Loop Quantum Gravity: Explained for Physics Laymen

[selfAdjoint]

They really mean that the math of spin does not apply to these particles. They are also called scalar particles, and they are frequent subjects in developing new ideas because they are easy to work with. Actually there are no scalar particles in today's physical theories except the hypothetical Higgs particle, and you bet these scal particles are not intended to model the Higgs.

 

[eigenguy]

Originally posted by selfAdjoint
---the math of spin does not apply to---scalar particles.

The math of spin does apply: spin-0 means lorentz scalar, which is where "scalar" comes from.

Originally posted by selfAdjoint
there are no scalar particles in today's physical theories except the hypothetical Higgs particle

There is the dilaton of ST.

 

[marcus]

Hello all, I'm quoting some exerpts to give an idea of context and what the article's about. This first quote was from page 3.

Freidel/Louapre hep-th/0401076

"In our paper, we consider the spin foam quantization of three dimensional gravity coupled to quantum interacting spinning particles. We revisit the original Ponzano-Regge model in the light of recent developments and we propose the first key steps toward a full understanding of 3d quantum gravity in this context, especially concerning the issue of symmetries and the inclusion of interacting spinning particles.

The first motivation is to propose a quantization scheme and develop techniques that could be exported to the quantization of higher dimensional gravity. As we will see, the inclusion of spinless particles is remarkably simple and natural in this context and allows us to compute quantum scattering amplitudes. This approach goes far beyond what was previously done in this context by allowing us to deal with the interaction of particles.

The inclusion of spinning particles is also achieved. The structure is more complicated but the operators needed to introduce spinning particles show a clear and beautiful link with the theory of Feynman diagrams [26]."

The next exerpt is from page 20:

Freidel/Louapre hep-th/0401076

"...
It is well known that, at the classical level, three dimensional gravity can be expressed as a Chern-Simons theory where the gauge group is the Poincare group. The Chern-Simons connection A can be written in terms of the spin connection ω and the frame field e,
$$A = \omega_iJ^i + e_iP^i$$
where Jⁱ are rotation generators and Pⁱ translations.

Moreover, since the work of Witten [44], it is also well known that quantum group evaluation of colored link gives a computation of expectation value of Wilson loops in Chern-Simons theory. Our result
therefore gives an exact relation, at the quantum level, between expectation value in the Ponzano-Regge version of three dimensional gravity and the Chern-Simons formulation...

[footnote] κ = 1/4G is the Planck mass in three dimensional gravity"

 

[marcus]

?

So why is the Planck mass different in 3 dimensions?

got kind of a glimmering
but has anybody thought thru this one and
got an explanation ready?

In 4D---the world we have----the Planck quantities are such and such.

But, according to this paper in 1+2 dimensions----their 3D world---the Planck mass is
$$\frac{1}{4G}$$

thats what the footnote on page 20 says, that i just quoted
anyone want to comment or differ with this or explain?

 

[marcus]

answered my own question

in 1+2D
Newtons constant has dimensions of
inverse mass
http://arxiv.org/hep-th/0205021
s'what I thought cause of force falling off
as reciprocal of distance instead
of sq. recip

the mass unit in 3D is basically 1/G
order one coefficients like 4 or 8pi are
mostly a matter of convention (how you
write the einstein equation, the 8pi business)

 

[marcus]

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

 

[nonunitary]

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]

Originally posted by nonunitary

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

What a coincidence! I posted that very same link yesterday evening
my comment was it "cooks the ES goose"
https://www.physicsforums.com/showthread.php?s=&postid=142694#post142694
he does seem to have some of the same arguments
so your posts have been in a certain sense prophetic

 

[marcus]

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
ad hoc made to ignore any j=0 edge
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]

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 which 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--
https://www.physicsforums.com/showthread.php?p=195126#post195126
I am trying to connect Sauron's post with earlier discussion we've had about LQG and entropy.