Is General Relativity Really About Physics on Curved Spacetimes?

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In summary, Carlo Rovelli mentioned that there is no background in quantum field theory, and this is the challenge for the 21st century.
  • #1
waterfall
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In the Physics World article "Loop Quantum Gravity" by Carlo Rovelli, he mentioned that:

"General relativity is not about physics on curved spacetimes, asymptotic space–times, or connections between theories defined over different backgrounds. It is the discovery that
there is no background; no space–time.The challenge for the physicists of the 21st century is to complete the scientific revolution that was started by general relativity and quantum theory.
For this we must understand quantum field theory in the absence of a background space–time. Loop quantum is the most resolute attempt to address this problem."

I thought General Relativity had Background and mass/stress/energy just curve the spacetime background. But Rovelli mentioned above there was no background, no space-time. What is he talking about?
 
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  • #2
The Minkowski metric isn't a background, it's just a particular solution of the field equations. It's no more fundamental than any other metric in GR.
 
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  • #3
Rovelli is talking about his Loop Quantum Gravity ideas, clearly not standard General Relativity which has a curved spacetime background as you describe it.
 
  • #4
Bill_K said:
Rovelli is talking about his Loop Quantum Gravity ideas, clearly not standard General Relativity which has a curved spacetime background as you describe it.

This is werid, Even if he is working on LQG, he should still refer to standard usage. For example. can he refer to an apple as a banana, so how could he refer to GR as having no background. Is he trying to redefine it.
 
  • #5
It's rather simple.

A picture where you have 'ripples' of spacetime on top of a given backround is misleading in GR; the idea is familiar from weak field gravitational waves, but in general it does not make much sense; how do you get the Schwarzschild solution from a 'deformed' Minkowski metric? The picture becomes seriously wrong when you try to define a canonical formalism quantum gravity.

In classical GR the picture of a backgrund spacetime is misleading and useless, but strictly speaking not wrong.
 
  • #6
tom.stoer said:
It's rather simple.

A picture where you have 'ripples' of spacetime on top of a given backround is misleading in GR; the idea is familiar from weak field gravitational waves, but in general it does not make much sense; how do you get the Schwarzschild solution from a 'deformed' Minkowski metric? The picture becomes seriously wrong when you try to define a canonical formalism quantum gravity.

In classical GR the picture of a backgrund spacetime is misleading and useless, but strictly speaking not wrong.

So you agreed with Rovelli that General Relativity "is the discovery that there is no background; no space–time." Who else agree with these two men. So it means there is no space-time. And if there is no space-time, there is no General Relativity either.
 
  • #7
waterfall said:
So you agreed with Rovelli that General Relativity "is the discovery that there is no background; no space–time." Who else agree with these two men. So it means there is no space-time. And if there is no space-time, there is no General Relativity either.

I think you're confusing "no background spacetime" with "no spacetime," though (judging by the above excerpt) you're not entirely to blame.An example of a background spacetime would be the weak field approximation to the metric:

[tex]g_{\mu \nu }=\eta_{\mu \nu }+h_{\mu \nu }[/tex]

In this case, the Minkowski metric ([itex]\eta_{\mu \nu }[/itex], flat spacetime) is the background.
 
  • #8
waterfall said:
In the Physics World article "Loop Quantum Gravity" by Carlo Rovelli, he mentioned that:

"General relativity is not about physics on curved spacetimes, asymptotic space–times, or connections between theories defined over different backgrounds. It is the discovery that
there is no background; no space–time.The challenge for the physicists of the 21st century is to complete the scientific revolution that was started by general relativity and quantum theory.
For this we must understand quantum field theory in the absence of a background space–time. Loop quantum is the most resolute attempt to address this problem."

I thought General Relativity had Background and mass/stress/energy just curve the spacetime background. But Rovelli mentioned above there was no background, no space-time. What is he talking about?
Good question; that remark is in direct conflict with Einstein's explanations. GR is a field theory with space-time description and in the absence of a background you have no field either. No background -> no field -> no GR.
 
