Comment by pimlottc
1 day ago
It’s not just drawing inferences, though; it’s saying you can determine exactly what’s happening in the box. But the pigeonhole principle would suggest there’s far more possible states in the 3-dimension volume than can be unique expressed on the 2-dimensional surface. That’s the part that defies common sense.
A 3d volume can contain a number of states equal to it's 2d dimensional surface.
All the extra states you would assume the 3d volume can contain are actually a single state called Black Hole.
There is a limit to how much you can fill a 3d volume before it's a Black Hole basically.
This is by far the most succinct, understandable, correct, description of the holographic principle. I don’t know all articles don’t just lead with this.
Does that mean that all the black holes of a particular volume have the same interior? Or does it mean that the black hole state is the case where you can’t tell what the interior is?
Classical understanding, yes. Black holes have no 'hair'. You can measure charge spin mass that's it
> a single state called Black Hole.
Quibble: A black hole still has a charge, mass, momentum vector, and spin vector. Which, yes, still vastly reduces the number of states needed on the surface of the enclosing container.
Is that result proven?
Depends on what hypotheses you are willing to accept, but, as far as I know, it is generally accepted by physicists: https://en.wikipedia.org/wiki/Bekenstein_bound
That's a purely mathematical result, the top comment of this thread has a link to the paper
I don't think it has been experimentally verified or anything
No.
That's the clearest description of how this dimension collapse via gravity thing works that I've ever heard.
I really think we live on the 3D event horizon of a 4D black hole, folks.
Why stopping at four dimensions?
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> All the extra states you would assume the 3d volume can contain are actually a single state called Black Hole.
How can that be? Don't different black holes have different masses?
Well the density goes down the larger the black hole so the extra states are still missing.
For exactly how that works, I'm a Comp Sci not a Physicist.
2d observed over time is also 3d. 3d over time would be 4d.
You still have less information than if you could observe the full 3d spatial volume over time, because presumably you won't know in perfect detail qnd precision what all the particles are doing internally?
Or does it not work like this?
Is it any weirder than the fact that there is a bijection between the unit interval and the unit square?
Yeah because you can prove that any such bijection cannot be a topological homeomorphism, for example. So necessarily some "nice to have" properties must drop out.
Those drop out in holography too — eg, information local within the interior can get smeared out across the surface.
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I'm not sure if I agree, but you certainly articulated it far more clearly than the original writer.
> That’s the part that defies common sense.
Does it? Isn't this basically the same as how cellular companies can figure out exactly where someone is calling from as long as their phone is pinging 3+ towers? Just connect the towers into a box and you have the same result.
Build an object out of legos and then reconstruct the shape of what you built by only looking at it from the sides and above.
Seems simple enough in many cases. But I think the difference is in the generality of it. Being able to do it for any interior arrangement of parts.
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If the events inside the box can’t influence events outside the box directly, only by changing the surface of the box, it’s fair to say they don’t happen at all, and all that happens is the change of the surface.
If you're willing to use continuous dimensions, the surface is the same size as the volume; I don't see why the pigeonhole principle would present any problems.
Interestingly enough, I believe there is a result that space-filling curves cannot be one-to-one, but the implication there is just that, by virtue of the continuity of the one-dimensional curve, it contains more points than the two-dimensional space that it fills.