About the results of trying to build quantum gravity from gravito-EM

[tade]

So one of the major topics in physics is trying to reconcile quantum mechanics and general relativity.
And the classical expression of electromagnetism is Maxwell's equations, and its linked to quantum models of electromagnetism.
And then there's also a gravitational analogue of Maxwell's equations, gravitoelectromagnetism (GEM), and it can function as a close approximation of GR within certain ranges of parameters.

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.
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.

 

[ohwilleke]

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.

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.

 

[tade]

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 in experimental sized applications. So, we don't have an urgent imperative to figure out how to make them work better today.

thank you for the detailed reply
and speaking of the same practical applications, have there been quantum models of gravity that are internally consistent and coherent, and which have been able to reproduce everything that we have experimentally observed and measured about gravity (and quantum mechanics)

such as these approximate Maxwellian gravitoelectromagnetic scenarios, but that then produce odd or counter-intuitive predictions at certain ranges of parameters which we are unlikely to be able to experimentally examine anytime soon?

as, considering the idea that it is difficult to experimentally examine quantum gravitational effects, whether this might make it possible for models which produce counter-intuitive results to still last for a while

EDIT: I'm putting this comment on hold at the moment as I'm still thinking about things and trying to figure them out

 

[tade]

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.

thank you for the detailed reply



and by the way, in this video Matt O'Dowd mentions "emergent phenomena from a quantum theory deeper than our currently accepted theories."

what are your thoughts about QG models which fall under this category which are background-independent?

 

[ohwilleke]

in this video Matt O'Dowd mentions "emergent phenomena from a quantum theory deeper than our currently accepted theories."

what are your thoughts about QG models which fall under this category which are background-independent?

Full disclosure: I didn't watch the video, because I hate watching podcasts and because I usually write at PF in an environment where it would be rude to listen to audio.

But, I suspect that Matt O'Dowd is talking about the loop quantum gravity class of quantum gravity theories when he mentions "emergent phenomena from a quantum theory deeper than our currently accepted theories."

In these theories, fundamentally, space-time and everything really is a network of nodes that each have a small number of connections to other nodes. Concepts like locality and continuity are emergent and not absolute. A node could have two connections a few zeptometers away from each other, and have a third connection that is on the other side of the Milky Way. From our human scale perspective, this looks like a universe full of tiny, random, non-local connections, which might even allow for faster-than-light transmission of individual photons that would allow communication between non-local points at faster-than-light speeds, although this wouldn't make traversable wormholes possible since the non-local connections would be random, dispersed, and tiny.

There is one small but tantalizing hint that favors this idea. This is the fact that when you do a path integral in quantum mechanics, for example, for the propagation of a photon, you have to consider paths in which the photon travels at more than, or less than, the speed of light, although these paths have a reduced weight the further away from the speed of light that they are. So, some of the paths considered in calculating the probability that a photon will go from point A to point B violate special relativity, even though the end outcome is always consistent with special relativity.

This would be consistent with a loop quantum gravity-type discrete space-time theory in which the speed of light is a number of node-hops per second, but in which the distance from point A to point B is not precisely the same number of node-hops in every path because while it averages out to the same, the fundamental non-continuity and non-smoothness of discrete space-time is such that some paths slightly differ from the average number of node-hops between points A and B.

On the other hand, there have been many efforts to observationally/experimentally look for any evidence of violations of special relativity (which are called "Lorenz Invariance Violations"), and these violations are ruled out to some of the highest precisions of any measurements in physics. So, if the deviations from the speed of light in the paths considered in the photon propagator path integral actually correspond to some physically meaningful reality, those deviations must be very slight and space-time must be extremely fine grained (perhaps even below the Planck scale with a Planck length of 1.616255(18)×10⁻³⁵ meters, which is twenty orders of magnitude smaller than the femtometer size scale of protons and neutrons, that has been hypothesized as a possible minimum distance in a discrete space-time).

Another notion of emergence from a deeper theory in loop quantum gravity theories is that particles of matter can be conceived of tightly knotted and bundled up networks of nodes of space-time itself.

This is a bit like the more commonplace reality that in quantum field theory, "particles" are really just stable, localized excitations of quantum fields, rather than truly distinct point-like objects, which is useful because elegantly eliminates the infinities associated with objects having zero volume and provides a framework in which the wave-particle duality is a naturally emerging concept.

