Gravity seems holographic. What does that mean for reality? | Hacker News Reader

Gravity seems holographic. What does that mean for reality?

quantamagazine.org

300 pointsibobev234 comments

Susskind's original paper is shockingly readable, at least the first section. It doesn't use a lot of fancy math or derivations to justify holography. Mostly it uses basic concepts from undergraduate physics to show how the idea of holography is consistent and makes sense, despite it seeming incredibly counterintuitive at first glance.

For instance, figure 3 shows how you can't hide a black hole behind another black hole, which has implications for how a 3D universe can be completely encoded in a 2D region.

https://arxiv.org/html/hep-th/9409089v2

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.

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

"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?

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!

Fortunately, it's very simple to navigate between pdf, html, and abstract, just put "abs" in the URL where it says pdf and so on.

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

space is 3D, but the information content can be encoded on a 2D hologram. general relativity works, mass-energy is curving spacetime, it just happens to do it in a way, that these curves and slopes and ... the whole 3D geometry can be flattened to 2D without loss of information.

So is there stuff below and above Earth

Yes, lots and lots of stuff. For all we know, space may extend infinitely in all directions.

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.

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.

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.

That is exactly what I was wondering about in my other comment: is physical nonlocality somehow equivalent to topological noncontinuity?

I am not a physicist but i presume that is the hope of some who pursue holographic modes

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.

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?

Oh sure. The parent universe could be the 4D event horizon of a 5D hole. It’s holes all the way up. If you draw little heads on them I guess they’re like round turtles so if this is true the turtles people weren’t as far off as we thought.

Since all the event horizons “touch” at N-1 dimensions I wonder if this is isomorphic with certain forms of string theory? Maybe there’s 11 levels of holes?

BTW this isn’t my idea. There’s papers on black hole cosmology. You can make the math work but no way to test it. Yet?

Legs, also little legs.

The people at Gillette are working on five.

That's old news. They solved five a while ago.

I heard they were researching up to 18, but most of the blades were curved and really short.

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

No.

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

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.

> 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.

> 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.

> Well the density goes down the larger the black hole so the extra states are still missing.

Huh? If the correlation between density and mass is perfect, that means two things:

1. There is an upper limit on the mass of the black hole, set by the volume of the box containing it.

2. The black hole's possible mass and density occupy a one-dimensional space and not a two-dimensional space.

Now, it appears to be true that the (possibly nonlinear) correlation between mass and density is perfect; for any mass a black hole can have only one density. But that doesn't make the space of possibilities finite. It certainly won't make it into a single point. And in fact black holes appear to have three independent physical dimensions: their mass, their electric charge, and their spin.

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

> There is a limit to how much you can fill a 3d volume before it's a Black Hole basically.

Which is exactly the part that "defies common sense" and is intersting

> 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.

Agreed, that was what I was trying to say. You can build a lego structure that you can not infer by just looking at from the top, bottom and sides.

I'm not sure if I agree, but you certainly articulated it far more clearly than the original writer.

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.

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?

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.

The metaphor as written is maybe bad, but the holographic idea really is outrageous and mindboggling. Because according to it the inside might as well be completely empty.

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.

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!

No. You are only counting the integral of the field on the surface, but if you take into account the orientation of the field on the surface, you can know the internal distribution of charges.

If the field is always radial, the charge can only be in the center, by symmetry. A different distribution of charges will not produce a radial field on the surface, even if it has the same integral.

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.

>"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."

Space filling curves with three dimensions could potentially provide us with some clues:

https://en.wikipedia.org/wiki/Z-order_curve

"In mathematical analysis and computer science, functions which are Z-order, Lebesgue curve, Morton space-filling curve,[1] Morton order or Morton code map multidimensional data to one dimension while preserving locality of the data points (two points close together in multidimensions with high probability lie also close together in Morton order)."

Also, to answer the question, potentially Octrees might be interesting to research:

https://mathworld.wolfram.com/Octree.html

"An octree is a rooted tree that represents a three-dimensional region by recursively subdividing it into eight congruent, axis-aligned cuboids, usually cubes (Meagher 1982, Samet 1990). Each internal node represents a spatial cell and has eight children, one for each octant of the cell. A tree leaf represents a cell that is not subdivided further."

But, since "a picture is worth one thousand words":

https://www.google.com/search?q=octree&udm=2

Another thing to consider is that according to the Knuth Transform (aka Left-Child Right-Sibling (LCRS) representation), apparently any k-ary tree (Octree = 8-ary tree) can apparently be converted into a Binary Tree without losing information:

https://en.wikipedia.org/wiki/Left-child_right-sibling_binar...

So, is there a 1D (or 2D) representation for 3D reality?

Well, I personally don't know!

What I do know is that a certain popular rock group sang the following lyric in one of their popular rock songs, back in 1999:

"Space may be the final frontier -- but it's made in a Hollywood basement..."

-The Red Hot Chili Peppers, "Californication"

So, you decide! :-)

> 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.

I remember thinking space filling curves were completely magical when I first learned about them. It feels like there should be some connection with holography although they don't get mentioned in the article.

> 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.

It is not outrageous. For example, conservation of energy tells you that if you observe the surface of a box, you can know things inside the box. If you observe how much energy enters or exits the box, you know the change of energy inside the box. And that's true independently of what is inside the box.

