[kamac]

Wow that was a tough read for a layman like me.

> [...] after the renowned physicist Juan Maldacena discovered that the bendy space-time fabric in its interior is “holographically dual” to a quantum theory of particles living on the lower-dimensional, gravity-free boundary.

What does "holographically dual" mean?

What boundary are we talking about here?

> The bendy fabric of space-time in the interior of the universe is a projection that emerges from entangled quantum particles living on its outer boundary

What is the "interior" of the universe? What is the "outer boundary"?

[roywiggins]

anti-de Sitter universes are bounded by a horizon. The example given in the article is an Escher print with an infinite number of tiles bounded by a circle. They get smaller as they get closer to the edge, but there's an infinitude of them, so you have a universe that is infinite from "inside", but "from the outside", there's an outer boundary. As far as occupants of a hyperbolic universe go, they can't see the horizon directly because there's an infinite number of tiles between them and the edge.

That boundary has lower dimensionality than the universe itself (the Escher universe boundary is 1D and the interior is 2D).

Holographic duality is where you can describe the entire interior of the universe by characterizing "stuff happening" on the boundary- that the stuff happening inside the universe looks 2D, but is fundamentally one dimensional. Real-world holograms work like this- they encode a 3D scene onto a 2D substrate.

Our universe is not anti-de Sitter- it appears to be flat and does not pack away nicely into a bounded area like the Escher universe does, so it's as yet unclear how to apply the stuff they've found in their model universe to our own.

[floatrock]

> They get smaller as they get closer to the edge, but there's an infinitude of them, so you have a universe that is infinite from "inside",

> Our universe is not anti-de Sitter- it appears to be flat and does not pack away nicely into a bounded area like the Escher universe

How do you tell from the "infinite inside" whether it packs away nicely into a bounded area? Or is figuring that out the trick?

[antidesitter]

> How do you tell from the "infinite inside" whether it packs away nicely into a bounded area?

Roughly speaking, you measure how fast the volume of a ball grows with its radius [1]. If it grows faster than you’d expect in Euclidean space, you know you’re in a hyperbolic space.

You can also draw a big triangle and see whether the interior angles add up to less than 180 degrees [2].

[1] https://en.wikipedia.org/wiki/Scalar_curvature#Direct_geomet...

[2] https://en.wikipedia.org/wiki/Hyperbolic_triangle#Properties

[roywiggins]

And we've done exactly that using our cosmological models of the Big Bang:

https://map.gsfc.nasa.gov/mission/sgoals_parameters_geom.htm...

One side of the triangle is the width of Cosmic Microwave Background variations (calculated from models of the early universe); the other two sides are known from how far away the CMB appears to be, which is known from independent measures of the expansion of the universe. Some trigonometry will tell you what the interior angle that should make with the Earth, which you'll see as the angular width of the variations in the sky. You can compare those two numbers (the one by trigonometry and the one observed), and determine whether they are different enough to exclude a flat universe.

In other words, if someone holds an 1 foot ruler at a distance, you can use trigonometry to work out how far away it is by using the apparent size. But if you know how far away it is, and the apparent size disagrees with the trigonometry, then the shape of the universe must not be flat. The longer the ruler and the further away it is, the greater the deviation will appear (if there is one). The CMB is very far away indeed so it makes for a good ruler.

[hammock]

> And we've done exactly that using our cosmological models of the Big Bang

What's the result- flat or not?

[roywiggins]

Flat, as far as WMAP can tell!

https://wmap.gsfc.nasa.gov/universe/uni_shape.html

Of course the curvature could maybe be arbitrarily small, but... it's definitely very close to flat.

[danbruc]

[...] whether it packs away nicely into a bounded area [...]

That is nothing you should worry about, with enough deformation you can make a map of any shape you like for any space. You must not conclude from looking at a map of the Earth using for example a Mercator projection that there are somewhere four straight edges meeting at right angles and where you can just fall off Earth. You also must not naively make conclusions about the relative sizes of things as they get heavily distorted. The same holds for this map of hyperbolic space, it is really misleading - in the space there is no boundary, there is no special point in the middle, it does not pack nicely into a circle in any meaningful way, ... Those are all just artifacts of the way this map is drawn and it has nothing to do at all with the underlying space.

