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Gravity, information, and cosmology (was Thoughts about the universe )

  1. Sep 7, 2011 #1
    Gravity, information, and cosmology (was "Thoughts about the universe")

    There was a thread here a few minutes ago, posted by a new user, called "Thoughts about the universe". It contained reflections about gravity, information, and the universe, that were probably inspired by the holographic principle, along with some less "scientific" thoughts. Some moderator has apparently deleted it, rather than just moving it. This is unfortunate, as I was about to make some extended comments on the scientific aspects - in effect, how to understand some of the things one hears about black holes (that time stops inside them, that they swallow "information"), and also about the meaning of "holographic cosmology", in which the whole history of the universe is supposed to be equivalent to a timeless field theory at its boundary in the infinite future. This is a genuine scientific theory and it has at least an impressionistic resemblance to some of what was stated in the post. (Fortunately, I knew the deletion might happen and saved a copy.)

    So this message is primarily for that new user - first, so they can know what happened to their essay; second, so they can get some feedback. There is a private messaging system in this forum and I am quite happy to talk privately about both the scientific and "non-scientific" issues that were raised. Perhaps there can also be some public discussion of those aspects of the "thoughts" that fall within the scope of the Cosmology forum.
  2. jcsd
  3. Sep 7, 2011 #2
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    Hey mitchell,
    thank you for clarifying what happened, I'm a little bit confused though... why did someone delete my post? Apparently there's some sort of rule against speculative posts which honestly I do not understand since all that is science is mostly speculations.. sure we have facts to interpret, but we can never be sure if our interpretation of things is right since we don't have all the information we need for that...
    I apologize though, I didn't want to break any rules, I just wanted to find people to discuss these thoughts with..

    I'm excited about this "holographic cosmology" you're talking about, I'd love to hear more about it :)
  4. Sep 7, 2011 #3
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    I am a physician not a physicist, but I read Einstein, Feinman, Schrodinger, Bohr, Wheeler, Brian Green, Susskind, Thorne, Gamow, etc. I recently learned of the Blue Brain project, lead by Henry Markram as well. It has occurred to me that the mysterious dark matter, detected as halos around all galaxies, may represent a two dimensional sphere surrounding each galaxy which holds the information for that galaxy. The altered dimensionality of that dark matter makes it impossible to detect and prevents it from interacting with anything but closed strings such as the hypothetical graviton or inflaton.
    My understanding is that though galaxies exist in local groups and superclusters, the galaxy is the fundamental unit of our universe. And dark matter and its motive closed string gravity is integral to holding these galaxies together.

    So if we propose that each galaxy is surrounded by the information that describes it (a holographic view), the galaxy itself may be the interior of a black hole with the physical embodiment of the "blueprint" expressed at the two dimensional shell or Shwarzchild radius. From the interior of a black hole, we should be able to see the other galactic black holes comprising our universe, and we may mistake the loss of energy by photons from the Schwarzchild limit (Hawking radiation) for “redshift”. As such, our visible universe composed of galaxies, may be more compact than we realize. This time dilated point of view may explain dark energy, an accelerative anti-gravity force, as well.

    Subsequently, a black hole at the center of a galaxy may represent another member of a “multiverse” with all the information to describe that universe on the surface. This bubble upon bubble multiverse is consistent with a number of multiverse theories in the “string multiverse landscape”.
    The blue brain project posits that among other things, the brain may actually project a sphere of reality around itself. This reminds me of the holographic view. The maximum amount of information that can be stored in a given volume of space is exactly the number of bits allowed by an event horizon of a black hole divided into two dimensional squares bounded by the Plank length. If the brain has very little entropy might it have a kind of more limited sphere of information surrounding it? And might our own conscious reality be an expression of that? Are our brains functioning from an informational level like a black hole? Is consciousness mysterious because it fundamentally exists on a two dimensional spherical shell which surrounds us encoding as much information as the number of Plank squares contained within that surface? And therefore the rules of that information (consciousness) may be described by describable but dissimilar rules. Might the universal mystery of the human soul reside on a relatively local manifestation of a minimization of entropy (the human brain) resulting in a sufficiently dense lack of entropy (concentration of energy and mass) to eventuate in a peripheral expression of that information on a lower dimensional membrane?