Inside the box, there may be one rat, a galaxy, a nuclear bomb, or whatever thing you can imagine, and still you know exactly the change in stored energy. It only depends on what happened on the surface of the box.

Also, when you solve a differential equation, you need the contour conditions. The contour completely determines what happens inside.

Sure but "total amount of energy evolution in the box" is much, much, lower-grained than "knowing exactly everything about the inside of the box"

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.

If you can convert back and forth between a 2D representation and a 3D representation, and different phenomena are more easily modeled in each, does it matter which is "real"? Unless of course you can come up with a specific prediction and experiment to test it.

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...

In 240p only? :-(

The YouTube video was uploaded 18 years ago, and looks like it was filmed on a VHS camcorder. I guess it could have been 480p as the original would have been 480i, but it wouldn’t look all that much better.

VHS has an effective resolution of ~240p anyway.

How much more knowledge are you hoping to extract from a 4K version?

There’s some physics-y Shannon entropy data or black hole joke in there somewhere I just am not mart enough to find it.

I haven't watched it so far, but I'd expect some diagrams on a chalk-, or whiteboard, maybe some 'overhead' projection. These will all be almost unrecognizable at that resolution, on current screens. Would have to try to upscale with AI. Which I won't.

I watched the whole thing, I didn't notice anything substantial lost.

what app do you use for yt-dl?

https://github.com/yt-dlp/yt-dlp seems to be a more currently maintained fork of the original https://github.com/ytdl-org/youtube-dl/

can concur

https://github.com/yt-dlp/yt-dlp is generally where the most up-to-date workarounds for Google's attempts to block downloads are.

This is a great video, thanks for sharing.

My favorite quote and a point where something really clicked was when he said "If you tried smaller you would instead be making a Planck-size black hole".

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?

It's Cauchy problem.

> 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.)

As a non expert who's just curious about science but also tries to talk like a normal person, from what I can tell holography really seems like it's now the leading candidate to be the next big conceptual revolution in physics.

There's not necessarily any breakthrough right around the corner and we shouldn't rush to coronation preemptively, but there's a lot of physics "voting with their feet" for holography as the article says, and I think it's officially time to start getting hyped. It could have sanity-restoring answers to questions of quantum weirdness, albeit at the rather expensive cost of giving up even more on our day to day intuitions about space and time in favor of an apparently informational substrate.

String theory had a generation of great science communicators writing its books and singing its praises, but holography doesn't yet have equivalent public champions, and I hope that's something that changes sooner than later.

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

Eh, 11 dimensions is just what the math predicts based on the theory’s postulate and observations of the universe.

Holographic gravity is no less fanciful if there’s no practical experiment to prove it.

No string theory (10d) or m theory (11d) map to lower dimensions (eg 4d) via (generalisation of) Kaluza Klein compactification. Vector boson (eg maxwell or Yang mills) are internal degree la of freedom-> 6/7d graviton becomes a photon/ gluon.

There’s holography in string theory: AdS/CFT but this rather maps 4d super Yang mills (on the boundary of AdS5) in an AdS5xS5 background: which is one holography correspondence we know works.

Holography is much more common, but we only really understand it on hyperbolic spaces.

Also since it has a theory at strong coupling on one side we cannot really do calculation on that side and verify it.

You can use it tho to make calculations.

Many concepts can be framed as projections onto lower dimensions. It’s the specific ways in which things are projected that makes things string theory. IOW don’t mistake the concept of a map for the territory that one type of map describes.

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 didn't intend to assert a clean distinction, you're exactly right about its connection to string theory. What I mean is that String Theory Writ Large enjoyed a lot of popular esteem in the 00s and 2010s in public communication as being our potential new framework for what lies beneath the quantum world, but string theory is huge in and of itself.

It's more a difference of emphasis (holography in particular) than something that's outside the scope of string theory.

> 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.

> could be mistaken

Could be forgiven?

Yes, thanks!

Damnit, I rewrote that sentence twice and still got it wrong.

You could be mistaken for that

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

I can't tell if you're aware that they're not synonyms.

Well the reason I couldn't tell if you were aware is because they aren't synonyms and your comment is perfectly reasonable, but I picked up an (incorrect, it seems) vibe that you thought they were unrelated. Which, they kind of are! It's a fairly interesting story how it came about as a property of string theory but appears to be leaving it behind.

I recommend growing your charitable interpretation muscle, it heads off avoidable confusions like these :)

PBS Space Time, could watch it all day, sometimes listen in the background all day

* https://www.youtube.com/watch?v=DoCYY9sa2kU

* https://www.youtube.com/watch?v=klpDHn8viX8

* https://www.youtube.com/watch?v=qYSKEbd956M

* https://www.youtube.com/watch?v=YNEBhwimJWs

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.

Ok so imagine we set up two sets of babushca dolls. Each larger one has two smaller ones nested inside. The total mass of the two smaller ones between the two sets is equal in mass and they are configured to have the same centre of gravity. But crucially the individual masses of the inner dolls are different between the two sets. So maybe the innermost one is made of a denser material in set A and the middle one a less dense material and in set B vice versa. And let's also say in each case the dolls are all locked into position relative to the outermost one, so there's no "play" if you move it around to infer a difference from.

