I've never understood why proof that the universe is "holographic" (= 2+1 dimensions of information projected as 3+1) does not fall out of the Schrödinger’s/Maxwell’s field equations.
After all, the equations, by their very nature as equations, constrain the dimensionality of possible universes (field configurations) by one, from 4 down to 3. The fourth is always derivable from the other three (e.g., X-Y-Z intial conditions at T=0 define X-Y-Z-T fields for all T).
To believe that the universe contains four dimensions of information (i.e., is not a hologram), would imply that the field equations do not universally hold. So what this experiment is actually testing is the truth of QED, which implies holography.
Does anyone know why this is not so? (I tried asking a while ago on Physics StackExchange and only got flippant responses.)
(As an analogy for CS types: consider the game of Life. It is 3-dimensional (2 space + 1 time), but constrained by the Life equation. So it cannot contain three dimensions full of arbitrary information; only a two-dimensional slice can be arbitrarily instantiated. The analogy is not perfect, as Life is neither reversible nor fully observable from any 2D slice, but it is close.)
I may be off base here, but I think the distinction is between number of degrees of freedom (what you describe) and density of bits of information. Bekenstein's result showed that the information in a black hole is proportional to its surface area, not its volume. This seems unintuitive in the sense that if you, e.g., stuff more ram chips into a box, its information content seems to increase as a function of volume; the disparity lies in the fact that bits in ram are not as densely packed as in a black hole.
I think there is no distinction to be made. Consider encoding information in a 4-cube (hypercube) constrained by Maxwell's equations. (Let's make the space discrete so our heads don't explode.) You will find that you can only encode an amount of information proportional to the cube of the 4-cube's edge length, not the 4th power, because you are constrained by Maxwell's equations. If you further insist on keeping the information unchanged with respect to time, you'll be restricted to an amount proportional to the square of the 4-cube's edge length.
Given that according to quantum mechanics, empty space continually experiences small, random fluctuations[1], I think you can argue that in the normal space, information does on average expand proportionally to the volume encompassed, even if the proportionality constant is rather low (edit: this applies to space-time volume too since the fluctuations are random, distinct on each timeslice).
Indeed, I think quantum mechanics would be the only system that guarantees this. I suppose a purely classical system that was entirely reversible couldn't contain information in the time dimension because each moment would imply every other moment. But claiming that any system determined by classical differential equations is "holographic" might be a stretch.
First of all, a spatial dimension is a degree of freedom per particle (two if you count velocity).
Second of all, physics equations often represent many constraints. For example, `p2 = p1 + v t` is actually three constraints. Each particle has these sorts of constraints, so all of them cut down the degrees of freedom in the system.
So it's not 4-1=3. In Newtonian mechanics it's 1 (time) + 3n (positions of particles) + 3n (velocities of particles) - 3n (velocities determined by forces) - 3n (positions determined by velocities) = 1+3n+3n-3n-3n = 1. Which makes sense, because otherwise you wouldn't get one solution per time step.
EDIT: jamii seems to understand that we are working with very different definitions of dimensionality.
My (and I suspect most readers') understanding of dimensionality is as follows. If I have a graph with x and y axes with six RGB-colored points on it, that does not make it a 30-dimensional graph. It's two dimensional because there are two independent variables in the 5-tuple relation that graph is representing.
Number of particles and number of dependent attributes do not affect dimensionality.
Correct. There's spatial dimensions, where you can put the points, and degrees of freedom, the number of numbers you specify when setting up a system. The word dimension can refer to either definition (and others), depending on the context.
What I was trying to communicate to the gp is that they were mixing the two concepts. Constraints reduce the number of degrees of freedom, not the number of spatial dimensions, so the intuition that you get the holographic principle by adding a constraint to 3d space simply doesn't type-check.
No, they really do reduce the number of spatial dimensions. Take EM fields. You have a 6-tuple relation, x×y×z×t×e×m. Maxwell's equations aside, this relation is four-dimensional, because two of its dimensions (e and m) are dependent on the other four (x, y, z, and t), making the relation a function: x×y×z×t→e×m. Meaning, for any values of x, y, z, and t, they are related to exactly one value of both e and m in the relation. Without any constraints, e and m may be freely chosen for each value of x, y, z, and t in the relation.
Now, if I assume Maxwell's equations, I am free to rewrite this relation as dependent on only three variables; let's say x, y, and z, but it really doesn't matter: x×y×z→t×e×m. To further refine the example, if I took t=0 for all x, y, and z, I'd have initial conditions at t=0 (very standard).
Given Maxwell's equations however, I can derive exactly one relation of the form x×y×z×t→e×m from my x×y×z→t×e×m initial conditions. Hence P(x×y×z×t→e×m) and P(x×y×z→t×e×m) are in bijection, |P(x×y×z×t→e×m)| and |P(x×y×z→t×e×m)| have exactly the same cardinality, and therefore the same spatial dimension, three.
I believe Strilanc is talking about dimensions in phase space rather than in physical space. If you plot all the possible configurations of those points on a graph, that graph would have 30 dimensions. Whether or not that is a valid point is beyond me.
Your point is very similar (equivalent IMHO) to Julian Barbour's case in The End of Time, that you can express the laws of physics without reference to time, since time can be defined with respect to a special distance metric between universe states (the Machian distinguished simplifier).
In fact, I think the analogy between Game of Life's governing rule and the Schrodinger equation is very clarifying!
The FAQ is very good. I wish the experimental section went into a discussion of error sources. There may be unexpected error sources which are just as interesting as the signal they're searching for (gravitational waves, who knows)
As one example of an error source, I can predict this thing would make a beast of a seismometer. Which in itself is interesting.
