Tuesday, April 01, 2014

Laymen's allergy to the holographic principle



Do we live in a hologram? Really??


In the second paragraph, she complains that our normal "reality" was referred to as three-dimensional. But it's normal to count the spatial dimensions only, even among physicists. For example, the word \(p\)-brane denotes an object with \(p\) spatial dimensions whose world volume has \((p+1)\) spacetime dimensions, however. This nomenclature doesn't mean that those who are using it are denying the theory of relativity. On the contrary, they are using it in a very fundamental way and the world volume of a \(p\)-brane actually does preserve the full \(SO(p,1)\) Lorentz symmetry.

A few more lines complain that the word "reality" isn't really well-defined. Philosophers like to say lots of redundant and ill-defined things about "reality" and I might agree with Sabine about it. And foes of quantum mechanics like to insist that "classical reality" has to exist even though it demonstrably doesn't.

But the Scientific American video doesn't intend to discuss any of these or similar controversial questions of the word "reality". The word "reality" is simply used to denote "how the world works according to the best theories we have, regardless of the potentially misleading appearances".

So now we will continue with the exchanges between the two laymen (one actual person and one fictitious person) that are specifically related to the holographic principle.
Q: Do we really live in a hologram?
A: What is “real” anyway?

Q: Having a bad day, yes?
"A" means Sabine Hossenfelder; "Q" is a fictitious third party. I already agree with "Q" that her first reply was inappropriately irritated and off-topic. "Q" didn't want to discuss any ill-defined esoteric aspects of "reality". He or she simply asked whether the proposition "our world is a hologram" is supported by the best cutting-edge science about this very question.

The correct answer to the first question is
Yes, assuming that the general lessons that have been established for the anti de Sitter space may also be applied to the approximate de Sitter space we inhabit.
OK, "Q" makes "A" a bit more cooperative for a while:

Unfortunately, what Sabine Hossenfelder says is complete junk. The holographic principle isn't a "conjecture" as of 2014. It is a physical principle whose specific realizations have been firmly established. In particular, the AdS/CFT correspondence hasn't been called a "conjecture" since Summer 1998 or so, less than one year after Maldacena's paper appeared, simply because it would be – and it is – utterly idiotic to suggest that it is a "conjecture". It is a scientific claim that is supported by a comparable amount of scientific evidence as any other established important insight of science.

And it is really exciting for hot babes.

The evidence involves tests of dozens of distinct (and pretty much all) types of dynamics in the bulk and at the boundary and it is spread in a big part of the 10,000 papers written on the subject. The evidence has a somewhat different character and composition than the evidence in favor of Darwin's theory or the existence of quasars or DNA. In some respects, it is less tangible; in others, it is much more exact. At any rate, it is a huge amount of evidence that immediately identifies a person who says "we don't know whether it's true" as a layperson. Such an answer is totally incompatible with the insights we have actually accumulated.

Even in a very strict way, the proposition that "there is no experimental evidence behind the holographic principle" is simply a lie. The principle says that non-gravitational CFT-like dynamics of a physical system may be equivalently and exactly described in terms of higher-dimensional quantum gravity and vice versa. It is backed by a substantial amount of evidence in condensed matter physics and other "non-particle" disciplines of physics.

More conceptually, it is silly to try to underrate a scientific claim by saying "some scientists only believe it because their theory supports it". Evolution is also "believed" only because a particular theory, Darwin's theory, seems to imply it. It doesn't mean that it is not as certain as you can get. Every robust enough claim about Nature is believed not just despite its dependence on a theory but because of its dependence on a theory. Every reliable enough insight about Nature is and must be rooted in a sufficiently deep theory, otherwise you would be building on sand. And yes, you should really imagine that you are building a tall building and you notice the difference between deep soil (theory) and some sand (claims that are not rooted in theory).

So her dissatisfaction with a theory-dependence of a proposition about Nature shows that she just doesn't feel comfortable with the scientific method as such. Indeed, her claim is fully analogous to some of the creationists' claims that "evolution is just a theory". Yes, no, but if the theory is robust, potent, contradicting no evidence, and passing a sufficient number of checks/predictions, a proposition's being rooted in a theory makes it as reliable as a proposition about Nature can possibly get.

