# Emergent gravity

1. Jul 4, 2012

### Chronos

Padmanabhan may have published his most brilliant, or misguided paper to date - http://arxiv.org/abs/1207.0505. This idea looks pretty solid to me.

2. Jul 5, 2012

### Drakkith

Staff Emeritus
Interesting. Just wish I knew more math and cosmology so I could make an educated opinion on it.

3. Jul 5, 2012

### Chalnoth

I didn't look at it in detail, but it sounds like an interesting idea. It seems, naively, that it might be investigated through a better measurement of the polarization of the CMB, which will provide us more detailed knowledge of the nature of inflation.

4. Jul 5, 2012

### Naty1

From the abstract:

Emergent perspective of Gravity and Dark Energy
Isn't this the very perspective that drives some in these forums nuts....I mean the idea of 'new space'....instead of merely a metric phenomena?? I just love it when such
protestations, based on a conventional view, get bypassed. Too many here seem to ignore the historical evidence that without new perspectives progress would be severely limited.

Anyway, When I got to equations 30 to 31, I though "HEY this sounds like Eric Verlinde's ideas", and sure enough a quick check in Wikipedia shows:

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

[I don't mean plagerism, just that the idea doesn't seem brilliantly original.]

and a few paragraphs later the Padmanabhan paper says:

I can't tell if this is just "one step for man or one giant step for mankind".....Did Verlinde think in terms of cosmological evolution moving to Holographic equipartition..or is this idea a radical/significant extension...

Cosmologists are not going to like this:

This seems on the surface to conflict with the idea expressed in these forums [regarding particle production, I believe] that the Hubble sphere is NOT a horizon.

Even a humorous name included:

Cool name!!!

edit: I see the author references Verlinde among many others...

Last edited: Jul 5, 2012
5. Jul 5, 2012

### Lino

Hi, Apologies if this is a very simple question but in relation to the name of this thread (emergent gravity) or even Padmanabhan's intro to the paper (which mentions "... gravitational field equations are emergent ..."), what is meant by "emergent" in this context?

Thanks in anticipation.

Regards,

Noel.

6. Jul 5, 2012

### Naty1

you can use the Wikipedia 'EMERGENCE'

Last edited: Jul 5, 2012
7. Jul 5, 2012

### Lino

Thanks Naty1.

8. Jul 6, 2012

### Naty1

Chronos...
What idea is that??

I'm not trying to be smart, far from it. I have not analyzed the math, but in general he seems to make [and perhaps draw upon] clever linkages between Einstein's equations, the FLRW solution, and thermodynamic degrees of freedom.

I am still plowing through the paper and it sure is interesting...I could have hardly found a single document that would better tie together many discussions in these forums.....but for the life of me I am unable to distinguish where the author begins 'new' ideas...In a number of cases he is integrating the work of others but which is which I haven't really figured yet. I have not had my 'socks knocked off' with some new and original insights, although they may well be present, as I can relate most of his explanations to discussions here in the forums.

I'll probably be back with some additional comments and questions on the paper.

Parts are difficult to understand for me because he doesn't consistently make clear some of the underlying logic/relationships. In other areas he makes those linkages very clear. Early on I wondered "Why does he pick the Hubble distance" and he doesn't explain that until much later ....all he had to say was "I pick THAT distance because it relates directly to the FLRW scale factor" and so may show a connection to the Einstein equations. Maybe pro readers are expected to find that association obvious?

Meantime, it seems around page 17 is the core of this paper: [N degrees of freedom, enclosing surface and the interior bulk] He is able to relate thermodynamic type degrees of freedom using an appropriate choice of proper time t and Hubble volume V. Are these new and original and dramatic new relationships...

from which he develops [around page 22] :

Last edited: Jul 6, 2012
9. Jul 6, 2012

### Naty1

Here is an example of 'logic over my head':

In section 5.1, page 28 this statement appears: [is charted in Fig 4, but that does not explain the underlying logic]

So the first two sentences are ok...but can someone explain the underlying logic from which I can understand why the 'Hubble radius remains constant'...yet wavelength is stretched as the scale factor [a] evolves???

I think it's time to quit this for today.

10. Jul 6, 2012

### Chalnoth

The Hubble radius is given by:

$$r_H = {c \over H}$$

So a constant expansion rate $H$ means a constant Hubble radius. This also leads to an exponential expansion because:

$$H = {1 \over a} {da \over dt}$$
With a constant Hubble rate we can substitute $H = H_0$, giving the following differential equaiton:
$${da \over dt} = H_0 a$$

The solution to this differential equation is:
$$a(t) = a(t=0) e^{H_0 t}$$

So we have exponential expansion.