From an outside mass/gravity point of view these are similar right? Yet the holographic universe theory seems to say we should be able to differentiate between the two sets of dolls purely based on space-time observations of the surface of the outer doll, despite each system having identical gravitational properties when viewed externally?

But doesn't that suggest a contradiction between this theory and what we have observed about gravity?

There seems to be a grand motivation to fit a holographic model onto how the universe seems to behave.

I recall a popular claim several years ago that we all lived in a hologram (whatever happened to that?).

I bet this has nothing to do with string theorists trying to make their 2D models apply to actual physical observations…

Matryoshka doll. Babushka = grandmother.

What if the dolls are all grandmas?

Then you'd have an infinite series, as each doll would have to contain two smaller copies.

But the real question is would you be able to determine this had happened from the surface of the outside doll if all of the masses of the inner dolls are half of the i-1 outer one, leading to a total mass of 2n?

I think the box explanation is misleading. There isn't literally a box whose surface you measure. The idea is that the state of a higher-dimensional gravitational system can, in some cases, be completely described by a theory in one fewer dimension.

For black holes it is quite literal tho.

So like describing the properties of a sphere by using a circle.

Not a circle but the surface of the sphere

Is the "in some cases" constraint really necessary? I thought Bousso's whole point in his talk linked elsewhere in this thread is that you can describe a 3D system in terms of 2D information.

Could you keep going, fully describing systems of higher order in less and less dimensions?

This is cool, but I've noticed that an idea of a "holographic universe" makes the news roughly once a decade.

Maybe fifth time's the charm. ;-)

Only time tells!

Fascinating article... reminds me once again why I went into EE/CS instead of physics, I just wasn't smart enough :-(

Some assumptions of holographic principle either do not match with standard model of cosmology or predict yet another consequences. This model acknowledges expansion of the Universe, observed via Hubble in 1990s and since then only more facts. Information limit of volume is measured by how much information (written into matter) can be put into volume before it becomes black hole and forcibly occupy as much volume as required to preserve area limits. But that expansion of the Universe, how does it interact with black holes?

If the space expands, that helps escaping black hole. And effective horizon of black hole should be smaller than without accounting for space expansion. And it is possible to put little more information than area permits. This is hard to verify since distances where space expansion starts being noticeable, are orders of magnitude bigger than radius of known most massive black hole. But consistent description of reality should combine them somehow.

There may be alternative solution. Area limit may turn out to be more fundamental than space expansion, and big radius black holes will have stronger gravitation to overcome space expansion.

> With gravity, mass plays the role of charge. It bends space-time around it, and it is always positive. There is no negative mass

Equations have not just mass, but also pressure, and space expansion is theoretically described by dark energy that has positive mass and negative pressure overcoming its positive mass.

This article seems to repeatedly blur the distinction between 'having space' to encode all the states inside a volume on it's surface and an actual theory of correspondence of states.

"Having space" is just a consequence of black holes. If you have more information in a volume than can be encoded on its surface in theory, you have enough mass inside the volume to make it a black hole and the event horizon then has enough space to encode the information even if the original surface did not.

The correspondence between information, thermodynamics, and mass that causes black holes to 'make it possible' to holographically encode all the information inside is what makes this theory so tempting. What if everything is information, and black holes aren't an expression of 'too much mass', but rather just a result of 'too much information to store'. This theory, if it existed, would demonstrate a key result of both relativity and quantum theory based on a very simple premise, and suggests it might then be possible to base both General Relativity and Quantum Theory on top of a simpler theory.

> That’s a violation of logic and geometry. It asks us to erase the categorical difference between square meters and cubic meters.

No, that's sheer nonsense.

> There is no negative mass, so you can always infer the one real arrangement of stuff inside from the warping of space-time at the surface of your box.

Positive mass does not make this argument work. Two bodies in GR can have different distributions of mass but identical exterior geometry. A counterexample is two spherically symmetric, uncharged bodies with the same total gravitational mass but different radial density profiles. By Birkhoff’s theorem, their exterior vacuum geometries are identical.

Isn't this the same as Newton's shell theorem?

Yep! Although it's different due to lack of superposition, I think it happens to work out for spherical shells.

> > There is no negative mass, so you can always infer the one real arrangement of stuff inside from the warping of space-time at the surface of your box.

> Positive mass does not make this argument work. Two bodies in GR can have different distributions of mass but identical exterior geometry. A counterexample is two spherically symmetric, uncharged bodies with the same total gravitational mass but different radial density profiles. By Birkhoff’s theorem, their exterior vacuum geometries are identical.

I thought I understood the holographic theory better after this article. But now it's clear I don't.

Lets imagine that we are the are the flat landers for a second. We're doing something, the laundry, and we feel an eerie feeling come over us as if we're being watched. No one else in the room, so you shrug it off. Come to find out, our 3D counterparts were actually observing us, unbeknownst to us (aside from that eerie feeling we got). Stay with me! So, while we are on the persons screen or a piece of paper in front of them (this of course assumes 2D existence is possible, just for the example) and they are viewing us, is this at all similar to what this article is talking about? In this scenario, can we label one Ads and one CFT? Another question kind of, but maybe not separate to that, asks if Ads/CFT is a mathematical description of how things project into seemingly completely separate things depending on your perspective? But they're indeed the same. An example of what I mean, so in our 2D existence we notice a pulsing circle, and then in our 3D existence we realize that pulsing circle is actually someone playing with a ball on a string and the pulsing is the ball getting closer to us in more dimensions than can be expressed properly in the 2D view. That's kind of what I mean...so is Ads/CFT description of the same kind of idea as my... admittedly weak example? Lastly, I would like to say that Quanta is fantastic. I don't understand a lot of what is written in their pages sometimes but that's not due to the writing by any stretch. But it makes me think, which is why I still read it anyway! If I'm not mistaken this is the 2nd time in as many days it was featured on the front page, and rightfully so, I think. Anywho, thanks for reading/taking time to respond if you do.

