I recommend when sharing arxiv links to link to the abstract. That way your reader can decide for themselves whether they want to bother with either a PDF or HTML version, especially since the HTML views are still experimental and have occasional display issues across devices.

Link to the abstract of that paper: https://arxiv.org/abs/hep-th/9409089v2

Thanks for sharing!

Much of Susskind's papers are like that. A few simple equations motivated by dimensional analysis, a couple of Penrose diagrams, and the rest speculation and insight.

"The World as a Hologram" (1994) https://arxiv.org/html/hep-th/9409089v2 .. citations: https://scholar.google.com/scholar?cites=1288333106183032878...

But can there be holograms within the outer hologram?

What shape is space? Like, how far does space extend "above" and "below" where the Earth hangs in space? What stuff is there in both areas?

My concept of space is informed by the hammock analogy where gravity is the result of the bodies' mass/density causing the fabric to sag and draw in approaching objectz

Thank you. This is far easier to understand than the OP.

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.

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.

> 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

You could ask, but that isn't possible, so the question is of dubious value. There are many states of the 3-dimensional world that will produce identical images in the surface of a mirror.

> 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)?

> 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.

No this is different. You can't classically encode an arbitrary 3D world on a camera sensor without losing information. It can only create a 2D projection of surfaces. It can't look inside opaque objects. Countless distinct 3D objects could correspond to one an the same 2D projection. There are actually many examples of optical illusions which show that a 2D image can be ambiguous with regards the 3D space it represents.

I feel the most interesting implication of the enclosing surface being a complete description of the enclosed volume and its contents implies the contents don’t need to exist. If you think physics as the set of rules that applied to one full state of reality can completely give it’s next state, then having redundant representations is wasteful and the interior of the enclosed volume, as the interior of the black hole, might not need to exist, or to be represented at all. If you extend this to the full spacetime we inhabit, it all would be the encoded in its boundary and, therefore, only the boundary is needed.

Yeah, there's a great talk about the physics of the holographic information encoded on the surface by Raphael Bousso (if you have an hour):

https://www.youtube.com/watch?v=GHgi6E1ECgo

HIGHLY recommend it for lay folks interested in this stuff. Which reminds me, I should yt-dl this so it's not lost, and I have a copy...

Is the physical nonlocality of the relationship between the bulk and boundary somehow related to the noncontinuity of any bijection between manifolds of different dimension?

> Mathematician, not physicist, but it seems reasonable to me that you could encode a sufficiently constrained 3D space on a 2D boundary. And if you have such an encoding, it also doesn't seem insane that some things might be more easily modeled on the 2D boundary than the 3D space.

Yes, you are missing the point entirely. Merely saying "you could encode a sufficiently constrained 3D space on a 2D boundary" as you correctly noticed, would be meaningless.

The observation is that the 3D space has properties that are weird in 3D but natural in its 2D representation.

> does it matter which is "real"?

No.

Also if you have different representations of something and your job/goal is to think and gain instinct then you should keep in mind all the representations, they very likely will be useful. (An observed property of mathematics is that if a mathematician pours 40 hours per week of work in an area for years in a topic other mathematicians haven't exhausted yet, she will find something there.)

It's Cauchy problem.

> String theory had a generation of great science communicators writing its books and singing its praises...

I would argue that has done more harm than good. Strong media personalities shouting "the next big breakthrough is here!" followed by 25 years of zero practical results have not done good things for public perception of field of physics. A layperson could be mistaken for assuming the field is literally regressing.

I don't think the distinction between holography and string theory is as clean as you're making it. The vague idea of holography predates string theory, but most of the working examples we have of holography come from string theory. That's what AdS/CFT is: It's an explicitly holographic description of superstring theory in an anti-Desitter space. It's frankly bizarre that the author of this article doesn't mention that fact. I suspect we are seeing a popular science rebranding of string theory without the word strings.

I can't tell if you're aware that the holographic principle came from string theory

isn't holographic universe a similar concept to string theory in that they both propose higher dimensions projecting into lower dimensions

string theory, 11 dimensions, is bonkers though, it's what happens when people are too smart for their own good imho lol

LOL, same. Usually I watch with a great, much deserved attention, but sometimes I need to work on something so I replay videos, and his voice, with such a fantastic cadence and soothing registry, talking about things I deeply enjoy and appreciate, makes work easier and better.