# And the experiment will explain the phenomenon of bitcoins

August 28, 2014 12:16 PM Subscribe

This is some World on a Wire stuff

posted by JauntyFedora at 12:43 PM on August 28, 2014 [2 favorites]

posted by JauntyFedora at 12:43 PM on August 28, 2014 [2 favorites]

Surely the easiest way to determine if the universe is a hologram is simply to tilt it forward and back and see if the image changes? Now it's a universe, now it's a bear waving a paw

posted by fallingbadgers at 12:47 PM on August 28, 2014 [61 favorites]

posted by fallingbadgers at 12:47 PM on August 28, 2014 [61 favorites]

*we could be clueless that our 3-D space is just an illusion*

Is there any current scientific model of the universe in which "our 3D space"

*isn't*"an illusion" in some sense?

posted by yoink at 12:48 PM on August 28, 2014 [5 favorites]

I, for one, intend to imprison these scientists in a tower if the result of this experiment invalidates my long-held belief system.

Just FYI.

posted by shmegegge at 12:51 PM on August 28, 2014 [8 favorites]

Just FYI.

posted by shmegegge at 12:51 PM on August 28, 2014 [8 favorites]

"I'm not sure all our readers have an inherent grasp of what 1-kw laser is. We need to clarify it somehow."

"What if we told them it was equivalent to two hundred thousand laser pointers?"

"You've done it again!"

posted by griphus at 12:52 PM on August 28, 2014 [15 favorites]

"What if we told them it was equivalent to two hundred thousand laser pointers?"

"You've done it again!"

posted by griphus at 12:52 PM on August 28, 2014 [15 favorites]

These scientists, they don't know how good they have it. Some poor buggers don't even have a universe and here they are looking this one in the mouth.

posted by George_Spiggott at 12:53 PM on August 28, 2014 [7 favorites]

posted by George_Spiggott at 12:53 PM on August 28, 2014 [7 favorites]

tags FTW

posted by SmileyChewtrain at 12:55 PM on August 28, 2014 [4 favorites]

posted by SmileyChewtrain at 12:55 PM on August 28, 2014 [4 favorites]

Thanks, scientists.

Thientists.

posted by fifteen schnitzengruben is my limit at 12:58 PM on August 28, 2014 [16 favorites]

Thientists.

posted by fifteen schnitzengruben is my limit at 12:58 PM on August 28, 2014 [16 favorites]

Zero results for "hologram".

Settled.

posted by George_Spiggott at 1:00 PM on August 28, 2014 [4 favorites]

Settled.

posted by George_Spiggott at 1:00 PM on August 28, 2014 [4 favorites]

"Has anybody tried saying, 'Computer, end program?'"

"Dude, that is a holodeck."

posted by ricochet biscuit at 1:01 PM on August 28, 2014 [3 favorites]

"Dude, that is a holodeck."

posted by ricochet biscuit at 1:01 PM on August 28, 2014 [3 favorites]

working on this experiment sounds like a great way to get infinite simulations of yourself tortured for eternity by a malevolent AI

just sayin

posted by threeants at 1:11 PM on August 28, 2014 [35 favorites]

just sayin

posted by threeants at 1:11 PM on August 28, 2014 [35 favorites]

Thanks, Roko!

posted by Revvy at 1:15 PM on August 28, 2014 [2 favorites]

posted by Revvy at 1:15 PM on August 28, 2014 [2 favorites]

ॐ

posted by nikoniko at 1:15 PM on August 28, 2014 [2 favorites]

posted by nikoniko at 1:15 PM on August 28, 2014 [2 favorites]

I've seen a bunch of articles like this, but it's never clear to me what they even mean by a third dimension being an illusion. Assuming pixellation and therefore countability, clearly you can define a bijection between a countable 2D space and a countable 3D space. But if the 3D space seems mathematically natural (e.g. go "right" from {x,y,z} to {x+1, y, z}, "up" from there to {x+1, y+1, z}, and "out" from there to {x+1, y+1, z+1}), which our seemingly 3D space does, then the corresponding 2D space will seem totally weird (e.g. go "right" from {x,y} and find yourself at {j, k} with some potentially very complex relationship between x, y and j, k). In what sense is the 2D space somehow better, then, and in what sense is it more "real"?

posted by Flunkie at 1:27 PM on August 28, 2014 [4 favorites]

posted by Flunkie at 1:27 PM on August 28, 2014 [4 favorites]

If I understand this correctly, the drive to do this experiment this came out of a philosophical paper that stated:

#1. Using virtual reality we should soon be able to create worlds inhabited by billions of people each with their own sense of existence.

#2. Such worlds will be so cheap to make that in the future there will be many of them.

#3. The number of such worlds will outnumber "real" reality.

#4. Somewhere out there, there is already an intelligent life form advanced enough to do this.

#5. Therefore, odds are, we are just a virtual world where the individuals believe in their existence.

#6. If we look hard enough (this experiment), we will see the sky is just a painted ceiling.

#7. ... in case I don't see ya, good afternoon, good evening, and good night.

posted by dances_with_sneetches at 1:32 PM on August 28, 2014 [9 favorites]

#1. Using virtual reality we should soon be able to create worlds inhabited by billions of people each with their own sense of existence.

#2. Such worlds will be so cheap to make that in the future there will be many of them.

#3. The number of such worlds will outnumber "real" reality.

#4. Somewhere out there, there is already an intelligent life form advanced enough to do this.

#5. Therefore, odds are, we are just a virtual world where the individuals believe in their existence.

#6. If we look hard enough (this experiment), we will see the sky is just a painted ceiling.

