Monday, April 05, 2021
Susskind's de Sitter rant
You may also read an interview in the Grauniad where he mentions string theory, colliders, and his view that it may be a stupid idea to obsessively contact the aliens. I can confirm the worries. Alza.cz, a Czech competitor of Amazon, allowed extraterrestrials to be hired. What happened? They have completely dominated the commercials from that moment on. Each ad has a stupid green extraterrestrial with a dwarf's voice. ;-)
But back to the main topic. David B. sent me this 6-year-old, 89-minute-long lecture titled "Old Man Leonard Susskind's Rant About de Sitter Space" which was introduced by Edward Witten.
The Covid-19 format sucks but many of you won't care, I guess. At the beginning, Susskind says that he more or less believes that the known wisdom about quantum gravity "softly predicts" (and incorrectly so) that we live in an anti de Sitter space or similar space (where the time is asymptotically bound to something); and the dynamics is supersymmetry, either with an unbroken supersymmetry or with an extremely weakly broken one.
Sorry, I don't agree it is the right summary of the knowledge. Anti de Sitter space and unbroken supersymmetry vacua play an important role in string theory and high-brow quantum gravity in general but that doesn't mean that they are predicted by the theory. Instead, the right interpretation is that these assumptions (AdS, SUSY) make the life of physicists who want to calculate something easier. But Nature doesn't give a damn whether something is easy to calculate.
In fact, I think it is right to say that relatively to an effective field theory in the swampland, our better sketch for quantum gravity – either explicit string/M-constructions or some more general wisdom respecting the paradigms and/or swampland criteria – only differs (1) at nearly Planckian distances, (2) by the rules that determine how larger massive objects are being built from the fundamental degrees of freedom and/or start to violate the regional independence or locality.
String/M-theory or quantum gravity do teach us new things about long distances, "infrared" non-locality around black holes, UV/IR-connections, and similar stuff but all these insights are really derived and from the possible dual descriptions, one may always find (at least) one that looks qualitatively just like the effective field theory. If you adopt this perspective of mine, the fundamental framework of quantum gravity doesn't – and cannot – predict something about the highly infrared distances, asymptotic regions of the spacetime, and maybe not even about the bubbling of the Universes from each other in the eternal inflation etc.
A heavily broken SUSY surely makes it hard to calculate something but you can't really prove (at least at this moment, as far as I know) that string/M-theory or quantum gravity ban a breaking of SUSY at energy scales that are much higher than the LHC scale. After all, there are still 15 orders of magnitude between that collider scale and the normal 4D Planck scale. The broken SUSY and/or the positive cosmological constant are still emergent, long-distant effects, even in string/M-theory or quantum gravity, and it is appropriate that it is difficult to calculate whether they occur. On the other hand, the apparent tiny cosmological constant is still a legitimate positive argument in favor of SUSY because SUSY makes the cancellations of the vacuum energy more likely or more plausible. The existing methods don't seem sufficient to get the tiny observed value but the qualitative statement is right, anyway. You make things worse by abolishing SUSY altogether.
Also, the degrees of freedom – what to calculate – are surely harder to be defined and calculated in de Sitter space (than in the AdS space). But it may even be impossible to define the precise ones. A fact is that even in the AdS setup which admits a precise, S-matrix-like set of observables, it is still possible to derive approximate predictions for a region which does not include the asymptotic region at infinity. Such a limited region is qualitatively the same as one in de Sitter space. That's why I think that it's obvious that if string/M-theory does allow the positive cosmological constant, it also makes it possible to calculate similar approximate quantities in a region of the de Sitter space. And everything else – predictions at a greater accuracy or observer-independence – may be physically prohibited or meaningless, due to a more massive version of the uncertainty principle.
I think that all existing versions of dS/CFT are wrong or at least physically useless and the whole logic that makes the people look for this kind of stuff is misguided for the reasons above. There is no reason why something like that should exist. On the other hand, one may derive effective field theories from the string vacua – and their parameters, like the gauge couplings and particle masses, are in principle calculable precisely. I think that this statement remains true and the possibility remains real even if the cosmological constant is positive and the spacetime ends up being de-Sitter-like. I think that nothing we have learned contradicts the possibility that we may derive totally precise parameters of an effective field theory expanded around a de Sitter space from string/M-theory. If you accept this way of linking string theory to detailed particle physics, the search for a "boundary of our de Sitter space" is perfectly useless and orthogonal to the things that physically matter.
Susskind also describes the de Sitter Penrose diagram, apparently identical to an enternal black hole, and discusses the entanglement between the "antipode" and the "pode" which Susskind believes to be the opposite of an "antipode". As a cultural European, I feel the moral duty to explain to the uncultivated American Mr Susskind that a "pode" isn't the opposite of an "antipode". An "antipode" is a person with the feet pointing in the opposite direction while a "pode" is just a foot, from the Greek πούς (poús). And a person with the misdirected feet isn't the opposite of the feet themselves. Thanks for your understanding. But I got distracted. ;-) I don't see much point in discussing the precise entanglement and correlations if one can't design an experimental protocol that will test this entanglement; and/or if one can't define the separate physics of the two Hilbert spaces. And it's obvious that we don't know how to make these exponentially precise measurements of the correlations in the dS space, isn't it? So why should we discuss it?