  • #9
Looks to me like post #2 and likely #5 are correct...at least I THINK I understand their meaning...but the terminology describing 'background' and utilized in posts here IS confusing because it apparently has different meanings to different people.

Rovelli [already posted above] says:

"General relativity is not about physics on curved spacetimes, asymptotic space–times, or connections between theories defined over different backgrounds.

I find this utterly confusing: I think he means GR is "not about physics with a fixed background of space time"...or maybe "GR is about physics IN curved spacetime"...not taking place against a previously selected background. Hence post #2.

GR is background independent unlike for example string theory, where extra dimensions must be manually CHOSEN. These are inputs to the formalism, not derived from the formalism as
in GR. This is fundamentally why we lack 'unification'.

So in post #5:
A picture where you have 'ripples' of spacetime on top of a given backround is misleading in GR...

IS MISLEADING because no background is GIVEN...none is selected...again in the context
of post #2.


Here is how Lee Smolin describes the situation in THE TROUBLE WITH PHYSICS,
in the chapter, 'The World as Geometry':



...For Newton, space and time constituted an absolute background...for theories that rely on such an absolute, fixed framework: we call them background dependent...
Einstein's theory of relativity is completely different. There is no fixed background. The geometry of space and time changes and evolves...we call such a theory background independent. ..The story that unfolds in this book turns on the difference between them.

Smolin goes on to describe how Kaluza-Klein extra dimension [and later string theory]:

The theory [with an extra dimension] relied on...an extra dimension too small to see (and) to get electromagnetism out of the theory the radius of the circule must be frozen, changing in neither space nor time. ...Freezing the radius undermines the very essence of Einstein's theory ...dynamical geometry...Tickle the Kaluza-Klein geometry just a bit and the small circle collapses quickly into a singularity marking the end of time.

[I still wonder why is this tiny dimensional change can 'stop time' why nobody reversed
the process to initiate a big bang...to begin time...that kind of miniscule perturbation seems more aligned with vacuum fluctuations that 'everything coming from nothing'...]
 
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  • #10
Here are some further insights...again Lee Smolin from THE TROUBLE WITH PHYSICS ,, 2007,
pages 119-127...(...)my added comments in parentheses.

",,,Because string theory is a background dependent theory...by choosing different background geometries we got technically different theories...these (geometric) constraints are part of the description of how strings propagate and interact with each other...the constants (experimentally determined) that denote the masses of the particles and the strengths of the forces (sounds like he is addressing the standard model here) are being traded for constants that denote the geometry of the extra six dimensions...each of the backgrounds on which a string theory is defined is a solution to Einstein's equations or some generalization of it... the theory that unifies them (a meta theory) MUST NOT LIVE ON ANY fixed SPACETIME BACKGROUND...what is needed to unify them is a single background independent theory..."
 
  • #11
What I think Rovelli is trying to say is that:

You can have a background with test objects in GR, but once we do physics with objects that play an integral role in 'shaping' spacetime there is no longer a physics on a background but the physics and the background are the same thing.
 
  • #12
Even Lee Smolin has same definition as Rovelli as when Smolin said in "Trouble With Physics":

"To say that the laws of physics are background independent means that the geometry of space is not fixed but evolves. Space and time emerge from the laws rather than providing an arena in which things happen."

Isn't it that in General Relativity space and time were simply curved by the laws or mass/stress/energy? What is Smolin talking about that space and time emerge from the laws?

Are these Loop Quantum Gravity Theorists trying to redefine classical GR? But some of you support them. What is the consensus about this?
 
  • #13
Classical GR is background independent. This is a traditional way of saying that GR has no prior geometry. In special relativity there is a prior geometry of flat spacetime. It is prior geometry because no matter how much matter you put on it, the spacetime is still flat. In GR, you cannot specify your geometry first then put matter as you wish, because matter curves spacetime. Nor can you put matter first, because there is no meaning to "where" without spacetime. So you must put matter and geometry on at the same time, so the geometry is not prior to the matter. This is the sense in which GR has no prior geometry.