In a sense it's the inverse of what you describe. A 3D creature could easily see everything happening in a 2D space because all the information describing the 2D space fits comfortably in a mere slice of the 3D space. It's trivial because 3D space is "bigger" than 2D space.

What AdS/CFT implies is the opposite: That all the information needed to describe a 3D space can fit in a 2D space, like a hologram. This is astounding and extremely counterintuitive.

The hitch is that our universe is (probably) not AdS; it's dS. And the astounding math doesn't work for the de Sitter space we live in.

Ahh. Okay...So, this is kind of like the 2D entities trying to make sense of their 3D counterparts, and the 3D counterparts getting the sensation of someone watching them, but its the 2D beings discussing the existence of the 3D entities instead of vice versa? I know this is quite a basic comparison but it helps me grasp it a bit better. Also, is there any particular reason that it's 3D and 2D? That is, is there any other dimension number that could accommodate the correspondence? Or does the math say it's only 3D to 2D and vice versa where this works? And do we know why or why not if so? Thanks

That's the idea, but it's like the 2D creatures know everything about the 3D creatures, which the 3D creatures find quite shocking.

The actual dimensionality is 4D to 3D once you add in time. But the math basically says an nD hyperbolic conformal manifold (AdS) can be completely described by its nD-1 boundary (CFT).* So I think it works in any number of dimensions.

*Oversimplified and probably wrong, but probably close enough for this discussion.

> That all the information needed to describe a 3D space can fit in a 2D space, like a hologram.

I'm not totally certain about this but I think you skipped over something important.

It's not that 3D space can be described by 2D space, it's that _our_ "3D" space appears to fit in 2D space because every time the universe puts too much information in the 3D space we get a black hole and a black hole is a 2D surface in 3D space.

It's not quite that: The math only works in Anti de Sitter space, which is not the universe we live in.

The tiny black holes that are suggested by non renormalizability are one of the mysteries that make AdS/CFT an attractive direction in which to explore our own universe, partially because Susskind has already shown that black holes in our universe can be described by their surfaces.

> You can “compress all of the three-dimensional world into two dimensions.”

That sounds a little like the sophons in the novel Three Body Problem. IIRC, aliens took a photon, unfolded it to a flat surface to etch circuitry on, then folded it back up and fired the photon at earth where it unfolded again and did the bidding of the aliens.

> you can decipher the entire contents of the box just by repeatedly measuring points on the surface

So if the box is both inside and outside of a black hole, is that a path for information to leave a black hole?

I immediately thought of the painter analogy (from the books which are astonishingly good) of "painting" 3D objects into 2D objects from the stories, and wondered if the author was exploring the reverse of this "perfect painting" that is still "functional". I'm definitely a lay person, I know enough physics to use a lever to lift heavy things.

Different topic, but the sophon idea in TBP revealed the author's complete ignorance of basic particle physics.

…it’s Science Fiction

More like space opera is my point. Science fiction projects out into the future to extrapolate from current science, it doesn't invent a parallel reality that is contradictory with already understood science.

There's no hard scifi story that doesn't have a big (often understated) magical physics moment. The harder it gets, the more understated the miracle. I would argue it's the very existence of this crucial violation of the Standard Model (and even current day alternates) that makes any of those stories compelling. They're what drive all the other actually realistic events forward.

I'm not claiming TBP is hard scifi btw. But the reveal which OP has spoiled already makes for a sick scene and pivotal point in the book.

It just struck more as a Marvel style ending than an Arthur C Clark style ending.

Was it just one violation of the standard model? It seems like it was referencing the pre-quantum classical model of protons, before we even knew about quarks.

It's touted as "hard science fiction" but it's riddled with this kind of stuff.

I think by definition if part of you is in a black hole, the bits inside it can't affect (or communicate information to) your bits that are outside.

Imagine we figure out that we are part of a simulation and that that simulation is nobody's, it just happened and keeps on happening, like the universe just happened and keeps on happening if we keep going back (or is it forth?) in time, and that we can't do anything to change that simulation. Would we lose all the purpose and meaning of life? Or will evolution, now simulated evolution, still manage to collectively pivot us into accepting that as the creation and move on? If we become capable of altering minds enough, this can be a very interesting and cruel experiment on human beings - a meeting of Westworld and MKUltra.

What does the word “simulation” mean in this context?

You can prove to me we’re just a video game running on the underpowered Game Boy of an interdimensional teenager, as long as I can make things with my hands, go out in nature, experience beautiful art, and have tasty food with people I care about, there’s no way I would “lose all the purpose and meaning of life”.

Same but we should both admit we would probably change what we made.

If you believe that every effect has a cause, then you might question the notion of “free will” that most people believe in. This means that regardless if it’s “simulation” or not, we can’t “change” anything.

