Musings

Understanding Holographic Space


I won’t purport to understand even a fraction of this union of String Theory and Quantum Physics, but I think the following snippets of information can help answer this question about a really exciting update in the world of Physics. Furthermore, I highly recommend that you read Anathem mainly because it was a fantastic, fun, and fascinating book that “tricked” me into understanding some complex thinking such as Configuration Space.

The reason I mention Configuration Space is that in addition to the below explanations of the Holographic Principle specifically, from what I recall in the book, the use of Configuration Space is sort of like a metaphor — housing many pieces of information in a reduced space. One point on a Euclidean Plane or Configuration Space can measure area, or angle, for example – unlike the familiar X/Y planes we use in basic math. In this way, I think physicists saying that a holographic model of the universe is one that expresses a lot of information in a fewer dimensions; but we are not literally flat, we’re just mathematically expressed as such.

*Please note: This it total conjecture and I might be completely wrong about everything, I’m not a physicist.

Sciency Sources:

The Holographic Principle
i.e. All the information in our three (spatial) dimensional universe can be “stored” on a two-dimensional surface.
Source article: PBS: Do Black Holes Destroy Information?


Configuration Space

A supplement to Anathem by Neal Stephenson

Anathem Configuration Space

“The dotted line track on the bottom shows just the x and the y,” Barb explained. “The track that it made across the floor.”

“That’s okay—it’d be confusing otherwise, if you’re not used to configuration space,” I said. “Because part of it—the xy track that you plotted with a dotted line—looks just like something that we all recognize from Adrakhonic space; it just shows where the bottle went on the floor. But the third dimension, showing the angle, is a completely different story. It doesn’t show a literal distance in space. It shows an angular displacement—a rotation—of the bottle. Once you understand that, you can read it directly off the graph and say ‘yeah, I see, it started out at twenty degrees and spun around to three hundred and some degrees while it was skidding across the floor.’ But if you don’t know the secret code, it doesn’t make any sense.”

“So what’s it good for?”

“Well, imagine you had a more complicated state of affairs than one bottle on the floor. Suppose you had a bottle, and a potato. Then you’d need a ten-dimensional configuration space to represent the state of the bottle-potato system.”

“Ten!?”

“Five for the bottle and five for the potato.”

“How do you get five!? We’re only using three dimensions for the bottle!”

“Yeah, but we are cheating by leaving out two of its rotational degrees of freedom,” I said.

“Meaning—?”

I squatted down and put my hand on the bottle. The label happened to be pointed toward the floor. I rolled it over. “See, I’m rotating it around its long axis so that I can read the label,” I pointed out. “That rotation is a completely separate, independent number from the kick-spinning rotation that you plotted on your slate. So we need an extra dimension for it.” Grabbing the bottle, and keeping its heel pressed against the floor, I now tilted it up so that its neck was pointed up from the floor at an angle, like an artillery piece. “And what I’m doing here is yet another completely independent rotation.”

“So we’re up to five,” Barb said, “for the bottle alone.”

“Yeah. To be fully general, we’d want to add a sixth dimension, to keep track of vertical movement,” I said, and raised the bottle up off the floor. “So that would make six dimensions in our configuration space just to represent the position and orientation of the bottle.” I set the bottle down again. “But as long as we keep it on the floor we can get along with five.”
[…]

Standard