It is beautiful to see how Dirac did put at first ideas about how tackling the problem of quantizing gravity from a canonical perspective. The canonical approach is to formulate things in terms of a Hamiltonian or to put an action and from there obtain the equations of motion. The way that things evolved (and the only seen) from this point did lead to the ADM formalism, a reformulation of the hamiltonian (supehamiltonian for being in 4 dimensions) and next to the Wheeler-DeWitt equation, that was not understood at all in its time, for saying so. From this line, using the introduction of Ashtekar of the so-called new variables, it was obtained by Rovelli and Smolin solutions to the Wheeler-DeWitt equation in form of loops (Wilson loops as in QFT). Now, from this, in Loop Quantum Gravity things are put in such a way that there are operators acting on an appropiate Hilbert space (and even for this space it was a little struggle in loops community) whose eigenvalues are Area, for example, that is space is discrete; for the case of volume things can be more or less stated but for time that appears to me a little bit philosophical and guess things are not well settled. Someone remember the uncertainty relations for momentum and position for example in classical QM and the uncertainity relation for energy and time? they are totally analogous in QM but turns out that the relation, formulated for position and momentum in terms of a root-mean-square-deviation of the operators, although totally analogue to the energy-time relation, there is no operator for time, and the derivation is (just) a little bit different. I guess both things could be related, as has been some suggestions that quantum mechanics should lie totally in operators, for example, but then time should be treated in equal footing (as operator, but things become very unclear; then one can think that time should dissapear and get only as a parameter, a very relativistic idea(a path parameter for defining for example geodesic equations in general relativity), but not compatible with usual QM, and you can check then some writings and articles of Smolin and Rovelli about the existence or not-existence of time (and can see how Smolin describes himself changing his point of view in www.edge.org if I dont remember bad). So, problems like this appears to be much the same that become irreconciliable QM and GR, and then quantum gravity. That really appears to me so, and guess any people working in LQG can have seen this but only a few see it as fundamental. Dont know how Ashtekar sees all this, but I can guess very easily that his hope is that with a better development the theory will get better answers, guess that Rovelli has convinced himself that of non-existence of time, and Smolin has changed his view from there to that of time-should exist as its own in a correct theory of QG (a view not that relativstic for me, but that could be surrounded aways that things discussed are local :S). It's enough for this introduction, hope the theme evolves in the near future and talk about other approaches for quantum gravity (QG).
Most of this ideas can be identified reviewing the article http://arxiv.org/PS_cache/gr-qc/pdf/0006/0006061v3.pdf by Rovelli.


P.S. I mentioned the page of edge.org, its nice in many aspects, its good to take a look some times in it. There are writings, interviews and others about evolution, psychology, sometimes physics, etc. There are very named contributors, just can remember L. Susskind, Smolin, R. Dawkins, H. Gardner.

Can you mention if someonelse here is directly related with QG?

What is Quantum gravity? I have a project im working on, somethin about infinite gravity. Is this related to Quantum gravity? :))

I haven´t seen anything about "infinite gravity" in any formal or informal publication of physics... whats this about? I don't see anything serious that use the term, and then I don't kno if it can be related to QG, may you tell a reference or explain the idea...

You people keep dragging me back, I'm supposed to be boycotting hi5's public groups!

I believe you are referring to the alternative formulation of gravitational theory whereby instead of gravity being a uni-directional pull generated by mass (and/or energy), it is a omni-directional push from infinity which is attenuated by passing through mass (and/or energy).

When done properly (which is not always the case when non-physicists discuss it online) the two formulations are mathematically equivalent and make identical predictions and no real-world experiment (as far as I'm aware) can distinguish between them.

I like the infinite gravity formulation because (1) it makes many physicists angry or crazy and (2) the value of the Gravitational Constant could depend upon the total mass/energy of the Universe in a way somewhat analogous to the pressure inside a balloon and could change if the total mass/energy changes.

The alternative gravity push has to be strong indeed if it can create black holes.

Does the "push from infinity" mean "push from all points approaching infinity", as the actual infinity would be infinitely distant and the interaction time would be infinite?

How does the push model relate with extreme or infinite redshifts at large distances?

Instead of saying "uni-directional pull" I should have said "omni-directional pull".

I was thinking about the case involving two masses which is often simplified as being an mutual pull along the line between their centers of mass. Or equivalently, as an attenuated push on each mass from the direction of the other mass, resulting in a net push on each mass from the opposite directions with all of the other non-attenuated forces balancing out to zero.

Assuming that a Black Hole is at or near 100% attenuation, you then have the "weight" of the entire Universe pressing down on that point from all directions unopposed. Is that strong enough for you?

> [...] you then have the "weight" of the entire Universe pressing down on that point from all directions unopposed. Is that strong enough for you?

Lacking a stronger gravity I will satisfy with that one. ;-P

Are you talking about Mach's principle? First, if it's so then this not deserves the nickname "infinite gravity" that is much more obscure...maybe it can appear to mainstream (nonrelativists) physicists as something more philosophical, but for relativists (I fit more in this scheme) it's something that is always seen in the first indagations about gravity.. in any case, it's irrelevant by the moment as it has nothing to add to the problem of QG, or even in the understanding of gravity or a calculation o any observable, so whats the point?. Again, guess there were cranky comments, Chrissy.