#7. ... in case I don't see ya, good afternoon, good evening, and good night.

posted by dances_with_sneetches at 1:32 PM on August 28, 2014 [9 favorites]

Well, really I mean the mapping of "right" within the 2D space will be complex in the 3D space. So more like go right from {x, y} to {x+1, y}, but f({x+1,y}) where f is the map from 2D to 3D is not necessarily near f({x,y}).then the corresponding 2D space will seem totally weird (e.g. go "right" from {x,y} and find yourself at {j, k} with some potentially very complex relationship between x, y and j, k).

posted by Flunkie at 1:33 PM on August 28, 2014

If you think you are real, and you act like you're real, and interact with others who also believe in their own reality, you are real, regardless of whether or not you're a hologram in some trans-dimensional horror's super-cellar or a Boltzmann brain or what have you.

posted by Mister_A at 1:34 PM on August 28, 2014 [1 favorite]

posted by Mister_A at 1:34 PM on August 28, 2014 [1 favorite]

Read the article. "Hologram" does not mean "virtual reality".

posted by Legomancer at 1:36 PM on August 28, 2014 [12 favorites]

posted by Legomancer at 1:36 PM on August 28, 2014 [12 favorites]

Well,

posted by Flunkie at 1:42 PM on August 28, 2014 [1 favorite]

*really*really I mean kind of the opposite direction of what I said: If you in your ignorance think you're going "right" from the 3D point {x,y,z} to the 3D point {x+1,y,z}, then really you're going from some 2D point {j,k} to some other 2D point {m,n} (with f({j,k}) = {x,y,z} and f({m,n}) = {x+1,y,z}, f defined as in my previous comment). But in 2D "reality", {j,k} and {m,n} aren't necessarily going to be near each other, and they'll have a pretty complex relationship with each other.posted by Flunkie at 1:42 PM on August 28, 2014 [1 favorite]

I've got root and if anyone says "wibbly-wobbly" I'm flipping a bit and giving them an unsightly boil.

posted by George_Spiggott at 1:43 PM on August 28, 2014 [8 favorites]

posted by George_Spiggott at 1:43 PM on August 28, 2014 [8 favorites]

*That would be Truly Outrageous.*

Truly, Truly, Truly Outrageous?

posted by TheWhiteSkull at 1:46 PM on August 28, 2014 [7 favorites]

*I've got root and if anyone says "wibbly-wobbly" I'm flipping a bit and giving them an unsightly boil.*

Timey-wimey?

**OW!!!!**posted by Thorzdad at 1:48 PM on August 28, 2014 [5 favorites]

PBS has a nice introduction to the ideas behind this experiment. For a more in-depth introduction, I like the lecture

posted by RichardP at 1:49 PM on August 28, 2014 [6 favorites]

*The World as a Hologram*from UC Berkeley's Raphael Bousso.posted by RichardP at 1:49 PM on August 28, 2014 [6 favorites]

I feel like the metaphors being used here—holograms, pixels, "not real"—create more distraction and confusion than they dispel. Anything you can measure is real, practically by definition—even if deviates from our (limited and fallible) intuition about how the universe works.

The analogy of a 2D projection of 3D world seems illuminating, though. When most people hear the word "hologram", they think of the fictional three-dimensional holograms of Star Trek and CNN stunt coverage (which aren't actually holograms—just special effects that people

When, in fact, the "holograms" in question are the more prosaic (but less fictional) 2D holograms—which are physically two-dimensional, but nonetheless contain a description of a three-dimensional object. And

Am I on the right track here?

posted by escape from the potato planet at 1:54 PM on August 28, 2014 [1 favorite]

The analogy of a 2D projection of 3D world seems illuminating, though. When most people hear the word "hologram", they think of the fictional three-dimensional holograms of Star Trek and CNN stunt coverage (which aren't actually holograms—just special effects that people

*call*holograms). So people hear "the universe is a hologram", and think "the universe is, in some sense, illusory, or virtual, or not real—just like Will.I.Am talking to Wolf Blitzer, or Captain Janeway's Irish heartthrob".When, in fact, the "holograms" in question are the more prosaic (but less fictional) 2D holograms—which are physically two-dimensional, but nonetheless contain a description of a three-dimensional object. And

*that's*the point of the hologram analogy—not that the universe is some kind of illusion.Am I on the right track here?

posted by escape from the potato planet at 1:54 PM on August 28, 2014 [1 favorite]

Yeah people are mixing up the "universe is a hologram" popular science articles with the "we may be living in a computer simulation" popular science articles.

posted by anazgnos at 1:59 PM on August 28, 2014 [15 favorites]

posted by anazgnos at 1:59 PM on August 28, 2014 [15 favorites]

This passage from RichardP's first link is illuminating:

Entropy is also a measure of the amount of information it would take to describe a system completely. The entropy of ordinary objects—people, sand buckets, containers of gas—is proportional to their volume. Double the volume of a helium balloon, for instance, and its entropy will increase by a factor of eight. But in the 1970s, Stephen Hawking and Jacob Bekenstein discovered that the entropy of a black hole obeys a different scaling rule. It is proportional not to the black hole’s three-dimensional volume but to its two-dimensional surface area, defined here as the area of the invisible boundary called the event horizon. Therefore, while theposted by twirlip at 2:03 PM on August 28, 2014 [17 favorites]actualentropy of an ordinary object—say, a hamburger—scales with its volume, themaximumentropy that could theoretically be contained in the space occupied by the hamburger depends not on the volume of the hamburger but on the size of its surface area. Physics prevents the entropy of the hamburger from ever exceeding that maximum: If one somehow tried to pack so much entropy into the hamburger that it reached that limit, the hamburger would collapse into a black hole.

