tag:blogger.com,1999:blog-22973357.comments2018-01-20T06:01:10.019-05:00BackreactionSabine Hossenfelderhttps://plus.google.com/111136225362929878171noreply@blogger.comBlogger47166125tag:blogger.com,1999:blog-22973357.post-51222505820987445412018-01-20T02:37:05.294-05:002018-01-20T02:37:05.294-05:00BHG
Then let me ask this question. Fix a boundary...BHG<br /><br />Then let me ask this question. Fix a boundary time t_0. There is some state psi(t_0) which is supposed to correspond to (or even *be*) a state in the CFT. But that state is also supposed to be, or correspond to, a state of the bulk. But as we have seen, unless you are assuming or have fixed some foliation of the bulk, no state that can be determined locally at the boundary can be Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-38519129823938933122018-01-20T01:57:22.822-05:002018-01-20T01:57:22.822-05:00im,
Yes, I am well aware that AdS is not globally...im,<br /><br />Yes, I am well aware that AdS is not globally hyperbolic and that this makes it different than asymptotically flat spacetime. In AdS we impose boundary conditions at the timelike boundary, and for generic matter fields there is a unique boundary condition that preserves the symmetry of AdS, so we use this. Once the boundary conditions have been chosen, the theory is "black hole guyhttps://www.blogger.com/profile/16669572196455299866noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-88806907883571617932018-01-20T00:59:05.623-05:002018-01-20T00:59:05.623-05:00I am not a contender, but Lynda Williams' &quo...I am not a contender, but Lynda Williams' "Cosmic Cabaret" album has 10 science-themed songs (all somewhat tongue-in-cheek), some of which I think are quite good.<br />https://www.amazon.com/Cosmic-Cabaret-Lynda-Williams/dp/B00004XS67 Olly Willyhttps://www.blogger.com/profile/05204608877360965504noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-57045483315248526392018-01-19T14:19:54.287-05:002018-01-19T14:19:54.287-05:00Con't
Since AdS has no Cauchy surfaces, the f...Con't<br /><br />Since AdS has no Cauchy surfaces, the first question is what sort of evolution one has any right to expect to preserve information in the first place. And here you have two choices.<br /><br />1) You are only interested in some sort of initial data from which the state on the *whole spacetime* follows. It looks like this is a perfectly fine thing to ask for in the case I Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-79999782089898947842018-01-19T14:19:22.392-05:002018-01-19T14:19:22.392-05:00BHG
Let's try to avoid the technical details ...BHG<br /><br />Let's try to avoid the technical details and think conceptually about what is going on. You seem to believe that the solution to all of this lies in some sophisticated math, but it does not. Let me make now one basic point that should have been recognized long ago, and which is implicit in what I have already written, but whose significance has not been appreciated (including Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-80470630526699986622018-01-19T10:56:25.956-05:002018-01-19T10:56:25.956-05:00Tim,
OK, just as long as we're clear that wha...Tim,<br /><br />OK, just as long as we're clear that what I said about the phase space variational principle is correct and indeed standard.<br /><br />However, this does raise a more serious problem that has me worried. In another recent message you wrote: ", I am trying to get you to think a different way about all this: instead of thinking of there being an initial value and then black hole guyhttps://www.blogger.com/profile/16669572196455299866noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-48504523091417644092018-01-19T03:00:46.449-05:002018-01-19T03:00:46.449-05:00BHG
Never mind about the phase space variational ...BHG<br /><br />Never mind about the phase space variational principle. I am still puzzled about it—I had to get straight what the exact form of the kinetic energy term is—and I seem to have even simpler examples of why the proper solution is not minimizing, and even seems not to be stationary—but this will obviously take us away from what we wanted to talk about. So just let it go. I'll get Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-43868610464322005502018-01-19T02:32:19.627-05:002018-01-19T02:32:19.627-05:00BHG
Looking over our last exchanges, I got myself...BHG<br /><br />Looking over our last exchanges, I got myself into unnecessary complications because of your remark about treating x and p as independent variables. So what I should have said (which is equivalent to what I did say, but simpler) is that the set of kinematical possibilities is just the set of all time-parameterized curves in *configuration* space, not *phase* space. Each of those Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-21627834135734589072018-01-19T01:57:34.146-05:002018-01-19T01:57:34.146-05:00BHG
