Friday, April 6, 2012

Holographic Universe

The idea that we, Earth, the stars, everything, live in a hologram seems stranger than any cooked up sci-fi fantasy, and yet that is exactly what a contemporary theory of the universe tells us.

Where Did this Weird Theory Come From?

The inspiration for this theory came from Stephen Hawking's work on black hole entropy. Entropy is the energy in a system that is available to do work. According to the second law of thermodynamics, the entropy of any closed system always increases or stays the same, and in many ways entropy can be described as the state of disorder in a system. Another law in physics states that all physical laws should work the same everywhere in the universe. Black holes, like the one shown below, present a big problem because they decrease entropy, and thus violate the second law of thermodynamics.

(Wikipedia copyright user: Alain r)

They reduce the entropy of the universe because the information encoded in objects that are sucked in is irretrievably lost.

What's just as strange about black hole entropy is the maximum possible entropy in any region of a black hole scales with its radius squared not cubed, as if a black hole were a flat two-dimensional object. This means that all the information about all the objects that have ever fallen into a black hole somehow seems to be confined to the spherical surface of the event horizon. The event horizon is like the outer shell of a black hole. It is the point of no return, where even light itself cannot escape, and no one knows what lies within this shell. Current theory tells us that all the mass of the original collapsed star and all the objects that have been swallowed since are reduced to a radius of zero at a central point inside the horizon, called a singularity.

The Holographic Principle solves two closely related important problems with black hole entropy. The first problem is that black holes decrease entropy, as described above. Second, they violate the law of conservation of information. This law, a more specific interpretation of the second law of thermodynamics, is most often described in a quantum sense. When an atom, for example, falls into a black hole, all of its information is lost. For an atom, that means its wave function, according to quantum mechanics, is gone from the universe. This loss violates an important principle in science - that information is conserved in the quantum sense.

Hawking showed us that black holes slowly radiate their energy away, they slowly evaporate in other words. According to the no-hair theorem in physics, this too is a problem. Hawking radiation should be completely independent of the material going into a black hole. It should be a mixed (think of it as generic) quantum state. Any particular initial quantum state of the material going into a black hole is therefore lost, and according to the law of information conservation, it can't be.

The problem of information loss can also be described by something called the entangled pure state situation. This is how it works: Let's say a photon has just spontaneously annihilated in space (they do this all time according to quantum theory). When it does so, an electron and a positron are spontaneously created. These two particles should quickly annihilate each other and release a new photon. But what if one particle is sucked into a black hole while the other one escapes? Half the information of the photon (called a partial trace) is lost from a closed physical system (the universe). This also violates the second law of thermodynamics on a quantum level.

From Black Hole Riddles to Holograms

The information problem led to a huge battle between physicists, with Hawking and Kip Thorn on one side insisting that quantum information must be lost, and Leonard Susskind and Gerard t' Hooft on the other side, insisting that that is impossible. Eventually, T' Hooft proposed a holographic theory as a solution to the problem and Susskind provided a string theory interpretation of that solution.

Hawking, recognizing the problem of information loss, suggested that quantum fluctuations on the event horizon could theoretically allow all information to escape from a black hole. As long as information comes back out, the information paradox is solved. From this solution they arrived at the idea of information being contained on the event horizon of a black hole, contained in a two-dimensional space in order words, and that is the kernel at the center of the Holographic Principle, introduced here in this 3-minute video:

(from MICHAEL COULSON on Vimeo)

What is the Holographic Principle?

A hologram is a three-dimensional image confined in two dimensions. Below is a mouse hologram for example. Two photos are taken from different views.

What's really interesting about thinking of the universe as a holographic projection is that it offers a possible description of quantum gravity, something that physicists have been seeking for decades. String theory allows us a lower dimensional description of the universe, in which gravity emerges from it in a holographic way. This could account for why physicists haven't been able to find a force-carrier particle for gravity. The other three fundamental forces each have a gauge boson, a virtual particle that mediates a fundamental force. It also offers an explanation for why gravitational force is so much weaker than the other three forces as well. It is so weak, in fact, that it can be completely omitted from quantum equations.