The inescapable conclusion is that all the information it takes to describe a three-dimensional object—a black hole, a hamburger, or a whole universe—can be expressed in two dimensions. This suggests to physicists that the deepest description of our universe and its parts—the ultimate theory of physics—must be crafted in two spatial dimensions, not three. ... Theorists were intrigued by the idea thata parallel set of physical laws, operating in fewer dimensions, might be able to fully describe our universe.

twirlip: "

They do this in ads for McDonald's, which show in 2D hamburgers that look to be 3D. But when you get the hamburger, it's in 3D but looks flat as if it were in 2D.

posted by chavenet at 2:15 PM on August 28, 2014 [12 favorites]

*The inescapable conclusion is that all the information it takes to describe a three-dimensional object—a black hole, a hamburger, or a whole universe—can be expressed in two dimensions.*"They do this in ads for McDonald's, which show in 2D hamburgers that look to be 3D. But when you get the hamburger, it's in 3D but looks flat as if it were in 2D.

posted by chavenet at 2:15 PM on August 28, 2014 [12 favorites]

*And that's the point of the hologram analogy—not that the universe is some kind of illusion.*

Well, philosophically, what would it mean to say that the world is some kind of illusion? I think it's beyond argument that the world as most people perceive it bears almost no relation to reality as we can measure it with scientific instruments. The world that most of us live in really is an illusion created by your brain based on sensory input. Our sense of being a unitary being, that we have free will, that objects are solid and have attributes like 'color', that time flows, etc....

posted by empath at 2:18 PM on August 28, 2014 [3 favorites]

I guess what I'm saying is that even if the third dimension were entirely illusory and we were somehow entities smeared across the surface of an event horizon a billion light years away, it would just be one more thing that people understand intellectually while continuing to live our lives as if anything we did mattered to the universe at large.

posted by empath at 2:20 PM on August 28, 2014 [1 favorite]

posted by empath at 2:20 PM on August 28, 2014 [1 favorite]

What If we are a Hologram, and the only thing that's real is Tupac

posted by hellojed at 2:23 PM on August 28, 2014 [7 favorites]

posted by hellojed at 2:23 PM on August 28, 2014 [7 favorites]

*I think it's beyond argument that the world as most people perceive it bears almost no relation to reality as we can measure it with scientific instruments.*

Well, yeah, but that's quite a separate matter from the universe-as-hologram thing, don't you think?

posted by escape from the potato planet at 2:26 PM on August 28, 2014

So... dividing the width of the observable universe into units the size of the planck scale, and putting that total into binary, how many bits are needed to store the resulting number?

That gives us the bit value of each axis of the coordinate space we live in, inside the computers of the gods.

From this we can calculate how much RAM their computers use.

From that, we can feel that our state-of-the-art computers are not as shiny as we thought. Also, I guess we should call them virtual machines.

posted by anonymisc at 2:32 PM on August 28, 2014 [1 favorite]

That gives us the bit value of each axis of the coordinate space we live in, inside the computers of the gods.

From this we can calculate how much RAM their computers use.

From that, we can feel that our state-of-the-art computers are not as shiny as we thought. Also, I guess we should call them virtual machines.

posted by anonymisc at 2:32 PM on August 28, 2014 [1 favorite]

*> #5. Therefore, odds are, we are just a virtual world where the individuals believe in their existence.*

"And that's why I'm not coming in to work today."

posted by The Card Cheat at 2:33 PM on August 28, 2014 [11 favorites]

*Well, yeah, but that's quite a separate matter from the universe-as-hologram thing, don't you think?*

Not really. Since it's a bijection (I think), there's no way to privilege either view of the universe.

Okay, imagine that you have a toy universe with a bunch of points moving in space, according to some basic physical laws. Just bouncing around in a box. You can define all the available information in that space by assigning locations in space and time to each point, and other physical attributes like mass, momentum, etc.

Let's say you've got all of that information in a database with columns for the X,Y and Z position, and X Y and Z momentum, and mass for each point, and a bunch of rules for how you update the table from moment to moment, including gravitational interaction.

What the holographic universe suggests is that you can basically write some kind of script that translates all of that to a new database and set of rules with only a new X and Y coordinate system (which might bear no relation to the original one), and with a new set of rules for updating it, that doesn't include gravity.

Is that one more real than the other? Not necessarily. It's just saying that there is a way to translate back and forth. Both systems are models. Our brain happens to have evolved to model a three dimensional universe internally, so that feels more real to us.

posted by empath at 2:35 PM on August 28, 2014 [1 favorite]

So this spacetime... it vibrates?

posted by dephlogisticated at 3:03 PM on August 28, 2014 [1 favorite]

posted by dephlogisticated at 3:03 PM on August 28, 2014 [1 favorite]

So which is the superflous dimension: length, width or height?

posted by klarck at 3:04 PM on August 28, 2014

posted by klarck at 3:04 PM on August 28, 2014

*"Has anybody tried saying, 'Computer, end program?'"*

"Dude, that is a holod

"Dude, that is a holod

**i**

*ck."*

posted by ryoshu at 3:10 PM on August 28, 2014

It's not that the universe itself is holographic, but rather that our best

It's similar to how you must turn an apple around in your hand in order to understand the entire apple. Those rotations you perform are not inherent in the apple itself, but you require those extra degrees of freedom in order to understand what's on every side of the apple all at once. A theory of everything is no different. We need to be able to "turn the universe around in our hand" in order to understand the universe, so we need some extra degrees of freedom to build the complete picture. How the universe appears to change as you turn it around in your hand tells you a lot about what the complete universe looks like. But those extra "dimensions" you added to perform this calculation aren't any more a part of the universe itself than the rotations are part of an apple. This is the essence of symmetry as it exists in the modern approach to physics.