Leave the computational error aside, and this...BHG<br /><br />Leave the computational error aside, and this isn't really important but look: if a trajectory locally minimizes the action in the mathematically complete set of trajectories, including the incoherent ones, then it obviously minimizes the action in any subset of that complete set that it is part of, and the deletion of any set of trajectories from the mathematically complete Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-11154863557010380982018-01-19T01:31:33.063-05:002018-01-19T01:31:33.063-05:00Tim,
Tim: "Your argument in point 1 is an a...Tim,<br /><br />Tim: "Your argument in point 1 is an argument by "clearly".... if you don't restrict your variation to the kinematically coherent trajectories, you don't even get the right answer! Some nearby kinematically incoherent trajectory will have a lower action" <br /><br /><br />You are just making a simple computational error here. I will explain black hole guyhttps://www.blogger.com/profile/16669572196455299866noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-36355374573642768552018-01-18T21:38:22.710-05:002018-01-18T21:38:22.710-05:00I feel that I have to comment on some deeply un-hi...I feel that I have to comment on some deeply un-historical remarks on epicycles made earlier in this thread.<br /><br />In the late middle ages there were (essentially) two competing cosmological systems: the system of <i>homocentric spheres</i> introduced by Eudoxus and championed by Aristotle (both 4th c. BC), and the system based on <i>deferents, epicycles and eccentrics</i> introduced by Hans Mühlenhttps://www.blogger.com/profile/12843348520853108444noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-66502859471907254862018-01-18T20:36:16.499-05:002018-01-18T20:36:16.499-05:00I often find it helpful to reformulate discussions...I often find it helpful to reformulate discussions about beauty-as-truth in terms of the (perhaps somewhat dated) distinction between the 'context of discovery' and the 'context of justification'.<br /><br />Most commentators here seem have no quarrel with scientists making use of powerful heuristics - like simplicity, (self-perceived) beauty, mathematical consistency, Hans Mühlenhttps://www.blogger.com/profile/12843348520853108444noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-20845653286353817992018-01-18T13:41:16.877-05:002018-01-18T13:41:16.877-05:00BHG
Your argument in point 1 is an argument by &q...BHG<br /><br />Your argument in point 1 is an argument by "clearly". What you characterize as clearly true is not at all clearly true! I am using a variational principle to identify—among a set of trajectories—ones that locally minimize the action. That is a purely local matter in the relevant mathematical space, i.e. the space of all trajectories through phase space. There can be a Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-27273255602140960262018-01-18T13:37:40.825-05:002018-01-18T13:37:40.825-05:00BHG
Regarding your point 2. In the case you descr...BHG<br /><br />Regarding your point 2. In the case you describe there is a 1-to-1 correspondence between solutions and points in phase space because the initial value problem is completely unconstrained. That is, you are using a Hamiltonian without constraints. If there are constraints, then not every point in the phase space may yield a solution. But more important, I am trying to get you to Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-18966924847263536392018-01-18T12:07:07.661-05:002018-01-18T12:07:07.661-05:00BHG-
I'll be brief so we don't get side-t...BHG-<br /><br />I'll be brief so we don't get side-tracked. What you say is "a big difference" is a difference, but not big—indeed of measure zero—in importance.What we are discussing are the principles that are validated (or not) by theories, e.g. "information preservation" (backward determinism). None of this has to do with what an actual observer could do. With a Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-55642282075735969732018-01-18T11:47:37.161-05:002018-01-18T11:47:37.161-05:003) "There is a little irony in your saying t...3) "There is a little irony in your saying that one needs the kinematically possible non-solutions—and even the kinematically incoherent non-solutions!—for the variational principle to pick out the solutions. That is, you are remarking on the mathematical necessity of having the non-physical trajectories in order to determine the physical ones. Earlier, you kept saying that the Hilbert black hole guyhttps://www.blogger.com/profile/16669572196455299866noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-27139805672452487562018-01-18T11:47:26.446-05:002018-01-18T11:47:26.446-05:00Tim,
