Quantum METRO-dynamics-reuter's no-frill QG

[marcus]

Quantum METRO-dynamics--reuter's no-frill QG

In straight classic GR, the geometry is described by the distance-function called the METRIC. the metric interacts with matter, and is a dynamical result, a solution, rather than being given

the metric is the variable (degrees of freedom) describing the geometry and the geometry IS gravity. that is how Einstein set it up. So if you want to quantize gravity the direct straightforward way is to quantize the metric. Not any particle like a "graviton" living on flat space or any force or anything else---the direct no-frill approach following vintage Einstein is to quantize the metric.

sometimes having an appropriate name for something helps to understand it and you could call classic Einstein GR by the name "metro-dynamics" because it is about the metric interacting with matter.

and you could call Reuter direct no-frill quantization of metrodynamics by the name
"quantum metro-dynamics" or QMD

and that would be analogous terminology to QED and QCD (quantum electrodynamics and quantum chromodynamics)
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Reuter calls it "asymptotically safe quantum Einstein gravity" but I want to sometimes call it QMD because it is remarkably analogous to QED and QCD.
The name makes me focus on the right things and helps me understand.

 

[marcus]

What message is sent by calling it "asymptotically safe".

Physicists communicate with each other partly by what can seem like sign-language to outsiders.
What Reuter accomplishes by calling his version of QG by the name Asymptotically Safe is he let's the other physicists know that he has solved the problem of making gravity RENORMALIZABLE using an idea called "asymptotic safety" that Steven Weinberg thought of around 1979, but couldn't make work.

It is a good idea and Reuter made it work roughly 20 years later. This is very much to the credit of Weinberg and Reuter both.

The history of QG from 1980 to present can be partly described by saying that people GAVE UP on a direct no-frills quantization of the metric and decided it was NON-renormalizable---and then for 20 years or so they groped around in all directions to find a different more indirect way. The ideas they came up with are not necessarily bad and some of them may prove useful. But some of the ideas may prove to simply be the Wild Goose that you pursued when you thought gravity was non-renormalizable.

So when Reuter uses the name Asymptotically Safe he let's the other physicists know that he has shown direct Einstein metric gravity to be renormalizable, after all, using Weinberg's idea.

the actual technical meaning of asymptotic safety may be less important for a general understanding than realizing the semaphoric purpose of what signal it sends
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But the technical meaning is interesting anyway! So as a kind of footnote or incidental comment let us look at that too.

We know from QED and QCD that coupling constants RUN in the sense that while they do NOT depend on location in space and time they do vary with the energy/proximity of an interaction. Other constants can run too. Some of the most vital constants in a theory can depend on the energy with which two things collide, or on how CLOSE they get. So there is this parameter k, which can be the inverse of a length (measuring proximity) or it can be a wavenumber or a momentum or an energy.

You imagine a THEORY SPACE consisting of all the versions of a theory, and, if it depends on N experimentally measurable constants, then the space is N dimensional. And you think that as k (the proximity/energy) changes then what is the right version of the theory also changes graduall---so by varying k you get a trajectory in theory space. You get this trajectory as k changes because the experimentally-measurable constants that go into determining the correct theory are gradually running as you change k, so the point representing the correct theory moves around in the space of theories.

these trajectories make up what is called a FLOW on the space of theories.
Now a flow can have a point called an attractor which is a FIXEDPOINT of the flow that trajectories tend to home in on.
WEINBERG'S idea was that even if the theory space is infinite dimensional, so that you could never succeed in identifying and experimentally measuring all the constants you need to specify the correct one, you can USE THE NATURAL FLOW to discover a fixed point and to find a trajectory which on the one hand has a section that matches observation of the everyday (low k) world and on the other hand goes to this fixed point under extreme conditions (high k, k going to infinity).

Applied to gravity, the so-called BARE theory, or BARE action, which is the fixed point, will have in it values of G and of Lambda which are the BARE Newton constant and the BARE cosmological constant. And these will be different from what we measure in everyday life and astronomy.
They will be the constants that ruled the universe in the ancient times
of extreme (high k) conditions.

This use of the word "bare" is the only place where the terminology gets at all vivid or evocative, as I have noticed. The rest of the time the terminology is sedate and does not stimulate the imagination. which is a good thing on the whole, in my view.

this stuff in interesting enough on its own without waxing rhapsodical like Brian Greene---it doesn't need poetic amplification.