    This point of view might allow for falling into a supermassive black hole and entering another very much time dilated universe not accessible by this universe. But rather than colliding with a "singularity" you enter a new universe which may evolve over billions or trillions of years. Such a multiverse is very interesting. The distant viewer's impression that the victim falling into the black hole is incinerated with all information being scrambled on the event horizon is consistent. Perhaps the thermodynamic end of the universe (heat death) which must lie in our future represents the final dissipation information (maximum entropy) and thus the dissolution of our universe. When all the black holes re-emit their information with Hawking radiation, space and time cease.

    Would these vast lower dimensional spheres of dark matter not contain enough information (low entropy, energy and hence mass) to have enormous mass?
    My question, has anyone ever looked at this blending of dark matter, black holes and the concept that the brain itself generates a kind of reality confined to three dimensional space been considered? What obvious flaws have I missed?
  5. Sep 7, 2011 #4
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    This is amazing! I've never heard of these theories before, so thank you for that :)
    I had the idea of atoms behaving like galaxies just before I read this. The experiments in CERN (Genf) where they smash atoms together and find anti-matter really got me thinking. Anti-matter does act like black holes, eliminating all matter it touches. This doesn't happen proportional to their size, but apparently to their mass, hence anti-matter must have a much higher density than matter, just like black holes have a higher density than planets (it makes sense if black holes have complete galaxies inside them).
    The idea of galaxies having some sort of bubble around them that is made of the same thing as the surface of black holes fits well here. When every black hole has another galaxy in it with another black hole at it's center (and so on), this would mean there is a universal law to all existence.
    Could this mean atoms are just like little galaxies?

    And what does this really mean? Everything is just a vast amount of layers of dimensions or galaxies within galaxies? Does it ever stop getting smaller or greater? Is it infinite in both directions and therefore the same?

    I apologize for these questions if anyone thinks they’re too speculative and wants to delete them.
  6. Sep 7, 2011 #5
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    It's just a thought. But does the notion of black holes containing universes endlessly not strike anyone as rather elegant? On the one hand, a universe suffers a heat death over trillions of years and vanishes, on the other hand Galaxies collapse in on themselves to form black holes containing new galaxies. The duality there is likewise interesting. That way information is conserved, yes?
  7. Sep 7, 2011 #6
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    I actually wanted to reply a real answer here, well at least one that could be true, but I just realized that it would be against the mainstream point of view hence I cannot post it.

  8. Sep 7, 2011 #7
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    I am brand new to this site. I did not read all the rules. Sorry, I'll read some more posts before I ask another question.

  9. Sep 7, 2011 #8
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    The best place to start is with a down-to-earth statement of what the holographic principle of quantum gravity actually says.

    The holographic principle in its most straightforward form says that you can enclose a volume of space in a sphere or other shape, and that you can make a description of the physics happening in its interior in a way which only lives on the surface of the sphere. Here I'm going to refer to pictures from http://www.sns.ias.edu/~malda/sciam-maldacena-3a.pdf" [Broken].

    To fix the idea, first consider the picture of the juggler at the start of the article. You see how she has a colorful image on the sphere that surrounds her. It's a bit like Plato's cave, except that ordinary shadows lose information; they only show an outline of the object casting the shadow. They don't tell you how far the object is from the wall, they don't tell you how thick it is, they contain no information about what's on the side of the object facing the wall or the other side facing away from the wall. The holographic "shadow" of the juggler has to contain all that information; for example, you can still make out, in her holographic image, the arm that is in front of her body, whereas in an ordinary shadow that detail would be missing.

    Now scroll down to page 61. You will see a picture of three wiggly strings on the boundary of a sphere, and three more strings in the interior of the sphere. The deeper that the inside string lies in the interior, the thicker its image on the surface. This is part of how the surface description manages to contain all the information about the interior - in this case, information about depth, how far it is from the surface to an object in the interior. Again, this is a lot like an ordinary shadow: as you move an object away from the cave wall and towards the light (maybe a fire burning in the cave), the shadow of the object on the wall will grow bigger.