Hmm, but isn't a statement that _every_ effect has a cause self-refuting?

I’m not that well versed in philosophy to dive deeply into theory, but I don’t see a self-refutation. There is obviously a problem of first cause, but I don’t think it refutes my argument about free will. Also, I think Universal Causation is mostly non-controversial and most people agree on it and operate accordingly.

Sorry, this wasn't a reply to the free will part.

And yes, I meant the problem of the first cause, but it probably isn't a strict refutation...

And also, when it's stated as "every effect has a cause" (not "everything," as I first understood it), then it's probably even a tautology :)

To the free will part itself - I can say that I decided to do B because of a reason A (so the effect B was caused directly by my decision and indirectly by A) and I still have a free will?

This is also a deep philosophical debate. I just meant that your decisions are based on internal and external circumstances, that are based on the physical world. Your decision is an effect of multiple causes (e.g. your mood, your beliefs, state of chemicals in your brain, weather, news that you’ve seen in tv, your genes, your childhood memories, etc). The “free will” as commonly understood would be then an independent act, a miracle that defies the constraints of physical world.

Purpose is found individually through daily lived experiences and not because we are or aren’t in a simulation

Hmmm. Just because you can take a 1D line of digits and combine them with another 1D line of digits to encode the information inside a 2D plane, that doesn't mean the 2D plane is a not a 2D plane, it just means you have a fancy encoder/decoder.

That is the holographic principle in essence, although that has more dimensions, but just because it is possible to encode the information pertaining to the contents of a nD area onto an N-1D set of surface coordinates does not mean the contents of the area are the surface which is what is being claimed.

If 3D space can be packed into a 2D hologram, then, can that 2D data be packed into a 1D hologram and so on?

The article touches on that:

In recent years, they’ve started to get more creative. Susskind and other teams have made progress [link] on holographic de Sitter models [link] that differ radically from AdS/CFT. Instead of squashing a volume into an area, these universes seem to cram all the dimensions into a lone quantum point.

If you read the article, one of the analogy points to this. Compressing everything to a point.

But I had the same question few months back. Asking Claude is fruitful in this case.

If unitarity and the no-hiding theorem are true and the Big Bag emerged from a point, doesn’t it follow that all the information about the universe was once contained in a dimensionless point?

At sufficiently high energies, interactions that appear distinct at low energies may be described by larger underlying symmetries. Symmetries reduce the amount of independent information needed to describe a system. So the early universe can admit a remarkably compact description.

Regarding unitarity, an initial state does not need to contain a record of a history preceding it; unitarity only requires that subsequent evolution preserve the information encoded in the quantum state. Later states may contain enormously complicated correlations that simply did not yet exist in the initial state.

And there is no general principle saying that a large amount of quantum information requires a large classical spatial volume. A Hilbert space can support an enormous number of possible states even when its geometric description is extremely compact.

More importantly, the universe didn't emerge from a dimensionless point. The (t=0) singularity is the limit where classical general relativity breaks down and stops being a useful description, so the ordinary picture of information as some number of independent "bits" packed into a 3D space is no longer obviously applicable. A coherent theory of quantum gravity would probably be needed to really break further ground.

It's a straightforward extrapolation. Big bang is extrapolation of Hubble law too. If the initial state was complex, why it would be consistent and why it would have low entropy?

1D = unus Deus

I feel like this article spends a lot of time on metaphysical speculation (what is "real"). However what i am left wondering is what exactly would the consequences be if this theory was true (for those of us living in a holographic universe).

Given that it’s always been true if true, then the implications are that things are as they’ve always been.

I think the point of the person you're responding to is what are the practical consequences for future scientific and technological leaps if this is accurate. Does that make FTL travel possible? Does it predict an outcome for the fate of the universe? etc.

i dont even mean big things like that. I'm more wondering, is there any experiment you could in theory do that would differentiate between the two cases? what does it affect? anything?

for most problems and perspectives it’s an irrelevant distinction

When all gravity runs out, and all forces fizzle into the vaccuum, entropy returns to a single maximally ordered state indistinguishable from any other. Identical conditions for a Big Bang.

Consider time itself: one beginning, and many endings. Why many endings? And who even asks the question in the first place? Many intelligent observers, with many endings, but the same beginnings. Perhaps the black holes are a hint to our own ending?

We're born and blink into existence. And then we die and fade into the void, carrying our varied stories with us.

Logically, it doesn't make sense, and we can't possibly know the answer. But what if all those ends wrapped around to the same beginning?

Would you look at the world differently?

> When all gravity runs out

what does this mean?

A theory is: blackholes give off Hawking radiation at the end of their lives.

I'm of course, oversimplifying things for a fun thought experiment. Everyone wonders about reincarnation, death, and the 'end of time'.

Just a thought experiment that's not grounded in anything. We all believe what we want and act accordingly.

> We all believe what we want

- Time is strictly perceptual. The Universe as a whole (including changes in the fourth dimension) has always existed and will always exist. There is no 'end of time'.

- When your portion of the universe runs out (death) you just rerun it again. Because linear time is an illusion that helps us make sense of it (and not fear the future) and in reality we're skipping all over the place constantly. Forever. So hope your life isn't terrible. You're going to be reliving it infinitely. Enjoy.

Compassion and good times run out too quickly. I hope we all do alright. It's naive but who cares.

