Verlinde's Entropic gravity and AdS/CFT Beyond the Standard
Model discussion is just a superstrings extrapolations.In fact,they confound the theory of informations witrh a real quantization.
In fact the works are not bad, but they are weak and not sufficient. The strings theories were just a faschion. Several convergence are relevant but it is time to be rational. The entropy is proportional with my rotating 3D spheres. Me I have explaine the gravity, him no !!! them , no !!!
The conformal group in 3+1 spacetime would then be SO(4,2) ~ SU(2,2). The connection to twisters of course is through this conformal symmetry. One can of course see this according to Desargues' theorem; Two triangles are axially perspective if and only if they are in perspective centrally. The projective rays in spacetime have a similar correspondence ω_a = ω(0)_a + ε_{aa'}π^{a'}, π^a = π(0)^a, which in the null construction is a projective Lorentz spacetime.
Your paper on 2+1 Chern-Simons SD has much the same structure as some work I just completed and will be sending to publication soon. The AdS_3 spacetime (2 space +1 time) has the CFT_2 on its boundary S^1xR. This CFT is SL(2,R)^2/Z_2, which with
1 --- > Z_2 --- > SL(2,C) --- > SL(2,R)^2 --- > 1
constructs spacetime symmetries in 4-dim. The S^1xR is the string world sheet or tube, and the CFT constructs the gravitons states. The holography here is with the boundary of the AdS_3. However, there is an additional symmetries on the string corresponding to four dimensions
There was some interesting discussion last week about commuting and anticommuting operators with SD and with causal set theory. I think this might have some interesting implications. It might provide some category theory of functors between spacetime and supersymmetry.
Cheers LC
"Moreover, the toy model may shed light on the nature of the Plank length. In this model, the Plank length is the emergent length arising ....
This dimensionful quantity, however, is not observable in this model. What is physical, instead, it the dimensionless ratio r=R. This illustrates how a dimensionful quantity can emerge from a scale independent framework. Size doesn't matter but a ratio of sizes does. The proof could be gravity."
Dear Sean
Be careful with Planck length and read Wilczek doubts about it
Wilczek:"we must extract roots",
"can be taken outside the square roots",
"In the strong system of units no square roots
at all appear in [M], [L], [T ]."
Read Wilczek http://arxiv.org/abs/0708.4361
Flavio
You said on Sept 12 "I'm reading your essay with interest...". I hope you have, or do, as I think it may be very important in context, and am looking forward to your comments.
Best wishes
Peter
Hi Tom,
Thanks for your kind words. You're right that there are many good essays in this competition and, unfortunately, too few prizes. I had a look at your essay. It seemed like there were some interesting points but I'm not knowledgeable enough with Joy and other's work to really make detailed comments. I certainly agree with the importance of the measurement problem though.
Good luck in the competition!
Sean.
Thanks for your comments Lawrence.
I think you're right that there could be some connections with causal set theory, but there is a subtly related to your first comment. Perhaps a point that is not clear is that, in SD, we have *spatial* conformal invariance so that the relevant group is the conformal group in 3 spatial dimensions, i.e., SO(4,1). I think the connection to causal sets could be through the causal structure of de Sitter space in 3+1 dimensions, whose isometry group is also SO(4,1).
A connection with supersymmetry in SD is hinted by the BRST algebra of the theory. This is explored in a paper by Gomes and Koslowski that you might find interesting: http://arxiv.org/abs/1206.4823. I could put you touch with those authors if you're interested.
Cheers,
Sean.
Sean,
Maybe my insight into this is not complete hogwash. It will take a bit to digest the Gomes and Koslowski paper. BRST quantization is a cohomology of supergenerators, where this is a modern cornerstone of SUSY. It does appear this is derived from shape dynamics without reference to causal set theory. I'd be interested in contacting these two authors.
I agree that the isometry of the anti-de Sitter spacetime plays a role. The anti de Sitter spacetime exhibits periodic time which is removed by considering a universal cover or a patch on the spacetime. The AdS spacetime on this patch is
ds^2 = (1/x)(dt^2 + dx^2 - Σ_idz^idz^i)
which in the limit as x --> 0 defines a Minkowski metric
dx^2 = -dt^2 + Σ_idz^idz^i
which is a Minkowski spacetime. This means that the evolute of AdS from a spatial surface is an entire spacetime. So there is a loss of causality here. What is then required is a conformal completion of AdS. In doing so the Cauchy data on the AdS is defined on a conformal set of metrics. The boundary space ∂AdS_{n+1} is a Minkowski spacetime, or a spacetime E_n that is simply connected that with the AdS is such that (AdS_{n+1})UE_n is the conformal completion of AdS_{n+1} which exhibits a conformal completion under the discrete action of a Klienian group. For the Lorentzian group SO(2,n) there exists the discrete group SO(2,n,Z) which is a Mobius group. For a discrete subgroup Γ subset SO(2,n,Z) that obeys certain regular properties for accumulation points in the discrete set AdS_{n+1}/Γ is a conformal action of Γ on the sphere S_n. This is then a map which constructs an AdS ~ CFT correspondence.
