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0:00
(upbeat intro music)
0:30
(audience applauding)
0:38
- Thanks, Tim. Thanks everyone. Thanks to the University of Michigan. I'll apologize ahead of time. They had me doing a lot of talking yesterday and my voice, not quite up to it. So I'm hoping that you'll be able to hear me during this talk today because we have some fascinating things to talk about. Quantum mechanics is this weird position in physics today. It's our most successful theory of physics of all time. It is the way the universe works as far as we know currently.
1:08
Of course, we might find out something better tomorrow, but right now the best theory we have, you can't understand the universe without quantum mechanics. At the same time, physicists don't know what quantum mechanics says, which is strange, right? I mean there might be individual physicists who know what it says. I know what it says, but not everyone agrees with me. This is very frustrating. I did write an op-ed for the New York Times a few years ago, complaining about the fact that physicists
1:40
don't understand quantum mechanics, and I was pleasantly surprised that only one of my colleagues emailed me to say, I understand quantum mechanics, what are you talking about? But I do think that we can understand quantum mechanics and that's the crucial thing. It's not that it's some ineffable mystery that we can't reach. We just have to be open to truly changing our view, our picture of how reality works. It's a radically different picture than what we had before quantum mechanics came along
2:08
and I want to push some of those implications front and center here. So, here's how radical it is. When you look around in the universe, there's a natural way to describe what you see, namely as stuff arranged in space. So we have space, it's three dimensional, right? We have stuff, we have tables, we have floors. Here's a photograph of a subset of the universe. Stuff arranged in space, in this case, is a chair in a room, right? And even that idea that what the universe is fundamentally
2:45
is stuff arranged in space is not true according to quantum mechanics. It's what you see, it's what you think there is, but it's not what is actually going on. The reason why quantum mechanics is hard is because it posits that what we see is not what there is. Reality is much, much richer than that. One way of thinking about it, as we'll see, is that reality, the whole thing is a superposition, an additive combination of many different versions of stuff arranged in space.
3:18
So we have access to just this infinitesimal sliver of all of reality. This rubs us the wrong way and we go into denial about it. And that's why it's very hard to accept what quantum mechanics says. So what I'm gonna suggest, arguing after many other people proceeding me, is that reality can be divided up into individual worlds, each one of which looks like stuff arranged in space. And the simple posit, I will argue, makes sense of the mysteries of quantum mechanics. But to get there,
3:50
I have to convince you that we should think about quantum mechanics in the first place. Let's do a little history. Physicists are terrible at doing history, by the way, because we forget all the messy parts and the mistakes, and we pretend that it's a beautiful sequence of brilliant deductions and that's what we're gonna do today. Brilliant deductions. You know, if you were in the early 20th century, it was a very exciting time to be a physicist. We were putting together this picture
4:16
of the world made of atoms. In the 19th century, chemists, we have to give them credit, they acknowledged the existence of atoms before physicists did, but they also made a mistake. They thought they were indivisible and the physicists instantly started dividing them. So by the early 20th century, we knew that an atom was a nucleus, a heavy, positively charged thing. Now we know it's made of protons and neutrons. And then electrons orbiting around the nucleus.
4:44
So a picture like this is what you'll very often see. It's the symbol of the atomic energy commission that we used to have in the United States and so forth. It's the icon of physics. It's also clearly wrong. This can't be what atoms are like. We knew that almost the moment that this idea, the Rutherford atom, named after Ernest Rutherford, almost the moment it was proposed, we knew it couldn't work. Because think about all the light that we have in this room. Where does this light come from?
5:14
Maxwell, James Clark Maxwell, in the 18th century, in the 1800s, explained that light is an electromagnetic wave. We have an electrical field, a magnetic field waving in empty space that those waves move at the speed of light. That's what we see as light. So if you take a charged particle like an electron, it has an electrical field pointing at it, and you move it, the field adjusts and the adjustments ripple out at the speed of light. And that is light, that is radiation.
5:45
If you had an atom like this, like a little solar system looking thing, those electrons orbiting the atom would be moving and therefore sending out electromagnetic waves and therefore losing energy and therefore spiraling in to the center of the nucleus. You can calculate this. It's kind of fun. If you're a beginning physics student, you can say, how long should it take for an electron orbiting a nucleus to just spiral into the middle? The answer is about a hundredth of a billionth of a second.
6:20
This is an experiment. Don't accuse me of not doing any experiments here, Saturday Morning Physics, let's do that experiment. There. We did it. It didn't happen.
6:30
Our atoms did not collapse. Okay? We would've noticed if this were true.
6:36
So we have on the one hand, an attractive picture. On the other hand, it doesn't work. So there's some fundamental problem and there were various steps towards solving the problem. The solution that eventually worked was sneakily radical. When physicists do come up with radical new pictures of the world, they creep up on them. They don't just say, it's not like some genius comes out of the cave and says, aha, a new paradigm for understanding reality. It's step by step.
7:04
So the step that worked in this case is to say that electrons are not particles.
7:10
They're waves. They have a profile. Rather than being a point with a location, there is a function over all of space that has a profile that can look like these different shapes. Again, if you are a chemist or you take chemistry, you've seen these shapes. These are the orbitals that electrons can fall into in atoms. And the thing is that there are only a finite number of shapes, or at least a countable number of shapes that you can write down.
7:39
All of these shapes are associated with different energies and there is a minimum energy shape. It's the one in the top left, right there. What is the chance this is gonna work, right there, minimum energy that an electron can have. And it's not sitting on top of the nucleus. It's spread out. So this answers why matter is stable. Matter is stable because electrons are not little points orbiting like planets in the solar system. There are waves that have certain shapes they can fall into.
