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26

How is the claim "information is indestructible" compatible with "information is lost in entropy"? Let's make things as specific and as simple as possible. Let's forget about quantum physics and unitary dynamics, let's toy with utterly simple reversible cellular automata. Consider a spacetime consisting of a square lattice of cells with a trinary ...


16

I don't know in which context Susskind mentioned this, but he probably meant time evolution is unitary. That means, among other things, that it's reversible, ie no information can ever get lost because you can essentially, starting from any time (time-like slice), run time backwards (theoretically) and compute what happened earlier. If black hole evolution ...


12

No, it cannot be enough. Stokes' theorem says that the volume ($\Omega$) integral of $d\omega$, a form that is the exterior derivative of another one (of $\omega$), may be written as a surface integral. But it doesn't allow us to rewrite the volume integral of a general integrand (which isn't the exterior derivative of anything) such as the Lagrangian ...


11

The utility of using branes to realize gauge theories in string theory, compared to using heterotic, lies in the ease with which we can decouple bulk gravity. Basically you can zoom in to the branes to isolate the degrees of freedom on them, forgetting the gravity. In contrast, in heterotic compactificarions, both gauge fields and gravity live in the same ...


10

The firewall is a new term in an extremely provocative paper http://arxiv.org/abs/arXiv:1207.3123 Black Holes: Complementarity or Firewalls? by Ahmed Almheiri, Donald Marolf, Joseph Polchinski, James Sully that claims that an observer who falls into a black hole gets burned at the horizon, after all. So the event horizon – the surface of a black hole ...


8

Let's clarify some common misconceptions here. Suppose we have a spherically symmetric black hole. Let's perform a mode analysis here. For simplicity, work with l=0 spherical harmonics for massless fields first. The same conclusion still applies to higher harmonics or massive fields, but the analysis is more complicated. Work in Eddington-Finkelstein ...


8

I believe one has to distinguish two kinds of dualities. AdS/CFT, even in the context where it describes an RG flow (so not the pure AdS_5xS^5 case), is an exact duality to a four-dimensional theory, which interpolates between one well-defined conformal field theory in the UV and another conformal field theory in the IR. So holographic renormalization is in ...


7

The following assumes that the holography to which the OP refers is that which is studied in high energy thoery. Holography is not just a framework that relates something (the RHS) on the region to something (the LHS) on its boundary It is a framework for studying the equivalence of certain theories, one of which is defined in the bulk of some ...


7

I decided to do the calculation and see what happens. According to Wikipedia, the radius of a Planck particle is $$ r = \sqrt{\frac{2Gh}{c^3}}. $$ Apparently, the surface area of a Schwarzchild black hole is given by $4\pi r^2$, the same as a Euclidean sphere. I found this surprising until user10001 confirmed that it's because $r$ is defined as ...


6

It is maybe an underappreciated fact that the old relation between the 2d Wess-Zumino-Witten model on a Lie group $G$ and the 3d $G$-Chern-Simons theory is an example of the holographic principle. See for instance Sergei Gukov, Emil Martinec, Gregory Moore, Andrew Strominger, Chern-Simons Gauge Theory and the AdS(3)/CFT(2) Correspondence ...


6

The holographic principle is a stronger proposition than the entropy bounds but what is the strongest possible formulation that is still valid is disputable. Nevertheless, some facts are well-known. The entropy bounds say that the maximum number of distinguishable microstates that may describe the interior of a region with a fixed boundary is $C\cdot ...


6

Explaining the math behind the holographic principle would be lengthy exercise. Is that really what you want? A short hand-waving argument would be that you can pack a limited number of qbits (in the form of photons) together in a given space. If you take long wavelength photons, you can pack a lot of them together before a black hole forms. Two ...


5

The holographic principle tells us that the description of what happens in a volume of space can be encoded on a surface that surrounds it. This is related to the Bekenstein bound that tells us that the amount of information in a volume of space cannot be more than the area of the surrounding surface in units of a quarter of a planck area. This in turn as ...


5

They are pretty much unrelated concepts. The only similarity is that both the holographic principle and the way holograms work can be described as encoding the information necessary to reconstruct an $N$-dimensional view on an $N-1$-dimensional surface. But beyond that qualitative description, there are not any meaningful similarities.


5

I'll forewarn that I'm no string theorist and Susskind's work is not therefore fully wonted to me (and likely I couldn't understand it if it were) so I do not fully know the context (of the supposed quote that entropy is hidden information). But what he maybe means by "hidden" information is one or both of two things: the first theoretical, the second ...


