## Monday, October 08, 2007

### Lenny Susskind & census taker's hat

In his new long paper, Leonard Susskind tries to reconcile these assumptions:
• inflation was long enough (50+ e-foldings) for us to know that the whole universe has at least 1000 times greater volume than the observable patch
• because the cosmological constant has begun to dominate, the observable patch no longer grows and the previous point will hold forever
• vacua in the string theory landscape are metastable
• complementarity holds in quantum gravity and requires one to specify a causal patch for quantum mechanics to be well-defined: the degrees of freedom are stored on the boundary
• inflation populates diverse pocket universes

These are pretty diverse assumptions. Moreover, Susskind wants to find a holographic version of the Wheeler-DeWitt equation.

According to him, his "obvious" assumptions imply that the universe has surely tunneled many times before it reached the present low cosmological constant. Where did it start? Well, it started in an "Ancestor" vacuum, Susskind thinks. He believes that the primordial background could be given these kinds of evidence:

• the spatial curvature of the cosmos is negative
• CMB has tensor modes but only with the minimum values of "l"

Together with his gang, Susskind considers eternal inflation, bubble nucleation, and a multiverse "all but inevitable". But he agrees that we lack tools to study this "most extravagant extrapolation in the history of physics", using Bjorken's words. So what does he do?

Stalin and the Central Committee

First of all, he realizes and exploits the fact that all people in his gang are leftists. Susskind agrees with Steve Shenker that in order to achieve a natural, egalitarian treatment of the patches, one needs a preferred observer to take care of everything. The preferred observer is called either "Stalin the Daddie" or "Kim Jong Il" but in the final version of the manuscript addressed to Western readers, Susskind used the moderate term "Census Taker" that was coined by Susskind and Shenker in a Palo Alto Café but none of the two gentlemen was the first one who said it! :-)

Susskind gave his talk in Korea but maybe he confused North Korea and South Korea. :-)

Stalin can't do everything so he has a "Central Committee of the Communist Party" known as "Census Bureau" in the Western edition. The committee is defined, they admit, as the end of history and the causal patch is therefore defined as its past light cone. A figure on page 4 indicates that the central committee is above Stalin and survives him.

Page 5 explains that the term "Stalin" was introduced for the "inevitable" observer who is responsible for other observers, Hydrogen atoms, galaxies, colliding bubbles, and civilizations beneath him. :-) At the bottom of page 5, Susskind assumes that government is an extremely intelligent entity who chooses a very good place where the committee should be located, and it's not the big crunch singularity.

Well, this is about 7th assumption that seems obviously wrong to me - this one is really bad - but let's go on reading. I still haven't understood what question he exactly wants to be answered. Equally seriously, I don't understand whether he thinks that his speculation about the location of the central committee is a hypothesis with some evidence, a nice hypothesis without evidence, God's ad hoc decision, or why does he exactly believe it.

Susskind suggests that the central committee should build its headquarters near the tip of the hat of an FRW geometry. His comrades will surely think it's a great idea but I am not refined enough to appreciate it. More importantly, he doesn't seem to say how Stalin is exactly supposed to control the causal patch i.e. what are the degrees of freedom. Can he define an S-matrix for every committee? His comments that "something" should be associated with the committees sound extremely vague to me and some obvious ways to clarify what he means seem to be either wrong or extremely ugly.

Physics is not about census taking. It is about quantitative causal relationships between observable quantities in the past and in the future. Neither of these quantities is "the number of patches or bubbles". These additional concepts can only be introduced if they're relevant for answering physical questions and physical questions are about observables such as the angular momentum.

Susskind then writes some FRW formulae and draws diagrams of the negatively curved spatial slices, including Escher's famous picture. He proposes the surface of the hyperbolic space to be the holographic screen except that it is infinite and the O(3,1) symmetry acting on the hyperbolic space seems to be broken in every realistic cosmology involving an "Ancestor". This breaking seems obvious but if you want a paper, read Garriga, Guth, Vilenkin. Susskind doesn't seem to agree or care about it, at least not at this moment which is why his text just seems to be plain wrong.

