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Does GR have Background?by waterfall
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#19
Feb1712, 11:15 PM

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#20
Feb1812, 12:22 AM

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Cook, Initial Data for Numerical Relativity, section 3.3.2 Weinberg, Gravitation and Cosmology, section 8.1  8.3 


#21
Feb1812, 12:34 AM

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What events do the harmonic coordinates exclude? Is harmonic coordinate related to linearized gravity? Lastly, are you saying that if gravity is a real physical field (versus mere geometry), it can't explain all gravity dynamics but only those belonging to a subclass compatible with harmonic coordinate? I wonder what dynamics it excludes. 


#22
Feb1812, 12:49 AM

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I'm not up on any of this, but I wonder if answering a primitive question might give me or others a grasp on the implications brought out in this thread:
Does background or no background have anything to do with whether an inertial frame mass is subject to any acceleration/momentum (or however the influence/interaction would be properly characterized?) due only to the general universal expansion of space geometry itself? 


#23
Feb1812, 10:23 AM

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#24
Feb1812, 04:52 PM

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#25
Feb1812, 06:39 PM

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#26
Feb1812, 06:56 PM

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And you said "Harmonic coordinates mean that the nonlinear curved spacetime is exactly equivalent to a spin 2 field on flat spacetime, so they don't imply linearization about a flat spacetime." And Lee Smolin said in "Trouble with Physics": "But Heisenberg and Pauli thought it would be simpler to first study cases in which the gravitational waves are extremely weak and can be seen as tiny ripples on a fixed background. This allowed them to apply the same methods they had developed to study quantum electromagnetic fields moving on a fixed background of spacetime. And in fact it was not difficult to apply quantum mechanics to very weak gravitational waves moving freely. The result was that each gravitational wave could be seen quantum mechanically, as a particle called the graviton  analogous to the photon, which is the quantum of the electromagnetic field. But at the next step, they faced a big problem, because gravitational waves interact with each other. They interact with anything that has energy, and they themselves carry energy." I'm still a bit confused about this connection with Harmonic coordinate. Both use the same concept of spin2 over flat spacetime. But like the Smolin quote, this can only occur when the gravity is weak. And you mentioned how the harmonic coordinate is related to the concept of spin2 over flat spacetime. So one thing in common for them is weak field. Yet you deny this. Why, can you model spin2 over flat spacetime in strong field? This isn't possible because in strong gravity, it is highly selfinteracting and there are no solutions! 


#27
Feb1812, 07:20 PM

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#28
Feb1812, 07:40 PM

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"Describing the selfinteraction of gravitons consistently turned out to be a tough nut to crack. We now understand that the failure to solve this problem is a consequence of not taking Einstein's principle of background independence seriously. Once the gravitational waves interact with one another, they can no longer be seen as moving on a fixed background. They change the background as they travel. Since this is outside the planck scale. So all gravity outside it can be described as spin 2 field on flat spacetime. Now why don't physicists accept this as primary instead. That is, that gravity is a spin 2 field on flat spacetime? Then one can apply gauge theory on it. In other words. Why assume the geometry dual context is the primary and the spin 2 field as secondary. Why not assume the spin 2 field as primary and the geometry just secondary? Please address this issue as it's the source of all confusion. Thanks. 


#29
Feb1812, 07:48 PM

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by Hinterbichler: The real underlying principle of GR has nothing to do with coordinate invariance or equivalence principles or geometry, rather it is the statement: general relativity is the theory of a nontrivially interacting massless helicity 2 particle. The other properties are consequences of this statement, and the implication cannot be reversed." and by Carlip: "Note that even though the perturbation theory described here does not provide an ultimate quantum theory of gravity, it can still provide a good effective theory for the low energy behavior of quantum gravity. Whatever the final theory, gravity at low energies is at least approximately described by a massless spin two field, whose action must look like the EinsteinHilbert action plus possible higher order terms. If we restrict our attention to processes in which all external particles have energies of order E ≪ M_{Planck}, we can write an “effective action” that includes all local terms allowed by dffeomorphism invariance." 


#30
Feb1812, 07:58 PM

P: 381

So Hobba was right in the other thread we were discussing when he said ""Up to about the plank scale the assumption it is flat is fine, with gravitons making it behave like it had curvature or actually giving it curvature (we can't determine which) works quite well." In reply to the above, remember Marcus wrote the following: 


#31
Feb1812, 08:00 PM

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#32
Feb1812, 08:16 PM

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"BTW, although massless spin 2 can be equivalent to Einstein gravity in spacetimes that can be covered by harmonic coordinates (or similar), I don't think the reverse is true that the existence of a spin 2 field is sufficient to produce Einstein gravity. Zhang and Hu, A Four Dimensional Generalization of the Quantum Hall Effect Elvang and Polchinski, The Quantum Hall Effect on R^4 Bekaert et al, How higherspin gravity surpasses the spin two barrier" How could that be. You said massless spin 2 in harmonic coordintes can produce Einstein gravity, then you followed it immediately with the conflicting passage " I don't think the reverse is true that the existence of a spin 2 field is sufficient to produce Einstein gravity." But you just mentioned in the first sentence that it can! This has been perflexing me for a week so hope you can explain the context of what mean in your conflicting paragraph. Thanks. 


#33
Feb1812, 09:42 PM

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#34
Feb1912, 11:04 AM

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#35
Feb1912, 11:53 AM

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http://arxiv.org/abs/1007.0435 


#36
Feb1912, 10:20 PM

P: 381

Also your analogy "A chair can be made of wood, but not everything made of wood is a chair." is not related to the above paper but as an answer to my other question, isn't it? 


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