Quantum mechanics describes the tiny subatomic world very well, and relativity describes the behaviours of massive objects in the vastness of space. The Holographic Principle could be the bridge between quantum mechanics and relativity that physicists have been searching for in their quest to find a single unified theory that can describe both the very small and the very big. String theory attempts to describe gravity as an emergent property of tiny fundamental vibrating strings. It doesn't attempt to describe gravity in terms of a force-mediating particle. Instead, gravity is an illusion. String (or strings as there is a whole set of these theories right now) theory is based on an elegant set of mathematical formulae but there are many physical phenomena it cannot describe and there is no way to test it, so far. Gravity, as an emergent holographic illusion, could bridge two competing (and as of now mutually exclusive) theories of how the universe works:

(QFT stands for quantum field theory)

Black holes present a riddle to physicists because they require both a relativistic and a quantum description in order to understand them, and the Holographic Principle offers a potential way to describe them in which both quantum mechanics and relativity can be satisfied.

Physicist Juan Maldacena came up with a mathematical description of spacetime, called anti de Sitter space, which describes the holographic universe. To us, the universe seems infinite yet we can deduce that it has some kind of boundary that has been expanding ever since the Big Bang. His mathematical metric solves this apparent anomaly. He used a three-dimensional analogue of what is called the hyperbolic plane, the boundary or surface of our universe. This plane is two-dimensional but it is wildly twisted (and impossible to visualize). We, living within this bounded surface, don't notice the twisting. It is sort of like the distortion you see when looking at a global map, a 2-D representation of a 3-D world. His 3-D analogue of this plane coupled with a fourth dimension, time, gives us a model holographic universe. String theory, describing the interior of the universe, has a sort of 2-D shadow on the inner boundary of it. Every fundamental particle has a 2-D counterpart on that boundary. Using this theory, you can describe any object in a gravitational field, whether it's a subatomic particle or a massive neutron star. You could describe a black hole. Try this 83-minute video from the 2010 World Science Festival called "Black Holes and Holographic Worlds," where the world's best physicists describe this topic for nonscientists:

As you can see, it has been very tempting to expand the holographic idea to the universe as a whole. In this sense, the universe is a two-dimensional information structure "painted on" the cosmological horizon, the edge of space analogous to the event horizon of a black hole. It even provides a new conceptualization of entropy - as the surface of the universe expands, more information can be stored on its 2-D surface and the entropy of the universe increases as a result.

According to this theory, our familiar three dimensions of space only work at the macroscopic scale and at low energies. When we look at very high-energy events or at the subatomic scale, or both simultaneously in the case of black holes, the underlying reality of a 2-dimensional space seems to become apparent. The event horizon of a black hole is, therefore, a peek at this inner reality of the universe. Leonard Susskind describes the Holographic Principle in his own words in this 13-minute interview:

In order for this theory to work, there must be a limit on information density. Entropy can be described as degrees of freedom in a system of matter and/or energy. There is an upper limit to the density of information that can be packed into a given volume that can be translated to two spatial dimensions. As you subdivide matter into its atoms and then into its sub-particles and finally down into various fundamental particles, you increase the degrees of freedom. The Holographic Principle implies that at some point there is a limit to the subdivisions you can make, and at that point you reach some kind of fundamental particle containing a single bit of information (like the zeros and 1's of a computer's binary language - or like a 1-dimensional string in string theory). And here is where the universe, according to the Holographic Principle, should ultimately break down into fundamental pixels of reality, like the pixels in a photographic image, in this case grains of spacetime calculated to be Planck length.

Searching for the Universe's Pixels First Try: Gravitational Wave Noise

Some scientists, such as Craig Hogan of Fermilab, believe that this graininess, equivalent to quantum fuzziness, can be scaled up across the holographic universe and detected as very minute gravitational waves. The GEO 600 in Germany is the latest and most sensitive gravitational wave detector built. Recall general relativity for a moment. Gravity bends spacetime. As a result it can shorten distances. Disturbances in spacetime caused by heavy-weight binary star systems made up of white dwarfs, neutron stars or black holes can ripple right across the universe as waves. The Hulse-Taylor binary, two neutron stars orbiting a common center of mass, has an orbital decay that is in exact agreement with the loss of energy through gravitational waves predicted by general relativity. These ripples, however, are expected to be very minute and none so far have been directly detected (by any instrument). The GEO 600 can detect relative changes in distance on the scale of 10-21 m, that's about the size of a single atom compared to the distance between the Sun and Earth! Along with detecting minute gravitational waves, noise in the GEO 600 may be holographic noise. Hogan's interpretation of the noise from GEO 600 caused quite a stir in late 2010. He suggested that the noise is scaled up Planck-length graininess, massively scaled up graininess. Planck-length is on the scale of 10-35 m, a difference of 1014 between Planck length and the detector's sensitivity! Hogan claims that the noise should grow grainier across great distances, much like a low-res movie played on a screen that is too big. So, larger scale (10-21 or more) changes in distance could be traced back to Planck-scale graininess at the edge of the universe, and it could be detected by the GEO 600.