8:08
Good. Huge progress. It was pretty radical to say that electrons are waves, not particles, but the stability of matter is an important consideration. Even better, we can invent an equation that these waves solve. Do not be alarmed. There will not be homework at the end of the lecture. You do not have to solve the equation, unless you're a physics student, in which case solving this equation is like half of the time you spend in the world. This is the famous Schrödinger equation,
8:39
the Greek letter capital Psi is what we now call the wave function. This is the most boring name in the world for the most important thing in the world. That little electron has a wave function. It's just a number at each little point in space, technically a complex number, but that's not really relevant. Schrödinger writes down this equation. Again, you don't need to know the details, but the spirit of it is, on the left hand side, you ask how much energy is in the wave function,
9:10
on the right hand side you have how rapidly is the wave function changing. So Schrödinger's equation is basically a quantification of the idea that the more energy the electron has, the faster its wave function is changing. Good. Physicists love this. There's an equation we can solve. We can write down homework problems for our students. It's paradise for physics. All you have to do is believe that electrons are waves, not particles. There's one little problem with this picture,
9:41
that when you look at the electrons, you don't see waves, you see particles. This is literally a little video of a radioactive substance in a cloud chamber giving off particles of radioactivity. And what you see are not big, puffy clouds. You see trajectories, little lines, as if what is escaping in the radioactive decay is a particle with a location moving away from the substance.
10:13
So, that's a puzzle. And that's a real puzzle, now. Now we're stuck with something. We had simple puzzles before. This is a deep one. It's almost as if,
10:22
in order to explain both what we see and the stability of matter, we have to say that electrons behave like waves when we're not looking at them. When we're not measuring them, we describe them as waves. There's a function, there's an equation, all good. When we measure them, suddenly they look like particles. Of course, this is crazy talk, right? How in the world could the fundamental nature of reality care about whether you and I as human beings are looking at it or not?
10:52
We like to think as physicists that reality exists outside of our observation and measurement. So, this is a puzzle. We assembled the world's greatest minds at this wonderful conference in 1927. The fifth Solvay Conference. Literally probably never a higher concentration of super smart people has ever been assembled. You have Einstein, there's Marie Curie, there's Lorentz, there's Dirac, there's Heisenberg, and Niels Bohr, and Pauli and all these great people.
11:23
And they were tasked with the job of reconciling. Why is it that it seems like electrons behave like waves when you're not looking and particles when you are? So they thought about it, they had a few fine Belgian ales, it was held in Brussels, and they came out and said, all right, we've got it figured out. Here's the answer. The answer is that electrons behave like waves when we're not looking at them and they behave like particles when we are.
11:54
And this is what we teach our students today. And if the student raises their hand and says, well, what do you mean by look at or measure or observe? I don't understand why nature should care about that. They're told to leave the physics department.
12:07
So what we teach our students is a recipe, not an understanding, not something that makes perfect sense, but something that fits the data exquisitely well. Which is to say when you're not looking at an electron or anything else in the universe, it is described by a wave function. So here's the function Psi, a function of X and Y position in space. But then when you measure it, it collapses. So the way function changes suddenly to be localized at a point.
12:37
And one of the things that rubs you the wrong way about this is you can't say where it will collapse. You can say the probability that it will collapse to different positions. But the fundamental rule that we teach our students is it randomly collapses, more likely to collapse where the wave function was big than where it was small. But there's a chance of it collapsing any of those places. So when we teach quantum mechanics, unlike any other theory of physics,
13:06
we need to teach two sets of rules. And I swear I'm not making this up, I'm just being honest about it. There's one set of rules for how nature behaves when you're not looking at it and another set for when you are. When you're not looking at it, Systems are described by wave functions. They always obey the Schrödinger equation. As soon as you measure something, as soon as you look at it, the wave function collapses and there's a probability that depends on the value of the wave function.
13:35
In fact, the probability is the wave function squared.
13:39
This is not like classical mechanics. It's not like, my friend always looks so good, but when I try to take a picture of her she doesn't look as good because I'm measuring her and changing her state, that's not what it is. This is a fundamental thing about reality. In classical mechanics, you could in principle measure things very carefully and get exactly their values. There's no barrier between you and the truth of reality. But in quantum mechanics, there apparently is.
14:08
So this is called the Copenhagen, or the textbook interpretation. It is what we teach our students honestly. And you're not encouraged to question what is really going on. That's too bad, because this is clearly nutso.
14:26
I mean it's not that it doesn't work, but if you're trying to claim that what we're interested in is a fundamental theory of reality, it's not that this is wrong, it's just it's not even defined. It's not even well posed. It's clearly unacceptable as a fundamental theory of reality because we haven't said what it means, really. So we can put our fingers on two problems. One is called the measurement problem. This is pretty obvious. What do you mean measure? When does a measurement happen?
14:58
When exactly does it need to be a conscious creature? Can I measure things when I'm asleep? Can a robot measure things? Can a cat? Can a single photon measure things? Why does it happen randomly? Is consciousness somehow involved? People talked about all these things and sometimes they still do. So, this is the fundamental issue. It's not that the theory is wrong, it's that it's just too vague. It's not a theory. We have to do better. The other problem, more subtle,
15:29
but lurking beneath all these discussions, is the reality problem. I told you we should think of the electron as a wave function. What is a wave function? Is that what the world is? Or is it just the tool that we use to predict the probability of measurement outcomes? Is it all the world? Or are there things in addition to the wave function?
15:54
Is somehow reality not described by wave functions at all, but not described at all when we're not looking at it, but reality is just built up by a series of measurement outcomes? And again, there are working, very smart physicists, who believe all of these options, I'm not making them up. We don't have agreement on it. This is very embarrassing, I think, that we don't, it's not embarrassing that we don't know the answer because all of physics is about not knowing the answers.
16:21
Not knowing the answers is fine. What's embarrassing is that we're not trying to know the answer. You might think given these fundamental mysteries at the heart of our most important physical theory, that the professors who spend their time working on this problem would be academic superstars. They would be the ones that the biggest universities threw giant salaries at trying to attract them and give 'em all the prizes and whatever. That is not what it is.