The right answer to the question by "A" is Yes. It is a harder thing to see but we inhabit a hologram in the same "real" sense as that we inhabit planet Earth.

We also inhabit a metric manifold with four spacetime dimensions and a Minkowskian signature in the sense that all of the physical theories describing sufficiently mundane, low-energy observations in the Universe may be organized as statements about degrees of freedom attached to points and places in such a manifold. The metric manifold isn't necessarily the complete and exact description of everything but it is an ingredient in a more accurate description of Nature than e.g. the description with the flat 3-dimensional space plus 1 time according to Newton, and this "improvement" is the reason why the morally correct answer must be Yes.

Hossenfelder is also wrong when she says that the holographic principle is a "mathematical statement". It is not really mathematical at all because the defining features of the two sides of the correspondence require physical criteria. The bulk dynamics must contain the gravitational force, for example, and whether or not a theory includes a gravitational force is a matter of physical interpretations. The holographic principle, much like the uncertainty principle and the equivalence principle, is a physical postulate, a constraint on current and future theories, a general observation about all theories that describe certain classes of phenomena in Nature (and phenomena in sufficiently similar theories describing fictitious or otherwise unobservable worlds that are sufficiently analogous to ours).

It's just wrong to classify such principles as "mathematical statements" because it makes them look disconnected from the real world (and indeed, this may be the very reason why Hossenfelder uses this bizarre description of a physical principle). But they are completely physical; they were discovered in physics, motivated by physics, using physicists' arguments and jargons, and implying things for physics. There is very little role in the principle that would focus on the "man-made mathematics" which may postulate axioms and rules more or less arbitrarily, independently of the observations. Mathematics is important for precise derivations of detailed things but the overarching principle, the holographic principle in this case, is physical exactly because it's both a "non-rigorous template" to produce more specific propositions; and a "proposition that is very important for very many situations and questions in physics". The same comments apply to postulates of relativity and quantum mechanics, laws of thermodynamics, the equivalence principle, and many other pillars of the foundations of physics. To attempt to dismiss them as "mathematical statements" means to completely misunderstand them.
Q: Well, do we [live in the metric manifold]?

The questions that "Q" is asking are actually much more physics-oriented, philosophical-babbling-avoiding than the answers by "A", at least so far! Sabine Hossenfelder complains that she doesn't want to drown in ill-defined philosophical debates on "reality" but at the end, it is no one else than her who is persistently pushing the exchange in that direction!

I think that the question of "Q" has a totally clear physical target. He is asking whether the description of physical phenomena as events affecting degrees of freedom attached to the metric manifold remains the physics' state-of-the-art framework to formulate the most accurate theory (or theories). The answer is Not quite. Just to be sure, the theory of relativity (neither of them) has been excluded and the symmetries underlying it (Lorentz symmetry, diffeomorphism redundancy) seem to be as correct and exact as 100 years ago.

But the description in terms of fields on this manifold is known or believed to be limited today and there are actually alternative descriptions of the same physical phenomena that are not defined as field theories on the target spacetime we easily "see". They're defined on "other spaces", e.g. boundaries of the spacetime or world volume, and they seem to be capable of a more accurate description of physics that continues to work in extreme conditions, too.

In the 1980s, people would think that physics fundamentally appears at the "world sheets of propagating strings" rather than the spacetime. In the 1990s, this viewpoint was rendered outdated by the duality revolution that shifted the physicists' attention back to the spacetime and downgraded the "fundamental string" to the status of "one object among many others that are comparably fundamental". The world sheets are only "more fundamental" than other world volumes (of branes) in the weakly coupled description of string theory.

The 1997 AdS/CFT correspondence allowed us to formulate theories of quantum gravity in the anti de Sitter space (AdS) using an alternative description, a conformal field theory (CFT) on the conformal boundary of the AdS space (at infinity). The two descriptions are equivalent except that the CFT, holographic description on the boundary seems "more exact" now because we actually have a full definition of the CFT while the description in the bulk is only known in various approximation schemes. In this sense of having the exact equations, the description saying that "we live in the hologram" is more real than the description in which we are living in the bulk.