5

As I said in the comment, the information is not lost simply because of the holographic image at event horizon. This was the result of a long 20 year battle between Susskind and Hawking. Susskind had the final laugh! I suggest you to read the wiki pages: Black hole information paradox,Holographic Principle I'll quote an excerpt from wiki, This idea ...


5

Quoting a deleted post of Dilaton: Joe Polchinski has just written a very nice guest post at Cosmic Variance titled "Black Holes, Complementarity and Firewalls".... Lumo has written a new article about what Raphael Bousso has to say about thi issue here: In response to Polchinsky, I gave this comment in the link, which I think answers the question ...


4

There is a resolution using the two-state formalism of quantum mechanics. Instead of a single state, we have two: $|\psi_i\rangle$ and $\langle \psi_f |$. $\langle \psi_f |$ is the postselected state. If $\rho_f$ is the postselection operator, then $\langle \psi_f | = \langle \psi_i | \rho_f$. Let the subscripts $e, f, i, o$ represent the early Hawking ...


4

The nonlocality of gravity doesn't mean that Lorentz invariance is broken, Lorentz invariance and locality are separate concepts. It just means that to define the state of the universe at a certain point, you need to know what is going on everywhere, the state space isn't decomposing into a basis of local operators. "Locality" is a bit of an overloaded ...


4

You can't say whether the scalings $S\sim R^2$ and $E\sim R$ are the same or different because they are relationships between different pairs of physical quantities! It's like comparing apples and oranges. Well, you could say that the scalings are different already because they contain different quantities but if you defined "different" in this way, $S\sim ...


4

In principle yes, but there are several conceptual and technical issues that make it unclear how this could be achieved. Even though the AdS/CFT correspondence is conjectured to be exact(with much evidence hinting at this), it is hard to prove this essentially because in order to do calculations, one still has to use approximations and perturbation theory on ...


3

To be clear what we're talking about (as I'm not totally sure this is what the question intended), I'll talk about the paradigmatic example of AdS/CFT, the equivalence between $\mathcal N=4$ Yang-Mills on the one hand, and IIB string on (asymptotically) $AdS_5\times S^5$ on the other (at general parameters: no t'Hooft limits etc). We are very much closer ...


3

The number 10^123 emerges as (roughly) the number of Planck areas contained within the boundary of the observable universe. If each Planck area can be (roughly) in two states, a total of 10^123 yes/no questions suffice to describe the boundary of the universe and - via the (still speculative) holographic principle - the whole universe. In other words, if the ...


3

you may begin by reading the reviews on the subject, e.g. http://arxiv.org/abs/hep-th/9611024 and more detailed http://arxiv.org/abs/hep-th/0503128 What type of charges do you have in mind?


3

You are right with your assumption - the special behaviour at the Dirac cone allows for an application of the holographic principle. But how is this possible? It turns out that since in this region of the band structure the Fermi velocity is very large, i.e. two orders of magnitude below the speed of light, graphene behaves effectively as a relativistic ...


3

I wouldn't say that "holographic theories are non-local by definition". On the contrary, in AdS/CFT the CFT is completely local and satisfies cluster decomposition. The cluster decomposition property in AdS can be proved using the CFT bootstrap for all CFTs in $d > 2$ (see http://arxiv.org/abs/arXiv:1212.3616, the proof only requires CFT `axioms', ...


3

Like many people have said here, he's probably talking about unitarity. Susskind is echoing the general view among physicists. I don't think we have (yet) a concrete way to even precisely formulate the principle, leave alone any kind of proof. But based on unitarity in quantum mechanics and (for what it's worth) physical intuition about gravity, it seems ...


3

The answer is quite simple. You should use eqs.(6.8) in the paper. You put them into the last term of eq.(7.11) then, a straightforward integration, I mean something like $\delta\tau\rightarrow\tau$, $\delta A_{\bar w}\rightarrow A_{\bar w}$ and so on, should do the job. So, let us consider (note that in your post there is a wrong sign) $$ \delta ...


3

There is a surface more or less at 13.7 billion light years from us which is where we see back to the big-bang (looking back in time, if you define "now" in a global way, although there is no reason that we should't define "now" by what we are seeing "now", i.e. along a past light cone). This surface is analogous to a black hole horizon, except it surrounds ...



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