The quotient space AdS/ Γ is a Kleinian structure. The group SO(2,n) is a map from the unit ball B_{n+1}, with boundary ∂B_{n+1} = S_n, into R^{n+1}. The discrete group Γ acts as a conformal on the sphere S^n by the action of the Mobius transformation on S_n. The discrete set of maps on S^n has accumulation points on the limit sphere S^n_∞ are determined by the limit set g_i \in G for i --> ∞. This is denoted by Λ(G), G = O(2,n). The discontinuous set is then the complement of this or Ω(G) = S_n - Λ(G). The manifold Ω(G)/G is an orbifold. This means that the Mobius transformation on the limit sphere S^2_∞ is equivalent to the conformal transformation of N^{n+1} which is equivalent to the isometries of AdS_{n+1}. The Ω(Γ)∩E_n/Γ is then a Lorentzian manifold ∂AdS_{n+1), and a set of discrete points in E_n pertaining to spatial hyperbolids of equivalent data. In this way the data on any spatial surface of AdS_{n+1} is contained in this conformal completeness of AdS_{n+1}. This is equivalent to the discrete action of Γ on S_n..
These discrete structures I think play a role analogous to causal set theory or to shape dynamics. I am of course not certain about this right now. I think this also has some connection to the AdS/CFT correspondence as well.
Cheers LC
Dear Mr. Sean and Mr. Flavio
Your explanation of distinction between space and time in special relativity is very similar as mine. The distinction is in minus sign in your equation (3), it implies causality. I wrote also pedagogically that imaginary distance means that interaction between two events is not possible.
But, it seems to me, that time is basis of everything and that space is only a consequence of time. I wrote also that time runs only in rest matter and that everything can be reduced to dimensionless masses of elementary particles. It seems to me that this is against your and Barbour's theory? I quickly read your and his article, but I did not found similarity. Please correct me if I am wrong. Otherwise I agree with Mach principle.
Your write also about measurement problem. I have my own solution, which is at the end of this essay . It says that every quantum collapse is a conscious decision of units of primitive consciousness. This does not disturb all quantum calculations. Thus every our decision is a quantum event.
Dear Sean Gryb,
I found your essay lucid, absorbing and relevant but I found the final section on solutions a little difficult to follow. That's OK though because the enjoyment of the rest of the essay more than compensated for the difficult bit at the end. (I would need to spend far more time on that bit to properly appreciate it.)You chose a really interesting selection of assumptions to consider. Well done. Good luck in the contest.
Dear flavio Mercati,
So sorry I should have addressed that last post to you as well. Well done, it is a very good essay, and good luck to both of you. Kind regards Georgina.
Dear Georgina,
Thank you for your flattering words. I understand that the last section was probably a little hard to handle. We tried to put in a little something for everyone but I'm glad that the technical discursion didn't ruin the essay for you!
Good luck to you too! I'm looking forward to having a look at your essay.
Cheers,
Sean.
ps. Flavio is a bit swamped with bureaucracy at the moment so I'm handling most of the posts on this forum.
I'm not really sure exactly what you're getting at here. We're suggesting that the flow of time may be intimately connected with the measurement process. This is suggested by the observation that the mathematics of coarse graining resembles the flow of time in general relativity. We are still not entirely sure what this means concretely, but we are working on it. One thing is certain, if the idea is right, it will mean a radical rethinking of time and measurement.
Cheers,
Sean.
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.
Thanks for the heads up. There are definitely better systems.
Sean, you will need to consider the following. Time is dependent upon the integrated and interactive extensiveness of space. That is ultimately dependent upon us. We fundamentally and ultimately depend upon gravity for our physical existence and physical experience (typical, ordinary, and natural experience -- seen, felt, AND touched). Time requires gravity. Physics happens in and with time. Outer space cannot be understood [fundamentally] in relation to time. The [real/actual/true/full] experience of outer space is impossible. Outer space is detached and disconnected from our thought/comprehension; as outer space destroys and precludes our being, experience, and thought/ideas. Gravity fundamentally relates to and involves distance in/of space, force/energy, feeling, visible space, invisible space, touch, and vision. Gravity, invisible and visible, is fundamental to distance in/of space. My essay proves this. Time requires distance in/of space. Importantly, vision and gravity relate to feeling, invisible space, visible space, distance in/of space, force/energy, and touch.
Einstein's GR never provided for fundamentally equivalent and balanced inertia and gravity in conjunction with: 1) Fundamentally demonstrating F=ma
2) Fundamentally balanced and equivalent attraction and repulsion 3) Fundamentally stabilized and balanced distance in/of space in and with time.
My essay, in this contest, provides for all of this.
I finally managed to read your essay. It is a very nice read. I have a number of questions regarding your essay. The first two are just technical:
1. In appendix A you say that equation (10) gives three constraints. 聽How is that? 聽Aren't we talking about motion in one dimension? 聽
2. I do not understand the first part of equation (11). 聽If you are looking for the moment of inertia why do you sum over all possible pairs? 聽The moment of inertia should always just contain a sum over the masses.