It seems to me that "Q" wanted to discuss physics, so it is puzzling why "A" offered a few incoherent words about Platonism and reality instead.

Again, "Q" formulated the question like a proposition that a physicist wouldn't be ashamed of. Even if we simply erase the question mark, it is a precious formulation of the status of "reality" of the holographic principle. If the principle holds for Nature around us, then we live in a hologram in an equally "real" sense as we learned that we lived in Einstein's curved spacetime.

If another layman manages to describe the situation this accurately, he or she should be praised because it's exactly right. Instead, "A" replies with tons of fog and erroneous claims.

Most importantly, Sabine Hossenfelder is completely wrong that one shouldn't take the nomenclature "holographic principle" too seriously. The hologram discussed in quantum gravity isn't made of the same "materials" as holograms on your credit card. But the ways how they encode the higher-dimensional information are totally analogous – I wouldn't be afraid to say that they are the same.

The dimensions along the hologram, e.g. \((x,y)\), represent the corresponding coordinates of the object in three dimensions. But the hologram – both in quantum gravity and on your credit card – also knows about the \(z\) coordinate of the three-dimensional object it describes. A point in the bulk isn't represented by a point on the hologram. Instead, there is always a network of waves, an interference pattern. Quite generally, values of \(z\) closer to the hologram are represented by denser interference patterns and values of \(z\) further from the holographic plate are represented by less dense interference patterns. Again, this claim holds both for real-world holograms on your credit cards and the holograms in quantum gravity.

So Sabine Hossenfelder's suggestion that "it isn't the same mathematics that is behind both cases of holography" and that "the Fourier transformation is only behind the credit-card holograms" shows that she has no clue what she is talking about. It is the same mathematical trick that is behind both cases of holography (only the precise details of the parameterization may differ) and the Fourier transformation is equally important and plays pretty much the same role in both holograms! It is surely not just the counting of dimensions that the credit-card holograms and quantum-gravity holograms have in common.


Here’s an example. Take a square made out of \(N^2\) smaller squares and think of each of them as one bit. They’re either black or white. There are \(2^{N^2}\) different patterns of black and white. In analogy, the square is a box full of matter in our universe and the colors are information about the particles in the inside.

Now you want to encode the information about the pattern of that square on the boundary using pieces of the same length as the sidelength of the smaller squares. See image below for \(N=3\). On the left is the division of the square and the boundary, on the right is one way these could encode information.

There’s \(4N\) of these boundary pieces and \(2^{4N}\) different patterns for them. If \(N\) is larger than 4, there are more ways the square can be colored than you have different patterns for the boundary. This means you cannot uniquely encode the information about the volume on the boundary.

The density of information that a volume of space (or its surface) may hold is one part of the issue. But the holographic entropy bounds are not the only aspect of holography, at least not in the AdS space. In the AdS space, the hologram is "real" also in the sense that the dynamics describing the evolution of the interference patterns on the hologram (in the boundary CFT) is local. (The letters on the custom declaration don't move just to their neighbors if the reality changes and you want the declaration to remain accurate.) It seems likely that this is a special fact related to the infinite warp factor at the AdS boundary and it can't be generalized to any "boundaries at a finite distance". Nevertheless, the locality of the boundary CFT is an important feature of AdS/CFT, one that makes the description using the CFT hologram more real than it would be otherwise, and it's plausible that some "approximate locality" holds for the hypothetical "holograms at a finite distance", too.

The possibility that "we live in a hologram" wasn't appreciated before the early 1990s. Nevertheless, it became totally viable, in some contexts proven, the would-be contradictions have been shown not to exist, sometimes for very clever reasons, and it is a shame that "A" didn't exploit the opportunity to explain these wonderful insights – that have led to a consistent picture – to "Q".