However, if one restricts to spacetimes which can be covered by harmonic coordinates, then GR does have an alternative formulation as a spin 2 field on flat prior background. Rovelli and Smolin are claiming that the "no prior geometry" view is better for generalization to quantum gravity than the spin 2 field view. This seems a matter of taste, unless there is experimental evidence showing that spacetime in our universe cannot be covered by harmonic coordinates.
 
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  • #14
atyy said:
Classical GR is background independent. This is a traditional way of saying that GR has no prior geometry. In special relativity there is a prior geometry of flat spacetime. It is prior geometry because no matter how much matter you put on it, the spacetime is still flat. In GR, you cannot specify your geometry first then put matter as you wish, because matter curves spacetime. Nor can you put matter first, because there is no meaning to "where" without spacetime. So you must put matter and geometry on at the same time, so the geometry is not prior to the matter. This is the sense in which GR has no prior geometry.

However, if one restricts to spacetimes which can be covered by harmonic coordinates, then GR does have an alternative formulation as a spin 2 field on flat prior background. Rovelli and Smolin are claiming that the "no prior geometry" view is better for generalization to quantum gravity than the spin 2 field view. This seems a matter of taste, unless there is experimental evidence showing that spacetime in our universe cannot be covered by harmonic coordinates.

What' harmonic coordinates? Is our GR not covered by harmonic coordinates? And when you mentioned "GR does have an alternative formulation as a spin 2 field on flat prior background" are you talking literally where gravity is a spin 2 field meaning gravity is field based and not really geometry? But there is still the flat geometry thing which signifies SR. Why not just use the original Euclidean Newtonian spacetime and add a field not just spin 2 but includes SR field as well?

In String Theory. The 6 dimensional "Calabi-Yau spaces" is the background of the Strings, but somehow the Strings themselves recover classical GR. Why did the String Theorists accept this formulation since the idea of strings in Calabi-Yau spaces are not really a background independent idea? Why did they ignore the basic idea of GR of BI?

I'm rereading Smolin "Trouble With Physics" and trying to understand the contexts from all point of views.
 
  • #15
In GR you can use any coordinate system you want. Harmonic coordinates are a particular choice of coordinates.
 
  • #16
atyy said:
In GR you can use any coordinate system you want. Harmonic coordinates are a particular choice of coordinates.

So our world can be described completely by this particular choice of coordinates called Harmonic coordinates hence making possible the spin 2 field or even combo spin 2, SR field on Euclidean physical space?
 
  • #17
atyy said:
Classical GR is background independent. This is a traditional way of saying that GR has no prior geometry. In special relativity there is a prior geometry of flat spacetime. It is prior geometry because no matter how much matter you put on it, the spacetime is still flat. In GR, you cannot specify your geometry first then put matter as you wish, because matter curves spacetime. Nor can you put matter first, because there is no meaning to "where" without spacetime. So you must put matter and geometry on at the same time, so the geometry is not prior to the matter. This is the sense in which GR has no prior geometry.

Here you are talking as if GR were already 100% proven. It's just a model and one can discard it and replace with another one in the future. Unless you are saying that this model is definite just like how Triangle obeys Pythagorean Theorem in Euclidean? But in Euclidean, we are not talking about time intermixing with space. Also note the time in SR and GR is just imaginary. So sometimes when we think of GR a lot. We assume this is automatically how the world works. My point is that. In the end, gravity can still be field based and not just geometry with geometry only as a result of symmetry of certain mathematical feature. This means a field based gravity can have more and richer degrees of freedom perhaps like anti-gravity which can't be allowed in GR, any objections?

However, if one restricts to spacetimes which can be covered by harmonic coordinates, then GR does have an alternative formulation as a spin 2 field on flat prior background. Rovelli and Smolin are claiming that the "no prior geometry" view is better for generalization to quantum gravity than the spin 2 field view. This seems a matter of taste, unless there is experimental evidence showing that spacetime in our universe cannot be covered by harmonic coordinates.

