are espectrum of Alekseev and colaborators is not well defined.
Too late, this guy must have read my posts and took part of them, added a new argument with graphs and posted:

http://arxiv.org/abs/gr-qc/0402064

I think I have to agree with him. What he didn't say though is that one might be abre to define a new operator that somehow "ignores" a j=0 edge, but there is some work involved in showing that it is possible.
Anyway, farewell to the ES-area operator of APS.

marcus
Gold Member
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marcus
Gold Member
Dearly Missed
Originally posted by nonunitary
... this guy must have read my posts and took part of them, added a new argument with graphs and posted:

http://arxiv.org/abs/gr-qc/0402064

I think I have to agree with him. What he didn't say though is that one might be abre to define a new operator that somehow "ignores" a j=0 edge, but there is some work involved in showing that it is possible...
again you were prophetic, the guy has added a paragraph to his
conclusions and updated the preprint
(it is now a little longer and is dated 17 February instead of 13 February)
and the addition includes the case where the operator is
so the spectrum is ES except for a double-size space at zero.
the author does not like this case but he includes it (with a warning) presumably for the sake of completeness

I checked the Gour/Suneeta paper (gr-qc/0401110) and it did not
seem to disturb their calculation of BH entropy
I could not see any reason to accept or reject, it appeared (at least for now) to be just an arbitrary ad hoc fix.

marcus
Gold Member
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I am looking for previous discussion of BH entropy, BH area, in LQG context.
Sauron recently posed some questions about entropy and LQG in another thread and hopefully there is something relevant to that here.

------here's some of Sauron's post-------
I have a few generic questions/reflections about some of the themes LQG is addressing.

Let´s begin by the question of entropy. My deal is whether the concept of entropy makes sense in GR at all. At least in the same sense as in ordinary statistical mechanics.

I know about two main results. The one, of wich i have a reasonable understanding , about the black hole area behaving like entropy. I also have notice about (but no understanding at all) results of Penrose relating the Weyl tensor to entropy, at least in cosmological scenarios.

The question is that in the microcanonical device the entropy is related to the number of micro-states compatible with an energy. But in GR there is no a good (and less local) definition of the energy of the gravitational field....
--end of exerpt--