Unfortunately, it is very common for gravitational wave detectors to detect a noise background - they are extremely sensitive instruments. And physicists are still in the process of identifying and removing sources of noise. And, as mentioned, gravitational waves have yet to be directly detected.

Searching for the Universe's Pixels Second Try: Gamma Ray Polarization

Some physicists calculate holographic noise, if it exists, to be on a much smaller scale than any current instrument can measure, much smaller than Hogan's estimate. And so they have devised another ingenious way to look for evidence of holographic graininess in spacetime. The European Space Agency used its Integral Gamma-ray Observatory in 2002 to look at gamma ray bursts. These are bursts of extremely high-energy gamma photons from supernovae. When the photons travel through spacetime, their polarization (you can think of it as a twist) is slightly affected. A polarized gamma ray preferentially scatters in a direction perpendicular to the direction of polarization. If spacetime is smooth, as Einstein predicted, the polarization should remain random. That means there shouldn't be any difference between higher and lower energy photons no matter how far they travel. But if spacetime is grainy as the Holographic Principle predicts, the degree of polarization of the gamma rays should depend on distance and energy. The detector should detect random polarizations if Einstein was right or it should detect a bias toward a particular polarization if the Holographic theory is right. I'm going to leave you in suspense for a moment about what they found, in order to introduce you to another very interesting problem that the Holographic Principle might solve, called locality.

A Fascinating New Look at Reality

Hogan's hypothesis violates a tenet of special relativity called locality. This means that an object is directly influenced only by its immediate surroundings. At first thought, this might seem to be a deathblow against the Holographic Principle. But, locality is already violated by a widely accepted (and experimentally verified) phenomenon called quantum entanglement. Let me give you an example to illustrate how this works: During nuclear decay processes, the events that take place must obey various conservation laws in physics. This means in the quantum world that various new particles that are generated as a particle decays must have specific quantum states. If a pair of particles is generated having a two-state spin, for example, one particle must be spin up and the other must be spin down. These particles are called an entangled pair. Lets say they fly away in opposite directions. Now here is the rub: when two objects (they can be subatomic particles, molecules or even diamonds have been observed to obey this!) interact physically and then become separated, each member of that pair is described as having the same quantum description. That means their state is indefinite until it is measured, according the the Copenhagen interpretation of quantum mechanics. They are each in an equivalent state of quantum superposition. Much later, when they are across the universe from each other, one person measures the spin of one of these particles. There is a 50% chance it will be spin-up and 50% chance it will be spin-down, depending on which one of the pair he measures. When one particle is measured, the quantum states of both particles collapses. If a second person then measures the second particle, its spin is 100% predictable - it will be the opposite spin of the first one measured. Let's say particle A collapsed into a spin up quantum state. How did Particle B instantly get wind of that news from across the universe and collapse into a spin down state?

Nonlocality implies some kind of across-the-universe instantaneous communication between two particles. That's a violation of special relativity, which states that nothing, star ships, light or communication, can exceed light speed. Experimental results have shown that effects due to entanglement travel at least thousands of times faster than the speed of light.

What does this mean? It suggests that either nonlocality operates in quantum physics or there are hidden variables we don't know about yet. Perhaps the measured spin of the particles is just one element of a larger yet unknown physical reality OR the assumption that we can measure a particle and collapse its spin into one definite state is not quite accurate. There is no transmission of information possible - no force transmission fast enough to account for projecting information across space between two separate physical systems. The fact that it happens is deeply unsettling. It is not easy to live in a classical world looking out into a quantum mechanical world, to use the words of physicist John Stewart Bell, who proposed the entanglement experiment described above and formulated Bell's theorem based on it. These results led to the Bohm Interpretation of quantum mechanics. This interpretation gives non-locality a place in quantum mechanics, where all particles in the universe are able to instantaneously exchange information with all other particles. Basil Hiley, Professor of Physics, describes the challenge of thinking about particles and locality, and extends it to the conundrum of Heisenberg's uncertainty principle, in this fascinating 10-minute video:

The Bohm Interpretation, as I understand it, does not provide us with an easy 1-step answer to the problem of locality. Instead, it asks us to rethink the problem of wave-particle duality and challenge our assumptions about particle reality.

