Progress In Loop Quantum Gravity

Over at physics forums, a discussion thread notes some important technical achievements in the process of formulating a model of quantum gravity within the spin foam formulation of the loop quantum gravity idea, where gravity arises from the structure of a discrete space-time.

For those familiar with the topic the key developments are that:

He shows that the method used by EPRL and FK is not sufficient to suppress the quantum fluctuations related to these constraints and that their method does not lead to the (correct) Crane-Yetter model! In addition he shows that the Immirzi parameter drops out in the final theory and that effects regarding its quantization are artificial.

EPRL is the closest approach that loop quantum gravity has to the leading formulation of the theory within this approach to developing a theory of quantum gravity, so pointing out a defect in the quantization method that it uses is not desirable.

The ability of a purportedly correct approach to formulating the equations to cause the Immirizi parameter, which is the characteristic physical constant of loop quantum gravity theories to drop out of the equations all together is absolutely unexpected and also encouraging as it narrows opportunities for fine tuning in a quantum gravity theory formulated in this way. The Immirizi parameter in this model looks a bit like the renormalization scale used in QED, necessary to intermediate calculations despite the fact that the value used is independent of the final outcome. In a related point, the author argues that this is suggestive of the possibilty that this solution is unique way to correctly fit the equations of general relativity to a spin foam model.

The remark that "effects regarding its quantization are artificial" seems clear at first read but grows rather cryptic as one really tries to articulate what it really means. This seems to be making a statement regarding phenomenology, but an examination of the pre-print itself suggests that at this stage that there are few phenomenological implications and that a true final spin foam theory, even in the absence of a matter field, is still a step or two away from being achieved even with this substantial step towards a final theory.

Forum moderator Marcus provides a more complete review of the prior literature related to this mathematical approach to spin foam models that is actually more complete to some extent that the citations in the pre-print itself.

The pre-print is: Sergei Alexandrov, "Degenerate Plebanski Sector and its Spin Foam Quantization" (22 Feb 2012).

The paper is also exceptionally well written for a paper in this field although at the bottom of the first page of body text the word "affordable" is used when the word "amenable" would be the correct useage. Similarly, it uses the non-ideomatic phrase "we went through a long way to get the partition function" at the start of Section 3.5 when the intended sense phased to avoid technical meanings of the word "path" in the field is that "we took a long road to get the partition function." These nits are obviously non-exhaustive, but aside from a few useage and errors in ideomatic English useage, is very well organized and laid out.

To back up and contextualize just a little more, there are about half a dozen different, possibly equivalent or nearly equivalent ways to formulate gravity in terms of the structure of space-time the way that Einstein's classical general relativity theory does, with a discrete space-time structure rather than a contious one. Spin foams is one of the more well established approaches to doing so.

Loop quantum gravity is only a theory of quantum gravity, and not a grand unified theory or theory of everything that describe fundamental forces of physics found in the Standard Model of particle physics. But, a discrete space-time formulation of general relativity at a quantum scale is not "allegeric" to the mathematics of quantuum mechanics reformulated into this discrete space-time the way that quantum mechanics is to a formulation in classical general relativity. The same basic quantum concepts apply to both.

Assuming one can iron out the remaining mathematical challenges associated with loop quantum gravity with matter fields, the path to formulating the Standard Model equations of particle physics within the discrete loop quantum gravity space-time that is four dimensional is considerably more straight forwards than the task of reconciling the Standard Model to general relativity, even though neither project has been successfully completed. One would hope, in turn, that the steps necessary to unify the Standard Model forces when formulated in LQG and the high energy modifications to the effective low energy theory that is the Standard Model might be more obvious in an LQG formulation. Preliminary suggestions have been made regarding how to proceed towards this end. If one leaps over that hurdle, moreover, one really does have something closely approximating a "theory of everything" applicable in all observable conditions. This would indeed be truly huge.