Flat spacetime + gravitons = Curved spacetime?

In summary, the conversation discussed the relationship between flat spacetime and curved spacetime in the context of gravitons and Einstein's field equations. Steve Carlip and Bill Hobba both agreed that a massless spin two interaction, coupled with the universality of the coupling, leads to the equivalence principle and the effective Riemannian space. This means that the initial flat background spacetime is unobservable and all observations detect the effective curved spacetime. This approach to Einstein's field equations can be summarized as "curvature without curvature" or "flat spacetime without flat spacetime". However, there may be testable predictions related to re-radiation from objects falling into black holes in these theories, but they have not been thoroughly calculated
  • #1
waterfall
381
1
Hi, does flat spacetime + gravitons automatically lead to curved spacetime?

In an old 2002 google thread sci.physics.research which is moderated:

http://groups.google.com/group/sci....Einstein+Field+Equations+and+Flat+Space+Time#

Steve Carlip seemed to agree when he said:

"There's a bit more to it. You also need, at least, a massless spin two interaction that couples universally. While this doesn't involve general covariance in an obvious way, a massless spin two field has a gauge invariance that's ``as big'' as diffeomorphism invariance (i.e., that's parametrized by a vector field), and the universality of the coupling rules out any noninvariant ``background.''

Steve Carlip"

Bill Hobba who is now a member of Physicsforums wrote this at sci.physics. (need comment how true it is).

Someone asked (in 2002) at sci.physics: "But in string theory, spacetime still has curvature."

Bill Hobba replied all the following:

"No it doesn't. It emerges as a limit - but the underlying geometry of space-time - if it has one - is not known."

"As Steve Carlip once explained, it is experimentally impossible to tell a theory formulated in flat space-time that makes rulers and clocks behave as if it was curved from a curved one, so the question is basically meaningless at our current level of knowledge."

"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. "

True? If yes, how much is it supported in String Theory? If not, why?
 
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  • #2
Looking at this matter further. I found out it was not even original claim by Steve Carlip but direct from Misner, Thorne, & Wheeler's book "Gravitation". I saw the following in Physicsforums:

https://www.physicsforums.com/showthread.php?t=278874

"Is spacetime really curved? Embedded somewhere?

Message #4:

"There's a fascinating analysis due to Deser ["Self-interaction and
gauge invariance", General Relativity & Gravitation 1 (1970), 9-18;
see also his later paper "Gravity from self-interaction in a curved
background", Classical and Quantum Gravity 4 (1997), L99-L105],
summarized in part 5 of box 17.2 of Misner, Thorne, & Wheeler's book.

Quoting from that latter summary:

"The Einstein equations may be derived nongeometrically by
noting that the free, massless, spin-2 field equations
[[for a field $\phi$]]
[[...]]
whose source is the matter stress-tensor $T_{\mu\nu}$, must
actually be coupled to the \emph{total} stress-tensor,
including that of the $\phi$-field itself.
[[...]]
Consistency has therefore led us to universal coupling, which
implies the equivalence principle. It is at this point that
the geometric interpretation of general relativity arises,
since \emph{all} matter now moves in an effective Riemann space
of metric $\mathcal{g}^{\mu\nu} = \eta^{\mu\nu} + h^{\mu\nu}$.
... [The] initial flat `background' space is no longer observable."

In other words, if you start off with a spin-2 field which lives on a
flat "background" spacetime, and say that its source term should include
the field energy, you wind up with the original "background" spacetime
being *unobservable in principle*, i.e. no possible observation can
detect it. Rather, *all* observations will now detect the effective
Riemannian space (which is what the usual geometric interpretation of
general relativity posits from the beginning)."

Comment?
 
  • #3
Check out the full arguments here in Misner, Thorne, Wheeler "Gravitation":

http://www.scribd.com/doc/81449908/Flat-spacetime-Gravitons

See the starting lines at :
5. Einstein's geometrodynamics viewed as the standard field theory for a field of spin 2 in an "unobservable flat spacetime" background

(body of arguments)

ending at
"
...[The] initial flat 'background' space is no longer observable." In other words, this approach to Einstein's field equation can be summarized as "curvature without curvature" or - equally well - as "flat spacetime without flat spacetime"!"

What do you think?
 
  • #4
Yes. If spacetime can be covered by harmonic coordinates, then spacetime curvature is equivalent to a spin 2 field on a flat spacetime.

An introduction can be found in http://arxiv.org/abs/astro-ph/0006423
 
  • #5
I think there should actually be some testable predictions if these theories are really taken seriously, about re-radiation from things falling into black holes. But it seems that the authors of these sort of theories don't really takes them seriously enough to calculate this in detail.
 

1. How does flat spacetime relate to curved spacetime?

Flat spacetime is a theoretical concept that assumes the absence of any gravitational forces. In this scenario, objects travel in straight lines at a constant speed. On the other hand, curved spacetime takes into account the presence of gravitational forces, which can cause objects to deviate from a straight path.

2. What role do gravitons play in the curvature of spacetime?

Gravitons are hypothetical particles that are believed to be the carriers of the gravitational force. In the theory of general relativity, it is proposed that the presence of mass and energy causes the curvature of spacetime, and gravitons play a crucial role in this process.

3. Can flat spacetime exist in nature?

In our current understanding of physics, flat spacetime is a mathematical concept that helps us understand the effects of gravity. However, it is not possible for flat spacetime to exist in nature, as there will always be some degree of gravitational force present in any physical system.

4. How does the concept of spacetime curvature impact our understanding of gravity?

The concept of spacetime curvature, as proposed by the theory of general relativity, helps us understand gravity as a result of the curvature of spacetime caused by the presence of mass and energy. This theory has been successful in predicting various astronomical phenomena and has greatly contributed to our understanding of gravity.

5. Is there any evidence for the existence of gravitons?

While gravitons are a crucial part of the theory of general relativity, they have not yet been directly observed or detected. However, there is ongoing research and experiments aimed at detecting gravitons, and their existence is highly supported by the current understanding of physics.

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