Does the Holographic Principle provide a viable answer to the nonlocality problem? Well, yes, in the sense that this principle implies a reality outside of spacetime, so that problems involving separation by space or time are transcended. Nonlocality means that no particle in this universe is separate from any other particle. An electron in Young's two-slit experiment, for example, seems to know beforehand where other electrons are going to be. According to this principle, we can view a particle such as an electron not as a material object moving through space but as something that unfolds out of a deeper level of reality that is outside of spacetime. In this reality, particles like electrons and photons can sniff out space before them. There is lots of evidence that they do just that. It's just that we can't observe their process because our perception of them is stuck in space and time.

The Holographic Principle, therefore, seems to solve two very tricky problems in physics - black hole entropy and nonlocality.

Experimental Proof of the Holographic Theory?

I left you in suspense over the gamma ray polarization experiment, so let's get back to it now. A gamma ray burst, such as the NASA artist's illustration below, is a random event and in order to detect and measure its photons, our detector (and Earth in general) must be in line with one of its bipolar jets (shown as yellow).

Luckily, such a burst happened in 2004 (well, for us anyway), called GRB 041219A. It was extremely bright and far away (300 million light years), making its data a perfect candidate to test the Holographic Principle.

No polarization difference was detected.

The Integral Gamma-ray Observatory detector is so precise it would be able to detect graininess down to a scale of 10-48 m, which is 1013 times smaller than Planck length. Some researchers, attempting to restore the Holographic Principle, have suggested that gamma rays perhaps don't behave as expected in this grainy universe.

To conclude, no one has yet experimentally verified the Holographic Principle. So far, two experiments appear to refute its existence. Specifically, they refute a measurable graininess or pixilation of spacetime. It might be possible that the assumption of underlying pixilation is itself incorrect but the idea of a three-dimensional projection of spacetime of a two-dimensional universe may still hold some validity. I suspect physicists right now are busy thinking of new ways to verify the principle.

The Next Step: Peering Past a Quantum-Uncertain Universe

When the Holographic Principle was introduced in 2010, it captured the imagination of people worldwide. We can play with the bizarre possibility that we, and everything around us, are merely projections cast from some distant 2-dimensional screen, that we are ignorant of our true flatness as we live out our lives inside an enormous sphere at least 13.7 billions of light years across as projections from its inner surface. Certainly this idea has huge philosophical implications. Can you imagine God observing us as characters in a moving film projected over the surface of the universe? What does this mean for time? How about free will? This notion is at once absurd and alluring.

This is why most physicists refer to the Holographic Principle as a principle. It is a reasoned argument, a starting point for a true scientific theory, which is a set of principles that can explain and predict phenomena.

This principle, perhaps a work in progress, has enormous implications for how we understand spacetime and it suggests possible solutions to some very vexing problems in physics. Rather than being abandoned by the scientific community because it has not been successfully verified through experiment, it seems destined to be a jumping-off point in physics where our very understanding of the rules themselves will be challenged to its core.


  1. I am writing a post about the Bogdanov brothers ("au commencement du temps _la cinquième dimension") and hypotesis of holographic Universe.This article passionated me.

  2. Fantastic article. I was hoping you could elucidate some things for me though.

    "This principle, perhaps a work in progress, has enormous implications for how we understand spacetime and it suggests possible solutions to some very vexing problems in physics. Rather than being abandoned by the scientific community because it has not been successfully verified through experiment, it seems destined to be a jumping-off point in physics where our very understanding of the rules themselves will be challenged to its core."

    I'm trying to better understand what this means. Does this mean that a holographic principle (or some variant of it) is - in a broad general sense - valid at some level of abstraction, yet the currently existing, empirically testable theoretical frameworks of such a principle must be re-conceptualized/re-formulated (as some experiments have not lent them credence)?

    And if the holographic principle is invalid, what other hypotheses have been proposed might explain phenomena like black hole radiation and (especially) quantum entanglement? Are these hypotheses as adequate as the holographic framework? Quantum entanglement is crying out for an explanation, and "holography" seemed very cogent.

  3. This is a very thoughtful and challenging question. I must admit that I avoided writing about the holographic principle for some time. Frankly I found this topic one of the most difficult in terms of keeping my personal feelings out of it. I personally don't like the principle. And yet as I researched the material I found myself shaking my head in agreement over and over, thinking, yes this makes sense.