The failure of volume-extensive locality isn't really "disturbing" in any realistic sense of the word. No freedom believed by common sense is ever violated by the holographic principle. Once you try to compress too much information into a given volume, the volume has to be equipped with too much mass as well, and even common sense is enough to see that the object collapses into a black hole. The reason is that memory chips require some matter to carry the information. And the matter can't be too light because too light particles have too long de Broglie wavelengths which means that the information has to be spread over larger volumes and its density can't be too high. Whenever you compress too much information into a region, you inevitably increase the (mass) density as well, and you're facing the risk of a collapse into a black hole. This collapse always occurs before you could violate the entropy bounds.

Pretty much every layman may understand that one can't create an object that is as geometrically large as a black hole but heavier. The black hole is simply the density champion. This uncontroversial fact by itself is enough to see that every simple enough method to make the non-independence of the information visible to plain sight is bound to fail simply because such an experiment needs too high a concentration of information which also needs too high a concentration of mass. At most, we create a black hole and it carries some entropy that just happens to be proportional to the area of its event horizon.

There is really no other "obvious experiment" that could be used to detect a "paradox" implied by the holographic principle. Because the gravitational collapse constrains how many memory chips may be squeezed into a volume, it automatically guarantees that the holographic information bounds are never violated. A truly counterintuitive situation would happen if the holographic principle implied "inevitable correlations between degrees of freedom we may comprehend", i.e. some bits of information known from long-distance physics. But that's exactly what never seems to happen. Whenever the information is carried in the intuitive, everyday-life-compatible, black-hole-entropy-ignoring degrees of freedom, its density is much smaller than the bound imposed by the black holes, and the holographic principle therefore allows all combinations of these mundane degrees of freedom.

But once again, the holographic principle is more than just the bounds on the information that may be squeezed somewhere. At least in the AdS space, it also says that the theory describing the dynamics on the hologram is actually known, and it is local. It is actually "more accurately known" than the theory in the bulk, so "we live in the hologram more really" than we live in the bulk.
Q: What then is the typical size of these pieces?

A: They’re thought to be at the Planck scale, that’s about \(10^{-33}\) cm. You should not however take the example with the box too seriously. That is just an illustration to explain the scaling of the number of different configurations with the system size. The theory on the surface looks entirely different than the theory in the volume.
First of all, the size of the cell for one bit isn't just "thought" to be the Planck area. It has to be \(10^{-70}\,{\rm cm}^2\) unless the holographic principle is "completely" wrong. Even in theories with old large dimensions or warped dimensions, the cells have this size – even though in these theories, we may rewrite the area constant in different ways as functions of the higher-dimensional Planck scales and the volumes or curvature scales of the compactification manifolds.

Second, it is not quite true that "the theory on the surface looks entirely different than the theory in the bulk". The bulk theory has gravity but its low-energy dynamics may be very analogous and, if the dynamical gravity is removed, nearly identical to the theory on the boundary. It's really a point of the holographic principle – and a major achievement of AdS/CFT – that the theory living on the boundary is as natural as the theories we know in the bulk. After all, the most intensely studied example of AdS/CFT has the \(\NNN=4\) gauge theory living on the boundary – and it is a close cousin of QCD, the theory that describes the quarks in the bulk (bulk of the real world around us).

So she is really contradicting the main facts about holography – that the boundary theory is completely natural and controlled by similar equations we have known from the bulk. Again, I think that she must know (or at least, she must have heard, which is a different condition) that her statement is untrue. She is saying it with the purpose of making the holographic principle look contrived to the readers. But it is not contrived at all. The theory on the boundary is a supernatural theory of the kind that theoretical physicists have loved for decades before the holographic principle was found.

Because she doesn't mention any black holes or event horizons or limits on densities etc. in this explanation of the experiments, you may be sure that Sabine Hossenfelder doesn't have the slightest clue about the actual phenomena that would be important for anyone who would try to test some of these elementary consequences of the holographic principle. She is just repeating the same kind of general claims about "experiments that may be made" that could be said in any scientific context but she doesn't have any specific knowledge of quantum gravity so you can't learn anything that actually matters in this scientific discipline.