These extra degrees of freedom are in some sense extraneous to the universe itself, but in another sense absolutely necessary for the small piece of the universe (humanity) trying to understand the bigger picture. So what you get is a bunch of people finding they need N+1 or more dimensions to describe a universe that should, by all accounts, have no more than N dimensions, and suddenly you have the analogy of a holographic existence. We are "inside" the hologram because inside a standard hologram there are 3 dimensions, but "outside" the hologram it's just two. Perhaps if we could stand "outside" the universe, we would see it as somewhat less dimensionful than our best models can tell us. In that sense reality would be a hologram.

That's as best I can tell, anyhow.

posted by grog at 3:13 PM on August 28, 2014 [7 favorites]

*descriptions*of the universe end up being holographic.It's similar to how you must turn an apple around in your hand in order to understand the entire apple. Those rotations you perform are not inherent in the apple itself, but you require those extra degrees of freedom in order to understand what's on every side of the apple all at once. A theory of everything is no different. We need to be able to "turn the universe around in our hand" in order to understand the universe, so we need some extra degrees of freedom to build the complete picture. How the universe appears to change as you turn it around in your hand tells you a lot about what the complete universe looks like. But those extra "dimensions" you added to perform this calculation aren't any more a part of the universe itself than the rotations are part of an apple. This is the essence of symmetry as it exists in the modern approach to physics.

These extra degrees of freedom are in some sense extraneous to the universe itself, but in another sense absolutely necessary for the small piece of the universe (humanity) trying to understand the bigger picture. So what you get is a bunch of people finding they need N+1 or more dimensions to describe a universe that should, by all accounts, have no more than N dimensions, and suddenly you have the analogy of a holographic existence. We are "inside" the hologram because inside a standard hologram there are 3 dimensions, but "outside" the hologram it's just two. Perhaps if we could stand "outside" the universe, we would see it as somewhat less dimensionful than our best models can tell us. In that sense reality would be a hologram.

That's as best I can tell, anyhow.

posted by grog at 3:13 PM on August 28, 2014 [7 favorites]

*So which is the superflous dimension: length, width or height?*

It doesn't work that way. You can draw coordinates an infinite number of ways, besides height, width and length(polar coordinates for example). The question is whether you need two numbers or three to model all the physical laws. You can't have a universe with gravity (that is a universe which is at all like anything we recognize) without three numbers. But you can create an alternative universe with two and no gravity that you can translate our universe into, let it evolve and translate back to get the same results.

posted by empath at 3:31 PM on August 28, 2014

If we're just bits, I want to run Photoshop on a few things.

posted by Brandon Blatcher at 3:43 PM on August 28, 2014 [3 favorites]

posted by Brandon Blatcher at 3:43 PM on August 28, 2014 [3 favorites]

Consider space/time coordinates as a way of describing the relationship that objects have with each other. You can tell how a planet will interact with a star based on it's distance from the star, which is calculated with a function that's based on their coordinates in space. No matter how you define those coordinates, you're going to need three numbers for each of them in order for physical laws

Now imagine that you can create an entirely new set of physical laws that work while requiring only 2 numbers to specify the relationship that objects have from each other. You can't imagine this as a flat section of our universe. You can't imagine it as existing in any way that you'd ordinarily understand reality to exist at all. All of the laws of physics are totally different. There's no gravity, the forces are different, the particles are different, everything is different.

What's special about this particular universe is that there is a way to take 3 dimensional coordinates, translate them into this two dimensional universe and then translate it back without losing any information.

Currently, we don't actually have this universe, or a way to make this translation, btw. We only believe it's possible because the maximum amount of information in a given space is proportional to it's surface area, rather than its volume. If it were proportional to its volume, there would be no way to construct such a universe without losing information.

posted by empath at 3:53 PM on August 28, 2014 [3 favorites]

**as we currently understand them**to work. If you plug our physical laws into a world with only 2 dimensions, they generally fall apart and behave in bizarre ways. If you drop one dimension and then run a simulation and go back to three dimensions, you've lost a ton of information and everything will be wrong.Now imagine that you can create an entirely new set of physical laws that work while requiring only 2 numbers to specify the relationship that objects have from each other. You can't imagine this as a flat section of our universe. You can't imagine it as existing in any way that you'd ordinarily understand reality to exist at all. All of the laws of physics are totally different. There's no gravity, the forces are different, the particles are different, everything is different.

What's special about this particular universe is that there is a way to take 3 dimensional coordinates, translate them into this two dimensional universe and then translate it back without losing any information.

Currently, we don't actually have this universe, or a way to make this translation, btw. We only believe it's possible because the maximum amount of information in a given space is proportional to it's surface area, rather than its volume. If it were proportional to its volume, there would be no way to construct such a universe without losing information.

posted by empath at 3:53 PM on August 28, 2014 [3 favorites]

This hour long video describing the underlying theory in lay terms expounds on what empath and twirlip are talking about.

(Thanks to symboid, from the previous FPP.)

(It looks like I missed RichardP's suggestion above.)

posted by johnnydummkopf at 4:07 PM on August 28, 2014 [1 favorite]

(Thanks to symboid, from the previous FPP.)