Amplituhedron geometry simplifies scattering amplitude calculations.

N-body gravity derived from QED with scattering amplitudes (without spacetime curvature, in a Flat Minkowski space)

[...]

From this chat: https://share.google/aimode/O0pKsl6nYdv8Nh2fD :

> The "shear-jamming" of Fedi’s fluid space is the physical, hydrodynamical translation of hitting a geometric boundary facet of the amplituhedron

And, normed tensor gaussian splatters work well as a simulation primitive for this too because they do conservation.

I don't think the author has relevant scientific background and it's frustrating this wasn't written by one of the Quanta journalists who does.

I often wonder if our brains are capable of understanding the Universe around us. Our brains were made to help us survive on this planet, not to understand the laws that govern our Universe.

The story that haunts me is the one where scientists attempted to understand how the brain of a simple organism worked. It only had 40 neurons yet they were unable to unravel the mystery on how it functioned.

I think about this sometimes too but I do believe we have at least for a fact described some aspects of the universe (speed of light for example) so we are at least capable of doing that, if not understanding much of the rest too.

Just as acceleration through space causes [the same effect as] gravity, could regular gravity be the movement through TIME?

Could gravity be a facet of time as electricity is to magnetism and vice versa? and the reason we cannot "isolate" gravity is because it's interwoven with time?

But then it would be weird that photos who don't experience time are affected by gravity..

Or maybe space, time and gravity are a trinity?

(no I'm not high, but maybe I should be)

is this why i increase in mass and volume every year?

Do you also attract more things?

no, and it's called the antigravitational theorem, taken to be proof that actually there is such a thing as "negative mass". To put it in vernacular terms, you do get more massive but not without a shrinkage in social currency. "Something's gotta give" is the textbook formulation of the principle.

Where did you get a photo that isn't effected by gravity?

fuck lol photon

Does that scale? Does a photo of a photo have antigravity.

To me (a total physics layperson with just an interest in it) space and time HAVE to be emergent and not fundamental because of the real phenomena of spooky action at a distance and dual slit craziness. All spacetime surely has to be connected is what it’s telling us.

Or hear me out here… we as a species have developed measuring methodology that is precise enough at human scale but not actually correct and breaks down at larger scales.

As far as I understand it,the relative time as we know it, is just something that emerges from the fact that all particle interactions travel with constant light speed.

So if anything moves, the interactions don't change their speed, they stay constant, but the delta to the movement changes, and thus time dilates.

Would be interesting to know if there is some absolute/fundamental global time that has nothing to do with the time we perceive.

"Spooky action at a distance" only happens in some interpretations of quantum mechanics, and not, for example, in MWI.

Somehow I’m expecting to see Bousso’s work here. Eg

https://en.wikipedia.org/wiki/Bousso%27s_holographic_bound

Going with the video game analogy, would the characters made out of pixels ever have a way to perceive the console and TV that created them?

This seems to resonate with the idea of the universe existing on the skin of an expanding hypersphere. Is there anything in that link?

That was so well written, a lovely read. So refreshing to be brought along on the authors journey into thought.

> space maybe an illusion..

space is an illusion...The only thing that is absolute is consciousness, on top of which all illusions stand.

This doesn't make sense. Which consciousness is absolute? Yours or mine? Because I can't see your consciousness; I can only infer its existence. You can't see my consciousness; you can only infer its existence.

>Yours or mine?

Ours. Or every ones..We can easily accept that we inhabit the same spacetime. Why is it hard to imagine the same for consciousness?

Because deceit and lies exist.

We inhabit the same spacetime, but we could be seeing different things.

Consciousness is the greatest illusion of them all.

Get a load of this. You can have only consciousness and still have a sensation of a full universe.

Tell me again how Consciousness is an illusion..

All possible subsets of a Universal Set can be considered as Observers. So a Power Set is collection of observers. Power Set of Power Set is another such collection. So on and so forth. Powersets all the way up.

> “You can ‘compress all of the three-dimensional world into two dimensions.’”

Would this imply that time is the third dimension?

Wouldn't time be one of the two resulting dimensions - the other being space?

Aside: Quanta magazine always has excellent design & visuals.

Ctrl+F Maldacena... 0 matches. Oh wow!

I think I have said it here before that it’s crazy we still don’t know what gravity is, we can tell its behavior but not what it really is. Probably when we figure this out we would create a time machine, because both are also connected.

If everyone was just taught quantum physics with lattice field theory at the beginning, everyone on earth would understand physics at any level, no clickbait mystic level black hole hologram physics trying to do mental gymnastics. want to study physics harder? Increase resolution add more parameters and bake into some formula for application ...done

My nitpick is with something the author said in passing about Hawking. Yes, around 1970 Hawking and the scientific community at large still used to believe nothing could escape a black hole, and between 1971 and 1973 Hawking along with Penrose and others expanded their evolving understanding and consequences of of Albert Einstein's breakthrough work.

But then Hawking argued back the opposite case, which in simple terms means that some things can, indeed, escape an event horizon. In fact, name dropping Hawking just to mention his views as they stood before his 1973 work, and his 1974 model of Hawking radiation seems dangerously incomplete journalistic reporting.