Your usage of terms like "solution spac...Tim,<br /><br />Your usage of terms like "solution space" and "kinematical space" are quite different from what appears in any of the physics literature I am aware of, and it will be important to arrive at some agreement on terminology. I will lay that out shortly, but first let me address your specific questions<br /><br />1) You ask "As I understand it, you claim that black hole guyhttps://www.blogger.com/profile/16669572196455299866noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-23575500495500153302018-01-18T11:24:11.524-05:002018-01-18T11:24:11.524-05:00So if in AdS/CFT, the CFT reflects the full state ...So if in AdS/CFT, the CFT reflects the full state of S2_in + S2_out in the bulk then naturally, the CFT will exhibit unitarity; if the AdS/CFT claim is that the CFT reflects only S2_out, then there is indeed another paradox.<br /><br />In particular, the claim seems to be that the state in S2_out and the CFT together can be "relaxed" to the vacuum. This "relaxation" doesn'Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-68928201057616096922018-01-18T10:52:48.803-05:002018-01-18T10:52:48.803-05:00Tim,
I do want to say one more thing about Hawkin...Tim,<br /><br />I do want to say one more thing about Hawking, because I think he gets the situation just right in the passage I quoted, and I don't agree with your criticism of it. To avoid issues about infinity, let's imagine performing experiments in a large sealed lab. In the context of non-gravitational physics, I think we all agree that we can prepare a pure state, let it evolve black hole guyhttps://www.blogger.com/profile/16669572196455299866noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-19930267076738334162018-01-18T09:19:13.776-05:002018-01-18T09:19:13.776-05:00Amos,
Thanks for pointing out, I've fixed tha...Amos,<br /><br />Thanks for pointing out, I've fixed that.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-63749074251976739702018-01-18T08:19:23.316-05:002018-01-18T08:19:23.316-05:00...the above mentioned ratio between the distance ...<i>...the above mentioned ratio between the distance the grasshopper jumps and the square of the lawn-area...</i> Square -> square root? Amoshttps://www.blogger.com/profile/00595591283398023248noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-55717593058576793142018-01-18T05:59:49.450-05:002018-01-18T05:59:49.450-05:00Nobody mentionned " The Simple Harmonic Oscil...Nobody mentionned <a href="http://theory.caltech.edu/people/politzer/SHO.mp3" rel="nofollow">" The Simple Harmonic Oscillator"</a> by David Politzer and the Rho mesonsEphraim Zymbalisthttps://www.blogger.com/profile/12549982959230732709noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-36326274919098482592018-01-18T03:58:10.188-05:002018-01-18T03:58:10.188-05:00Tim,
I am not motivated to add further papers to ...Tim,<br /><br />I am not motivated to add further papers to the pile on a questions that, as I explained above, I consider to be impossible to make headway on without experimental input. <br /><br />I also didn't mean that there is anything to expand on in your paper (at least not that I see) but that it wasn't hard to see the way you presented it would just make everyone in the field saySabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-85402521763032952042018-01-18T03:15:49.241-05:002018-01-18T03:15:49.241-05:00Sabine,
Well, I am glad that we seems to be comin...Sabine,<br /><br />Well, I am glad that we seems to be coming to a bit of agreement! Let me try to expand the circle of convergence.<br /><br />I certainly agree that there is some new physics needed if you want to cure the singularity. My paper just isn't about that problem. If you can completely cure the singularity and extend the space-time there, that alone does not touch the supposed Tim Maudlinhttps://www.blogger.com/profile/17918668471205376513noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-46804058306856080072018-01-18T03:09:16.052-05:002018-01-18T03:09:16.052-05:00Fun problem.
My intuition suggests that for very l...Fun problem.<br />My intuition suggests that for very large d, the solution should consist of very many small stripes, almost dots. In statphys problems there are generically no ordered phases in 1D, so the solution in 1D - many disconnected points - is the disordered phase. So when the disorder parameter grows large in higher dimensions, the solution should be similar to the 1D case.<br /><br />Thomas Larssonhttps://www.blogger.com/profile/01207766078592840926noreply@blogger.com