Internal Relativity

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  • #1
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 !...
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.

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  • #2
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 draw any overall conclusions.

Seems like the key assumption is on page 5:

By putting ourselves in an Einstein elevator gravity disappears. Locally there
is no gravity. Gravity is in the non-trivial effect that moving from one Minkowski space
to another has.
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 the first part seems ok, but other experts might interpret the text differently.

We have seen that the vacua for many-body systems provide a similar
structure.....then locally the physics would be indistinguishable from a constant vacuum but globally there are effects because the map v is not constant. We claim that these effects constitute gravity
Here is what seems to be a giant 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:
It is a remarkable experimental fact that there is a constant C such that m = Cm.
, 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.
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  • #3
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

..... As of 2008, no deviation from universality, and thus from Galilean equivalence, has ever been found, at least to the precision 10−12. More precise experimental efforts are still being carried out.
  • #4
Thank you Naty, it is indeed puzzling.
Are there some parallels with Verlinde ideas ?..
  • #5
40 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:
LQG and allied QG approaches are about geometry. For geometry to have entropy it MUST have microscopic degrees of freedom. This opens up a big field of investigation (where Loop is already an active program) namely, what are the underlying degrees of freedom of geometric relationships. String researchers can be expected to follow suit.
a prior post of mine:
....If anyone has determined that one or several of these [physical entities] is "fundamental" meaning it is the first to emerge and precipitates the others, I have not seen that yet. My only personal hesitancy is that quantum theory, incomplete though it may be, suggests there is no space and time at the tinest scales....Planck size I personally wonder if geometry/time is the first to emerge....

For further insights:

Induced gravity
From Wikipedia, the free encyclopedia

Induced gravity (or emergent gravity) is an idea in quantum gravity that space-time background emerges as a mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics approximation of Bose–Einstein condensates. The concept was originally proposed by Andrei Sakharov in 1967......

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

The Einstein equation is derived from the proportionality of entropy
and horizon area together with the fundamental relation _Q = T dS
connecting heat, entropy, and temperature. ,,,,,,,,Viewed in this way, the Einstein equation
is an equation of state......

How did classical General Relativity know that horizon area would turn out to be a form of entropy, and that surface gravity is a temperature?.......
That causal horizons should be associated with entropy is suggested by
the observation that they hide information. In fact, the overwhelming
majority of the information that is hidden resides in correlations between
vacuum fluctuations just inside and outside of the horizon...

On the Origin of Gravity and the Laws of Newton
Erik Verlinde (69 pages)

Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.......In this paper we will argue that the central notion needed to derive
gravity is information. ......The most important assumption will be that the information associated with a part of space obeys the holographic principle
How entropy evolves:

When gravity matters as it did in the high density early universe, clumpiness - not uniformity- is the norm.
[my prior post:]....So shortly after the big bang uniformity actually means LOW entropy as gravity was 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.

When gravity flexes it's muscles to the limit it becomes the most efficient generator of entropy in the universe. Since we can't see inside a black hole, it's impossible for us to detect any rearrangements.....
..,meaning hidden information (entropy) is maximized.

(3) Post#6: [someone posted doubting a Roger Penrose claim:]
Penrose also argues (his Fig. 27.10) --- without seeming to provide any proof --- that any gravitational condensation (perhaps into galaxies or stars) will increase the entropy of a uniform distribution of matter, and hence conform with the Second Law of thermodynamics

Greene: [confirms Penrose perspective:]

In calculating entropy you need to tally up the contributions from all sources. For the initially diffuse gas cloud you find that the entropy decrease through the formation of orderly clumps is more than compensated by the heat generated as the gas compresses, and ultimately, by the enormous heat and light released when nuclear processes begin to take place...The overwhelming drive towards disorder does not mean that orderly structures like stars and planets...can't form...the entropy balance sheet is still in the black even though certain constitutents have become more ordered.

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..."

[Roger Penrose has been working on spin[foam] networks since the 1950's because he thinks spacetime and physics is fundamentally discrete. ]
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  • #6
Science Advisor
Did any of you, read this new paper by Olaf Dreyer ?..
Can someone elaborate a little, what this paper is about.
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
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.

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