Does this harmonic coordinates have black holes and other dynamics in it or allowed? Because it seems you are saying that it contraints the field based approach of gravity. But this is not a priori or the argument totally sound.
 
  • #18
waterfall said:
This means a field based gravity can have more and richer degrees of freedom perhaps like anti-gravity which can't be allowed in GR, any objections?
Who says so?

It is unusual if it does not but in GR matter does not necessarily have to be attractive.
 
  • #19
Passionflower said:
Who says so?

It is unusual if it does not but in GR matter does not necessarily have to be attractive.

How do you model negative curvature in GR such that an object with gravity shielding can just float in air without propulsion?
 
  • #20
waterfall said:
Does this harmonic coordinates have black holes and other dynamics in it or allowed? Because it seems you are saying that it contraints the field based approach of gravity. But this is not a priori or the argument totally sound.

I'm unsure of this point, but I think that harmonic coordinates include the event horizon of a black hole, as well as the expanding universe. Some references that discuss this are:
Cook, http://relativity.livingreviews.org/Articles/lrr-2000-5/index.html, section 3.3.2
Weinberg, Gravitation and Cosmology, section 8.1 - 8.3
 
  • #21
atyy said:
I'm unsure of this point, but I think that harmonic coordinates include the event horizon of a black hole, as well as the expanding universe. Some references that discuss this are:
Cook, http://relativity.livingreviews.org/Articles/lrr-2000-5/index.html, section 3.3.2
Weinberg, Gravitation and Cosmology, section 8.1 - 8.3

I tried to read the reference above. But not completely understood it.
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
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
waterfall said:
I tried to read the reference above. But not completely understood it.
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.

I don't know what harmonic coordinates exclude, my guess is that they fail close to black hole and cosmological singularities, or when the spacetime topology gets weird. 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. They are related to linearization on flat spacetime, since using them makes it easy to see gravity as a nonlinear field on flat spacetime. Then, when the nonlinear gravitational field is weak, it can be successfully approximated as a linear field on flat spacetime. (There may be other sorts of linearizations about curved spacetimes.)

bahamagreen said:
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?

As long as harmonic coordinates are possible, you can view gravity both as having a background, and as having no background. In the no background view, an inertial frame is only local, due to the curvature of spacetime, which in our universe can be approximately described as an expansion of space.
 
  • #24
atyy said:
I don't know what harmonic coordinates exclude, my guess is that they fail close to black hole and cosmological singularities, or when the spacetime topology gets weird. 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. They are related to linearization on flat spacetime, since using them makes it easy to see gravity as a nonlinear field on flat spacetime. Then, when the nonlinear gravitational field is weak, it can be successfully approximated as a linear field on flat spacetime. (There may be other sorts of linearizations about curved spacetimes.)

We know that gravitons or gravitational waves self-interact and distort the spacetime as they travel. Except the case when these gravitational waves are very weak, where they can be seen as tiny ripples disturbing a fixed geometry. Is this what you were describing? the latter directly related and what is the true meaning of harmonic coordinates where spacetime is not distorted significant by strong gravitons? But wherever you are, gravity is still strong such that if you go outside the windows of your 2nd floor, you'd fall to the ground. Does this approximate flat spacetime?

As long as harmonic coordinates are possible, you can view gravity both as having a background, and as having no background. In the no background view, an inertial frame is only local, due to the curvature of spacetime, which in our universe can be approximately described as an expansion of space.
 
  • #25
waterfall said:
We know that gravitons or gravitational waves self-interact and distort the spacetime as they travel. Except the case when these gravitational waves are very weak, where they can be seen as tiny ripples disturbing a fixed geometry. Is this what you were describing? the latter directly related and what is the true meaning of harmonic coordinates where spacetime is not distorted significant by strong gravitons? But wherever you are, gravity is still strong such that if you go outside the windows of your 2nd floor, you'd fall to the ground. Does this approximate flat spacetime?

