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You would observe the theory not blowing up. :)

The key feature she never names is known as a "UV fixed point".

UV = UltraViolet, which in this context simply stands for "high energy".

Fixed point... for that you need to know that the effective values of coupling "constants" aren't actually constant in quantum field theory; they depend on the interaction energy (i.e. how hard you bang your particles together). So they are called "running" coupling constants. Yes, it's contradictory.

That dependence on interaction energy is described by differential equations (known as the renormalization group flow equations, which may sound impressive but is actually a misnomer), which you can integrate to see how a coupling measured in the lab at low energy will change when your descendants finally get enough funding for a larger accelerator.

One interesting behavior is the coupling going to zero when you increase the energy towards infinity. That happens in QCD: counterintuitively, the harder you bang quarks together, the less they affect each other (via QCD, that is; they also have other kinds of interactions which behave differently). So QCD is called "asymptotically free": in the limit of infinite interaction energy, as far as QCD is concerned, quarks are free particles, completely unaffected by each other's presence.

In asymptotic safety, as opposed to freedom, the coupling does not go to zero as you increase the energy; instead, the rate at which it changes goes to zero, and it does so at some finite value of interaction energy. So, as you crank up the interaction energy toward that value, the coupling constant "runs" slower and slower, and once you get there, it stops "running" altogether. From there on, you can raise the interaction energy all you want, and the coupling constant stays... constant.

And that is a UV fixed point.




This helps, but doesn't say what the theory says gravity will do at higher energy levels.

To me it seems to imply gravity will get weaker at higher energies? Something about that makes me feel like it violates conservation of energy, so maybe that's not it.


Having the theory behave at all, in the sense that calculations do not result in infinities, is big enough.

But there is a prediction which has been made pretty much since Reuter et al. picked up asymptotic safety again in the mid-2000s, and which is directly related to the way it supposedly tames those infinities: at higher resolution, i.e. when spacetime is probed at higher interaction energies, its dimensionality is reduced, going from 4 at the macro scale to 2 at the microscopic scale [1].

[1] https://arxiv.org/abs/hep-th/0508202


Also begs the question of how that reaction could even take place if gravitons are totally unreactive with anything other than their source - mass. How would you accelerate a graviton. Gravitons always move at C just like light. Do we have any idea what kind of production and annihalation products will give us gravitons?

Just a guess - dark matter/energy might be the only way to create a graviton without associated mass generating it. That is..the pair production of a virtual dark photon and a graviton.

In that case what are our options?


Are gravitons a thing - i.e.a generally accepted concept in the scientific community? I thought their very existence was highly controversial...


I've always had the naive and hand-wavey understanding that gravity is spacetime, while all the other quantum fields happen in spacetime.

So there may be issues trying to use a particle theory to describe something that may be more fundamental than the other fields.

But IANAP, so this could be completely wrong.




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