    Your question really gets to the heart of the matter. As I reread my article I found myself basically saying yes it has this and this and this going for it but because it can't produce this one bit of evidence we've tried so far to test it (holographic graininess) we can't call it a proper theory. As I rethink this article, and as I understand the definition of scientific principle, the holographic principle stands as perfectly valid. As an experimentally verifiable theory, well, what other concept embraces quantum entanglement and black hole radiation, you ask – and as far as I know there is none. Does it need further experimental verification? I want to say yes but why? Furthermore, it can also be described mathematically using anti de Sitter space.

    I seem to find myself tenaciously hanging on to some notion that atoms and other elementary particles have at their core something "real," that they have their own independent reality. Since I wrote this article I've found myself even deeper in uncomfortable territory – take a look at the article "Quasiparticles" if you have a chance – it again gave me the queasy feeling that the core of matter might just be some kind of artifact after all.

    I believe you are asking why I'm not embracing the holographic framework at least for now, as it is a very practical approach to some real problems. In that spirit, I thank you for nudging me back to a difficult point. If I were to write this article again, I would come to a different conclusion and I'd admit why I don't like it. It's too hard to swallow all the implications.

  4. The standard explanation for mapping an n dimensional space onto an n-1 dimensional surface necessarily requires the loss of an arbitrarily large amount of information. This is apparent from the (to me questionable, but at present canonical) limit of the recording surface as one bit per Planck area. This, taken together with the amount of information contained in the n dimensional “original,” leaves us with the difference between the number of spaces (Planck limited) available in an n dimensional structure versus the number of spaces available on the n-1 dimensional surface. 

If it were not for the Planck limitation, the orders of infinity available in n dimensions versus n-1 dimensions would be equal, as implied by the paradox of Hilbert’s Grand Hotel. That is, as (I believe) Cantor also demonstrated, the number of real points on a line is equal to the number of points in a surface. However, once the Planck limit is imposed, the number of points in, for example, a three dimensional object is far greater than the number of points in a two dimensional surface which contains its hologram. I suppose this objection can be met by removing the plane to an arbitrary distance, so that it becomes large enough to have a number of Planck points equal to those of its contained 3D object, but this starts to smack of ad hoc requirements. Perhaps more importantly, the removal distance involved would seem to prohibit liminal communication between the hologram and any sufficiently complex object. At this point, we must think very carefully of whether the holographic principle is literal or metaphorical.

  5. It's been a while since I wrote this article. Rereading it yet again, after thinking over your fascinating comment, has been another trip down the rabbit hole for me. I had never heard of the paradox of Hilbert's Grand Hotel so I Wiki-d it. Thank you for pointing this out! It seems to me too that there is some very intriguing connection between that counterintuitive state and this one, and, as you said, at the very least we should be questioning why Planck scale is the written-in-stone limit, which all this graininess is based on. Isn't it fair to say that Planck limits are not the limits of physics itself but only the limits of the current theoretical framework? I've been reading and writing about gauge theory and supersymmetry lately and these two theories only reinforce this need, I think you are alluding to, to be careful about what to put down as the "foundation posts" of a theory.

    Placing Planck limits maybe more properly into a softer interpretation, forces a rethink of the graininess, this limit to information imposed on the universe. Imposing it, as you said, puts us in a quandary – now we have to think about how far away the two dimensional matrix must be in order to store all the information contained in "our" more complex higher-dimensional space. I'm not convinced that the distance, however, affects subliminal communication, because it seems to me, by introducing a hologram, you are transcending that whole sticky business – distance (and time!) becomes meaningless.

    I spent some time mulling over your suggestion to think of the holographic principle as metaphorical. I have this creepy feeling that alluring new ideas like the holographic principle make the imagination run off too fast, at least it does mine. Lately I've been trying to get my head around the idea of mathematical space-time matrices transforming in various ways (gauge theory) to give us our fundamental particles of matter and force. Lets say we let go the ramifications for a moment and go back to the anti de Sitter space framework (as an Lorentzian analogue of hyperbolic space, where it operates with special relativity). I didn't write this article from a mathematical perspective and I am not a mathematician, but I wonder if that is where we last left off before imagination went running. The space-time matrices and their transformations in gauge theory are mind-boggling and just plain impossible to our Euclidean brains, yet they are the foundation of particle behaviours as basic as electron spin. It seems to me there is the math and there is how we interpret it, if we can. Is the holographic principle an example where we should trust that the math is solving two fundamental problems and let the chips fall where they may, or maybe better yet not let the chips fall at all just yet? I am trying to say I agree, I think it's metaphorical too.