    So a first simple way to think about the holographic principle is to imagine that we have enclosed a region of space in a sphere, and then, all the things that were happening inside the region of space are now being represented by images on the surface of the sphere. Let's say there was a flock of birds inside the sphere, flying around in circles. We would have an image of each bird moving around on the surface of the sphere. When the bird's path took it deeper into the sphere, away from the surface, its image would get larger. The images of the birds can pass through each other - because inside the sphere they're not colliding, they're just on the same "line of sight" from the surface. And each individual image has the X-ray quality of the image of the juggler from the beginning: the back and the front of the bird and all of its insides are somehow depicted, it's not just an outline like a shadow is.
    Last edited by a moderator: May 5, 2017
  10. Sep 7, 2011 #9
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    Now I'll try to bring more physics into the picture. According to physics, everything that happens is because of the interactions of elementary particles. The birds flying around are complicated assemblages of atoms which have a lot of rigidity and which move because of internal releases of energy, and the stiffness of the molecules and the flows of energy ultimately result from lots of electrons and quarks interacting in their specific ways... Maybe it would have been simpler to talk about planets orbiting each other. :-) ... But whether it's planets or birds, the holographic description has to extend right down to the atoms and the subatomic particles. Every particle must have its image on the boundary. And here's the really interesting thing: Just as we have the ordinary physics of electrons and quarks which determines how they interact inside the space, we can define a different "physics" which applies to the holographic images of the electrons and quarks moving around on the surface of the space, which also makes the larger images of atoms, birds, and planets move around appropriately (changing size, and passing through each other without interaction if they are at different sizes).

    I will add a further detail, at the risk of confusing you with too much new information, just to emphasize the difference between the "physics on the boundary" and the "physics in the interior". In string theory, electrons and quarks are indeed little strings that vibrate and move around. Those strings will have their holographic images on the surface, as in the picture in Juan Maldacena's article. But in the surface physics - the separate set of rules which describes in a self-contained way how the surface objects move around - the strings are not fundamental, they are condensed out of fields that live on the surface.

    So if we back away from all these details and review the big picture, what do we see? We have a world of objects moving around in space - atoms, birds, planets - according to a fundamental physics of electrons and quarks (that are actually superstrings). We also have the holographic projection of all those moving objects onto an imaginary surface enclosing that region of space; and we have a different physical theory, describing the interaction of fields confined to that surface, in which the fields condense into strings which form structures which behave exactly like the holographically projected images of the atoms, birds, and planets. In other words, we have two apparently equivalent descriptions of the same physical processes, built up from theories of fundamental physics which are distinct and yet completely equivalent; but in one theory, the sphere has an inside, while in the other theory, we only talk about images moving around on the surface, not inside it.
  11. Sep 7, 2011 #10
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    The whole reason that anyone even thought of looking for the holographic description of events in space is because of black holes. A black hole is a region of no return surrounding a very dense mass that was predicted by Einstein's theory of gravity, and Stephen Hawking and others studied what happens when you apply quantum mechanics to the matter inside and outside a black hole. They found that because of the uncertainty principle, the matter inside the black hole can sometimes "tunnel" or "quantum leap" out of the black hole - something that wasn't possible in Einstein's pre-quantum version of gravity - and so the black hole leaks radiation, and shrinks microscopically as a result. The smaller it gets, the faster this process goes, so a black hole starts out big and cold, but over cosmic time it very slowly loses mass, and when it gets very small, it gets hot and completely disintegrates in a bang. All the energy is conserved, but now the mass that once fell into the black hole is converted to a random spray of particles moving away from where the black hole was. At least, this is what our best theories say; no-one has ever observed Hawking radiation. The big black holes we can indirectly see in astronomy are basically at absolute zero temperature, we'd need to somehow get a micro black hole for the Hawking radiation to be detectable, and then we'd only get one burst of it as the micro black hole completely blew up.

