# Flat spacetime + gravitons = Curved spacetime?

1. Feb 13, 2012

### waterfall

Hi, does flat spacetime + gravitons automatically lead to curved spacetime?

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?

2. Feb 13, 2012

### waterfall

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:

"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;
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. Feb 13, 2012

### waterfall

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. Feb 13, 2012

### atyy

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. Feb 13, 2012

### pervect

Staff Emeritus
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.