OK, I am still distracted. Juan Maldacena has been too shy for almost 3 decades but he should have taught Susskind and others that his name isn't "One" (at most "The One"). "One" may be OK in Mexican Spanish, e.g. for Susskind's Mexican janitor, but Maldacena is Argentinian and Juan is pronounced "Khoo-un" Thank me very much, Juan, you are welcome. ;-)
As far as I can see, what is going on is that these de Sitter or dS/CFT rants have been trying to find "elegant, precise, or integrable constructions" analogous to the unbroken SUSY or AdS/CFT ones at least for 20 years – I would say it is at least 22 years now – but it seemed pretty self-evident to me (and it still does) that nothing like that exists. So why would you waste 20 years with such a thing? On the other hand, the fact that the ugly de Sitter space without a mixed-signature asymptotic region and without the niceties of unbroken SUSY prevents us from a nicely controllable, integrable construction does not mean that it isn't the right background recommended by string/M-theory or quantum gravity for our world.
Then there is the whole issue of the de Sitter temperature. Susskind says that it is the only temperature at which de Sitter may have the right symmetry. Well, let me tell you something. Quite generally, if the temperature is totally precise, it means that the system is described by the very precise density matrix \(\exp(-\beta H)\). The tiny but nonzero temperature of the de Sitter space primarily means that you can't cool it to zero, without destroying the basic shape of the space, i.e. the very existence of pure states is banned in the de Sitter space! There is almost certainly some (application of the) uncertainty principle that prevents you from building a complete set of commuting observables that would be consistent (all of them) even with the rough de Sitter geometry or topology. And that impossibility means that you can't prepare the system in a pure state and all the doable calculations are density-matrix-like. Any effort to discuss a precise construction of Hilbert spaces with pure states may very well be impossible and I think that it is. But this still doesn't mean that there is something wrong with de Sitter as a possible background of string/M-theory. It's just a background where you can't produce pure initial (or final) states. The preparation of the initial density matrix may very well depend on some priors, like in Bayesian inference, and this dependence on the priors may be as impossible to remove as the uncertainties for \(\Delta X,\Delta P\) in regular quantum mechanics. In de Sitter space, the thermal noise is unavoidable and the occupation numbers in the deeply infrared modes (whose wavelength is comparable to the de Sitter radius) are unavoidably uncertain! Also, you shouldn't compute scattering amplitudes but the inclusive cross sections (like in the usual treatment of infrared divergences, the de Sitter radius is the infrared cutoff)!
Susskind has also placed the holographic screen on the de Sitter horizon, surely not the first person who makes the guess. It may be right or wrong and neither possibility seems to have terribly interesting consequences. The horizon etc. is a fast scrambler but I couldn't see anything new in the comments using this sexy buzzword. OK, after some combinations of these ideas, Susskind talked about the Boltzmann fluctuations and combined them with the \(ij\)-bilocal degrees of freedom in Matrix theory. I have tried to generalize them in many contexts but here I didn't quite understand whether he claimed to "derive" the relevance of the Matrix-theory-like degrees of freedom from some properties of de Sitter, or he just combined two ideas that have nothing to do with each other, and if he did, I didn't understand what this combination was good for.
Some Susskind's Boltzmann fluctuation formula only worked for \(D=4\), as Juan pointed out, and Susskind didn't care, apparently suggesting that \(D=4\) is required for a consistent de Sitter. I don't believe it, it is an extraordinary claim. Instead, Juan's observation that the formula only had the right scaling for \(D=4\) meant that the justification of the formula was wrong.
We also saw Susskind's successful effort to simplify the everyone-to-everyone graph so that the system is still a fast scrambler and he decided that a graph that is as sparse as cabbage ("expander graphs") is still OK but parsley is no longer enough for fast scrambling. Excellent, probably a nontrivial mathematical result but I don't see how it could be interesting for a physicist. It seems to me that they have answered a similar question to the question "how many screws you may remove from a Michelson interferometer so that it still disproves the aether wind". No screws, one screw, 11 screws, a cabbage of screws? Unless you have another result that makes the answer important, I just don't care. It is not physically relevant.
Various comments and questions were contributed by Banks, Bousso, Maldacena, and Witten.
To summarize, I have the constant perception – and it gets manifested at so many, a priori independent, places – that Susskind conflates "what is true" (or compatible with string theory or quantum gravity) and "what is simple or admitting integrable structures". In particular, I find it almost self-evident that there is no AdS/CFT-like beautiful "integrable structure" in the de Sitter space and it's been foolish to look for one. De Sitter is warmer and messier than AdS, it has new kinds of unavoidable uncertainties and upper bounds on the precision of experiments. I would add that a complete set of commuting observables is impossible to be found in dS theories and consistent with the approximate dS locality, and that's why you can't work with pure states and you need to compute inclusive probabilities with the de Sitter radius as the infrared cutoff, just like in the calculations with infrared divergences.
The focus on the expander graphs has been a new example that struck me. Susskind and pals may be right that expander graphs produce "fast scramblers" much like some matrix models or Yang-Mills theories for black holes and their horizons. But clearly a complex or non-integrable enough systems are generically fast scramblers. It is not "unusual" to get a fast scrambler – a fast scrambler is some generic "non-integrable" dynamics which is the rule, not the exception. At most, one may get a psychological toy model for the fast-scrambling, complex behavior. But a "toy model for a complex behavior" sounds pretty stupid to me me because as long as the toy model is a good representation of what we're interested in, it will still be messy because by definition, we are interested in a messy thing! This worshiping of fast scramblers looks like Wolfram's worshiping of non-integrable systems of rules and I find it totally silly because non-integrable rules are the rule, not the exception.