    Anyway, the key discovery was that a black hole has a temperature - the amount of Hawking radiation being emitted - and this means it has an entropy. Entropy is famous as a measure of "randomness" in a physical system, and this is tied up with the distribution of heat inside a physical system. Heat is vibration, and if the energy of vibration is spread throughout the parts of an object, the vibrations are more homogeneous and random-looking, and that gives it a high entropy. Back in the 1970s, people didn't have a model of what the matter in a black hole is like - they represented it as having been gravitationally crushed into a single point - but the Hawking radiation is still just energy that was inside the black hole getting out, and before it got out it must have been doing something, such as moving among the "parts" of the black hole, whatever those are.

    If you do the calculations, based on the work of Hawking and others like Jacob Bekenstein, you find that the entropy of a black hole is proportional to the area of the event horizon, the surface of no return. This was highly unusual. People thought that the mass of the black hole was collapsed into a point, then there was a finite distance from that point to the event horizon, so there was a volume of space inside the black hole. You would think, therefore, that the parts of the black hole, swapping energy among themselves at a particular temperature and occasionally losing energy to the outside world, were somehow free to move throughout the three dimensions around the central singularity, and this ought to show up in the calculations of the entropy. But instead the entropy looked as if the parts of the black hole, its "degrees of freedom", were restricted to the surface of the event horizon. This was the first indication of the holographic principle.
  12. Sep 7, 2011 #11
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    Hey DrZ, it's not like your questions were too speculative, my answer just would have been ;)

    And thank you mitchell for explaining the holographic principle. Seems like a good way to picture information on a two dimensional surface.
    Is it possible that the information is simply encoded as radio waves since that's all black holes emit? Or is there some other way to get the information decoded?

    Did I understand this right, this theory says the surface only reflects or holds information about what's inside? Or is there any way it could be just a reflection of all the information surrounding the black hole?
    Seems to me this surface is like the one of water, which is kind of transparent from outside the water but almost mirror-like when you look at it from under water.
    Could this apply for the surface of the sphere? That we may be able to see what's inside but wouldn't be able to see outside our own or the other way around?
    I hope I'm not confusing anyone ;)

    And honestly, I'm not even sure if my questions could be seen as too speculative or anything.. do you know where to stop? Is the suggestion of the spheres being the surface of black holes too speculative? Or is there actual research on this stuff?
    I'm so confused
  13. Sep 7, 2011 #12
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    If we have a fundamental theory of physics - that the world is made of electrons and quarks, or that it is made of superstrings, or something else entirely - it has to apply inside the black hole as well as outside. And one of the very basic features of fundamental theories of physics is the thermodynamics that they predict - what they say about energy, entropy, and temperature; the ways in which the basic entities share and swap energy. What black hole thermodynamics was telling us is that in a black hole, basic physics behaves in the way you would expect from a theory with one less dimension of space. So Leonard Susskind and Gerard 't Hooft - who first stated the holographic principle as a principle, or at least a hypothesis - proposed that this always happens, if your theory includes gravity: whenever you have gravity, a holographic description of physics with one less dimension will exist.

    I should pause here to explain a few things about the speculative and mathematical side of theory-building in physics. We start out in life not knowing what the world is made of or how it interacts. Over the centuries, we have learned how to state mathematical hypotheses along the lines of, "these fields and particles exist, with certain properties, interacting in a certain way", and the aim of the game is to find a hypothesis which explains everything we know about and doesn't make wrong predictions.

    But although there's ultimately just the one reality that you're trying to match, in principle you have great freedom to make a hypothesis, or you can even describe worlds which are definitely not the one we inhabit. In the real world, we have three visible dimensions of space, six known types of quark, and they all have a mass, but you can say, let there be a world with five dimensions of space, fifteen quarks, and they are all massless; and you can calculate what happens in that world. (Actually you would have to specify a lot of other details, like how the quarks interact, before you could make any "predictions" for the imaginary world.)

