Undergrad Flat arena for quantum gravity?

[gerald V]

TL;DR

Will background independence hold down to the quantum scale? Is there research on alternatives?

In a textbook, which is not in Englisch language unfortunately, I found a passage saying that intrinsic curvature of spacetime is just a specific definition. The alternative definition is that spacetime is flat, whereas clocks and rods have variable lengths - which is just Feynman’s bug.

Currently one thinks that the above two definitions are equally good and that the flat spacetime is unobsorvable. This is supported from observation, which however has not yet reached the quantum scale. Regarding theory, quantum gravity has not been achieved a century after Planck and Einstein because of the lack of an arena. Disconcertingly, one obesssively removes any reference to an arena even where it would appear quite naturally. „Background independence“ is a strict dogma, which however has Einsteinian gravity (using Riemannian mathematics) as its only scientific justification.

To me it appears as highly likely that at the quantum level it will turn out that the said definitions are not equal. Rather, there actually is a prior intrinsically flat space, and variable clocks and rods live in this arena. This variability has a dynamic, which can be quantized above the flat background.My questions:

- Why does one so strongly believe that background independence will hold down to the quantum scale?

- Didn’t the genius Einstein make a couple of highly sophisticated mistakes (the introduction and withdrawal of the cosmological constant, as well as the assumed locality of quantum interactions as the most prominent), and isn’t background independence likely to be another such sophisticated mistake?

- Is there research and respective literature on the possibility of a flat arena for quantum gravity?

Thank you very much in advance.

 

[haushofer]

Actually, background independence was not something Einstein demanded or anticipated of his theory of general relativity. It took him 2 years to appreciate this aspect of the theory. See the infamous "hole argument".

Afaik it's not clear whether background independence is GR's deep lesson for quantum gravity. But e.g. in string theory it's quite odd to quantize on a flat spacetime, only to find out dozens of pages with calculations later that due to the very existence of a spin-2 oscillation and its corresponding beta-function (giving the Einstein vacuum eqns) that this is consistent to start with in the first place. For me that's a reason to suspect that string theory should be formulated in a background independent way.

How? I don't know obviously.

 

[aleazk]

Afaik it's not clear whether background independence is GR's deep lesson for quantum gravity.

Really? Most relativists will tell you it actually is. In fact, the only people I have seen casting doubt on that are precisely string theorists, with very little convincing argumentation. Time to stop giving these people so much credit and start to challenge their BS. Decades have passed, none of the promises delivered.

 

[haushofer]

Really?

Really.

 

[aleazk]

Really.

Thank you for your argumets... as usual in this topic. Sigh.

 

[haushofer]

Thank you for your argumets... as usual in this topic. Sigh.

I'm giving an argument why I suspect that string theory in its current background dependent formulation is lacking, an argument pro background independence, and you start a rant about string theory. So yeah, you got me a bit puzzled here.

And btw, I'm not a string theorist. But e.g. Fierz-Pauli theory shows how a bbackground dependent theory can become background independent by imposing the right principle.

In my experience some critics of ST treat background dependency as some sort of disease. But the Fierz-Pauli example shows them wrong. Also, a background dependent formulation allows you to do scattering calculations, define propagators, show that Minkowski spacetime is a classical vacuum solution, etc. Things which, e.g. in LQG, afaik are much more difficult to obtain than in ST. So then an honest question is: how much should one value such a background independent formulation?

Sorry for my bullshit, I won't bother you with it anymore.