[spenczar5]

Thank you for a terrifically clear description of difficult concepts. This helped me a lot!

[badloginagain]

They talk about black holes being possible in AdS universe- in the Escher universe does that look like a group of the fish "missing"?

Also, near the end they get into black hole information preservation. What information are they referring to? My assumption has always been that black holes essentially zero out all information, like making all bits zero on a hard-drive.

[hammock]

Maybe a black hole looks similar to the boundary, but instead centered on a single point- the fish closest to the point getting smaller and smaller.

[nabla9]

How do black holes fit into this picture? Are they anti-de Sitter locally?

I mean if our universe maps to 2d boundary, you could find it out if you try to pack 3d volume of space full of information/matter. The volume must become full earlier than if the the information is limited by the surrounding area and not by the volume.

[0db532a0]

What do you mean by saying that our universe is flat. Are you saying that it’s a 2-manifold?

[pixl97]

https://en.m.wikipedia.org/wiki/Shape_of_the_universe

[0db532a0]

Makes sense. Thanks.

[raattgift]

Flatness is a property of the Robertson-Walker metric, as the k parameter at https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr... where you'll find a reasonably rigorous discussion.

More figuratively, if you take any circular planar slice of the spatial part of an expanding spacetime such that all points in the plane have the same coordinate time and then evolve the slice forward in time or examine it over cosmological distances (meaning more than megaparsecs) the plane is always flat like a disc rather than curving like a bowl.

With the constraint that there are cosmological observers -- they just float with the metric expansion of space and always observe the largest-scale distribution of matter as isotropic and homogeneous: mostly meaning similar-looking galaxy clusters (and cosmic microwave radiation) along every line of sight -- then a Robertson-Walker metric has identical constant curvature everywhere, so it doesn't matter what planar slice you choose: you'll always see the same circular disc, spherical cap, or their equivalent on a negatively-curved plane. Moreover, it does not matter when we take the planar slice; the spatial curvature is constant in the whole spacetime. [1]

Thus, we have excellent evidence for the spatial flatness of the universe from the small variations in the blackbody temperature of the Cosmic Microwave Background, and the evidence improves as we compare those variations with galaxy clusters at different redshifts (and other measures of distance).

In his last paragraph (which provoked your question) roywiggins means that our universe is expanding and at cosmological scales matches the Robertson-Walker metric extremely well. If we look into the far future, the matter dilutes away enough that it will look very similar to de Sitter space (an empty expanding spacetime) rather than anti-de Sitter (an empty collapsing spacetime).

- --

[1] Just to clarify: we are talking about spatial curvature here, where we have sliced up the 4d spacetime into 3d spaces indexed by time. In an expanding universe, whatever the spatial curvature (even if it's exactly zero), spacetime curvature is large: freely-falling objects diverge with the expansion. The spatial curvature mostly deals with relative distortions of the shapes of similar galaxies (e.g. barred spirals, or ellipticals) at different distances. With zero spatial curvature, faraway barred spirals have the same shape as nearer barred spirals.

With positive spatial curvature, further away barred spirals would be less arm-y and more core-y than nearer ones, while with negative spatial curvature they would be more arm-y and less core-y. The light from the outer parts of the arms and the core are all emitted essentially as parallel rays. With positive spatial curvature, the rays converge, so the arm-rays get squashed towards the core-rays as they travel cosmological distances. With negative spatial curvature, the initially parallel rays diverge.

We don't see that kind of distortion in images like this, with a large number of faraway galaxies looking very similar to foreground galaxies like Andromeda (M31) https://en.wikipedia.org/wiki/Hubble_Ultra-Deep_Field

[toufiqbarhamov]

There isn’t an exterior in this model, just a boundary you can’t get “outside of” because everything including space and time are part of the universe. What this is all based on is the observation that the information required to describe the volume of (for example) a black hole, can be encoded on its event horizon. The theory says that the universe and it’s horizon(s) can be similarly modeled. In essence that we live not in the volume of a soap bubble but in the fluctuations of the skin of the bubble. It’s only to us, at our energy level and scale that a higher dimensional volume appears to emerge.