    So the holographic principle of 't Hooft and Susskind can also be understood as a statement about the mathematical properties of imaginary physical worlds. The purpose of the game of theoretical physics is to identify the "imaginary world" that we are actually living in, but in practice you have to study many possible worlds, because you don't initially know which one you're in - so you have to use trial and error - and also because the simpler worlds are practice for analysing the more complicated and realistic ones.

    As a statement of mathematical physics, 't Hooft and Susskind's holographic principle says something like this: If you have a quantum field theory in n dimensions of space in which one of the fields is gravity, then that will have an equivalent description in terms of another quantum field theory in (n-1) dimensions of space that doesn't include gravity. And Juan Maldacena - who wrote the Scientific American article that I linked to earlier - discovered the first exact example of this. He found that string theory in five dimensions (with the other five dimensions being "compact" and small) is equivalent to a field theory in four dimensions. He's famous among physicists for this discovery, which occurred in 1997, and hundreds of other examples have been discovered since then.
  14. Sep 7, 2011 #13
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    I'm going to take a short break from all this exposition in a moment, but I'll say a few more things.

    First, the holographic dual description of the real world is not yet known. The real world is described at low energies by the "standard model" of electrons and quarks and other known particles, and possibly those are actually superstrings moving in a particular hyperspace geometry. If the world really is made of strings, then it should have a holographic description, as in the case that Maldacena discovered. In fact, a common line of research says that our three dimensions of space are already an almost-holographic description of a higher-dimensional reality; this is connected with the idea from string theory that we are living in a "braneworld", a three-dimensional "membrane" to which the strings are attached. Something about the extra dimensions off the braneworld should be holographically implicit in the physics of electrons and quarks. It's very unclear - to me, and not just to me - how this relates to the holographic description of black holes inside the braneworld. Although the holographic principle is supposed to involved stepping down one dimension from a world with fields including gravity, to an equivalent set of fields not including gravity, it seems that sometimes you can apply the principle repeatedly, going from a higher-dimensional space with stronger gravity to a lower-dimensional space with weaker gravity. Ultimately, there may be a description of the world in terms of matrices that doesn't involve dimensions of space and time at all, but which implicitly contains all those higher dimensions, and out of which they can be unfolded in diverse but equivalent ways.

    Second - in response to one of Alex's questions - this is all genuine theoretical physics, there are thousands of papers going into great mathematical detail about all of this - though some of it is far less understood than other parts. That's what I'm trying to do with these responses, give you some recognized theoretical constructs and results that can then interact with the thoughts of yourself and DrZ. :-)
  15. Sep 7, 2011 #14
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    Let me get this straight. So if you think of a universe with five normal dimensions and five tiny dimensions you end up getting the right results for other universes?
    So why are there five tiny dimensions? Does it have anything to do with anti-matter?
    To me that would actually make sense, for example if we look at a galaxy with a black hole at the center... black holes do contain anti-matter, right? Or did I mix something up there?
    Cause they both seem to have similar properties like high mass in tiny spaces and the ability to eliminate matter.
  16. Sep 7, 2011 #15
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    By the way, I think you should be fairly uninhibited in expressing ideas now. Hopefully the thread is now safe from deletion, and the moderators will instead show up and urge us to "stay on topic" if it begins to sound too strange.
  17. Sep 7, 2011 #16
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    Maybe you're right :) thanks again for explaining so much!

    And of course I have more questions ;)
    Do I understand string theory right when I imply that every reality with x dimensions has almost the same information and might even follow the same laws as a reality with x+1 dimensions?
    This reminds me of derivation, every formula with x variables being a simplification of the formula with x+1 variables.
    So with the universe in which all galaxies have holographic bubbles around them and they're all stacked into one another like babushka dolls, the mathematical connection between the different dimensions is derivation and integration? And wouldn't this mean that we can never truly find out what the mathematical equation of the next higher-dimensional reality is (we don't know what the constant C is), but we can always look down at lower-dimensional realities?
    Looks like everything is connected again - Yay! ;)

    oh and I also have some more questions about black holes..
    So black holes grow smaller as they "lose" the information to the outside.. And grow when they suck information in.. Sounds to me like black holes are breathing ;)
    But how sure is it that they simply explode (or implode) when they become very tiny? I don't understand how they should just blow up out of nowhere. Is entropy the reason for this?
    This concept of things blowing up just doesn't get into my head. Just like the big bang theory and the heat death of the universe. It would be such a waste to create all this matter and this complex concept of reality if it would someday all just vanish from existence (or turn into a huge explosion.. ). Wouldn't this mean that information is lost?
    Nature always makes sense, and this really doesn't make any sense to me.