This was probably the only marginally okayable answer in this dialog and I don't want to be picky in this case.

11 spacetime dimensions is the total spacetime dimension of the bulk of M-theory; string theories have 10 spacetime dimensions and they are equally fundamental as the 11-dimensional M-theory.

At any rate, the hologram to describe 11-dimensional theory only has 10 dimensions, and the holograms that describe 10-dimensional string theory have \(8+1=9\) spacetime (world volume) dimensions. Well, some of these dimensions shrink to zero size. For example, the most carefully studied example of AdS/CFT involves \(AdS_5\times S^5\) of type IIB string theory (yes, \(5+5=10\) dimensions, the right critical dimension of superstring theory had to be generated) but the boundary theory is just a 4-dimensional supersymmetric gauge theory. The spacetime hologram was expected to be 9-dimensional but the fives dimensions of \(S^5\) became "invisible" because the five-sphere is infinitely smaller than the typical distance scales near the conformal boundary of the AdS space; the five-sphere shrinks to a point in the boundary CFT. The dependence on the five \(S^5\) coordinates is encoded into the way how we use the 6 scalar fields of the gauge theory (or the fermions); the (angular) momenta dual to these five-sphere coordinates are given by generators of the \(SO(6)\) R-symmetry in the gauge theory.

So it surely is true that if we counted the dimensions of the holograms, we would have to say that the spacetime dimension is 10 for M-theory and 9 for string theory.

Also, it is important to point out that holography always removes one dimension only – that's true for credit-card holograms and quantum-gravity holograms, too. The subtraction of one is a part of the holographic principle and "analogous" principles that would try to subtract or add different numbers of dimensions would simply not work! As I argued under a picture above, the extra coordinate normal to the holographic plate is encoded in the "density of the interference pattern" (or its "wavelength") and there simply exists only one such "extra" quantity to be used.

A: The reflection on his glasses.
I thought that the reflection was appropriate because a human was concentrated on a two-dimensional plane, too.
Q: Still having a bad day?

A: It’s this time of the month.
My understanding of the answer was along these lines.

A: You’re so awesomely attentive.

Q: Any plans on getting a dog?

A: No, I have interesting conversations with my plants.
The "happy end" is that "Q" has been brainwashed by this anti-physics propaganda, too.

The statement "The holographic principle is an unproved conjecture supported by string theory and black hole physics" is nothing else than a demagogic anti-science sleight-of-hand. The truth is that every fundamental insight of science may be dismissed by a science hater in this way. Darwin's theory is also just "an unproved conjecture supported by some fossils and genetics". What is the purpose of such hostile and morally wrong comments? Both Darwin's theory and the holographic principle are fundamental pillars of our scientific understanding of the corresponding classes of phenomena and observations.

And the sentence "It is only surprising that information can always be encoded on the boundary of a volume if you request to maintain the resolution, but then it is quite a mindboggling idea indeed." shows that she has never actually thought about the phenomena that occur if one tries to approach the limit (of information).

At any rate, I find her rant to be fully analogous to creationists' anti-evolution diatribes. The only difference is that creationists get rarely employed by scientific institutions that were established with the realistic plan to be at the cutting edge. Nordita was founded by Niels Bohr in 1957 – so it could have been a continuation of the Copenhagen school, if you wish: quite a brand – and you may see the deterioration we witness 50 years later. Low-brow rants against the pillars of theoretical physics of the last 20 years.

I think that she must suffer more than anyone else because the people around her are trying not to tell her that her knowledge is totally inadequate for a professional researcher in theoretical physics of the early 21st century. Still, I am sure that she may "see" in between the lines, see that everyone who knows some physics actually agrees with me and only tries to maximize the hypocrisy because hypocrisy has become more important for many physicists than the question whether institutes founded by giants like Niels Bohr are taken over by mindless mediocre anti-science kibitzers.

Physicists, please, tear down this wall of hypocrisy and political correctness run amok. Save the institutes founded by the likes of Niels Bohr and reclaim them for proper physics research by those who actually love and can do this research. So far you're being pathetic in this respect.