There's also a theory that our universe is a 3-D hologram that was spawned from a black hole in a 4-D universe [1]. Would there be any way to test this theory as well?
That actually makes a lot of sense. For quite a while, I've been trying to imagine some rules for how some parent system might guide the laws of physics behind our universe, and your comment seems to have lit a bulb in my head. I haven't yet read the source link and I wish I could offer more input on it right now, but I'll have to check it out later.
Great lecture. When information moves outside of the shell of our observable universe due to expansion, shouldn't we be able to receive Hawking radiation from this process?
I'm very excited about this experiment. Even if it completely fails, we're bound to learn something interesting. Spacetime fluctuations haven't been examined at this level before, so anything they find out is new.
Someone educate me. Isn't this farcical at the core? If we are living in a hologram, then why is our world visible inside of structures, even when devoid of light (eg: buildings, dark tunnels, etc).
They're not saying the universe is a light hologram like the one on your credit card, they're saying it might be holographic in the sense that our 3d space could be a projection of a 2d boundary.
The idea came about as a way to resolve the black hole information paradox in a way compatible with string theory (the idea is that information can never be destroyed, but black holes appear to destroy information). One interesting consequence would be that our universe could be the result of a black hole in some other universe.
Last I read about holographic projection was the idea that our universe is a 3D projection of a 4D star. Is this a completely different theory or maybe just easier to test?
Where does the idea come from that information cannot be destroyed? Is that supported by strong evidence, or is it just an assumption, axiom, or hypothesis?
My intuitive sense is that information can be created and destroyed. For example if I arrange wooden block letters to form a sentence, I have expended energy to encode information. If I scatter the blocks randomly, I have expended more energy to destroy information.
It's supported in both classical mechanics (Liouville's theorem, which is a vital component of the proof of Newton's second law) and in quantum mechanics (quantum unitarity).
The term hologram is more of an analogy than anything else, you shouldn't think of it as a projection produced by light. The idea is that we're living on the edge of a high-dimensional membrane and that our 3 dimensions (+ time) form the surface of that membrane. One of the interesting thing about membranes is that the surface encodes a lot of information about the interior structure, or stated differently, the interior determines the surface. That's what they mean by hologram.
The other replies here reference a 2D encoding of a 3D space. That's a simple example of this kind of holograpy but it's not the one being tested for. Most of hte holographic theories reference a much higher dimensional space on the inside and a 3 dimensional surface.
The 'hologram' in holographic physics doesn't refer to the standard 3d optical illusion things. It's a more general term for 3-dimensional information being encoded on a 2-dimensional surface. Just like the hologram you're thinking of constructs a 3d image out of a bunch of 2d dots, so the entire physics of our 3d universe are constructed out of information on an imaginary 2d surface.
The optical holograms we see often are an example of holograms in general, but they're far from the only ones.
Indeed, it's amazing tech. It's even better than you think: size of the image is dependent on projection, not size of the medium. If you cut it it will show the same size as before, but with lower resolution. That is one of the things that blows my mind every time: the less data points there are, the less precise it is, but it's all still complete.
I don't think they mean literally a hologram. As far as I can tell, they're checking to see if the universe is actually a 2d sheet like an infinitely thin piece of paper. It's like a computer game displayed in 3d, but all the data exists in a 2 dimensional structure (ram).
Or maybe I just don't get it at all. (I know next to nothing about quantum theory)
I really enjoyed reading "The holographic universe" (http://www.amazon.com/gp/aw/d/0062014102) some time ago but how can an experiment which is entirely based on science, physical laws, empirical evidences and so on, prove something which would make all these means... meaningless. This looks like a paradox to me.
The August 2014 issue of Scientific American had an article by Afshordi, Mann, and Pourhasan entitled "The Black Hole That Birthed the Big Bang" on a holographic theory of the universe.
The article [0] is paywalled, but the preview contains a note from a reader suggesting "the holographic principle shares the same problems of all Idealist notions: rather than relying on evidence, it puts the elegance of the model first as an argument in its favor."
I hope the Fermilab experiments provide some useful data.
That's definitely a valid criticism, and one that can be levelled to a lot of popular theories like string theory (where holographic theory originates from) and quantum loop gravity. It's a short-term problem though, since we're more and more capable of searching for the needed evidence.
Yeah, formalizing thoughts into models, and then testing them to validate or invalidate them is sooo idealist. I wish scientists would only rely on common sense and holy books, trusting their guts to do the right thing.
Seems to be a bit dangerous experiment. I remember reading something in some kind of a manual that it is definitely dangerous to put to much information in one place. It gets hungry for more information and then things get complicated pretty quickly.
I was referring to a physics textbook, Bekenstein Bound [ http://en.wikipedia.org/wiki/Bekenstein_bound ] and a gravitational collapse. Doesn't look like downvoters had gotten the point through though ;)
After all, the equations, by their very nature as equations, constrain the dimensionality of possible universes (field configurations) by one, from 4 down to 3. The fourth is always derivable from the other three (e.g., X-Y-Z intial conditions at T=0 define X-Y-Z-T fields for all T).
To believe that the universe contains four dimensions of information (i.e., is not a hologram), would imply that the field equations do not universally hold. So what this experiment is actually testing is the truth of QED, which implies holography.
Does anyone know why this is not so? (I tried asking a while ago on Physics StackExchange and only got flippant responses.)
(As an analogy for CS types: consider the game of Life. It is 3-dimensional (2 space + 1 time), but constrained by the Life equation. So it cannot contain three dimensions full of arbitrary information; only a two-dimensional slice can be arbitrarily instantiated. The analogy is not perfect, as Life is neither reversible nor fully observable from any 2D slice, but it is close.)