    There's something else.
    The experiments with particle exhilerators show that there's a vast amount of types of subatomic particles that are all different from each other.
    Assuming there's a possibility of different dimensional galaxies existing somewhat like layers around each other, couldn't the reason for the seemingly never ending number of subatomic particles be that atoms kind of like resemble higher-dimensional realities? If you smash two galaxies into each other at high speed, you might think the bits of matter that are being catapulted out of their orbit could very well be regarded as subatomic particles by huge creatures that simply live in a much higher-dimensional reality.
    Last edited: Sep 8, 2011
  18. Sep 8, 2011 #17
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    I want to make a comment about how to think about these changeable numbers of dimensions. At one extreme there are matrix models in which there are no space dimensions at all, and all the physical objects correspond to "blocks" on the matrix diagonal. It's a highly abstract description. At the other extreme, you have all these higher-dimensional theories, with more dimensions than we actually see. And the contemporary research is producing many equivalences between physics in different dimensions.

    One way to think about this would be to say that space and time are illusions (or at least that they are appearances), and that the basic reality is an inconceivable commingling of all things. The opposite extreme would be to say that the picture with the maximum number of unfolded dimensions is always the correct one, and the holographic compressions, all the way down to the matrix models, are encryptions or enfoldings of a fundamentally higher-dimensional reality. I don't want to presuppose either interpretation as correct, I just want to point out the existence of competing or complementary perspectives.

    Now I want to say something about DrZ's cosmology. Maybe the main point is that the existence of a holographic description on the boundary of a region of space is not the same thing as the existence of a black-hole event horizon there. An event horizon is a special type of surface in space, and the holographic description of the interior will be correspondingly distinctive (basically, when there is a black hole inside the holographic surface, the holographic fields on the surface are in a plasma state). But even regions of space containing no black holes will have holographic descriptions.

    The other comment is that the idea of other universes inside black holes isn't how we describe them now. It's a somewhat old-fashioned idea that derives from the early attempts to understand the distortions of space and time inside the event horizon. The string theory model of a black hole is more like a giant atomic nucleus: it's a big bundle of strings and branes all tied together and spinning hard (and that includes rotational motion in the extra dimensions), which stretches out to the event horizon (the surface of no return for something falling into the black hole). The branes are all curved around on each other, they are quivering with energy and emitting and absorbing strings, and sometimes a string gets away (that's the Hawking radiation) and the black hole shrinks as a result. (This isn't just vivid metaphor, by the way; there are differential equations describing bound systems of branes which obey the laws of string theory and which exhibit all these behaviors.)

    It's very possible that dark matter and dark energy are somehow a side effect of the holographic principle - they might be an extra aspect of gravity arising from the holographic property. By the holographic principle, each galaxy should indeed have a holographic description on a shell in space surrounding it, just like the sphere with images of the flock of birds on its surface. (It's such an insane idea that we might "actually" be living on the surface of a sphere surrounding our galaxy that I want to repeat my initial point about the different possible perspectives on holography. The interpretation which says that the higher-dimensional picture is real, and the holographic descriptions are just a sort of mathematical origami trick, would imply that the three-dimensional picture of life in the galaxy is the real one, and the two-dimensional holographic description is just a projection you can make.) And maybe, if we understood real-world holographic duality better, we would see that it implies that there are subtle modifications to how gravity works on very large scales, which would explain dark matter and dark energy. But it also remains true that dark matter and dark energy might just be new types of particles and fields that we don't know about. That's what most people think; the holographic explanation for dark forces is very speculative and doesn't have a convincing expression so far.
    Last edited: Sep 8, 2011
  19. Sep 8, 2011 #18
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    In an attempt to keep at least part of the discussion grounded, I want to bring up another concept from physics which suggests a less exciting interpretation of the holographic principle: http://en.wikipedia.org/wiki/Gauss%27s_law" [Broken]

    Gauss's law can be interpreted as a relationship between a fact about a surface and a fact about the volume which the surface encloses. The fact about the surface is the amount of electric flux through it; the fact about the volume which the surface encloses is the amount of electric charge within that volume.