  1. Yay! Can't wait to read this... to me the holographic principle is the most glamorous, enchanted one, in QM.

  2. Lubos, a nice article. I liked your demonstration of encoding the inside of a square on its perimeter - "this means, basically, that some of the patterns for the squares can’t happen". But I am free to select any pattern for the squares, meaning that in this simple model a holographic principle does not hold. What are limits of applicability of the holographic principle?

  3. “If another layman manages to describe the situation this accurately, he or she should be praised because it's exactly right.” Well, thank you much for doing so by writing this fine article. I’m a fairly long-time reader of your blog and I can say
    that munching your magic mushrooms in many occasions painted a small on my face even after having a bad day. Now, this peculiar Amanita Muscaria deserves to be dried to its boundary and preserved for later consumption in winter!

  4. "small" should be read as "smile", it's getting late, the mushrooms' effect...

  5. Did David Bohm get much right in his Wholeness And The Implicate Order outlook and book? Also, Rupert Sheldrake's ideas in his banned TED talk about causation memory? If holography or a sort of super Fourier enfolded order dominates physical theory now, that sounds like the stuff of an equation based simulation, a kind of convenient compression of reality, or backwards being a projection out into it from algorithmic code.

    You make a good chemist, claiming that all real information has mass.

    Darwin's follower D'Arcy Wentworth Thompson in his “On Growth And Form” pointed out that far from (then unknown) DNA coded genetic programs having to specify each square nanometer of biological order, that vast simplification was at work dud to how simple principles of self organization and mathematical entrancement found afford macroscopic function and symmetries and overall elegance, akin to only ages variables being needed in a parameterized model to make an elephant wiggle it's tail, here literally so.

    But does the math for any of these popular ideas relate to today's essay about serious physics?

  6. I think she's trying to get some popularity with that title, and I think she will attract the less interesting kind of popularity.

  7. "The theory on the boundary is a supernatural theory of the kind that
    theoretical physicists have loved for decades before the holographic
    principle was found." . Supernatural statements existed long before string theory . Have you heard of the Akashic rehttp://en.wikipedia.org/wiki/Akashic_recordscords ? .It is funny, but in my metaphysical phase years ago, one of my skeptical hold outs was that I could not think of a physics theory that could account for Edward Casey's Akashic records readings :).

  8. Thank you for all your efforts that you have put in this. Very interesting info. TRUCK TRACKING

  9. Can any N-dimensional content be wholly recoverably reduced to (N-1)-dimensional content? Can any entity be rewritten as a non-crossing Schlegel diagram? Kuratowsky's theorem says "no." One therefore suspects an unlimited number of pathological entities falslfy the holographic principle.

    Reality has positive feedback. The holographic principle can be spare, elegant, rigorous, all-encompassing and - like quantum gravitation, SUSY, and dark matter - empirically wrong at the founding postulate level.

  10. ",,,but in my metaphysical phase years ago...". Hmm, don't you mean "seconds ago"?
    Yes, supernatural statements existed long before string theory. In fact, history is rife with supernatural claptrap...btw, I can think of a theory that accounts for Casey's ravings--in fact, several :)

  11. The most galling thing about Sabine's post was undoubtedly how she "endured" holography posts and papers. I guess she "endures" any post 1915 physics as well. Sabine, like barbie says, "Math is hard" and "Let's find a Lagrangian" :)

  12. "The black hole is simply the density champion."

    Of course, that isn't really true. The greater a black hole's mass, the lower its density (assuming that you define the volume of a black hole based upon the dimensions of its event horizon from the point of view of an observer outside the black hole and define density to mean aggregate mass/aggregate volume for the black hole, as one conventionally does).

    A really big black hole at the center of a huge galaxy, for example, has a density that is lower than, for example, the density of an atomic nucleus or a neutron star. The highest density black holes that have been observed are those with the lowest masses. No black holes at all are all are observed with masses small enough to permit them to have densities more than a few percent in excess of the density of a neutron star.

  13. You tore it from the context. I was clearly saying that the black hole is the density champion among either equally large or equally heavy objects.

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