wrote and excellent posting about holographic principle was motivated by a Youtube hype stating that "Many physicists now believe that reality is not in fact, 3-dimensional". This type of "many/leading physicists believe now" hook has become familiar from science lobbying. Sabine makes it clear that the holography principle is strongly theory dependent proposal.
Lubos reacted strongly to Sabine's comments and wrote a response full of negative emotions. It is a pity, since this posting was preceded by several excellent guest posts about Bicep2 discovery of evidence for gravitational radiation in microwave background: also Lubos wrote a nice post about the topic. I am just wondering why Lubos cannot get his emotional brain in control to avoid this kind of flops.
Lubos did the usual mud slinging with a lof of "silly":s and other similar attributes. Lubos even accused Sabine for being creationist. Towards the end Lubos's emotional brain took the lead totally and he closed the posting with a series of personal insults. Lubos writes otherwise excellently and could become a good science journalist if he only could get his aggressions in control and widen his rather narrow intellectual horizon limited by blind beliefs in string theory, supersymmetry in standard sense, in Boltzmann's thermodynamics as a final truth, recent mainstream interpretation of quantum mechanics, etc...
Is holography principle true?
A fictitious character Q starts a discussion with Sabine by posing the following question.
Q: Do we really live in hologram?
Sabine reacts to "really" and quite correctly states that its content is far from clear. "Reality" indeed leads to long philosophical discussions. Sadly, most colleagues see these discussions as esoterism. It is a pity since this attitude has halted the development of theoretical physics for almost a century. This kind of discussions were possible during the first year of quantum theory but should have been continued.
To specify what "we" means requires a quantum theory of consciousness and of life and I can only refer to the 9 books concerning the TGD view about "really" and "view" (see this)!
A more technical formulation avoiding "we"s and "realities" would be following.
Q: Is holography principle true?
And to avoid the misleading impression that there exists some universally accepted form of this principle as science lobbyist would want us to believe Q should ask:
Q: Could some form form of holography principle be true?
- Sabine quite correctly states that gravitational holography principle is a specific conjecture stimulated by AdS/CFT correspondence introduced by Maldacena and being inspired by string model. It relates conformal quantum field theory ( N=4 SUSY) at the 4-D boundary of AdS5, which is 4-D conformally compactified Minkowski space to string model in 10-D AdS5× S5. These assumptions are very strong and not generally true in quantum field theories - say standard model. Lubos claims that a fundamental physical principle is in question. One must of course notice that now hologram is 4-D Minkowski space and something totally different from 2-D hologram provided by say black-hole horizon. A lot of conceptual sloppiness is involved with holography hyping.
- Space-time according to standard cosmology is not conformally compactified M4 and standard model is not conformally invariant theory so that holography in the sense AdS/CFT correspondence is a rather specific conjecture! Certainly not a fundamental principle.
Lubos however states without any justification that this conjecture can be applied also to AdS4 that we habit. This statement of Lubos contains several bad inaccuracies since AdS4 represents inflationary cosmology in the first approximation, and inflationary cosmology is only one of the many proposals, and inflationary cosmology does not apply during say radiation dominated period. In Lubos's own blog a string gas cosmology was discussed as a guest post and this cosmology is certainly not inflationary cosmology! By the way, in TGD framework string gas is replaced with cosmic strings and there are many common elements between these views about cosmology.
- Both Sabine and Lubos talk about holography in quantum gravity sense: 2-D or 3-D holograms in 4-D space-time defined by black hole horizons. This holography is rather speculative notion and in principle something very different from AdS/CFT correspondence since in this case one would reduce 4-D physics to 3-D or even 2-D and in the case of Maldacena n-D physics would represented as part of n+1-D physics (Sn excitations are trivial).
It should be also made clear that the AdSn
/CFT correspondence is application of the mathematics of string theory and not a part of string theory. In string theory S10-n
replaced with Calabi-Yau space so that the relationship is far from obvious.
Various forms of holography principle
There are very many forms of holography principle with varying degree of mathematical and physical feasibility.
- t'Hooft proposed a holography principle relating gauge theory description to string model type description: for gauge theory in M4 the strings would live in M4 and intuitively correspond to planar Feynman diagrams forming net like structures.
- In general relativity it is natural to make the conjecture that 2-D black-hole horizon is hologram. It is often assumed - an ad hoc assumption is in question - that single bit corresponds to an area of Planck length squared so that horizon area would could carry only finite number of bits. Sabine talks about this form of holography. Also Lubos speaks about this holography instead of better established AdS5/CFT holography as he starts to put down Sabine.
- Maldacena introduced super-string inspired holographies using 10-D target space with decomposition AdSn× S10-n. I guess that in M-theory speculations this decomposition would be replaced with AdSm× S11-n. AdSm has m-1-D conformally compactified Minkowski space as boundary. For AdS5/CFT hologram the boundary would be 4-dimensional and correspond to conformal compactification of M4 appearing also in twistorial approach and being motivated by 4-D conformal symmetry. QFT in M4 would have higher-D stringy/gravitational description.
Maldecena holography must be distinguished from the gravitational holography in which one conjectures that 4-D gravitation allows 3-D or even 2-D QFT type description in terms of black hole horizons. These are quite different holographies but for some reason neither Sabine nor Lubos do not emphasize this distinction.
I do not know how feasible all these conjectured AdSn
/CFT correspondences really are.