Does that help any?

11. Jul 6, 2012

### Chronos

It's not, imo, so much a bold new idea as it is the synthesis of existing knowledge into a broader perspective. The term emergent suggests gravity is not a 'first principle', rather it is the product of more fundamental interactions.

12. Jul 7, 2012

### Naty1

Chalnoth:
Oh, That must be it..... I never thought about inflation as a constant H.....that explanation is great!!! Thank you.

I thought inflationary expansion slowed at the end analogous to radioactive decay. Perhaps that 'decay' period was immaterially short relative to the overall expansion.

Getting around this kind of mental obstruction is why I so admire people who have studied on their own, outside formal instruction.

I'm about 2/3 of the way through Allan Guth's INFLATIONARY UNIVERSE [which for the first 2/3 of the book disappointingly seems about everything EXCEPT inflation] and I'll be interested to see what if anything Guth says about this and what I hope will be a more interesting last 1/3 of the book.

Chronos:

I'm about 3/4 of the way through, and I think that may well be it. He lists a number of his own papers as references, more than anyone else referenced, so it could also be he has filled in missing theoretical pieces and new perspectives in those. Regardless, this paper does tie in a wonderful range of concepts.

unrelated footnote 1: Here in NJ, USA, we are due for a near 100 degree day today 7/7...so of course last evening my air conditioning quit as I was reading Padmanabhan's paper... I found a diagnostic LED flashing in my furnace/ a/c unit [and had logged the same code from several years ago] which suggested possibly shorted thermostat leads....I called a friend who does a/c mtc...He said "Check the compressor outside and see if a mouse chewed somewires"....not the first time I have fixed one of those!!....So I spent nearly two hours outside in heat and sure enough I had forgotten two thermostat leads [for a/c] go all the way outside to the compressor and two were stripped of insulation and touching....Voila!!! as I type this is air conditioned comfort!!!

note 2: 'Padmanabhan" is tougher to spell than 'Schwarzschild'!!!

Last edited: Jul 7, 2012
13. Jul 7, 2012

### S.Daedalus

Padmanabhan's been at this a lot longer than Verlinde, though; this paper from 2002 was the earliest of his on the subject I've been able to pull up on a quick search. Both Verlinde's and Padmanabhan's ideas, in turn, can be considered as part of the 'horizon thermodynamics' approach to gravity initiated in '95 by Ted Jacobson (see here), which in turn probably owes a debt to Sakharov gravity, proposed originally in 1967 (that's what Jacobson worked on just prior to his seminal 'Einstein Equation of State'-paper). Personally, I found his most recent paper to be quite illuminating.

14. Jul 7, 2012

### Naty1

My Summary notes of the paper:

Emergent perspective of Gravity and Dark Energy

A static universe is represented by a universe with constant Hubble radius. Some unknown quantum gravitational instability triggers the universe to make a transition from the initial static state, to one of increasing Hubble distance [currently] and eventually in the final evolution of de Sitter space, to another significantly larger static state.

“The precise description of the transition between the two de Sitter phases is the standard domain of conventional cosmology in which.... a radiation dominated phase {gives} way to a very late time matter dominated phase.”

One can insert some ’hbar’s’ into the FLRW solution to Einstein’s classical theory of gravity to get equivalent statements in equal partition theory [a form of thermodynamic equilibrium] . “Interpreting gravitational field equations as emergent allows us to obtain the gravitational field equations by maximizing the entropy density of spacetime.”
This means [in the static case] the degrees of freedom [N] of a surface equals those of the enclosed bulk [volume] and this equality drives cosmological evolution: Nbulk = Nsur

This bulk volume is taken to be the Hubble volume in which the enclosed bulk space is taken to be the cosmic space that has already emerged;The surface is the Hubble sphere. The emergence of matter [degrees of freedom] along with cosmic space occurs during the current expansion era when the universe is making the transition from one de Sitter phase to another.

The emergence {expansion} of cosmic space is driven by the holographic
discrepancy (Nsur + Nm − Nde) between the surface and bulk degrees of freedom where
Nm is contributed by normal matter and Nde {dark energy} is contributed by
the cosmological constant.

“In a way, the problem of the cosmos has now been reduced to understanding one
single number N closely related to the number of modes which cross the Hubble radius
during the three phases of the evolution.”

edit: So IMO my post #8 does seem to appropriately capture a major aspect of the paper....exactly whose idea it is seems unimportant....

