## emergent gravity

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

 Quote by Naty1 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....
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...

 Quote by 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
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!

 Recognitions: Gold Member 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.
 Recognitions: Gold Member In the first slide of Jacobsen's talk he has: " The entropy scales with the area because the entanglement is dominated by vacuum correlations which diverege at short distances." Can someone paraphrase this?? Maybe explain 'entanglement', 'vacuum correlations' and why they might diverge at short distances....just a few sentences for perspecgtive...
 I'll try: Let's say you've got two systems, $A$ and $B$, each of which can be in the states $|0\rangle$ or $|1\rangle$ (perhaps think of a fermion with spin up/down states), or of course in any superposition of both, $\alpha|0\rangle + \beta|1\rangle$, with $|\alpha|^2 + |\beta|^2=1$. The combined system then can be in any of the states $|\psi\rangle_{AB}=\sum_{i,j}c_{ij}|i\rangle_A \otimes |j\rangle_B$. If this state can be written in the form $|\psi\rangle_A \otimes |\psi\rangle_B$, it is called separable; if not, it is entangled. An example of an entangled state is $|\Psi^-\rangle = \frac{1}{\sqrt{2}}(|0\rangle_A \otimes |1\rangle_B - |1\rangle_A \otimes |0\rangle_B)$. Its entangled nature comes to light if we let $A$, conventionally called Alice, perform a measurement. If she obtains the outcome 0 (with probability $(\frac{1}{\sqrt{2}})^2 = \frac{1}{2}$, the state collapses to $|0\rangle_A \otimes |1\rangle_B$, and we know with certainty that $B$ (Bob) will obtain 1 upon measuring the system; conversely, if Alice obtains 1, the state afterwards will be $|1\rangle_A \otimes |0\rangle_B$, and thus, Bob's subsequent measurement will yield 0 as a result. Now, the state $|\Psi^-\rangle$ is what's called pure, which basically means that it can be represented by a unique ray in Hilbert space (i.e. a single ket vector $|\psi\rangle$). The converse of pure is mixed. A state is mixed if it consists of an ensemble of pure states -- you can picture this as being uncertain about what state the system is actually in. So if you have an apparatus with a randomizing element that prepares you state $|\psi_1\rangle$ with probability $p_1$, and state $|\psi_2\rangle$ with probability $p_2$ (such that $p_1 + p_2 =1$), you describe whatever comes out of the apparatus by the statistical mixture of these two states. Unfortunately, the bra-ket formalism is not well suited to the description of mixed states; to do so, one typically turns to the density matrix formalism. For a mixture of states such as the one above, the density matrix is: $\rho = \sum_i p_i|\psi_i\rangle \langle \psi_i|$; it gives the probability with which the system is found in either of the states $|\psi_i\rangle$. Now, a consequence of entanglement is that you can't associate to either of the systems $A$ or $B$ a pure state anymore. This is intuitive -- because of the entanglement, the systems considered on their own do not describe the complete state. Rather, the state of the system $A$ is described by the partial trace over $B$ of the density matrix of the whole system: $\rho_A = tr_B \rho_{AB}$ (nevermind the mathematical terminology; this just means 'whatever's left over when I forget about all the degrees of freedom associated to $B$). The last little fact we need is that pure states have zero entropy, while the entropy of mixed states is always nonvanishing. So effectively, if I have an entangled state as above, and restrict my attention to one part of it (say one particle of an entangled two-particle system), then I must describe the state of that part as having nonzero entropy, even though the complete entangled state has no entropy. Because the situation is completely symmetric, the entropy of one part is equal to the entropy of the other, if I remove (say, hide behind a horizon) the remaining one. I.e. if $S$ denotes entropy, $S(A)=S(B)$. This almost directly leads to the 'area law' scaling of entanglement entropy: if I have some volume uniformly filled with some field, and remove a (spherical, for convenience) portion of it, then the entropy of the removed part relatively to the rest must be equal to the entropy of the rest relatively to the removed part (from inside the sphere, effectively the rest of the universe has been hidden behind the 'horizon'); but the area of the sphere's boundary is the only quantity both sectors have in common, so the entropy must end up proportional to it. (Vacuum correlations are just the correlations -- i.e. entanglement -- that are naturally present in the field.) Unfortunately, while the Bekenstein-Hawking entropy has a definite upper bound, given by the Planck area, the entanglement entropy hasn't -- I can always go to smaller and smaller distances and find higher and higher modes that contribute. What Jacobson's now claiming, essentially, is that gravity, which emerges from the thermodynamics of the horizon (recall, what has entropy, also has temperature), serves to regulate this divergence (if I understand correctly). Does this help?

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Gold Member
The math is above my paygrade, but the last paragraph helps:

 Unfortunately, while the Bekenstein-Hawking entropy has a definite upper bound, given by the Planck area, the entanglement entropy hasn't -- I can always go to smaller and smaller distances and find higher and higher modes that contribute. What Jacobson's now claiming, essentially, is that gravity, which emerges from the thermodynamics of the horizon (recall, what has entropy, also has temperature), serves to regulate this divergence (if I understand correctly).
Although I don't really get 'entanglement entropy'......for another time...
Thank you.

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Jacobson's 1995 paper mentions this on 'entanglement entropy':

 ....That causal horizons should be associated with entropy is suggested by the observation that they hide information[3]. In fact, the overwhelming majority of the information that is hidden resides in correlations between vacuum fluctuations just inside and outside of the horizon[4]. Because of the infinite number of short wavelength field degrees of freedom near the horizon, the associated “entanglement entropy” is divergent in continuum quantum field theory. If, on the other hand, there is a fundamental cutoff length lc, then the entanglement entropy is finite and proportional to the horizon area...... {The cutoff seems to be on the order of Planck length}
Thermodynamics of Spacetime:
The Einstein Equation of State
http://arxiv.org/pdf/gr-qc/9504004v2.pdf

Sorry about the delay in responding. I had been traveling and occupied with a variety of other tasks. Please find a simpler explanation of the work in the attached file.

regards
sunu
Attached Files
 Simplicity of the Universe.pdf (96.4 KB, 29 views)

 Recognitions: Gold Member Science Advisor Very nice, sunu. I think there may be more observational tests than proposed.
 Thank you, Chronos. The question of observational tests and further generalizations of this work is what is being discussed at present. I hope you have had a look at the evolution of the idea through the different papers (which may be a bit esoteric in its language) of Prof. Jacobson, Prof. Padmanabhan, Prof. Verlinde, Prof. Visser and others who have been working in the field. It is a very entertaining trail of thoughts and explorations. regards sunu
 Recognitions: Gold Member Science Advisor I'm still reading the other papers. I concur some of them are rather difficult to digest. I am partial to the works of Dr. Padmanabhan. He has a unique ability to render complex ideas comprehensible to mere mortals.