16:52
What it is is you're fired if you work on this, or at least you're not hired. Let's put it that way. It amounts to the same thing. We have decided to go on using quantum mechanics without understanding it until today.
17:08
So let me give you a hint as to how I'm gonna propose to solve this reality problem. There's a famous experiment in quantum mechanics, the double slit experiment. This was a experiment first in classical mechanics trying to decide whether light was a wave or a particle. You send light through two slits. You see it interferes with itself. This is evidence that light is a wave. What it means is that there is something going up and down, waving, and as it goes through the two slits,
17:37
it can either constructively interfere if it's going up at the same place from both slits, or destructively interfere, if it's going in opposite directions. So what you observe at some detector screen on the other side is this pattern of fringes, interference fringes. Now if instead of something very obviously wavelike, like light or water waves or something like that, send a single electron through the two slits, you just get a dot on the screen
18:08
'cause you measure it and it looks like a particle when you measure it, right? Those are the rules. But now you do this over and over again, you keep doing it, keep sending electrons individually through, and they build up to form an interference pattern. So even though each individual measurement looks like a particle, when it's going through the slits, that doesn't count as a measurement. Don't ask me why. I mean you can ask me why, 'cause I know why, but you're not supposed to ask why.
18:34
Does not count as a measurement until it hits the screen and then it's done interfering with itself. And you see this pattern of waves, interference fringes.
18:43
This is evidence that you should take the wave function as something real because it's interfering with itself. It's not like a probability distribution. It's not like the electron is somewhere. The electron goes through either the top slit or the bottom slit. We just don't know which one. If that were the case, then it couldn't interfere with itself. It would either go through the top or the bottom, but it goes through both. It's a wave that goes through both slits.
19:11
That gives you very strong evidence that the electron's wave function is a real thing. We should take it seriously as what nature is doing. But that leads to a puzzle that was pointed out by Professor Einstein. Einstein gets a bad rap when it comes to quantum mechanics. He gets this story told that he got kind of too old. He didn't grasp all the newfangled craziness.
19:36
At the time of the Solvay Conference, Einstein was 10 years younger than I am now. So I resist believing that he was too old to grasp this stuff. And in fact, he understood quantum mechanics as well as anyone. He just didn't think we were done. He was not happy with the existence of these puzzles that we're talking about. So here's one of the thought experiments he put forward in a famous paper, the EPR paper, Einstein, Podolsky and Rosen. He says, consider, this is not exactly what he said,
20:07
but it's pretty close. Take a particle, it has a wave function, but let's just imagine that it's pretty localized so we know where it is, but it's an unstable particle. Maybe it's a nucleus that's going to decay. What does quantum mechanics say? Quantum mechanic says it's going, to the Schrödinger equation in particular, says the wave function will decay into the wave function of two particles. So it's more or less spherically symmetric, honestly.
20:33
So you have basically, this is a little bit hand wavy, but you get the idea, a green particle number one, a red particle number two, maybe the red particle's a little bit heavier so it's moving more slowly. But both particles get emitted. They have wave functions. That's why they're all smeared out over this sphere. But then we detect them, we look for them. Quantum mechanic says you can't say what direction you're gonna detect the particle moving in. But let's say we measure particle one
21:03
and we find that it's moving in this direction, okay?
21:06
There is something called conservation of momentum. So if you just detected particle one moving in that direction, since the initial particle had zero momentum, it wasn't moving at all, you know the other particle has to be moving in the opposite direction.
21:24
So even though both particles were uncertain as to where you would ever see them, when you observe one, you instantly know what the measurement outcome is going to be for the other one.
21:38
And that's true, no matter what observational outcome you have, that particle one is moving that way, particle two would definitely be moving that way. This is true even if you let them go for a light year before you did the measurement, no matter how many things you do. So somehow this is what Einstein called spooky action at a distance. How does particle two know that we detected particle one?
22:06
Let's not worry about that. Let's just get down to the implications here. The implication of the EPR thought experiment is this idea called entanglement. In classical mechanics, if I have two objects, the earth and the moon, I can tell you the state of the earth and the state of the moon. Here's the earth, here's the location, here's where it's moving, here's the moon, here's its location, here's where it's moving. They're separate, they're distinguishable things. Two different systems.
22:32
You might think that in quantum mechanics, if I have two different particles, I have a wave function for particle one, a wave function for particle two, like it says here. No, that wouldn't work. If that were the case, you would separately predict the probability of where you would observe the particle going. But that's not how it is. There's a relationship, there's a correlation between your measurement outcome for one or the other. The way to make that work is to say
23:01
there is only one wave function for the two particle system. Unlike classical mechanics, where you can separate out the two particles, there's one quantum mechanical state describing both particles at once.
23:16
So the wave function that you square to get a probability is not separately the probability of particle one and then the probability of particle two. It's the combined probability of both particles being seen at two different locations. And there's nothing special here about two particles. This would work with three or four or all the particles in the universe. So this is completely standard. Everyone accepts this. In quantum mechanics,
23:42
there is something called the wave function of the universe. One wave function that says, for every possible configuration of stuff in the universe, I'm gonna give you a number, and I square that number to get the probability of seeing the universe in that particular configuration. So we can think of the wave function not as a wave, really. It's not like there's at every location in space, some value of the wave function of the electron. The wave function is something much more profound
24:13
and deep than that. It is a superposition of all possible ways that the entire universe can be arranged. It's an assignment of a number to every possible configuration of stuff. Here's a chair in space, there's another way you could arrange that stuff. You could move the chair somewhere else in space. The wave function of the universe assigns a number to every possible configuration and gives you the probability that that's the configuration you are in.
24:46
So just taking straightforwardly what quantum mechanics is trying to tell us, and here is where physicists' nerve clearly fail 'cause they don't quite wanna do this, but if you just take what the equations are telling you at straight value, reality is not chairs and things like that arranged in space. It is a superposition, a combination of all the possible ways that that could happen. Each configuration contributes to reality as a whole.