It’s important to say that this is all entirely speculative, based on the physical possibility which allows for the resolution of some outstanding problems in physics. That doesn’t mean it is in any way real, it is just another possible model, and one without observation to support it as the way our universe actually works.

[wallace_f]

Perhaps a stupid question:

If a 3d universe can be encoded in a 2d space, then I suppose a 2d universe can be in a 1d space? And could 1 dimeneion be encoded in 0? Just some bits or fluctuations?

[saalweachter]

With the caveat that I am neither a physicist nor a mathematician:

1. My understanding is that some kinds of 3d universes can be encoded on a 2d surface. Whether our universe is one of those is an area of research.

2. You can't always generalize from one dimension to another in mathematics. The most common example is that knots can only exist in three dimensions; they don't exist in 2 or 4.

[drdeca]

You can knot surfaces in 4D though.

Edit: not to say that 3D space isn't special though. There are plenty of special things about it.

[toufiqbarhamov]

You’re not wrong, but all such knots are trivial in 4D. The math is discussed here: https://math.stackexchange.com/questions/1426501/why-are-all...

[drdeca]

That link appears to be about unknotting any embedding of the circle into R^4 . Indeed, these can all be unknotted.

I am saying that if instead of having a 1-d curve (a circle) embedded in 3-space, you instead have a 2-d surface embedded in 4-space, that such surfaces can be knotted in 4-space just as the circle can be knotted in 3-space.

Iirc, one way to construct these surfaces is to start with a knot in a particular 3D slice of 4-space, put all of it on one side of a plane in that 3D slice, stick the knot to that plane at 3 points (remove the bit of the knot between them), and then revolve what is left of the knot around the plane (so, the projection of the knot as it is revolving into the 3D slice will look like the knot is being squished into the plane, unsquished on the other side, and then doing that backwards. But this is only the projection into the 3D slice. Really, when revolving around the plane, as the direction normal to the plane within the slice gets scaled to zero, the same amount is added first in one direction normal to the 3D slice, and then as- ... blah, I am going on too long in describing this. I'm typing on my phone, so I can't effortlessly see all that I wrote, so I might be repeating myself. It rotates around the plane. Each point in the original knot traces out a circle in 4-space. )

[debatem1]

At some level of approximation you can encode any higher dimensional space into a lower dimensional one. The usual approach is to use a space-filling curve, like a z-order curve or Hilbert space filling curve, then describing a point in the higher dimensional space as a distance along the curve.

[late2part]

It’s easy to encode the universe into a single binary bit. It’s the decoding bit that presents a challenge.

[ars]

Here's a possible answer. Imagine a 2d universe - a piece of paper. Cut that paper into infinitely thin lines, and line them up.

You have converted the 2d paper into a 1d line, but in the process have made the line much longer than the 2d version. (Like the difference between Aleph 0 and Aleph 1.)

I don't see any way to go lower than that though.

[mcxlog]

To go lower you cut the line into infinitely many points and stack them together :-) ?

[avmich]

I think a good illustration could be provided by the Gauss law. https://en.wikipedia.org/wiki/Gauss%27s_law

It states that if you have a volume of space - say, a cube 1 meter side - containing some electric charges, and you calculate the total flux of the electric field across the boundary of that volume - that is, across the surface of that cube - then you'll find that total charge Q and total flux FF are proportional, FF = Q / epsilon_0 , where epsilon_0 is a fundamental constant. And that ratio doesn't in fact depend on shape or size of that volume of space.

That means Gauss law allows you to go along the boundary surface, calculate total electric flux and calculate the total charge inside the volume within that surface.

Similarly here, "holographically dual" means that you can derive important properties of matter inside some volume from properties which are observable on the boundary surface of that volume. What are those properties is another matter - but this duality principle says that there is a certain relation between them.

[aaaaaaaaaab]

That’s a bad analogy. You can’t deduce the charge distribution within a volume from the flux through its boundary. You can only deduce its magnitude.

[beambot]

Parent correctly referred to "total charge", not its distribution.