(It looks like I missed RichardP's suggestion above.)

posted by johnnydummkopf at 4:07 PM on August 28, 2014 [1 favorite]

Physicsmatt did a really great post on this here:

one of the things Hawking did was demonstrate that the entropy of a black hole is proportional to its surface area (in particular, it's the surface area in units of the squared Planck length over 4). So, this means that the maximum entropy of any volume is set by the surface area of that volume. To see why this is a huge problem, imagine what happens if you double the dimensions of your room (say it's 20 feet by 20 feet by 20, instead of 10 x 10 x 10, for instance), then you increase the volume by a factor of 8, but the surface area goes up by only a factor of 4. This means that even though you have way more volume, and so way more places for quantum fields to fluctuate and particles to be, so you'd EXPECT way more possible ways for them to be arranged (entropy), in fact you get only a little more entropy to play with (i.e., not enough to account for all the states you thought you'd have). As you extend this to bigger and bigger volumes, the problem just gets more severe: you can't have as many quantum states in a volume as you'd expect, and nothing in quantum field theory (or our normal classical intuition) prepares us for this. It's almost as if there's one *fewer* spatial dimensions around than we think there is.posted by Ryvar at 4:36 PM on August 28, 2014 [8 favorites]

This is the holographic principle, and what it essentially means is that everything that CAN occur in any volume can be encoded by physics on the boundary of that volume. So I should be able to tell everything that can happen in a room just by looking at the walls, somehow.

Could someone--such as, oh, i don't know, say, PHYSICSMATT--do me a solid and explain how, if at all, time figures into holography? I guess holography is based on a toy universe of some kind, which maybe doesn't include time; and I guess the basic laws of physics are time-symmetric, so they don't contain any time terms; but then again, as i understand it, the accumulation of entropy, which is at the heart of this whole shemozzle, flows forward in time. So I just wonder if holography includes or addresses anything resembling a time-like dimension.

posted by Zerowensboring at 5:33 PM on August 28, 2014

posted by Zerowensboring at 5:33 PM on August 28, 2014

*So... dividing the width of the observable universe into units the size of the planck scale, and putting that total into binary, how many bits are needed to store the resulting number?*

Using the value of 46 billion light-years as the radius of the universe, that's 2.69 * 10^61 planck lengths. The volume of that sphere is about 8.28 * 10^62 planck lengths. I believe that's about 206 bits.

posted by WaylandSmith at 6:20 PM on August 28, 2014 [2 favorites]

If the entire universe can be expressed in 206 bits, I may have to reconsider my opinion of Twitter.

posted by sfenders at 6:32 PM on August 28, 2014 [4 favorites]

posted by sfenders at 6:32 PM on August 28, 2014 [4 favorites]

That's the number of bits needed (at least in the claim, which I make no judgment about) to describe the number of planck lengths. That's a totally different thing than the number of bits needed to describe the universe. For example if there's one bit of information per planck length, then (according to the claim) you need 8.28 * 10^62 bits, not 206 bits. The fact that you can write the number 8.28 * 10^62 in 206 bits is not relevant to how many bits you'd need to describe the states of 8.28 * 10^62 things.

posted by Flunkie at 6:42 PM on August 28, 2014 [1 favorite]

posted by Flunkie at 6:42 PM on August 28, 2014 [1 favorite]

I think you are calculating wrong. If this is a pixelated world then the stars are not full-sized and as distant as we believe any more than the stars in a Pixar movie is the size of stars. They merely need to be large enough for us to not be able to tell the difference (assuming we are the center of the virtual reality presentation. There does not have to be a core to the earth, at least the programmers don't need to make one until we go there. (They do need this imaginary core to affect other materials according to physical rules)

posted by dances_with_sneetches at 6:50 PM on August 28, 2014

posted by dances_with_sneetches at 6:50 PM on August 28, 2014

So if I knew what was going on fully with the Holographic Principle, I think you guys would have heard about it by now. We have a clear understanding that something is going on in the Universe that requires explanation, and we have examples of theories of physics which are not our Universe that realize the holographic principle. But I can't for example, explain HOW it is possible that all information that we think need 3+1 dimensions can be fit into 2+1.

Zerowensboring's question actually gets at something really interesting about this whole thing: the relation between gravity, time, and entropy. The reasoning that led us to the Holographic Principle came to us via Hawking's (and other's. For example, Bekenstein and Bousso) work on black holes.

The one natural law that I am most convinced can not be violated is the 2nd Law of Thermodynamics: entropy always increases with time. Other than this, all the laws of Nature are reversible. The thing that maybe defines the arrow of time is that the future is the direction with more entropy. Now, luckily for us, gravity increases entropy when objects collapse into each other. So, you start with a near-uniform early Universe and you get clumps built by gravity, which give you galaxies, stars, planets, New York and so forth.

Now, according to what we know from general relativity, if you get enough mass together, it collapses into a black hole, which has an "event horizon," beyond which nothing can escape. (This differs from a Newtonian "black star," which has an escape velocity greater than the speed of light. In a black star, you could in principle climb slowly out, using finite energy to escape. A black hole requires infinite energy to escape from inside the horizon to the outside).

So that seems fine. The problem comes when you remember that entropy always increases. If I build a black hole, in standard quantum mechanics, it has exactly one state (the state of being a black hole with mass M, charge Q and spin S). That means it has zero entropy. Now, if I throw a dictionary into the black hole, the dictionary had entropy, but after it passes the horizon, the black hole appears to again have zero entropy (mass M+mass of dictionary, charge Q, spin S). This violates the 2nd Law.

Now, if we want to assign entropy to black holes, we run into the problem that entropy implies a temperature. And things with temperature radiate as a "black body" (unrelated in terminology to black hole. Which is only going to get more confusing in a moment). But a event horizon is impassible, how can the black hole radiate?