"Both Verlinde's and Padmanabhan's ideas, in turn, can be considered as part of the 'horizon thermodynamics' "

That seems like another good way to capture the transition from relativity to thermodynamic cosmological evolution.

Jacobsen puts it this way: "...the Einstein equation is an equation of state..." referring to 'horizon thermodynamics'

Last edited: Jul 7, 2012
15. Jul 8, 2012

### Naty1

Thanks Daedalus for the reference to the Jacobson paper.....here is a quick summary....it
provides some basic relationships utilized in the current Padmanabhan paper...At 9 pages it's a quick read for concepts...

My comments enclosed thus:{}

Thermodynamics of Spacetime:
The Einstein Equation of State
Ted Jacobson

Summary: [mostly quotes patched together]

Last edited: Jul 8, 2012
16. Jul 8, 2012

### Naty1

Draakith:

It's a tall order for us casual, part time, amateurs to understand the scope of the math and science such full time science people amass over a career. And you would also need a better knowledge of thermodynamics than I to understand all the details of this paper.

I pretty much skip the math..... except to see if I recognize any basics...and look for the logical connections....the theoretical underpinnings.....how theories link together, as I posted from the Jacobson paper, for example. People often don't agree on what the math means, or perhaps it's better to say the math has multiple valid interpretations.

17. Jul 8, 2012

### Naty1

Daedalus:

Well if you, or anyone else, can highlight a few central ideas from that paper:

Gravitation and vacuum entanglement entropy

Ted Jacobson

(Submitted on 28 Apr 2012)
http://arxiv.org/abs/1204.6349

I'd sure appreciate it.... I don't think I understood one paragraph....

Abstract:

18. Jul 12, 2012

### sunu.engineer

Hello, I am new to this forum and my name is Sunu Engineer. I am a cosmologist by profession and a student of Prof. Padmanabhan whose work is being discussed here. I am familiar with the work (over a very long period of time) and its evolution as well as the related work of Prof. Jacobson and Prof. Verlinde. Please feel free to ask any question that you may have. The work as all of you have indicated, while related to earlier work of Prof. Jacobson, has many important and novel aspects to it. It is also complete and consistent.

Regards
sunu

19. Jul 12, 2012

### S.Daedalus

I'd love to, however, I'm a bit pressed for time at the moment... So the key idea is, roughly, that the entanglement entropy in QFT scales with the area rather than with the volume, like black hole entropy does. To get a rough idea about this, consider a universe permeated with some scalar field in a pure state, so the entropy is zero. Then, 'hide' some part of the universe from the rest, say a sphere, i.e. integrate out the degrees of freedom in that part. This will generate an entropy, which by direct calculation can be seen to scale with the area. This I think was originally shown by Srednicki. The wiki article gives some more insight on the issue of entanglement entropy.

Now this is already very suggestive of black hole thermodynamics. If it were the case that the QFT entanglement entropy is equal to (or bounded by) the Bekenstein-Hawking entropy for a certain appropriate space-time volume, then one could apply Jacobson's arguments and derive the Einstein equations from there. However, in general, the entanglement entropy diverges at the horizon. What Jacobson now points out is that if you have gravity, then the entanglement entropy is automatically finite.

So the program is roughly to get general relativity from quantum theory, via space-time thermodynamics. I'll be happy to expand once I get more time (view the above only as a very rough, qualitative sketch), in the meantime, maybe you find this talk by Jacobson interesting...

Hello sunu! Thanks for joining in to the discussion. Unfortunately, I don't have the time right now to think off and ask good questions, but if I get a few hours to spare to sit down with Prof. Padmanabhan's paper, I'll jump at the opportunity... Perhaps, seeing how I'm more familiar with Jacobson's work (and there, too, only an interested outside observer), you could point out some differences, and say a few words about what you think the most significant aspects of Padmanabhan's work are (I realize this is a lot to cover, perhaps you could just provide some pointers to get the discussion started). Again, thanks for joining in!

20. Jul 12, 2012

### Naty1

Sunu: My compliments on your last name!
When I read "Engineer" as a surname I was harkened back in time to college when a bunch of fellow engineering students and I would make up names for each other often involving 'engineer'....

I'd be interested in what you view as a few of the key 'novel aspects' to Professor Padmanabhan's paper. Not knowing the history of the development of this subject made it
difficult to sort out the 'new ideas'.
Also, Jacobsens 1995 paper was an easy read....but anything you can add to the prior post regarding his 2012 paper would be appreciated. I found that paper opaque, maybe because I don't understand 'entanglement entropy'.

I hope to listen to the Jacobsen talk, referenced above, in the next day or so.