In 1974 Hawking formulated what we now know as Hawking Radiation, which is the *exact opposite* of what was previously believed about the impossibility of anything coming back from a black hole. Whilst still not conclusively proven as a physical fact, this did win him the Special Fundamental Physics Prize in 2013. specifically for his discovery of Hawking radiation from black holes and his deep contributions to quantum gravity and quantum aspects of the early universe.

I find myself not agreeing with a lot of nitpicks, but this is a good one! The article says "Contrary to what Stephen Hawking argued, black holes are not inescapable prisons." But information escaping black holes is named after him! He definitely, in the full scope of his career, was perfectly agreeable to the idea of information escaping black holes.

Those claims are backwards.

Hawking found that energy/mass can escape but the information remains destroyed. You can't run a black hole backwards in time and reconstruct the matter that created it and hawking radiation bears no resemblance to anything that was ever beyond the horizon.

Shucks, you're right. Well, mostly. I misunderstood Hawking radiation as a solution when it actually contributed to the motivation for holding that info was not recoverable. However, he did famously "concede" a bet on the question that he believed was resolved against this belief and it's still the case that his belief by the end of his life was not that it was a "prison" the way the article suggests.

Not sure I follow your comment exactly, perhaps I am misunderstanding it but Hawking radiation doesn't involve anything escaping a black hole.

The radiation never originates from within the event horizon. Furthermore the radiation itself does not encode any information about what fell into the black hole apart from the electric charge, angular momentum, and mass (all of which must remain conserved).

The only caveat that I'd ask about is the death of a black hole after it evaporates away too much mass. If that explosion does occur, is that matter/energy that was from inside the singularity itself?

AFAICT nobody has a consistent theory proven by observations. Some theories offer an explosion in which the singularity vanishes, but this has trouble with information / entropy. Some say a microscopic remnant stops radiating because the original assumptions of Hawking radiation mechanism do not apply at near-Planck scale. Some say that as the curvature grows with the diameter shrinking, the black hole pops off from "our" spacetime and forms a parallel universe, without an explosion.

The current age of the Universe is way small compared to the time needed for evaporation, so observing anything like that happening (or not) is hardly possible.

At Planck scale it becomes a big particle, and such particles are known to be unstable and quickly decay.

Indeed All Hawking radiation takes from a black hole is some mass. It's a bit like radiation resulting from annihilation of matter and antimatter: it does not "escape", it "gets born" in the process.

I'm not sure that is a meaningful distinction. All a black hole _is_, is mass. If you take away the mass, you are taking away the black hole.

It's also information / entropy, hence the https://en.wikipedia.org/wiki/Black_hole_information_paradox

And electric charge, which is conserved!

The entire blackhole will eventually evaporate, so yes it is literally escaping from the black hole.

We can play with words all day, but in the sense of a particle entering into the event horizon of a black hole and then at some point in the future exiting from inside of the event horizon, that simply never happens and Hawking radiation does not propose that.

I don't know the slightest about this but... That list looks like it is supposed to be limited but that sounds like infinitely more information than zero?

>> Not sure I follow your comment exactly, perhaps I am misunderstanding it but Hawking radiation doesn't involve anything escaping a black hole.

>> The radiation never originates from within the event horizon. Furthermore the radiation itself does not encode any information about what fell into the black hole apart from the electric charge, angular momentum, and mass (all of which must remain conserved).

> I don't know the slightest about this but... That list looks like it is supposed to be limited but that sounds like infinitely more information than zero?

I don't know about electric charge, but can't you observe mass and angular momentum of a black hole from outside? I think the "no information" thing means the Hawking radiation won't let you tell you if the black hole was made from a dead star or just a really big pile of meat or what's going on inside of it.

IIRC, all Hawking radiation does is provide a mechanism for a black hole to eventually decay.

Hawkings radiation doesn't tell you anything about the contents of the black hole, just that it lost energy/mass. That reduces the event horizon, so there is now a (miniscule) amount of space that has become "visible". It'll be empty space, no extra mass is leaked in that way.

It's been ages since I read it and I am 99% sure I'm remember horribly wrong, but I was thinking it's something like this? Also - your "the only information" is precisely what we can measure of quantum states, so information is still preserved. That's more a limit of what we know?

I think that with Hawking radiation you have quantum entanglement of two pairs. You have a matter-antimatter pair production near the horizon. When the antimatter falls into the blackhole without being destroyed via mutual annihilation, the matter particle at the boundary now "radiates" away. HOWEVER.

The matter inside boundary which the anti-matter DOES interact with is destroyed, and the information of that interaction is is "passed" to the outside via the the anti-matter's entanglement with its co-created pair.

Something like that, isn't it? Please any physicists clarify :)

> I think that with Hawking radiation you have quantum entanglement of two pairs. You have a matter-antimatter pair production near the horizon. When the antimatter falls into the blackhole without being destroyed via mutual annihilation, the matter particle at the boundary now "radiates" away. HOWEVER.

That's not how Hawking radiation actually works. It's just a "lies-to-the-children" explanation. Antiparticles have positive mass, so the black hole would be _growing_ as a result. This mechanism also violates the equivalency principle, as you shouldn't be able to detect the event horizon with only local observations.

Reality is more interesting. In flat space, the ground state of quantum fields is actually non-zero. But black holes "bias" the fields in such a way that their ground state becomes _negative_ from the viewpoint of a remote observer.