25:17
Nobody said this in the 1920s or 1930s. The sort of psychological breakthrough came in the 1950s. Hugh Everett was a graduate student at the time, and what he said was, you're working too hard. You're so attached to your observations and the reality of what you see that you're not really internalizing what quantum mechanics is trying to tell you. Let's just try the simplest, most straightforward thing we can try. Every version of quantum mechanics needs wave functions. They seem to be real.
25:59
Let's just imagine they're real. That's what reality is. It's a wave function. And this collapse business, this "I measure something and I make it collapse," just forget about that. Just get rid of that. We have the Schrödinger equation. It tells us how things evolve. Let's just take it seriously, not only for the electron, but also for the observer doing the experiment.
26:23
And Everett's, in some sense, his entire contribution was to say, and that's okay. We can live in that simple world. So what we teach our students is there's two sets of rules for quantum mechanics. What Everett said is, no, there's only one set of rules. Forget about all this measurement stuff. Just say systems have wave functions. They obey the Schrödinger equation. This is the Everett interpretation of quantum mechanics. It's not an interpretation in the sense
26:52
of literary criticism or something like that. It's a theory. This is a well posed physical theory. Unlike the Copenhagen interpretation, where words like measurement appear but are never defined, here all the words that appear are perfectly well-defined.
27:09
Why isn't this obviously true? Why do people not immediately say this is right? And the answer can be explained using the thought experiment stylings of Erwin Schrödinger.
27:20
The famous Schrödinger cat experiment, which you've probably heard about before, many of you have, in the original version of the experiment, Schrödinger invents this crazy Rube Goldberg machine that tries to put a cat, a macroscopic object, not just a little electron, into a quantum superposition. And he tells the story in such a way, that superposition is of the cat is alive and the cat is dead. As a cat person, I object to this.
27:49
As Schrödinger's daughter once said, I think my father just didn't like cats.
27:54
So what I do is I put the cat into a superposition of awake and asleep, which many cats you might think already are. But the idea is you have a little radioactive source. So the Schrödinger equation tells you the radioactive source evolves to be in a superposition of, I have decayed and I have not decayed. So there's a Geiger counter, a detector that clicks if the source decayed. So the Geiger counter is now in a superposition of, I've clicked and I have not clicked.
28:25
If it clicks, it opens this box of gas, sleeping gas, and it puts the cat asleep. If it doesn't, the cat remains awake. So the cat is now in a superposition of awake and asleep. Okay? And the point that Schrödinger is trying to make is not like, wow, look how cool quantum mechanics is. He was on Einstein's side in being skeptical that we truly understood what quantum mechanics was saying. So his point was, surely you don't believe this.
28:55
And I wanna emphasize the difference between the classical story and the quantum story. The classical story would be, okay, there's a cat in the box, maybe it's awake, maybe it's asleep. We don't know. There's some uncertainty due to our lack of perfect knowledge. Quantum mechanics is saying something profoundly different. In the box, the cat is in a superposition of awake and asleep. It's a different kind of thing. So to bring it home, I'm gonna use square brackets for classical ideas
29:25
and parentheses for quantum ideas. So, what I'm trying to do is to tell you why Everett's simple interpretation is not obviously true. It is true, but not obviously true,
29:39
because we never feel like we ourselves are in a superposition. So Niels Bohr and his friends who helped invent the Copenhagen interpretation of quantum mechanics insisted that they never felt quantum mechanical. They never went through life as if they were in a superposition of different states. So they said you must treat the observer as classical. So their explanation of the Schrödinger cat thought experiment has a classical observer, here played by Niels Bohr, quantum mechanical cat,
30:15
and the story is the observer opens the box, observes the cat, the wave function collapses, and now either the cat's awake and the observer saw it awake or the cat's asleep and the observer saw it asleep. That's the Copenhagen story.
30:31
Everett says, you're not that special. You're made of atoms. Atoms obey the rules of quantum mechanics, therefore you obey the rules of quantum mechanics. Therefore I should put parentheses around you and treat you, the observer, as if you have a wave function. What is gonna happen to you? Solve the Schrödinger equation. That's all you have to do. And happily, in this case, it's actually pretty easy to do that. The measurement is just a particular physical interaction.
31:03
There's nothing weird or special about measurements. But what happens, and this is unambiguously true as a prediction of the Schrödinger equation, is that the combined system, remember there's only one wave function for the whole universe, so the combined cat plus observer system evolves into an entangled superposition,
31:24
part of which says the cat's awake and the observer saw it awake, part of it says the cat's asleep and the observer saw it asleep. But they're both there.
31:35
The puzzle is, Niels Bohr would come along and say, this says I'm in a superposition of seeing the cat awake and seeing the cat asleep. And that has never happened to me. This is empirically wrong. When I measure things, I always feel like I've perceived a definite measurement outcome. How is this compatible with what's going on here? And Everett's answer is, you have misidentified yourself in the wave function. And to make this clear, let's be even a little bit more honest
32:06
because remember I said there's only one wave function for the entire universe, but then I showed you a wave function that has a cat and an observer, what happens to the rest of the universe? What about that? We should include that too. And so we can. We put it in, we call it the environment. It is represented by a picture of leaves of grass. But this literally means everything else in the whole universe, okay? So in this room, if I were to do an experiment on the table,
32:33
the environment would be all the air molecules in the room, all the photons of light in the room, all the things you don't explicitly keep track of. Classically, you wouldn't have to keep track of them, they would just bounce off harmlessly, not make a big difference. But quantum mechanically is a different story. And this is the more modern way of thinking about these things by an idea called decoherence. Because think about that cat in the box in a superposition of awake and asleep.
