tade said:
So I was wondering about the attempts to apply existing quantum models through the Maxwellian parallel between EM and GEM at those certain ranges (where the approximation to GR is close) in order to shed more light on possible or potential quantum models of gravity.
tade said:
What have been the results of such attempts?
And clearly the attempts ran into certain problems since we still haven't been able to reconcile the quantum world and GR, and I'm also wondering what those problems have been.
Serious efforts to formulate quantum gravity have been an active area of inquiry for more than fifty years.
The biggest problem is that a naïve attempt to quantize gravity with a massless spin-2 graviton (which is what a graviton ought to be) by analogy to photons is "non-renormalizable" which means that the perturbative renormalization based path integrals that are used in the Standard Model have fundamental theoretical problems with them.
Renormalization is the mathematical trick that makes it possible to do calculations for the electromagnetic force (quantum electrodynamics or QED for short), the weak force, and the strong force (quantum chromodynamics or QCD for short) possible, and it doesn't work in a straightforward frontal attack way to do the same thing with gravity.
At an intuitive heuristic level, this isn't too surprising. Electromagnetism doesn't produce singularities and Maxwell's equations don't blow up into infinities. Renormalization is a way to remove non-physical infinities from quantum calculations. But, GR has singularities and infinities that are physical and supposed to be there. So, it isn't too surprising that a tool designed to remove infinities from calculations in the quantum version of GR unsurprisingly don't work.
Also, a quantum gravity theory should be non-Abelian, in common with QCD, and in contrast to QED and the weak force. The main reason that this is so is that gravitons ought to interact with other gravitons in proportion to their mass-energy in the same way that they interact with anything else.
Thus, even if we could overcome the problems associated with it being non-renormalizable (which might be possible to overcome, for example, by using non-perturbative techniques analogous to discrete Lattice QCD approximations), the calculations are wickedly hard because you have to consider graviton-graviton interactions in addition to all other possibilities.
It could be worse. The fact that QCD is non-Abelian is not the only thing that limits QCD calculations to precisions of parts per thousand rather than the parts per million or billion of QED and the weak force.
The other thing that makes QCD calculations so hard is that the QCD coupling constant, α
s, is very large compared to the electromagnetic couple constant and the weak force coupling constant, which makes the truncated infinite series approximations in powers of α
s (which are how the path integral calculations of Standard Model physics are done) converge much more slowly, so you need more terms of the series to get a reasonable approximation of the true value of the quantity you are trying to calculate. But a large coupling constant isn't a problem for quantum gravity theories which have a much smaller coupling constant than QCD (it is smaller than even the weak force coupling constant when converted from the dimensionful Newton's constant to the dimensionless coupling constants of that three Standard Model forces in an appropriate way), so it converges in fewer terms.
The comparative weakness of gravity also makes direct detection of individual gravitons essentially impossible because their expected mass-energy would be so small. So, there are really no ways to confirm this possibility.
There are some instances where very low energy approximations of quantum gravity are used in a very specific situation to make some predictions, doing their best to avoid the parts of a quantum gravity theory that are difficult theoretically or practically.
There are also questions about whether you should really work from the Standard Model paradigm of a force carried by a carrier boson (photons, gluons, W and Z bosons), or whether the way to go for quantum gravity is to quantize space-time itself. Loop quantum gravity and kindred quantum gravity theories take that approach.
One fruitful approach, although it hasn't produced any real major breakthroughs yet, is the QCD squared approach.
Graviton based quantum gravity is, in mathematical form, quite similar to its fellow non-Abelian gauge theory, QCD. And, in many instances, if you take a quantum gravity problem and formulate it as a parallel QCD problem, and then square the result and switch out a QCD coupling constant for a gravitational coupling constant, you can replicate the results you would get from doing it the hard way from first principles as a quantum gravity problem. Being able to get answer to a calculation in a theoretically non-renormalizable theory, by doing a parallel calculation in renormalizable theory and then making some minor manipulations of it, is pretty crazy. It isn't a trivial matter to figure out why that should work. But it has been fruitful so far.
Classical GR does its thing just fine in its domain of applicability, but its classical deterministic physics formulation doesn't play nice with the quantum physics involved in Standard Model physics.
There are core widely accepted concepts in GR, as it is generally operationalized and formulated, like "gravitational energy can't be localized" and "gravity is deterministic" and "gravity is background independent and geometric" that are inherently problematic for a quantum theory in which gravity is carried by gauge bosons (e.g. gravitons and photons).
Fortunately, there aren't that many applications where you need to use both the relativistic regime of GR and the Standard Model in the same practical application. GR is basically relevant in astronomy and astrophysics applications. The Standard Model matters most often in Earth based experiment sized applications. So, we don't have an urgent imperative to figure out how to make them work better today.