No. Harmonic coordinates don't assume weak field, so the weak field condition is not the "true meaning of harmonic coordinates". For example, the proof of local existence of solutions to the nonlinear Einstein equation relies on harmonic coordinates. How about the glocal existence? Well, maybe there is no global existence, if the spacetime contains singularities.
 
  • #26
atyy said:
No. Harmonic coordinates don't assume weak field, so the weak field condition is not the "true meaning of harmonic coordinates". For example, the proof of local existence of solutions to the nonlinear Einstein equation relies on harmonic coordinates. How about the glocal existence? Well, maybe there is no global existence, if the spacetime contains singularities.

In the Weinberg Gravitation book you mentioned above. I saw inside the line "Another related advantage of the harmonic coordinate condition is that, as shown in Chapters 9 and 10, its use produces a very great simplication in the weak-field equations, similar to the simplication brought to Maxwell's equations by the use of the Lorentz gauge."

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 spin-2 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 spin-2 over flat spacetime. So one thing in common for them is weak field. Yet you deny this. Why, can you model spin-2 over flat spacetime in strong field? This isn't possible because in strong gravity, it is highly self-interacting and there are no solutions!
 
  • #27
waterfall said:
In the Weinberg Gravitation book you mentioned above. I saw inside the line "Another related advantage of the harmonic coordinate condition is that, as shown in Chapters 9 and 10, its use produces a very great simplication in the weak-field equations, similar to the simplication brought to Maxwell's equations by the use of the Lorentz gauge."

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 spin-2 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 spin-2 over flat spacetime. So one thing in common for them is weak field. Yet you deny this. Why, can you model spin-2 over flat spacetime in strong field? This isn't possible because in strong gravity, it is highly self-interacting and there are no solutions!

By strong field, Smolin means when the curvature is Planck scale. I'm talking about cases where the field isn't as strong, but still strong enough to be in the nonlinear regime.
 
  • #28
atyy said:
By strong field, Smolin means when the curvature is Planck scale.

No. He was not referring to Planck scale, the context he was referring was this:

"Describing the self-interaction 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.

I'm talking about cases where the field isn't as strong, but still strong enough to be in the nonlinear regime.

So when you say "strong", it means the Planck scale. So you mean outside it when you said "Harmonic coordinates mean that the nonlinear curved spacetime is exactly equivalent to a spin 2 field on flat spacetime"

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
waterfall said:
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.

That's what I like to think. You can find this view in reviews

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 non-trivially 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 Einstein-Hilbert action plus possible higher order terms. If we restrict our attention to processes in which all external particles have energies of order E ≪ MPlanck, we can write an “effective action” that includes all local terms allowed by dffeomorphism invariance."
 
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  • #30
atyy said:
That's what I like to think. You can find this view in this review 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 non-trivially interacting massless helicity 2 particle. The other properties are consequences of this statement, and the implication cannot be reversed."


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:

"Waterfall it seems to me that you do not a one "map" and a "territory", you have two maps. One is GR, which has been tested to exquisite accuracy in a lot of subtly different ways and fits nature remarkably well. The other map is something you (or Bill Hobba? don't know of him) have made up---it does not correspond to string theory or anything else I know. In this map, things called "gravitons" are responsible for all the geometric effects including those I mentioned. Expansion, inflation, accelerated expansion, black hole collapse, the gravitational field outside the BH horizon. I mentioned some others...

Your second map, that you call "territory" would have to be formulated exactly in order to be tested and would have to be tested (as GR has been) and my guess is would turn out to be a dud. Everything the whole universe, would be happening in some fixed eternal Euclidean space, and everything includes BH collapse. Your theory would then have to explain how a "graviton" gets from the heart of a black hole out past the horizon to exert a "pull" on somebody orbiting the BH. And all the stuff about how the clock on the mountain top runs faster than the one in the valley. I guess because the "gravitons" slow clocks down.