33:04
There's air in the box, there's light in the box. These parts of the environment are going to interact with the cat long before we open the box. So the environment becomes entangled with the cat. The light particles and the atoms in the box will interact with the cat differently depending on whether the cat is awake or asleep, because it's literally in a different position in the box. And so that entanglement is really when the wave function evolves at a superposition of two different things
33:42
and then the measurement just goes along for the ride. You open the box and you become entangled with the cat as well. So what we're left with is this final state of the universe. There's one term that says cats awake, environment saw the cat awake, observer saw the cat awake, plus a whole nother way of thinking about reality. Cat's asleep, environment saw the cat asleep, observer saw the cat asleep.
34:10
And because of this decoherence effect where the environment is different in these two things, these two parts of the wave function will never influence each other ever again.
34:22
Remember in the double slit experiment, the electron could go through either slit and then interfere with itself, but it interferes with itself because it's exactly the same electron doing exactly the same thing. This part of the wave function can never interfere with this part because these environments have gone their separate ways. They're completely perpendicular to each other in the literal mathematical sense. So it is as if they have become completely separate worlds.
34:51
Nothing that happens in this part of the wave function can be affected by, or affect that part. They're independent of each other now. So Everett's insight is to say, you don't think you're ever in a superposition because you are not the combination of this observer who saw the cat awake and this observer who saw the cat asleep. You are one or the other.
35:15
But there is also the other one. So if you saw the cat awake, quantum mechanics predicts, there's another one of you that saw the cat asleep. When I say quantum mechanics, I mean everyone agrees this is straightforwardly what you would get if you just let the Schrödinger equation do its work. The disagreement is about whether or not you should let that happen. So this is the Everettian, or many worlds interpretation of quantum mechanics, because he says if you believe
35:47
in superpositions of electrons, you should be able to believe in superpositions of worlds. And the Schrödinger equation makes those worlds become real, whether you like it or not. There is no need for measurements or observations. There was just decoherence according to the usual Schrödinger equation. So, not everyone agrees yet. So there's some objections. And there are objections to the many worlds version of quantum mechanics. I would say that within the physics community,
36:18
there's a healthy fraction of people who do accept many worlds. But there's also those who don't. There's not any agreement here. There are reasons to object to many worlds that are bad reasons, and there are also legitimate worries. So I don't mind if you object to the theory, but I want you to object to it for the right, sensible reasons. So let's get rid of some of the bad reasons. One bad reason is just you kind of are annoyed by all these universes. It's just too many. I don't like it.
36:47
Like three or four, I could understand. But you're talking about an infinite number of universes, or at least a very, very large number. If that's your objection, then your objection is not to many worlds. Your objection is to quantum mechanics. And that's hard to object to 'cause it fits the data really well. Once you have quantum mechanics, once you have wave functions that are superpositions of all these different possibilities, the worlds are there as possibilities
37:17
in the set of all possible wave functions. Every version of quantum mechanics includes wave functions that describe many worlds. The only question is whether you take them seriously, or just hold your breath and refuse to believe that they're actually there.
37:32
So if you accept the reality of wave functions at all, you can't object that there are just too many worlds, you don't like it. Another bad objection is that this can't be tested. Well, it depends on, not to parse things too carefully, depends what you mean by the word "this."
37:51
The Everett interpretation of quantum mechanics is 100% testable. Remember the Everett interpretation is not a postulate that there are multiple worlds. It's a postulate that the Schrödinger equation is always right. That's a very testable thing. Just look at systems, don't measure them, don't disturb them. See if they always obey the Schrödinger equation. There are alternative theories in which they don't, in which wave functions suddenly collapse all by themselves.
38:22
And there are experiments looking for exactly those things. And if they ever find it, many worlds will be falsified just like that. It's a perfectly testable scientific theory.
38:35
Another easily answered objection is where does the energy come from to make all of these worlds? I mean the world, by which we mean the universe, certainly seems like it contains a lot of energy.
38:48
You make multiple copies of it, where do you get all the energy? There's an energy crisis already. This makes it worse. But it doesn't really. And this is a difficult objection to talk about because at the level of the equations, there's no worry whatsoever. The equations are perfectly clear about what happens. There's energy in the wave function of the whole universe, the wave function of the universe, that includes all of the branches all at once and that energy is conserved.
39:16
But the branches which represent the individual copies of classical reality that we find ourselves on contribute less and less to the energy of the whole shebang. So there's a weight that you can attach to any one branch of the wave function of the universe. And as time goes on and it splits apart into more and more branches, the branches get thinner.
39:42
Now you might say, I look at the energy in the earth, or the sun or the moon or the stars, it doesn't seem like they're getting thinner. That's 'cause you are getting thinner too. Relative to each other, everything in the universe looks like it always has the same energy, but the contribution of that branch to the overall energy becomes less and less as time goes on. So energy is 100% completely conserved. There's no problem with that. The final slightly askew objection
40:12
is what about my personal identity? This is a vague objection, because it's more psychological than physical or philosophical. But you like to think of yourself as having a history, as being born, growing up, having a story to tell, et cetera. And many worlds says, now suddenly there's many copies of you.
40:35
Should you feel kinship toward those other copies? Should you try to arrange the world so that other versions of you in the multiverse are happy or something like that? And the answer is, you just gotta think this through.
40:48
There's something new going on in many worlds, no doubt. The thing that is new is that the history of a person is more like a branching tree than a single line. But once those branches happen, they're now separate people. Identical twins start as the same single cell, but they split apart and become different people. No one tries to say like, oh, it's okay if one twin dies, 'cause we have the spare over here. They're two separate people. Likewise for the copies of you in many worlds,
41:23
they're all separate people. It's not like, I don't mind if all the other copies of me die because I'm still here or vice versa. Every one of them has some personal dignity. You just have to sort of update your idea of what an individual person is. But you can change, you can do that. It's actually not that hard. It's very different than what we're growing up intuitively to think about. But it makes perfect sense. It hangs together quite nicely.