[aaaaaaaaaab]

That wasn’t the issue with their analogy.

The issue was that the holographic principle states that the boundary completely determines what’s inside a volume, as opposed to Gauss’s law which only talks about the total amount of charge.

[avmich]

You're right, Gauss law only talks about magnitude, not distribution. I chose this example because it's simpler than explaining reversal of wave fronts, so the formula FF = Q / epsilon_0 is shorter. Note I mentioned "what those properties are is another matter".

The choice of analogy is less precise but hopefully easier to understand. The idea is just that there could be relationship between boundary conditions and internal conditions.

[jahnu]

Not sure if it's related but this lecture gave me some basic grasp on the notion of holographic representations

https://www.youtube.com/watch?v=2DIl3Hfh9tY

[psychometry]

Quanta is great, but there's definitely a limit to what can be portrayed to a popular audience and this is well past it.

[kamac]

I think anything can be portrayed to the popular audience. Other comments here explaining the terms used in the article suggest that this is possible. The only problem is that some fine information would most likely be lost with a simplified explanation.

[klank]

I think there's an additional difficulty when those unfamiliar with more rigorous (as compared to pop sci anyway) physics/mathematical discussions.

There is simply a great deal of unintuitive interactions to keep in mind all, at once, when attempting to rationalize how many of these interactions happen. Physicists and mathematicians combat this by working with specific abstractions enough to become intuitively familiar with the behavior of said abstractions.

Unfortunately, this packing away of unintuitive complexity behind intuitive interactions is unavailable to the lay reader. Any specific interaction can be explained in simple enough language, eventually, if the curious reader keeps asking why. However, when they attempting to pop back up the why stack and get back to the big picture (i.e. the world people can understand intuitively), lay readers lose the nuance in the noise created by the volume.

[theoh]

The verb "portray" doesn't mean what you guys seem to think it means.

[klank]

Perhaps you could elucidate us with the way you feel people are misusing the word?

[ada1981]

Fine information on both sides, as they say.

[labster]

On the contrary, this is the perfect article to explain to audiophiles why to buy my cable with quantum error correction. By increasing the qubit parity, we bring your sound system to a whole new level of clarity.

[kakarot]

Go one step further and sell a box that does quantum error correction for the entire room, like those "ambient room conditioners": https://www.lessloss.com/blackbody-p-200.html

[IIAOPSW]

Like grandma used to say: if you can't do something right, do something profitable.

[empath75]

So, let's imagine you have a function that takes a phase space (ie, the positions, momentum, etc of a bunch of particles in normal 3+1 space time) as an argument and produces an evolution of that phase space in time. It's got a bunch of rules in the function regarding gravity.

Now imagine you've new function, which also takes a phase space as an argument, but instead of operating in 3 spacial dimensions, it has five. And that it doesn't have any rules regarding gravity.

Now imagine, you have a one to one mapping between states in those functions. So you can take a state in 3d space, translate it to 4d space -- run both functions for the same amount of time, and they both should produce states which you can still map to each other.

[ojosilva]

To my computer scientist mind this can easily be a parallel to checksum and hashing. Quantum error correction is analogous to using checksum to validate file integrity. Memory chips use similar schemes (ie parity bits) to correct errors. The same is being applied to quantum computing, ie. a sort of quantum hashing scheme based on (spacial) logic gates.

Now new research is being conducted where this quantum hashing scheme could be used to solve some of physics hardest problems. One of them could be Hawkins paradox, where "data" gets corrupted while being "processed" by a black hole. Maybe, scientists argue, error correcting data is stored at the black hole entrance so that it can be somehow applied as correcting code at the exit, ie when Hawkins radiation is released.

Or maybe the entire universe has gone through a hashing function and now there's error correcting code keeping information error-free using the "hash value". That's what the boundary stores that describes the bulk in certain theoretical universes.

Hashes have always fascinated me. The fact that a relatively short binary sequence can uniquely describe all of Shakespeare's works. What if we could completely reverse hashes, creating the most powerful compression ever? Well quantum physicists just might do that at cosmic scales!

