Holographic universe experiment begins(symmetrymagazine.org) |
Holographic universe experiment begins(symmetrymagazine.org) |
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.)
EDIT: misspelled Bekenstein
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.
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.
In fact, I think the analogy between Game of Life's governing rule and the Schrodinger equation is very clarifying!
As one example of an error source, I can predict this thing would make a beast of a seismometer. Which in itself is interesting.
[1] http://gizmodo.com/our-universe-might-just-be-fourth-dimensi...
Sadly, Mr. Talbot died in 1992, six months after this interview.
Holometer site: http://holometer.fnal.gov/
I've also asked Fermilab directly and they confirm the article is from today, the holometer came online very recently: https://twitter.com/FermilabToday/status/504286464637939712
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.
[0] http://www.scientificamerican.com/article/the-black-hole-tha...
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.
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.
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 optical holograms we see often are an example of holograms in general, but they're far from the only ones.
https://en.wikipedia.org/wiki/Holography
If you cut a hologram (a real hologram), no matter how you cut it it still shows the whole image, just smaller.
Or maybe I just don't get it at all. (I know next to nothing about quantum theory)
There are a number of reasons this might make sense. For one, the maximum entropy of a volume increases with its surface area, not its volume (IIRC).
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.
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.
Is this true for N=2?