# Internal Relativity

1. Mar 17, 2012

### John86

Did any of you, read this new paper by Olaf Dreyer ?..
Can someone elaborate a little, what this paper is about. Looks interesting and new i can't get my head around yet !...

http://arxiv.org/abs/1203.2641
Internal Relativity
Olaf Dreyer
(Submitted on 12 Mar 2012)
General relativity differs from other forces in nature in that it can be made to disappear locally. This is the essence of the equivalence principle. In general relativity the equivalence principle is implemented using differential geometry. The connection that comes from a metric is used to glue together the different gravity-free Minkowski spaces. In this article we argue that there is another way to implement the equivalence principle. In this new way it is not different Minkowski spaces that are connected but different vacua of an underlying solid-state like model. One advantage of this approach to gravity is that one can start with a quantum mechanical model so that the question of how to arrive at a quantum theory of gravity does not arise. We show how the gravitational constant can be calculated in this setup.

2. Mar 17, 2012

### Naty1

I might be able to elaborate a LITTLE.....but just a little!!! As will be become immediately apparent, I don't know enough about the many body model, in particular equation #5....to draw any overall conclusions.

Seems like the key assumption is on page 5:

For GR, local spacetime [Minkowski space] is flat and when we connect local spaces where curvature [gravity] exists, we find geodesics become curved...more curvature, more gravity....so the first part seems ok, but other experts might interpret the text differently.

Here is what seems to be a giant leap...is it correct or not? And are their subsequent conclusions the correct ones. It reminds me of the Unruh effect where accelerating observers record a different vacuum energy than do inertial observers.

I won't comment much further now so as to allow 'experts' to possibly offer their own insights rather than correct possible errors on my part. [edit: I could not help myself, so I ramble on!!]

One other point:
, equation 12.

Maybe someone who has knowledge of experimental results accuracy of inertial and gravitational mass can comment on the authors value for the C....and equation 23.

I know gravitational and inertial masses have been found experimentally to be very,very close....perhaps identical, but I also understand there is no reason they must be identical.
So the result in theory [close to unity] is not surprising, but does it fall within experimentally verified results?? Presumably the author thought about this.

This seems their overarching conclusion [page 8] :
"We have argued here that quantum gravity is very different from a theory of quantized metrics. First we have argued
that gravity is not part of the fundamental theory but instead is an emergent feature of the low-energy theory. Then we have argued that gravity is not an excitation of the theory but
a non-perturbative feature. Gravity is due to the spatially changing vacuum of the theory..."

That's above my paygrade for sure!!

But from the perspective that at the moment of the big bang vacuum everything was unified [energy, mass, spacetime, you name it] and became 'emergent' so today we observe many 'different' phenomena ....including multiple forces and gravity, I like the concept of the author. Did gravity emerge from a low energy or high energy phenomena?? I don't think anyone knows nor have we any consensus theory.

Last edited: Mar 17, 2012
3. Mar 17, 2012

### Naty1

So it looks like inertial and gravitational mass are identical experimentally to within an accuracy of one part in a trillion:

Equivalence of inertial and gravitational masses

http://en.wikipedia.org/wiki/Inertial_mass#Equivalence_of_inertial_and_gravitational_masses

4. Mar 18, 2012

### John86

Thank you Naty, it is indeed puzzling.
Are there some parallels with Verlinde ideas ?..

5. Mar 18, 2012

### Naty1

John...you need some experts here for more authortative discussion....we are now way "above my paygrade"...

But Verlinde's idea seem clearly related [see below] to the current paper....if you search these forums you can find a lot more; try subjects like ...emergent gravity....Verlinde....
to get started....

If you check below you'll see information, entropy, gravity, degrees of freedom, spacetime[geometry] and lots more, even Bose-Einstein condensates and black holes, are all related.....but nobody, I think, seems to know exactly how. So various researchers start from different points, different perspectives....

