Thread

1. anigbrowl · 1790380260 · focus · HN ↗

   Pause for a moment to reflect on how outrageous this assertion is. You can’t see into the box at all. Nevertheless, holography says that you can learn exactly what’s happening everywhere in the box without any access to the interior. Observing the surface alone is enough. In this sense, the amount of stuff that fills a box is the same as the amount of paint that covers it. That’s a violation of logic and geometry.

   The breathless tone of this article obscures rather than illuminates its subject. It sounds as if the author describes a box with some particles bouncing around inside, and every time a particle bounces off the wall of the box the outside glows briefly indicating the location and intensity of the collision. The author is amazed that by repeatedly measuring this, you can draw inferences about what's going on in the box.

   I can't see what's 'outrageous' about this. You need a lower surface which registers information about activity inside a higher-dimensional volume, some way to accurately read that information, and the time/patience to repeat the measurement many times. Isn't this how radar works, or feeling your way around a pitch-dark room using only the 2-dimensional surface of your hands (or shins)? We know from computer science that you can mathematically encode any structure of arbitrary dimension into a binary tree. One might as well ask how it's possible that our complex 3 dimensional world can be contained in the flat surface of a mirror, film strip, or camera sensor.

   1. yshklarov · 1790397352 · focus · HN ↗

      Indeed. A "violation of logic and geometry"? Reading the author's own description, it's hard to see what the big deal is:

      "Put a box around any region of space (space-time, really, but I’m going to drop time throughout this essay for ease of visualization, as physicists often do). The holographic principle asserts that no matter what’s going on inside — from gas molecules pinging around to black holes colliding — you can decipher the entire contents of the box just by repeatedly measuring points on the surface."

      Well, if we're bounding a region of space-time then, in a purely classical universe governed by deterministic ODEs or PDEs, the statement reduces to a triviality: having information about the boundary amounts to knowing all boundary conditions. Of course I understand that this isn't really the statement of the holographic principle, but the article's formulation is rather underwhelming.

      1. ridiculous_fish · 1790468882 · focus · HN ↗

         Say your boundary is a spherical shell, with a radially constant electric field. Based only on those boundary conditions, you cannot know the distribution of charges inside the shell. It could be a point charge, a solid sphere, a smaller shell, etc.

         So classically you cannot decipher the entire contents of the box just from its surface!

         1. yshklarov · 1790553088 · focus · HN ↗

            You are correct if you mean a 2-sphere, but a spherical shell in space-time would be a 3-sphere, which gives quite a lot more information. To make things a bit simpler we could consider a 2-sphere × an interval -- the boundary of a 4-dimensional cylinder -- which is to say, your spherical shell at all points in time from t_0 to t_1, and also the entire interior of the spatial region at both the initial time t_0 and the final time t_1.

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