The loop quantum gravity class of theories were motivated in the first place, in part, by the conviction that graviton based gauge theories of quantum gravity didn't take the background independence and geometric nature of general relativity seriously enough.

The Standard Model is formulated in Minkowski space-time, which is like Euclidian space-time but incorporates special-relativity. If you just try to insert gravitons into a Minkowski space-time, you get something very similar to the more "sophisticated" space-time of Minkowski space-time, but it probably isn't quite the same, and theorists developing loop quantum gravity and kindred approaches to quantum gravity think that the discrepancies between the two approaches are material and a hint that a spin-2 massless graviton gauge theory in Minkowski space-time is the wrong approach to quantum gravity, and that this is part of the reason that quantum gravity has been such an intractable problem.

Loop quantum gravity and kindred theories, because they start much closer to scratch, rather than being able to borrow heavily from Standard Model quantum mechanics and structures, have been slow going. The Holy Grail of LQG type theories is to establish that these theories can be well approximated classically by GR. There is dispute over how close theorists have come to achieving this goal. If LQG theories have a classical approximation that is too different from GR, then they are just an interesting mathematical exercise with no physics relevance.

 

[tade]

Full disclosure: I didn't watch the video, because I hate watching podcasts and because I usually write at PF in an environment where it would be rude to listen to audio.

But, I suspect that Matt O'Dowd is talking about the loop quantum gravity class of quantum gravity theories when he mentions "emergent phenomena from a quantum theory deeper than our currently accepted theories."

oh, so O'Dowd was saying that one possible path to solving the conundrum is considering deeper quantum theories, and he mentioned string theory as opposed to LQG, but i think that one of the main problems with string theory its that its not background-independent, and so i was asking about theories which are

 

[ohwilleke]

oh, so O'Dowd was saying that one possible path to solving the conundrum is considering deeper quantum theories, and he mentioned string theory as opposed to LQG, but i think that one of the main problems with string theory its that its not background-independent, and so i was asking about theories which are

It might be possible to develop a background independent string theory, but no one has done it yet. As explained at the link:

String theory is usually formulated with perturbation theory around a fixed background. While it is possible that the theory defined this way is locally background-invariant, if so, it is not manifest, and it is not clear what the exact meaning is. One attempt to formulate string theory in a manifestly background-independent fashion is string field theory, but little progress has been made in understanding it.

Another approach is the conjectured, but yet unproven AdS/CFT duality, which is believed to provide a full, non-perturbative definition of string theory in spacetimes with anti-de Sitter asymptotics. If so, this could describe a kind of superselection sector of the putative background-independent theory. But it would still be restricted to anti-de Sitter space asymptotics, which disagrees with the current observations of our Universe. A full non-perturbative definition of the theory in arbitrary spacetime backgrounds is still lacking.

Topology change is an established process in string theory.

Another problem with string theory is that no one can pin it down out of countless vacua which realize string theory. The other problem is that lots of those vacua (maybe all of them) are in the "swampland" which can be ruled out on grounds like the weak gravity conjecture.

No one has found a way to make string theory fit the Standard Model and GR-like universe with a positive cosmological constant in which we appear to live.

One of the things that made string theory so attractive is that it overcame some "no go" theorems about quantum gravity. Some string theory advocates claim that it is the unique solution to those "no go" theorems, although this isn't the consensus view. But, since string theory is a package deal, and since our world doesn't appear to have the 10 or 11 space-time dimensions that it wants (which requires additional effort to explain away), fitting that into the world of the Standard Model is challenging. It isn't a modular theory that you can pick one piece of and fit into another theory. It is a quintessential theory of everything.

As a result, while string theory has lots as professionals working on it, as much as anything out of inertia, and can provide some mathematical tools used to develop it for use elsewhere, it is pretty much stalled and at a dead end when it comes to being a viable quantum gravity theory at this point.

This is why I discussed loop quantum gravity which has background independence as one of its key motivating axioms.

 

[tade]

It might be possible to develop a background independent string theory, but no one has done it yet.

Right I see. and yeah have there been other types of QG models which are background-independent and which are under the category of "deeper theories" as O'Dowd mentioned?
and also I guess that O'Dowd placed LQG under the other category

 

[tade]

Right I see. and yeah have there been other types of QG models which are background-independent and which are under the category of "deeper theories" as O'Dowd mentioned?
and also I guess that O'Dowd placed LQG under the other category

@ohwilleke by the way sorry I was just wondering about this question