Some time ago Marcus [a widely read participant here] posted about emergent gravity and entropy and a long discussion ensued: I did not record the thread identity itself but saved some explanations/posts and references which somewhat clarify entropy, information, and gravity:

I had forgotton [as usual] about some earlier discussions from which I kept some notes:

This may have been Marcus:
a prior post of mine:

For further insights:

http://en.wikipedia.org/wiki/Emergent_gravity

Induced gravity

Thermodynamics of Spacetime:
The Einstein Equation of State
Ted Jacobson (1995, 9 pages)

http://arxiv.org/PS_cache/gr-qc/pdf/9504/9504004v2.pdf

On the Origin of Gravity and the Laws of Newton
Erik Verlinde (69 pages)
http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.0785v1.pdf

How entropy evolves:

[my prior post:]....So shortly after the big bang uniformity actually means LOW entropy as gravity was huge...one DOES NOT expect uniformity under such conditions of high gravity to reflect high entropy. (I think Penrose agrees.)

(2) Post #6
Then he points out (by invoking the Bekenstein-Hawking formula) that a universe which has gravitationally condensed into black holes has an even higher entropy. ...
Black hole entropy IS maximum because gravity is maximum in a given region of space.

Greene:
..,meaning hidden information (entropy) is maximized.

(3) Post#6: [someone posted doubting a Roger Penrose claim:]
.

Greene: [confirms Penrose perspective:]

edit: I happened to just read this which sounds like a 'relative' of Dreyer's approach:

"Spin networks provide a language to describe quantum geometry of space. Spin foam does the same job on spacetime. A spin network is a one-dimensional graph, together with labels on its vertices and edges which encodes aspects of a spatial geometry.....

A spin network is defined as a diagram (like the Feynman diagram) that makes a basis of connections between the elements of a differentiable manifold for the Hilbert spaces defined over them. ..... A spin foam may be viewed as a quantum history..."

http://en.wikipedia.org/wiki/Spin_foam

[Roger Penrose has been working on spin[foam] networks since the 1950's because he thinks spacetime and physics is fundamentally discrete. ]

Last edited: Mar 18, 2012
6. Mar 18, 2012

### strangerep

This idea of different vacuua at different spacetime points is analogous to situations in advanced interacting QFT. Typical interaction terms in the Hamiltonian mean that the "natural" Fock space at time=t is inequivalent to that at t+dt. (This is closely related to Haag's theorem.)

A number of authors have tried to exploit such inequivalent Hilbert spaces by constructing a very large space containing all of them, and working in that. Condensed matter theory exploits related ideas: the ground state is obtained from a free vacuum by a so-called Bogoliubov transformation that mixes the annihilation and creation operators.

Now back to Dreyer. He appears to envision a very simple model in which the transformation between these inequivalent vacuua is governed by a single parameter $\theta$ which calls an "order parameter". But I didn't find a very good explanation of what he really means by that, neither in this paper, nor in his previous paper "Why things fall" (referenced in arXiv:1203.2641). Both papers are flimsy and highly speculative.

The notion of inequivalent vacuua (representations) in curved space has been around for ages. An introduction can be found in Birrell & Davies ch3. Dreyer's flimsy idea then seems to be that instead of thinking about patching together little Minkowski spaces continuously to get curved spacetime, we should patch together a continuous family of inequivalent representations (vacuua). OK, fine, that gives you a framework maybe -- he doesn't show whether or not the total space is/isn't nonseparable, and that can make or break an approach from a practical perspective.

As for his purported "derivation" of the gravitational constant, I don't see that he's getting any more out of his "theory" than he's putting in -- since he inserts an arbitrary constant $a$ just before eq(18).

7. Mar 20, 2012

### John232

I am no expert, but I think it is easy to see that the only discovery made here is how to not solve for the gravitational constant. There could only be two objects in the universe where this would work. It takes into account the mass and the radius of the object, but the gravitational constant is just that a CONSTANT. If this value was changed it wouldn't work for anything, I think any solution for solving for the gravitational constant should at least come to almost the same value for any object.