- It is argued that one can think that S10-n excitations do not contribute to the physics in the scales much longer than S10-n size so that higher-D space effectively reduces to AdSn. Hence one would have hologram as n-1-dimensional representation for physics in n-dimensions rather than for 9-D physics in 10 dimensions.
- This is not not enough: if one wants gravitational holography in the sense suggested by blackhole physics and t'Hooft's original argument one should be able to replace AdSn× S10-n with 4-dimensional space-time of general relativity and in quantum gravity one should speak about quantum superpositions of space-time surfaces. One would have "quantum holography". Whether holography extends in this manner is far from obvious. AdS3 with 2-D with conformally compactified M2 as boundary would be analogous with this holography.
What about experimental side? AdS5× S5 holography have been applied in attempts to explain RHIC and later LHC results but with a rather modest success: even qualitative predictions are wrong as reported by Sabine in her earlier posting.
What looks strange to me that one is ready to introduce strings in 10-dimensional space to explain these findings in conflict with perturbative QCD but refuses to consider the possibility that a fractal copy of hadronic physics modellable using hadronic string like objects in 4-D space-time could explain the findings much more elegantly (see this)! But this is sociology of science which rational mind is not able to understand.
AdS/CFT holography has been applied also to nuclear physics and condensed matter without any breakthroughs. The description of atomic nuclei or condensed matter as blackholes in 10 dimensions has not led to any breakthroughs. Amusingly, in TGD framework atomic nuclei can be described as wounded string like objects in the familiar 4-D space-time but this is of course too science-fictive and speculative as compared to blackholes in 10 dimensions;-). Wikipedia article contains comments about these applications (see this).
Holography in TGD framework reduces to General Coordinate Invariance
In TGD framework holograms are effectively 2-D as they should be if quantum gravitational intuition is correct. The pair formed by AdS5 and its boundary which is 4-D Minkowski space M4 is replaced with 4-D space-time surface in M4× CP2 and its space-like boundaries or light-like "boundaries". The holography holds trued for single space-time surface in quantum superposition of them.
- Holography in TGD sense follows from General Coordinate Invariance (GCI) in TGD framework in which gravity becomes sub-manifold gravity. Single big principle instead of two means quite a dramatic increase in conceptual economy and was in ancient times seen as a signal that theory has been able to catch something very profound about reality.
- Also a stronger form of holography is possible. Suppose one requires that light-like "boundaries" identified as regions at which induced metric changes its signature from Minkowskian to Euclidian inside lines of generalized Feynman diagrams and space-like 3-surfaces at the ends of causal diamonds provide dual descriptions of quantum physics. If this is the case, one obtains strong form of GCI and consequently strong form of holography. The universe is effectively 2-dimensional: partonic 2-surfaces defined by intersections of these two kinds of 3-surfaces and tangent 4-D space - data at them would code for physics.
It is amusing that strong form of holography is very nearly the same as the holography as we encounter it in everyday world and in sensory perception we see things as 2-dimensional! Note however that the representability of space-time as a 4-surface of M4× CP2 is essential.
"Effectively" is an important limitation.
- Quantum states contain information about actual 3-dimensionality. For instance, the integers characterizing the modes of induced spinor fields restricted at string world sheets code for this kind of information. These string world sheets accompanying magnetic flux tubes carrying monopole fluxes and connecting various partonic 2-surfaces are the counterparts of strings connecting points at the boundary of AdS5× S5 so that these two holographies have a lot of common. In TGD one might perhaps speak about dual descriptions provided by partonic 2-surfaces and string world sheets. The situation is not however completely clear.
- Zero energy ontology originally motivated by the failure of the strict determinism of Kähler action implies a hierarchy of causal diamonds (CDs) so that one obtains holography only in given UV and IR resolutions (considering single CD). Also Sabine emphasizes the importance of measurement resolution but formulates this in terms of finite area per bit condition. Discretization at space-time level is the number theoretic manner to express finite measurement resolution. Inclusions of hyper-finite factors of type II1 provide the mathematical language to express the notion of finite measurement resolution and leads to the emergence of quantum groups and quantum spinors.
- An additional complication is due to the fact that one does not have single space-time surface but quantum superposition of them. If quantum classical correspondence is taken really seriously, one is led to the conjecture that all space-time surface in allowed superpositions have the same classical n-point functions for coordinate invariant field like quantities as functions of M4 coordinates and that these n-point functions are identical with their quantal counterparts. This is very powerful constraint on quantum states and without further specifications could be too strong. "Modulo finite measurement resolution" is one such additional specification.
- The hierarchy of CDs implies that we are 3- (or 4-) dimensional in the same as a 3-D lattice consisting of 2-D (3-D) objects is 3-D (4-D). Although quantum states are coded by data assignable to partonic 2-surfaces at boundaries of CDs, the understanding of what happens in quantum measurements requires both quantum states and and their space-time correlates since every measurement outcome is formulated in terms of classical space-time physics. Quantum numbers such as momenta, spin, charge, etc.. label quantum states whereas in space-time description one has frequencies, field intensities, etc... Both are needed.
For these reasons and as a habitant of TGD Universe I cannot agree when someone says that we live in (2-D or 3-D) hologram/are hologram. Nature just represents same information in many manners just as computers provide a large number of different representations of the same data. This does not diminish the mathematical power of strong form of GCI/holography.