Hawking proved that, in quantum field theory, the vacuum state that observers close to the black hole horizon see is different from the vacuum state infinitely far away. What this means is that an observer "at infinity" sees the horizon as radiating away particles, according to a blackbody spectrum with an entropy set by the black hole horizon area (in units of the fundamental length, the planck length squared), which increases with the black hole mass. The temperature goes inversely with the mass and area. Big black holes are colder. Macroscopic black holes are cold enough that we cannot see the blackbody radiation over the background radiation of the Universe. So while we have no direct experimental evidence yet, Hawking's argument is so compelling we can treat it as true for the purposes of further theoretical work. One day, 100 or 1000 years from now (maybe earlier if I'm lucky to be alive during it), we will measure the blackbody spectrum of a black hole. And that will be a great day. Or we will measure that it isn't there, and that will be a more interesting day.

So, this solves the entropy problem of black holes (other people before Hawking thought along these lines. Hawking provided a mechanism to explain it, if I understand my history correctly). When you throw a dictionary into a black hole, the dictionary entropy "disappears," the mass of the black hole increases and so, as always the entropy of the Universe increases. As black holes radiate away blackbody radiation, the black hole mass decreases, but the decrease of black hole entropy is balanced by the radiation's entropy.

Now, notice something weird: I assumed that black hole entropy must increase more than whatever the entropy of the dictionary I threw in was. That turns out to be something you can prove analytically. The black hole ALWAYS increases in entropy more than any other configuration of mass you can throw into it. If you try to cram enough entropy into a box before you throw it into the black hole to beat this bound, you turn out cramming enough energy into the box that the box collapses into it's own little black hole. The maximum entropy of ANY collection of mass is the entropy of an equivalent-mass black hole.

Now, this is where things get bizarre. The entropy of a black hole is set by the mass. The mass sets the surface area of a black hole (the area of the event horizon). So what I'm saying is that the maximum entropy I can fit into a volume (the volume of the black hole) is bounded by the surface area of the volume. The volume in 3 dimensional space does like the radius of the space cubed. The surface area goes like the radius squared.

This is holography: the information inside a volume (the entropy, loosely defined), is bounded by the surface area, which has lower dimension. And somehow this has to do with horizons, and entropy, and thus time. This is something that standard quantum field theory can't explain: the number of configurations of quantum fields (which will relate to the entropy) should be set by the volume you have available, not the surface area. And how the hell does the surface area know what's going on inside all the time, despite lightspeed lag? Something's wacky.

There are examples of theories where this works. Something called the AdS (anti-de Sitter space)/CFT (conformal field theory) correspondence is an explicit realization where the physics of a 5-dimensional anti-de Sitter space can be mapped to a conformal (scale invariant) field theory on the 4-dimensional surface of the de sitter space. We live in neither AdS space or have perfect CFTs. However, I am sure the string theorists will make progress on this, and the whole thing is amazingly interesting.

So what we suspect is that the Universe can be explained fundamentally with a theory with only 2+1 dimensions, rather than 3+1. We don't understand is how that works out. But the arguments that led us to this unusual conclusion come from a deep relationship between entropy, which in many ways defines the arrow of time, and gravity. Throw in the fact that this is telling us that our quantum field theories go horrifically wrong somewhere around the time you have a black hole (so at the Planck scale), and wow, that's a fascinating problem. I don't know the answer though. Wish I did.

posted by physicsmatt at 7:08 PM on August 28, 2014 [26 favorites]

Zerowensboring's question actually gets at something really interesting about this whole thing: the relation between gravity, time, and entropy. The reasoning that led us to the Holographic Principle came to us via Hawking's (and other's. For example, Bekenstein and Bousso) work on black holes.

The one natural law that I am most convinced can not be violated is the 2nd Law of Thermodynamics: entropy always increases with time. Other than this, all the laws of Nature are reversible. The thing that maybe defines the arrow of time is that the future is the direction with more entropy. Now, luckily for us, gravity increases entropy when objects collapse into each other. So, you start with a near-uniform early Universe and you get clumps built by gravity, which give you galaxies, stars, planets, New York and so forth.

Now, according to what we know from general relativity, if you get enough mass together, it collapses into a black hole, which has an "event horizon," beyond which nothing can escape. (This differs from a Newtonian "black star," which has an escape velocity greater than the speed of light. In a black star, you could in principle climb slowly out, using finite energy to escape. A black hole requires infinite energy to escape from inside the horizon to the outside).

So that seems fine. The problem comes when you remember that entropy always increases. If I build a black hole, in standard quantum mechanics, it has exactly one state (the state of being a black hole with mass M, charge Q and spin S). That means it has zero entropy. Now, if I throw a dictionary into the black hole, the dictionary had entropy, but after it passes the horizon, the black hole appears to again have zero entropy (mass M+mass of dictionary, charge Q, spin S). This violates the 2nd Law.

Now, if we want to assign entropy to black holes, we run into the problem that entropy implies a temperature. And things with temperature radiate as a "black body" (unrelated in terminology to black hole. Which is only going to get more confusing in a moment). But a event horizon is impassible, how can the black hole radiate?

Hawking proved that, in quantum field theory, the vacuum state that observers close to the black hole horizon see is different from the vacuum state infinitely far away. What this means is that an observer "at infinity" sees the horizon as radiating away particles, according to a blackbody spectrum with an entropy set by the black hole horizon area (in units of the fundamental length, the planck length squared), which increases with the black hole mass. The temperature goes inversely with the mass and area. Big black holes are colder. Macroscopic black holes are cold enough that we cannot see the blackbody radiation over the background radiation of the Universe. So while we have no direct experimental evidence yet, Hawking's argument is so compelling we can treat it as true for the purposes of further theoretical work. One day, 100 or 1000 years from now (maybe earlier if I'm lucky to be alive during it), we will measure the blackbody spectrum of a black hole. And that will be a great day. Or we will measure that it isn't there, and that will be a more interesting day.