41:50
There are no ethical, moral, political implications of the idea of all of these different worlds.
41:58
Nevertheless, there are perfectly legit physics problems here. And so now I wanna shift gears as we close the talk a little bit, because many physicists will say, who cares. Like sure, you get a well-defined theory, et cetera, et cetera. But I care about making predictions and things like that. I'm not gonna be bothered about whether it's many worlds or not. But I think that's wrong. Because there are puzzles that we have in physics that we haven't yet answered.
42:30
And maybe part of that is because we don't understand quantum mechanics. I don't think it's a leap of speculation to say that if we understood quantum mechanics better, maybe that would help us understand some of the other puzzles that we have. So one way of thinking about it is as an additional set of questions that arise when you think about things from the many world's perspective. In other theories, you would start with a classical theory, the ball rolling on a hill,
43:04
or an electron in a hydrogen atom. And then we teach our students a set of rules to quantize these classical theories. But nature doesn't do that. Nature just is quantum mechanical from the start. You get a classical limit, et cetera. But really if you think about it, the way to construct the correct theory of the world should be to think about wave functions and Hamiltonians and the Schrödinger equation from the start. Not to start with some classical theory and quantize it.
43:34
But that turns out to be kind of hard and challenging. Not impossible but something that we haven't really put our attention to yet. And that's important. So if you're thinking about quantum mechanics first, the quantum state of the universe is this wave function which John von Neumann, famous mathematical physicist, taught us years ago, can be thought of mathematically as a vector, in a fancy vector space called Hilbert space. Who cares? You don't need to know that.
44:05
The problem is the starting point of a truly quantum description of reality is not stuff arranged in space, it's this vector, this quantum state. But we have to recover our usual everyday way of thinking about the world in terms of stuff arranged in space from this abstract vector picture. How are we gonna do that? That's the challenge for Everettians, to start from a purely quantum mechanical description of the world and explain why the world looks pretty darn classical, or even better,
44:40
why the Copenhagen interpretation that we teach our students suffices to get the experiments right.
44:47
My own hope, and this might only be a hope, is that this is not just a challenge but an opportunity. One of the big unanswered questions in physics is quantum gravity.
44:58
We know, you probably know, if you come to this kind of Saturday Morning Physics thing, that we have not yet achieved a fully working quantum mechanical theory of gravity. We don't understand quantum gravity, but we also don't even understand quantum mechanics. Maybe it's not surprising that we don't understand quantum gravity, and maybe the mistake we've been making is trying to take a classical theory of gravity and quantizing it rather than starting
45:27
with quantum mechanics and finding gravity within it. So this is just to give you a hint about the kind of research that I've been doing most recently trying to extract the world from the abstract quantum wave function. So, here is famous physicist Albert Einstein.
45:48
One of the things that he said that was successful was gravity is the curvature of spacetime.
45:55
This is a whole other lecture, but I already gave the lecture yesterday. You can find versions of it online. But the upshot is, this equation, this is Einstein's equation of general relativity. It's the mathematical expression of the idea that the geometry of spacetime is influenced by and influences the energy and mass and matter and radiation and all that stuff in the universe. Okay? This is a purely classical theory of gravity. Relating energy and mass, et cetera,
46:28
to the curvature of spacetime. Obviously, this is another equation that has a lot of symbols in it that are very intimidating. Fortunately for you, you could buy a book that explains what all those symbols mean in exquisite clarity. You could buy it on your phone right now. There's no reason to wait until you get home.
46:49
But this book only talks about the classical world. There'll be a sequel coming out in the spring talking about the quantum world. And what we're trying to do in this project is to take clues from what we know about the quantum mechanical world we observe, and use those clues to show how to extract the world that we see. So one of those clues, is that it's not just quantum mechanics that is so successful at describing the world, but something called quantum field theory.
47:22
So field theory classically became very popular in the 1800s with electromagnetism. You have a little magnet here, put iron filings around it. They trace out the lines of the magnetic field. Even though you don't see, when you look at the magnet, the magnet is surrounded by a magnetic field and you can see what it's doing by looking at these lines that the filings line up into. Modern physics says that's the whole of reality. Everything you know is a vibration
47:53
in some quantum mechanical version of this field, these fields fill all of space. There's the electromagnetic field, the gravitational field, but there's also the electron field, the quark field, the neutrino field. All the particles you've ever heard of are vibrations in underlying quantum mechanical fields. So that suggests a very different picture of empty space.
48:16
If you had a theory that was primarily based on the idea of particles, space is just kind of a container, right? You have particles here, particles there, in between, space is empty, nothing is going on.
48:29
In field theory, in quantum field theory, that's not exactly right. Even empty space is kind of an exciting place. There's all these fields. Now, they're doing the least they can do. They're in their minimum energy state, what a physicist would call the vacuum state of the field. But quantum mechanically, they're still there. So empty space is characterized by having these quantum mechanical fields with a very specific wave function, doing some very specific thing.
49:00
Again, this is a clue from what we know. So this is not something we derive, this is our best current understanding of how to think about nature at a deep level.
49:11
And there is a feature that you get out of this quantum field theory way of thinking about empty space. Namely, guess what? These different regions of space are entangled with each other. 'Cause there's only one big wave function for the whole universe. And so for any little region of space, you can ask, is there quantum entanglement between this little region, the modes, the vibrations in the quantum fields in that region, and the vibrations in this region? And the answer is yes,
49:42
for any two regions of space, in completely empty space, no particles, no nothing, there is still entanglement. And there is a feature that that entanglement has that if the regions are nearby, there's a lot of entanglement. If the regions are far away, there's a little bit of entanglement. Not quite zero, but much less.