Basically I'm skeptical of your second map. Ask Hobba to give you a reference to the paper by Steve Carlip and see exactly what Carlip said. I doubt a Euclidean cosmology (with "gravitons") has ever been formulated in a way that comes near matching what we observe. But I think it is probably dear to your heart and you are not going to change your ideas. So AFAICS we have to agree to disagree on that. Agreed?"

Marcus thought it was my idea when it was not even mine nor Hobba's but from others which you also saw. Hence Marcus was wrong here or not aware of the source you also have, agree? Try to agree and case closed.. it was what confused me a week ago because I thought he was right that I and Hobba were wrong.
 
  • #31
waterfall said:
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."

Yes, I think Hobba was right.
 
  • #32
atyy said:
Yes, I think Hobba was right.

Ok. But there was something you said later in the thread that perplexed me. You said:

"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 higher-spin 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
waterfall said:
Ok. But there was something you said later in the thread that perplexed me. You said:

"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 higher-spin 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.

A chair can be made of wood, but not everything made of wood is a chair.
 
  • #34
atyy said:
A chair can be made of wood, but not everything made of wood is a chair.

Ok. So you mean full GR includes black holes dynamics *near* singularity which spin-2 field over flat spacetime doesn't cover. Good. Thanks for the clarification.
 
  • #35
waterfall said:
Ok. So you mean full GR includes black holes dynamics *near* singularity which spin-2 field over flat spacetime doesn't cover. Good. Thanks for the clarification.

Yes, that's true, but not what I meant. I meant that there may be spin 2 fields that produce "gravity" that is different from that of GR, even below the Planck scale.

http://arxiv.org/abs/1007.0435
 
<h2>1. What is General Relativity?</h2><p>General Relativity is a theory of gravity developed by Albert Einstein in 1915. It describes how massive objects interact with each other and how they affect the curvature of spacetime.</p><h2>2. How does General Relativity differ from Newton's theory of gravity?</h2><p>While Newton's theory of gravity describes gravity as a force acting between two objects, General Relativity explains gravity as the curvature of spacetime caused by the presence of mass and energy.</p><h2>3. What is meant by "curved spacetime" in General Relativity?</h2><p>In General Relativity, spacetime is a four-dimensional fabric that is curved by the presence of mass and energy. This curvature affects the motion of objects and is responsible for the force of gravity.</p><h2>4. How does General Relativity explain phenomena such as black holes and gravitational waves?</h2><p>General Relativity predicts the existence of black holes, which are regions of spacetime where the curvature is so strong that nothing, including light, can escape. It also explains the existence of gravitational waves, which are ripples in the fabric of spacetime caused by the acceleration of massive objects.</p><h2>5. Is General Relativity still considered a valid theory in modern physics?</h2><p>Yes, General Relativity is still considered a valid theory and is widely used in modern physics. It has been extensively tested and has accurately predicted various phenomena, such as the bending of light by massive objects and the precession of Mercury's orbit.</p>

1. What is General Relativity?

General Relativity is a theory of gravity developed by Albert Einstein in 1915. It describes how massive objects interact with each other and how they affect the curvature of spacetime.

2. How does General Relativity differ from Newton's theory of gravity?

While Newton's theory of gravity describes gravity as a force acting between two objects, General Relativity explains gravity as the curvature of spacetime caused by the presence of mass and energy.

3. What is meant by "curved spacetime" in General Relativity?

In General Relativity, spacetime is a four-dimensional fabric that is curved by the presence of mass and energy. This curvature affects the motion of objects and is responsible for the force of gravity.

4. How does General Relativity explain phenomena such as black holes and gravitational waves?

General Relativity predicts the existence of black holes, which are regions of spacetime where the curvature is so strong that nothing, including light, can escape. It also explains the existence of gravitational waves, which are ripples in the fabric of spacetime caused by the acceleration of massive objects.

5. Is General Relativity still considered a valid theory in modern physics?

Yes, General Relativity is still considered a valid theory and is widely used in modern physics. It has been extensively tested and has accurately predicted various phenomena, such as the bending of light by massive objects and the precession of Mercury's orbit.

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