[stubish]

Hashes do not uniquely describe things. There are an infinite number of alternative texts that also match your hash that describes all of Shakespeare's works. A hash function is pretty much just a very lossy compression algorithm.

[irrep]

> What does "holographically dual" mean?

> What boundary are we talking about here?

"Boundary" refers to the boundary of Anti-de Sitter (AdS) space. The model that is typically studied is that of five-dimensional AdS space for which the boundary is four-dimensional. One can now formulate a quantum field theory on this boundary that is "dual" to the theory in the interior in the sense that there is precise dictionary between quantities living on the boundary and quantities in the interior ("the bulk"). "Holographically" refers to the difference in dimensions of the theory living on the boundary and the one living in the bulk.

[scottlocklin]

Its cod profundity which the author shouldn't have attempted to popularize. People haven't even demonstrated quantum error correction in a single qubit in an actual quantum computer, and suddenly it's the source of space and time. Chyeah, dude; whaddevah.

The model universes they're talking about, FWIIW, are all just models, with very little relationship to the world of matter we all live in.

[logfromblammo]

In our universe, construct an object that is perfectly spherical, and perfectly reflective. Now glue it to a table somewhere. Put another 3D object on the table. It has mass and volume, and felt real when you held it. Now look at the sphere. The 3D object is mapped onto the 2D surface of the sphere.

Now turn reality inside out. Because of various symmetries, it looks pretty much the same as it did before. Mathematically, it isn't all that important whether the signs of various things are positive or negative.

Instead of placing a 3D object on the table, draw a 2D shape on the surface of the sphere. Because you everted reality, this causes a 3D object to be reflected onto the table. The math can't really tell whether the object causes the reflection on the sphere, or the pattern on the sphere causes the object to exist.

Now turn the sphere inside out. Put the entire universe on the inside, and all of the stuff inside it (that you knew nothing about anyway, because it's perfectly reflective) on the outside. Now that your sphere encloses the entire universe, you can draw a 2D shapes on the outer boundary and reflect them as 3D shapes somewhere in the interior.

[galaxyLogic]

I don't know much about it but from what I've read imagine that we are inside a black hole. Every black hole is a universe of its own. The boundary of the black hole is the outer boundary if we are inside it. From the outside it would be just the surface of the black hole. Something like that perhaps

[rightbyte]

Should be verifiable on the inside with stuff popping up at the boundary, right?

When I read these quantum articles I think it's might as well be mambo jambo. Are the fundamentals of quantum physics even falsifiable?

[antidesitter]

What do you mean by “the fundamentals of quantum physics”? If you’re talking about phenomena like superposition and entanglement, the answer is absolutely yes.

[croo]

First observations of quantum physics was that if you light through two slices of holes in a paper it makes more than two marks on the wall behind it - this proves that the light is some kind of a waveform or could act like one. As far as I know the fun starts when you try the same experiment with exactly one photon emitted. The single photon will simultaneously go through the two hole. This caused some confusion and we now call this phenomenon and related things "quantum". But thid is just my understanding based on a book, other commenters seems to be much more knowledgeable about the topic.

[int_19h]

The single photon registers in a single spot on the screen, as a particle should, and so there's no problem with assuming that it went through one hole or the other.

The fun starts when you start sending single photons through the holes one by one - again, every photon registers in a specific spot; but when taken in aggregate, those spots form the same interference pattern as with multiple photons.

[roywiggins]

The boundary would likely appear to be infinitely far away, and so you could never see it actually happen.

[vnnkov]

I really liked cosmological natural selection of Lee Smolin in that regard. For me it's just looks so simple and obviously. https://en.wikipedia.org/wiki/Lee_Smolin#Fecund_universes

[rubyn00bie]

Sounds like if you imagine the universe as a sphere, like we (me?) "normally" do (3 dimensions), you use volume to describe its contents. Well... I think what they're saying is that the outside of the sphere, in this case the universe, just its surface, describes everything (all the information) inside of it... because in fact the volumetric area we know as the universe is a projection of a "flat" surface.

And... like I'm not very smart, but this is probably a bit like the non-euclidean space demo from yesterday's front page, where the geometry is doing really weird things... perhaps someone smart will come along and give a proper explanation.