50:05
Again, this is a clue from conventional, perfectly accepted physics. In empty space, the entanglement between nearby regions is large, the entanglement between faraway regions is small. We want to turn that on its head. We wanna go backwards. We wanna start with pure quantum mechanics. So there's no such thing even as space, there's no such thing as distance, but there is a wave function, there is entanglement. So we're suggesting rather than saying,
50:40
when regions are nearby they're highly entangled, when they're far away they're a little bit entangled, you go the other way around. You say when regions are highly entangled, we call that nearby.
50:50
When regions are only a little bit entangled, we call that far away.
50:54
So what you're doing is you're defining a geometry. You're starting from a purely quantum mechanical set of ideas and words and you're defining space, you're emerging the idea of distances and lengths and areas and all that stuff, from this underlying quantum mechanical information. So there's very naturally a relationship between geometry of space and entanglement.
51:22
Meanwhile, there's also very naturally a relationship between entanglement and energy. I told you that in empty space there's a certain amount of entanglement between the quantum fields in any one region and the quantum fields somewhere else. If space is not empty, that means I put a particle there, and that means that I have changed the nature of the quantum fields in that region. In particular, I have broken the entanglement between this region and other regions.
51:51
So adding energy, adding particles, means changing the entanglement structure. There's very naturally a relationship between entanglement and energy. So what we're left with is natural relationship between the emergent geometry of space and the underlying quantum entanglement. And very naturally a relationship between quantum entanglement and the energy that you would describe in space. But that is just Einstein. That is Einstein's relationship in general relativity.
52:27
Between the curvature of spacetime and the energy in spacetime. So in other words there is this crazily hypothetical, alternative history of physics in which Einstein did not invent relativity, but we invented quantum mechanics and we thought about it really hard and we wondered how spacetime could arise from it. And we realized that if it did, it would naturally be curved and dynamical, and that curvature of space would be interpreted as gravity to you and me.
52:55
Now I have to be honest, this all might fail. This is all very speculative research project kind of stuff. We're working on it, trying to make it better. But I like it because it plays by the rules. It plays well with the nature of how quantum mechanics works. It's an illustration that thinking of quantum mechanics carefully for its own sake can lead you to certain ideas about existing problems like how to quantize gravity. So I think we spent over a hundred years
53:28
with quantum mechanics without quite understanding it. It is time to climb out of the box and take our quantum world seriously. Thank you very much. (audience applauding)
53:57
- Wow, thank you so much. We're gonna move. Can they hear me? - Don't think so.
54:08
- We are going to move to the question and answer period.
54:14
We are going to ask you to, if you're here in the room, to actually move to where we have a microphone here with Professor Goldman. And I'll give this one to Case for the other side. So, if you wanna ask a question here, we also have some questions online. And while we get organized with that, if you'd like to ask a question just line up.
54:40
At the end, Sean said that he will sign books if you brought books to get signed. And we're also gonna try to do that fairly efficiently. So we'll ask you, I'll remind you again, to come down on this side, and we'll sort of move across here and take care of that. All right, so let's start with the questions over here in the maize and blue.
55:05
- Hi there, my name's Anthony. I'd like you to talk a little bit about emergence. And on a podcast recently, you talked about top down emergence and how things that might emerge out of some smaller underlying systems, how they might affect things underneath them. If you have anything to say about that. - Yeah. So the question is about, can you hear me? Is this happening? Okay, I can barely hear myself. The idea of emergence is one that philosophers
55:33
and scientists have talked about for a long time. It's a slightly misleading word 'cause it seems like you're talking about something crawling out of the mud and emerging from it. But this notion of emergence has nothing to do with evolution over time. It's just when you have a system that has one microscopic description, like the air in this room, it's made of molecules, there's oxygen and nitrogen and CO2. But there's a whole nother way of talking about it that is maybe an approximation,
56:01
but captures a lot of what matters. Namely, you can talk about the air in the room in terms of its density and pressure as a fluid, right, with temperature and velocity and things like that. So when there is a pattern hidden implicitly inside some microscopic theory, we talk about an emergent macroscopic version of it. The whole classical world, in the picture I just told you today, is an emergent approximation to the underlying quantum mechanical world. Now there's a debate
56:32
about whether emergence only works in that direction, from the microscopic world to the macroscopic world, or whether under certain circumstances, the macroscopic world affects the microscopic world in some way that the microscopic theory was insufficient to account for. I think that when it comes to physics, that just doesn't happen. I think that our theory of physics at the microscopic level does the trick. You don't need to know whether an electron is in empty space
57:03
or a rock or a brain to tell how the electron behaves. All that matters is the fields affecting it at that one point in space. Other people disagree, bless their hearts.
57:16
- Hi, thanks for the talk. Very nice. I had a question- (microphone cuts) (audience member speaking quietly)
57:35
- Yeah, this i that appears in the equation here is the square root of minus one, the imaginary unit. You know, it's not really imaginary. There it is. I can see it, I can square it, I can get one.
57:48
The word imaginary doesn't mean it's not real. We're borrowing a word from a different context here. The fact is that it's just more convenient to express the Schrödinger equation using imaginary numbers, or complex numbers more generally, than purely real numbers. You don't have to. You could choose to write the Schrödinger equation as multiple equations interacting with each other, all of which just involve real numbers. It's just that you're doing more work for yourself.
58:19
So it turns out to be easier and more convenient to do it this way. Nothing more profound than that.
58:27
- Good morning. So when we're doing quantum mechanics in class, sometimes we'll have situations where, we have particle A in a superposition of some states and particle B in a superposition of some states, and they become partially entangled. So that when we measure A, or discover which branch we're on of A, we eliminate some of the possibilities for particle B. Now when I'm doing these problem sets, we renormalize particle B so that all of the new answers still add up to one.
59:00
In the many worlds interpretation, would it be possible to think of that, instead of renormalizng, the rest of the missing probabilities have now gone down a different branch, and I could maybe recover some of the points on that problem set?