    The difference between Gauss's law and the holographic principle, is that in quantum gravity, the information about what's happening on the surface completely determines the physics inside the surface, it doesn't just tell you one fact about the inside. Nonetheless, the holographic principle has a lot in common with Gauss's law. All you have to do is replace electromagnetism by gravity, replace classical physics by quantum physics, and replace "charge" and "flux" by "mass" and "conformal dimension". :-)
    Last edited by a moderator: May 5, 2017
  20. Sep 8, 2011 #19


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    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    That does not solve the problem of initial conditions - which is a bigger issue.
  21. Sep 8, 2011 #20
    Re: Gravity, information, and cosmology (was "Thoughts about the universe")

    Sorry, what doesn't solve the problem of initial conditions? :-)

    But this gives me a chance to go into more detail about the "timeless field theory" mentioned in my opening post. This is http://arxiv.org/abs/1108.5735" [Broken]. In this, an expanding universe with a scalar field, a gravitational field, and an infinite set of massless higher-spin fields, is supposed to be holographically equivalent to a Euclidean field theory defined on a space equal to the spatial cross-section of the expanding universe; this space is identified with the behavior of the expanding universe at "future infinity". The Euclidean field theory is one of spin 1/2 particles, and the spin 0, spin 2, spin 4... fields from the history of the universe are identified with conserved currents in the Euclidean field theory, found by combining the spin 1/2 particles. So it's not the universe we know, but it's the first mathematical realization of holographically emergent time, and a more complicated form of the correspondence may apply to reality.

    I was reminded of this by the section in Alex's original post where the possibility of somehow detaching oneself from one small location in space and time was raised. If physicists say that space and time are illusions, it's a natural idea. But here again I will bring up my two perspectives on holography - that no space is fundamental, vs that higher dimensions are fundamental - and another principle to use when judging or trying to understand weird claims about the nature of reality: that they must "add up to normality". At least some part of reality must correspond to what you are seeing, the mundane or not-so-mundane reality that you personally experience. Therefore, even if someone is saying that space and time aren't real, and reality is just a matrix, or whatever whacked-out mathematical metaphysics they have going, you know that if it is true, there must be a way to interpret it so that it looks exactly like the world you are seeing.

    In the present instance, that means that, even if the mathematics appears to be saying that the universe we know is holographically equivalent to a timeless field theory located at future infinity, we know from experience that time and change are real, that events actually happen, that there is such a thing as spatial separation, and so on. So once again one has the option of taking the attitude that the fundamental reality is one of changing irreversible time and spatial separation, and that the timeless field theory representation of reality is just a sort of trick, a way to collapse the whole infinite future of the universe into a single compressed description. It's interesting that it's possible to do this at all, and also that the description looks like a quantum field theory in Euclidean space, but that doesn't mean that time isn't real. I think that would be the sensible, cautious approach to these ideas. I don't mean to dogmatically exclude other interpretations, or even the possibility that experienced reality could, under the right conditions, start to look very far from the "normality" that we have hitherto experienced. I find it very plausible that the long-run consequence of revolutionary physics ideas about space and time will be to alter the way they are experienced as well, though that might have to wait for a transhuman civilization that can do funky things with neurobiology. But you have to admit that reality as we know it looks pretty three-dimensional and "timeful".

    By the way, Chronos, in this "dS/CFT correspondence", it's a little hard to see how the initial conditions work. There are comments in the first appendix to the paper about this, but I haven't parsed them yet.
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