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  7. It is really incredible and amazing holographic images especially that universal holographic image was blowing my mind for some moments. This images are reminds me about a watch which contains holographic 3d images of universe shown in malaga main digital market in sector.

  8. There is only one optimal solution to the black hole information paradox and black hole merger paradox... only one...

    1. Hi Jimmy,

      First, thanks for reading my article. I am always excited to find fellow explorers! As I read through your webpage, I found one point in your short list, concerning homogeneity versus anisotropy in the very early universe that I think can be explained as two competing pressure effects of photons and baryons, which make their first appearance at this time. The competing effects set up acoustic vibrations ( that are magnified as the universe expands. That, along with growing gravitational instability created by these growing oscillations, sets in motion the events that are required to amass the first stars and galaxies. At least for me this solves the transition from perfectly smooth to asymmetries caused by the appearance of different kinds of particles, but I also see your point and see the possibility of "missing steps" between being smooth and then symmetry-breaking into particles, assuming you agree with gauge theory . . .

      Your Point 1 in your 'please consider' section is very interesting. Again, degeneracy seems to make a leap between neutron degeneracy and the assumed total degeneracy of a black hole. It looks like there are some missing physical processes there, or missing physics in general to describe it.

      And point 2 – again, you make a bee line to some very interesting missing steps that we seem to gloss over a bit when thinking about black holes. What's the mechanism for conservation of information? Where do the wave function and all the other physical info go? If I understand your theory, though, doesn't the idea of two merging black holes, with one purging information and thus creating a new universe, also require a jump or two in logic as well? Or at least some more descriptive mechanism about how that is done is a better question.

      I don't follow your treatment of magnetism in this theory. For example, you describe magnetism in a volume of space as non-temporal mass, or as dark matter. It seems to me that magnetism as one side of the two-sided coin of electromagnetism arises as a consequence of an electrically charged electron with intrinsic spin, as well as from the electron moving through space. To me this is part of a more fundamental question of where intrinsic properties such as spin and charge come from. Are they actually properties of space-time itself? I think I get the information transfer and conservation argument for black holes but I always find myself wondering if the place to look first in understanding them is with space-time itself, which seems, thanks to developments in quantum theory and the discoveries of dark matter and energy, to be an incomplete picture of what the fabric of the universe consists of. If that fabric is better understood (for example, maybe Euclidean geometry and/or differential calculus are not the best formulations for this theory), then the puzzle of the black hole might be better revealed.

      Anyway these are some of my thoughts on this matter. I hope you continue to develop your theory, and keep your passion!

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  10. To me, the Holographic Principle makes so much sense, scientifically as well as for myself spiritually. I've viewed everything as an illusion for awhile, well the material world anyhow.

    I think people get confused when you say hologram or illusion, because it doesn't mean that you don't feel or that you don't hurt or that your perceptions aren't real to you. It just means the physical world is not what it seems, it is not really the fundamental truth/reality.

    I see the hologram of our 3D world as a result of a 2D 'map' which holds all the information, which projects itself. This is why instant communication can occur. The fundamental particles don't actually have to travel through space like our 3D world does. They all sit on the 2D map, interconnected as one.

    This also answers questions about gravity. Why gravity is so weak, because it is shared in this other dimension.

    When particles begin to unify and build molecules so they take physical space, gravity then effects them because they are now in the 3D world 'hologram'. We see this interaction, this effect, because of our space time and our gravity there, but fundamentally they exist on the 2D plane.

    This principle also addresses black hole entropy and I love the idea of information not being destroyed, though lost to us.

    But then I also tend to think the 2D map could be a hologram itself of a 1D map which in turn is a hologram of a 0D map-or Infinity.

    1. Thanks for your thoughts! It's an intriguing notion isn't it? It's a great example too of how, if we want a greater understanding of theoretical physics, we have to come at it with an open mind, something not at all easy to do! Here in "the West" we tend to think of everything as concrete, here or there, real or not real. Eastern thought, such as Zen Buddhism, tells us that reality doesn't have to be an either/or matter, and that illusion not only has a place in our experience but it has central place. The fields of cosmology and quantum mechanics could take something valuable from that perspective.

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