This in turn permits it to create new particles from just nothing. This in turn adds _negative_ energy to that space, resulting in the black hole decreasing in mass.

But crucially, the event horizon itself is NOT involved. Particle creation can happen anywhere in the vicinity of the black hole, not just on the event horizon.

Please correct my understanding as I am not a scientist, but why do you assert that Hawking radiation "escapes" or "comes out of" a black hole? Nothing crosses the event horizon. Isn't it more correct to say that Hawking radiation is produced by the extreme warping of the spacetime very near the event horizon, and the black hole shrinks to conserve the energy? Black holes can also shrink as gravitational waves are produced, but we don't say that the waves "escape" the black hole.

My understanding is that Hawking radiation is where:

1. a particle/anti-particle pair is created at the event horizon;

2. the particle is on the outside edge of the event horizon, so "escapes" the black hole;

3. the anti-particle is on the inside edge of the horizon, so decreases the size of the black hole due to particle/anti-particle annihilation (with a corresponding particle on the inside of the black hole).

This is often used as an explanation in pop-sci materials, but it isn't particularly accurate, IIRC.

For example, Hawking radiation is always photons, with the wavelength corresponding to the size of the black hole. That isn't explained purely by virtual particles.

Also, for that explanation to work, it would always have to be an anti-matter particle that is selected to cross the event horizon, and I don't see how that would be the case.

Minor quibbles: Hawking radiation has a blackbody spectrum, so we get a variety of wavelengths, with a peak determined by the size of the hole. The outgoing particles should eventually include any kind of particle that can be created in the Standard Model, not just photons and gravitons.

Strangely, it is _not_ the instrinsic curvature of spacetime that produces Hawking radiation. There's a variation on Hawking radiation -- called Unruh radiation -- experienced by accelerated observers in flat spacetime. Any two observers will agree on the value of a field (e.g. the electric field) at a point, but an accelerated observer will experience empty spacetime as a _thermal bath of particles_, with a temperature proportional to the acceleration. Relatively accelerated observers don't agree on what the vacuum is.

You’re missing a big issue here… Hawking Radiation doesn’t escape from within the event horizon, and there’s no physical process preventing that. It’s radiation from the surface of the black hole, not the interior.

When I read "But holography really starts to bite only after..." my LLM-dar goes off. Everything I read up to that point was comprehensible, but man, I have developed a shudder reaction to any language suggesting AI was involved ibn its creation.

I find AI written stuff to be hard to read. Part of my career is being a writer and I take great pride in my outout. AI written materials is a slog because you can see how it's pumping out words to hit various metrics rather than what's needed for the task.

> Holography implies that you can do that — reconstruct every fold, vessel, and neuron in three dimensions — without actually looking inside. Simply photographing the surface of the brain somehow suffices.

Gah I am not a fan of pop-sci simplifications like this for the sake of a soundbite. The author goes onto explain how no, a picture is not enough, you need to actually measure the distortion of spacetime at the surface. Somebody is going to walk away thinking this stuff is possible, that maybe psychics really can detect something wrong with them.

I know what you mean and I think you're right, but I take it as the cost of doing business when trying to turn frontier physics into layperson analogies. You're not going to use an analogy to successfully complete a calculation of black hole entropy, you're going to use it to convey the high level intuition that "stuff on inside = stuff on boundary".

Because if we litigate the imperfections of analogies all day long, then you're going to react to videos titled "black holes described at five levels of difficulty" by saying the first four levels were all wrong, which may in a sense be technically true but not in the spirit of the exercise.

It's okay as long as they call it out, but the author doesn't and instead states it like a fact. They could have easily caveated it with "but a magical camera that can see magnetic and gravitational fields" or something. The analogy is fine, but it's not presented as one, so it's not clear how far the analogy actually goes. So the takeaway is "wow technically it's possible!"

It is Quanta, the home of sensationalist oversimplifcations. What did you expect, solid science?

Yes, the rest of the article is pretty good.

This was the low point for me:

> Consider a video game sun passing behind a video game tree. The sun pixels touch the tree pixels directly, yet the tree does not burst into flames. This is because the sun pixels are independent of the tree pixels.

With apologies to Babbage, I am not able rightly to apprehend the kind of confusion of ideas that could provoke such an explanation.

lol yikes. Some of the other illustrations quoted seemed OK esp if you already have a layman's understanding of the major concepts... but this just seems.... bad.

All particles and molecules move with cosine and sin in unison (maps our existence) therefore producing a shadow encoding our conscious in 3D realm

> With gravity, mass plays the role of charge. It bends space-time around it, and it is always positive. There is no negative mass, so you can always infer the one real arrangement of stuff inside from the warping of space-time at the surface of your box.

This is a simplification to the point of just being wrong. Gauss’s law works for gravity; if you put a shell around Earth you have no way of knowing whether it’s a planet or an Earth-mass black hole inside. Assuming spherical symmetry of density, anyway.

> This is a simplification to the point of just being wrong.

Is it? If you project a "3D" singularity onto a surface, it's still a point. If you project a roughly spherical object, it's roughly circular.

Gauss' law in this case would apply to the total force of gravity exerted by the mass within the shell, not its distribution across the surface of the shell.

I assumed the analogy meant that just by measuring the gravitational field outside the shell, you could figure out the mass distribution inside. And you can't, not in the general case.

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