The next three are more important:
3. You say that the entropy is exactly the Hawking-Bekenstein entropy. 聽I guess by exactly you mean that it goes like a length squared. 聽Is that correct?
4. This r^2 result gives the correct black hole entropy only in 3+1 dimensions. 聽The black hole horizon of a D-dimensional black hole is a (D-2)-dimensional surface and the result should thus be proportional to r^(D-2). 聽Isn't that correct?
5. I am trying to understand how this entropy gives rise to gravity. 聽Should I be able to understand from what you said why the particles with masses m_i attract each other with a force that is an inverse square law? 聽I somehow don't see that.
Two more general remarks:
6. I think your view of renormalization is too rosy. The view that renormalization is the key to understanding large scale structure is somewhat too optimistic. It would be great if one could just start with a large system and obtain the low energy behavior by just running the renormalization group. Unfortunately this is not the case. One can see this in almost all interesting solid state phenomena. E.g. the ground state physics of the fractional quantum hall effect is not found by performing a renormalization group analysis but by hard work, intuition, and luck (which is then rewarded with a Nobel prize).
7. I have a question about the emergence of time in your framework. 聽This is mainly a question regarding the answer to the question by G. Ellis. 聽I have spent a long time thinking about the role time plays in physics. My original conviction was that time should not be fundamental but should emerge somehow in the theory. After a lot of thought I convinced myself that there is no way to think about emergence that does not already presuppose the notion of time. I think you run into the same problem here. Can you make a measurement without having a time? Isn't time already there when you make anything?
All the best from Rome!
Cheers
Olaf
Hi Olaf,
Thanks for the detailed questions! I'll try to respond in order.
1. This is a typo. An old version of the draft was in 3d.
2. This is Julian Barbour's favourite way of writing the moment of inertia (because it is more "Machian"). It takes some rearranging, but it's possible to get it into the right form (note the M^2 in the denominator).
3.Yes.
4. You are correct.
I have two possible responses to this issue:
i) The result we get is that Shape Space leads naturally to 3d emergent space only (and no other dimensions). So that the model we are considering is some microscopic model where 3d space with gravity emerges.
ii) The result is simply a coincidence and means nothing deep.
We thought that it was a "cute" result but still don't know what to do with it. Fortunately, we have a much better, and more clear, toy model with Matteo Lostaglio's Masters thesis and extensions of this look promising.
5. The short answer is 'No'.
What we wanted to focus on is that, in 3d, the entropy appears to be holographic. Then, the claim is that this is a microscopic model for an entropy of the kind discussed by Verlinde to get gravity out of an entropic force. Of course, the details are very sketchy. But, like I said, we are working on better models.
The key point is: *** We think that Shape Space may be a way to realize some aspects of Verlinde's idea. In particular, the idea of holographic renormalization.****
6. I think we may have misrepresented our view here. What we are really suggesting is that the RG flow equation for some 3d theory with two *asymptotic* conformal fixed points: one in the IR and one in the UV, might be interpreted as Hamiltonian flow in GR/SD. That is, RG time is essentially replaced with real time! We are working on a particular proposal for this and have some toy models to support it.
7. I think I agree with your point. I suppose it's all about wording. I'm not convinced that time doesn't exist. I think it might be part of our very perception of the world. That's why I say in the essay that Platonia, the timeless shape space, cannot be our world. Nothing happens there. In order to describe our world, I think we need something more. Whatever this "something" is, that is what we perceive as time. I think you can also call it measurement. So, for me, the ability to do measurements could be the manifestation of time. It's not that you need to assume time in order to have a measurement, it's that time and measurement are essentially the same thing. That is what I meant when I say that time and measurement are inseparable. Also, I think it might be possible that this is compatible with Julian's view of time. From my perspective, this would certainly be the "End of Time" as we know it!
Hello!
Ultimately, physics is all in the eyes of the beholder.
This conclusion comes straight from the so-called "problem of perception" in philosophy, that has not been solved so far.
In simpler physical approaches to reality, we may wish to pretend that we, somehow(!), observe the independent, objective reality. This is called in philosophy: "naive realism".
Dear Zbigniew,
It may interest you to know that I have addressed this problem. There is an explanatory diagram in my essay and a high resolution version of the diagram correctly oriented in my essay discussion thread. In that thread there is also a link to a web site giving some more detail about it.
Dear Sean and Flavio,
If we accept the existence of absolute time and that a clock second represents a different amount of absolute time in different frames (different states of absolute motion) then all the perceived paradoxes of SRT are resolved. The GPS suppoorts the existence of absolute time. A GPS second is redefined to have 4.46 more periods of Cs 133 radiation than the ground cloock second. This redfinition of the GPS second is designed to make it contain the same amount of absolute time as the ground clock second and thus making the GPS permanently in synch with the ground clock in terms of absolute time.
Sincerely.
Ken Seto