So, this solves the entropy problem of black holes (other people before Hawking thought along these lines. Hawking provided a mechanism to explain it, if I understand my history correctly). When you throw a dictionary into a black hole, the dictionary entropy "disappears," the mass of the black hole increases and so, as always the entropy of the Universe increases. As black holes radiate away blackbody radiation, the black hole mass decreases, but the decrease of black hole entropy is balanced by the radiation's entropy.

Now, notice something weird: I assumed that black hole entropy must increase more than whatever the entropy of the dictionary I threw in was. That turns out to be something you can prove analytically. The black hole ALWAYS increases in entropy more than any other configuration of mass you can throw into it. If you try to cram enough entropy into a box before you throw it into the black hole to beat this bound, you turn out cramming enough energy into the box that the box collapses into it's own little black hole. The maximum entropy of ANY collection of mass is the entropy of an equivalent-mass black hole.

Now, this is where things get bizarre. The entropy of a black hole is set by the mass. The mass sets the surface area of a black hole (the area of the event horizon). So what I'm saying is that the maximum entropy I can fit into a volume (the volume of the black hole) is bounded by the surface area of the volume. The volume in 3 dimensional space does like the radius of the space cubed. The surface area goes like the radius squared.

This is holography: the information inside a volume (the entropy, loosely defined), is bounded by the surface area, which has lower dimension. And somehow this has to do with horizons, and entropy, and thus time. This is something that standard quantum field theory can't explain: the number of configurations of quantum fields (which will relate to the entropy) should be set by the volume you have available, not the surface area. And how the hell does the surface area know what's going on inside all the time, despite lightspeed lag? Something's wacky.

There are examples of theories where this works. Something called the AdS (anti-de Sitter space)/CFT (conformal field theory) correspondence is an explicit realization where the physics of a 5-dimensional anti-de Sitter space can be mapped to a conformal (scale invariant) field theory on the 4-dimensional surface of the de sitter space. We live in neither AdS space or have perfect CFTs. However, I am sure the string theorists will make progress on this, and the whole thing is amazingly interesting.

So what we suspect is that the Universe can be explained fundamentally with a theory with only 2+1 dimensions, rather than 3+1. We don't understand is how that works out. But the arguments that led us to this unusual conclusion come from a deep relationship between entropy, which in many ways defines the arrow of time, and gravity. Throw in the fact that this is telling us that our quantum field theories go horrifically wrong somewhere around the time you have a black hole (so at the Planck scale), and wow, that's a fascinating problem. I don't know the answer though. Wish I did.

posted by physicsmatt at 7:08 PM on August 28, 2014 [26 favorites]

So much question! Such interesting!

If the singularity in a black hole is, as relativity (i think) says, the end of spacetime, this should imply high, if not infinite, entropy. So how then does that square with the fact that black holes have low entropy?

Is it going to prove useful to you physicists to think of gravity as entropy in another guise?

Mock theta functions?

In AdS/CFT theories, is one of those five dimensions time-like? Or is that even a meaningful question?

And if light is only time thinking about itself, what is gravity thinking of?

posted by Zerowensboring at 8:08 PM on August 28, 2014

If the singularity in a black hole is, as relativity (i think) says, the end of spacetime, this should imply high, if not infinite, entropy. So how then does that square with the fact that black holes have low entropy?

Is it going to prove useful to you physicists to think of gravity as entropy in another guise?

Mock theta functions?

In AdS/CFT theories, is one of those five dimensions time-like? Or is that even a meaningful question?

And if light is only time thinking about itself, what is gravity thinking of?

posted by Zerowensboring at 8:08 PM on August 28, 2014

Black holes don't have low entropy. They have the most entropy possible in a given volume.

posted by empath at 8:16 PM on August 28, 2014 [1 favorite]

posted by empath at 8:16 PM on August 28, 2014 [1 favorite]

But i thought they could be described only in terms of mass, spin and charge, which, as Physicsmatt said above, implies zero entropy. is that not right?

posted by Zerowensboring at 8:25 PM on August 28, 2014

posted by Zerowensboring at 8:25 PM on August 28, 2014

A black hole in our understanding of quantum field theory has zero entropy. I don't know why you think the singularity would have infinite entropy, I suspect it is that a singularity is where space-time curvature hits infinity, so you're extrapolating that all properties must infinite there. This is probably not correct. Also, notice that this is a discussion of horizons, not the singularity. Nothing here requires that a singularity actually form. The same thing happens with Unruh radiation seen by accelerating observers, and no singularity exists there.

Entropy counts the number of ways we can describe a particular configuration without changing the macroscopic properties of the configuration. As far as we know, in the theories we understand well, there's only one way to describe a black hole of given mass, spin, and charge (and presumably the same one way would describe the singularity, but I don't need to worry about it in this argument). The point is that real black holes don't have zero entropy, they have enormous entropy, the largest possible per volume actually. This forces us to conclude that our QFT description is wrong, and somehow the true theory will have multiple descriptions of a configuration we can call the black hole (or any space-time horizon). So we know there are these problems, but not a clear solution.

