Non-geometric approach to gravity impossible?

yuiop

Yes, that is what I meant, more precisely I should of said for an observer at rest in the centre of mass frame.

I agree that it is true that in the rest frame of the the Earth that more massive objects fall faster than less massive objects (as long as they are not dropped at the same time) but the point that I was making (and I am sure you understood what I was getting at) in the rest frame of centre of mass of the Earth and falling object, the acceleration of the falling object is independent of its mass in Newtonian physics. Agree?

Put it another way. In the rest frame of the Earth the acceleration of a falling object is proportional to G(M+m) where M is the mass of the Earth and m is the mass of the falling object. It is easy to see that if m goes to zero, that the acceleration does not go to zero.

PAllen

Yes, this is fine now for Newtonian gravity.

waterfall

So since everybody believe there must be a quantum theory of gravity, then it's almost definite and categorical that "classical curved spacetime (that can be covered by harmonic coordinates) is a coherent state of gravitons on flat spacetime" then why don't we hearing from say sci.am or other news items reporting that "Universe is really flat spacetime a priori!". Hmm.. maybe I should write an article in sci am and make it a cover subject or someone else with credentials write it because sci am doesn't seem to accept contributions by unknown people. But in the book "Philosophy Meets Physics at the Planck Scale". It seems they are saying there that there is a quantum gravity programme where spacetime is really curved and gravitons just quanta of it without any flat spacetime underneath.

This proves that in string theory, spacetime is really flat with the curved spacetime as only coherent state of strings.. although I'm still trying to imagine how these two can co-exist together.

Why didn't you answer this question "2. Can Loop Quantum Gravity be formulated as spin-2field in flat spacetime? Or does LQG stay valid only if spacetime is actually curved?" anyone else knows the answer?

atyy

The gravitons on flat spacetime is a quantum theory of gravity, but it only works below the Planck scale. The question is how do we get a quantum theory near and above the Planck scale? LQG says maybe quantum spacetime is really curved, and there is no flat spacetime underneath it. AdS/CFT indicates that even curved spacetime is not radical enough, and completely different degrees of freedom than what are indicated classically are required.

waterfall

In other words. LQG is about spacetime that is really curved, with no flat spacetime underneath it even far below the planck scale. But this is the confusing part, in LQG, there are also gravitons. But these gravitons can't be modeled as occuring on flat spacetime even far below the planck scale? If you say they can. But LQG is about spacetime that is really curved, with no flat spacetime underneath it even far below the planck scale. Please resolve this confusing part. Thanks.

atyy

LQG hopes that its predictions for experiments occuring far below the Planck scale will be almost identical to that of gravitons on flat spacetime.

waterfall

Yeah and I think this describes how it is done http://arxiv.org/pdf/gr-qc/0604044v2.pdf
"Graviton propagator in loop quantum gravity"

If you have read it already before, please comment on it on the important issues related to our discussions. Thanks.

atyy

Yes, that is a proposal for how it's done. I don't know if the proposal is correct. Why don't you start a thread in the BTSM forum about it?

waterfall

btw.. how do you model Big Bang Expansion using spin-2 field on flat spacetime? Anyone got an idea?

atyy

Weinberg exhibits harmonic coordinates for the FRW universe in his text book.

I'm not sure whether the positive cosmological constant changes things.

waterfall

Gee.. they have even addressed that.. maybe one can imagine say a flat paper size thing expanding to the size of the universe, so the minkowski metric can stretch too.. if anyone has objections.. please say so.

atyy

There's a famous rewrite of the Minkowski metric as expanding space called the Milne universe. It's not relevant to our universe, since it has no matter (in GR, flat spacetime has no matter).

The FRW universe is expanding space with matter, and corresponds to curved spacetime.

waterfall

if flat spacetime has no matter, then how does the spin-2 field in flat spacetime expand with matter? I can't find anything in the internet from goggling "expanding flat spacetime". Hope you have some references.

atyy

It's a silly trick (nothing to do with spin 2 - since it's pure flat spacetime - spin 2 adds spacetime curvature). Try googling "Milne universe".

waterfall

I know. I have read it. Milne Universe doesn't describe out universe so let us forget it. My question is simply how spin-2 field on flat spacetime expand in the Big Bang? Pls just describe how. Thanks.

atyy

The basic idea is expanding space (not expanding spacetime) is just curved spacetime. Spin-2 on flat spacetime produces curved spacetime.

waterfall

atyy.. i think you missed my question here... that was why I had to start the FRW thread just to inquire about this confusion. Well. I'm referring to the Field Theory of Gravitation. I was asking how space expanded in Field Theory of Gravitation. Someone said space didn't expand in it. Knowing my question now. If you have answers to this correct question, pls let me know. Thanks.