Preferred holographic screens

Susskind asks why flat and AdS spaces allow simple rigorous descriptions of string theory and others don't. Well, it's because these descriptions are associated with simple rigid holographic surfaces at infinity - the AdS boundary or ScriPlus/Minus - where the asymptotic states can be easily defined and "solved" (i.e. they are independent of the exact location of the screen at infinity). He gives essentially the same answer although, in my opinion, his "cold" comments make it look more complicated than it is. But I agree with him that the time-dependence is at most a technical complication and has nothing to do with the essence of the problem how to describe quantum gravity at a causally non-trivial background.

Several comments about the Wheeler-DeWitt equation are written so that they look completely non-stringy. I would disagree that it's natural to choose the metric as a set of privileged degrees of freedom or that the "Hamiltonian" is a preferred operator. Susskind says that the WDW equation is useful if you avoid extreme quantum environments. I think that if you avoid extreme quantum environments - or, equivalently, if you also avoid tiny corrections that quantum phenomena imply for ordinary environments - then the whole problem with complementarity in patches is absent. In other words, you can't solve these deep problems in the semiclassical description. At this level of approximation, complementarity is inconsequential.

Some standard lore about the emergence of time from the WDW equation follows.

Holographic WDW

His holographic WDW equation seems to be nothing else than a dimensional truncation of the WDW equation to the boundary. I have no idea how it actually looks like for the N=4 background or another background. More precisely, I think that this whole concept is incorrect because the very essence of the boundary descriptions is that the gravitational character (and diff symmetry) completely evaporates so it is completely wrong to use WDW-like equations for these boundaries. Moreover, the Hamiltonian becomes physical, nonzero, and well-defined on the boundary.

Susskind uses some contour calculus and AdS/CFT basics to check the locality of a boundary theory.

A minute ago, Susskind incorrectly postulated a WDW-like equation for the boundary. In Section 6, he correctly shows that this incorrect assumption also forces him to incorrectly introduce a non-existent Liouville sector responsible for the metric fluctuations on the boundary. In reality, the very point of the boundary in all working descriptions is that these fluctuations are suppressed or they become unphysical. An exact description of a superselection sector of quantum gravity is possible exactly when it becomes effectively non-gravitational.

His bizarre Liouville sector is responsible for diff transformations on the boundary that are locally perpendicular to the boundary - diff transformations that are identified with RG flow, according to another lore, but it doesn't seem that Susskind uses this lore in a new or coherent way. He also tries to incorporate Bousso's bounds but it is hard to follow the role of these comments at this place, too.

Section 7 finally combines some RG scalings with Stalin's government.

As Stalin moves closer to the central committee, he is supposed to make some RG-like scaling procedures when he counts the observers. This section seems to highlight the problems I have had previously. The goal of a physical theory is to predict relationships between the actual degrees of freedom such as spins and momenta of asymptotic particles, not just to count them. As far as counting goes, RG flows are OK in a field theory because the number of degrees of freedom is infinite anyway. If the number of degrees of freedom became finite or even small, it would be impossible to have RG-like flows that would still preserve the accuracy of the equations.

I have a feeling that Susskind tries to present some approximate RG constructions as accurate ones. Moreover, he doesn't want to write the scaling prescription for the actual degrees of freedom but rather for some meta-degrees of freedom such as the "number of patches". That's a misunderstanding of dynamics of quantum gravity because the "number of patches" is surely not an observable in the technical sense - and even more clearly, it is not a complete set of observables. The very goal of the complementarity principle is that you shouldn't be asking about physics behind your patch which is why e.g. the number of other patches should be excluded from the menu of recommended policy measures. ;-)

In other words, I still don't understand how to relate these speculations with dynamics i.e. the relation between observables.

In Section 8, it is explained that the idea to introduce Stalin was originally meant to define a measure on the landscape. Well, that's why all these Stalin-like ideas are incompatible with the complementarity principle. In a couple of subsections that follow, Susskind simultaneously tries to generalize the conclusions of Garriga, Guth, Vilenkin, as well as deny their basic setup (where the O(3,1) symmetry is broken). I don't think it's possible.

The last Section 10 is a warning to Stalin written in italics.

These causally non-trivial aspects are confusing. I am also confused about some of them but I feel that I am almost certainly less confused than Susskind. It might be a good idea to write a coherent presentation of these things instead of comments about an incoherent one. ;-)

And that's the memo.