I understand there are some possibilities in string theory to describe what exactly those multiple configurations of fields and strings are, but this is not my area of research, so I can't speak to them.

posted by physicsmatt at 8:34 PM on August 28, 2014 [3 favorites]

Entropy counts the number of ways we can describe a particular configuration without changing the macroscopic properties of the configuration. As far as we know, in the theories we understand well, there's only one way to describe a black hole of given mass, spin, and charge (and presumably the same one way would describe the singularity, but I don't need to worry about it in this argument). The point is that real black holes don't have zero entropy, they have enormous entropy, the largest possible per volume actually. This forces us to conclude that our QFT description is wrong, and somehow the true theory will have multiple descriptions of a configuration we can call the black hole (or any space-time horizon). So we know there are these problems, but not a clear solution.

I understand there are some possibilities in string theory to describe what exactly those multiple configurations of fields and strings are, but this is not my area of research, so I can't speak to them.

posted by physicsmatt at 8:34 PM on August 28, 2014 [3 favorites]

*But i thought they could be described only in terms of mass, spin and charge, which, as Physicsmatt said above, implies zero entropy. is that not right?*

This is known as the No-hair theorem btw. Otherwise, what physicsmatt said.

Black hole entropy being maximal instead of minimal isn't the only place where current physical theories give obviously wrong answers - there's the "worst discrepancy in physics" - the fact that QFT theories predict a value for the cosmological constant about 10

^{120}times larger than the observed value. I can't think of any other predicted values that are similarly outrageous though: are there any you know of physicsmatt?

posted by pharm at 9:48 AM on August 29, 2014 [1 favorite]

If the information content of a black hole is maximal, and is determined by the surface area, doesn't that imply that the surface area of a black hole of given mass must be constant? So if you start it spinning, it will take the form of an ellipsoid with constant surface area, not constant volume?

posted by Joe in Australia at 2:32 AM on September 1, 2014

posted by Joe in Australia at 2:32 AM on September 1, 2014

Black holes are described by one of the following metric solutions: Schwarzschild (uncharged, unrotating solution), Kerr (uncharged, rotatating), Reissner-Norström (charged, unrotating), or Kerr-Newman (most general: charged and rotating). In all cases, the event horizon, the point of no return, describes a sphere, not a oblate spheroid. Equality relationships must be satisfied which basically require a charged, spinning black hole to have "more" mass than charge and spin (with appropriate Planck factors to make these quantities have the same dimension and thus be comparable). Violating the equalities formally leaves you with a naked singularity, and various theories predict that such black holes which are more than "extremal" cannot actually exist.

Inside the event horizon, the world-line of any object points "in." That is, as you fall in towards the black hole, the radial spatial dimension and the time dimension start becoming intermixed, and after the event horizon, what you as an infalling observer call "the future," someone outside the black hole would call "towards the center." (though the outside watcher cannot actually see you anymore). There is no future in which you do not move towards the center of the black hole, where formally our equations require a singularity.

For rotating black holes, there is a surface that describes an oblate spheroid, but it is not the event horizon (and horizons are what the holographic principle cares about). This surface is the ergosphere: it is wider than the event horizon along the equator of the black hole, and grazes the event horizon at the poles. Inside the ergosphere, an effect called frame dragging has taken hold. Just as with "future" and "inward" inside the event horizon, inside the ergosphere, the future is in the direction of "spinward." There is no future in which you are not rotating in the direction of the the black hole's spin. Between the ergosphere edge and the event horizon, it would take infinite energy to stay stationary with respect to the "fixed stars" at infinity. You can escape from the ergosphere with finite energy though, unlike trying to escape the event horizon.

In fact there are ways in which you can "mine" the black hole for energy by throwing particles into the ergosphere, letting them gain energy and then pulling them back out. This is called a Penrose process, and it is possible that such black hole energy mining in Nature is or was fueling some of the very energetic processes we see in the Universe, such as quasars and gamma ray bursts. However, while quasars are now considered to be related the accretion disks of massive black holes, I think it is still not settled whether the relativistic jets emitted from the disks are fed by Penrose processes or not.

posted by physicsmatt at 5:39 AM on September 1, 2014 [2 favorites]

Inside the event horizon, the world-line of any object points "in." That is, as you fall in towards the black hole, the radial spatial dimension and the time dimension start becoming intermixed, and after the event horizon, what you as an infalling observer call "the future," someone outside the black hole would call "towards the center." (though the outside watcher cannot actually see you anymore). There is no future in which you do not move towards the center of the black hole, where formally our equations require a singularity.

For rotating black holes, there is a surface that describes an oblate spheroid, but it is not the event horizon (and horizons are what the holographic principle cares about). This surface is the ergosphere: it is wider than the event horizon along the equator of the black hole, and grazes the event horizon at the poles. Inside the ergosphere, an effect called frame dragging has taken hold. Just as with "future" and "inward" inside the event horizon, inside the ergosphere, the future is in the direction of "spinward." There is no future in which you are not rotating in the direction of the the black hole's spin. Between the ergosphere edge and the event horizon, it would take infinite energy to stay stationary with respect to the "fixed stars" at infinity. You can escape from the ergosphere with finite energy though, unlike trying to escape the event horizon.

In fact there are ways in which you can "mine" the black hole for energy by throwing particles into the ergosphere, letting them gain energy and then pulling them back out. This is called a Penrose process, and it is possible that such black hole energy mining in Nature is or was fueling some of the very energetic processes we see in the Universe, such as quasars and gamma ray bursts. However, while quasars are now considered to be related the accretion disks of massive black holes, I think it is still not settled whether the relativistic jets emitted from the disks are fed by Penrose processes or not.

posted by physicsmatt at 5:39 AM on September 1, 2014 [2 favorites]

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> “If we see something, it will completely change ideas about space we’ve used for thousands of years.”That would be Truly Outrageous.

posted by The Card Cheat at 12:33 PM on August 28, 2014 [21 favorites]