59:19
- You're welcome to say that I say, you should get full credit for that problem set just 'cause you're here this morning. I would say basically, yes, I don't want to go too far and too definitively 'cause I think it depends on how far you wanna push this story. But yeah, in the wave function of the universe, the total sets of coefficients of the wave function that we square to get one and add up to get one, remain with that feature. You never have to renormalize
59:47
the whole wave function of the universe. The renormalization is a way of saying, it's actually quite, what she's talking about, is very closely related to this picture, where the thickness of the branch of the wave function you're on gets thinner and thinner, but you get thinner in this description as well as everything else. So you don't notice it getting thinner and thinner. But if you're doing a problem set in a physics course, you have to mathematically take account of that
1:00:13
by dividing by the thickness that you've lost. And so it's totally okay to say that the rest of the thickness is there in the rest of the wave function of the universe.
1:00:32
(audience member talking quietly) Just keep talking.
1:00:37
(audience member talking quietly)
1:01:03
- Is that the same space, or a version or supposition, of say string theory space?
1:01:19
Other things that define spaces? Do they have any relationship?
1:01:24
- They might. So the question is, are the space that we're getting emerging from our quantum mechanical wave function, is it related somehow to the space and the spacetimes that string theory talks about? String theory is a very popular attempt to unify all the forces of nature, including gravity, by postulating that instead of little particles, the world is made of little strings. String theory is extremely successful and probably is at least adjacent to the truth in some regime.
1:01:53
But it is an example of this idea that you start with a classical theory and you quantize it. And so it leads from that starting point to certain very, very specific ideas, like space has to have nine dimensions, spacetime has to have 10 dimensions. We don't see them therefore we have to curl them up and hide them in these tiny little compact manifolds. Maybe that's right, but in this picture you don't need any of that. Again, maybe you might fit it in if you wanted to,
1:02:21
but here you're just treating space as not something fundamental. Space is just emerging from an underlying quantum mechanical theory. So there's no obvious reason in this picture why you would have to use all that extra structure.
1:02:36
- Let me ask a question from online if that's okay. And there are several, but I had to pick one. And this one is to ask you to see if there's a connection, or tell us if there's a connection, between the multi-world and the multi-universe. - Right, to make things difficult for you, cosmologists and physicists talk about many worlds of quantum mechanics. But separately what you might call the cosmological multiverse. The cosmological multiverse is actually much more down to earth.
1:03:04
It's just the idea that very, very far away, in some direction, the universe might look very different. Even the local laws of physics could be different. So the many worlds of quantum mechanics is right here in this room. I can do an experiment. You can literally download an app for your iPhone called universe splitter, which will branch the universe into multiple copies. So conceptually, they're very, very different. In some ultimate, more elevated theory of physics,
1:03:29
they might turn out to be related, but that's not obvious to us right now.
1:03:36
- Jonathan, may I ask a philosophical question? Isn't it possible that these brains that evolve to survive and procreate in a very specific environment are simply incapable of understanding these things and our impulse to latch onto a particular explanation is an evolved reaction to the mystery of life? - My brain is not incapable of understanding these things. I have no problem.
1:04:06
Look, you'd never know, I don't even know how you would ever know, if there was some feature of reality that was literally impossible for us human beings to understand. What I do know is that we've understood an enormous amount about reality. It's been less than a century since the Solvay Conference and the first strict formulations of quantum mechanics, and we've gone enormously far. To me, if history is telling us anything at all, it's not that we're about to bump up into fundamental limits,
1:04:34
it's that we are pretty darn awesome at understanding reality.
1:04:42
- So, towards the end, you gave a brief overview of the relationship between geometry, entanglement, and energy. And one of the questions I have is classically we know, you mentioned it early in your lecture, that if you have two particles, two photons, let's say, and you entangle them, isolate them perfectly and separate them across the universe, those two particles, the moment you detect them, the entanglement relationship is conserved. How does that fit into this geometry
1:05:07
and entanglement picture? Because you stated earlier, and I know this is a bit of a overview of the topic, that we can describe highly entangled particles as being close together, but if you separate these highly entangled particles across the universe, they still follow that relationship. - Yeah, this is, I feel like I am not obeying my own advice here because this is a question I get, or a version of it, every single time I give this talk.
1:05:33
So I clearly need to do better at explaining it in the talk. But the point is that, the entanglement we're talking about here is the entanglement between regions of empty space. It's not the entanglement between particles. Particles are something extra, something over and above the region of empty space. So if I have a little box, a cubic nanometer or whatever, and I have a particle in that box, that means that one of the quantum mechanical field modes is vibrating. But the overwhelming majority
1:06:08
of the quantum mechanical field modes are still in their vacuum state. So even in the middle of this room, even the middle of a neutron star, as far as quantum field theory is concerned, it's almost empty space. Almost all of the quantum fields are still in their vacuum state. So in terms of calculating the entanglement between one region of space and another, the fact that there's a particle there, it might two particles that might be entangled, is entirely irrelevant.
1:06:34
The regions of empty space are still doing most of the entangling.
1:06:41
So the point of the question is that, if I have two particles, there's zero relationship between their entanglement and their distance from each other. The relationship only exists for regions of empty space.
1:06:56
- I think you might have just answered my question, but I'll ask it anyway. Is entanglement a binary or is it a spectrum? As in, are you entangled or are you not entangled? Because when I think about quantum computers, they go through great lengths of entangling particles, but here we talk about highly entangled versus not very entangled. So it seems like it's a spectrum. - 100% a spectrum.
1:07:20
That was a good one.
1:07:24
- Can I ask, or try to put together two questions from online about time.
1:07:31
And I'll preface it. The Schrödinger equation describes how the wave function changes in time, but their questions are concerned with the past, the present and the future, and the fact that time only really seems to go in one direction.
1:07:51
So can you you comment about that?
1:07:55
- Sure. This is a whole separate talk. Maybe I'll come back and give it some other day about why is there an arrow of time in the universe? The arrow of time is simply the fact, the past, present, and future, are very different from each other, manifestly so. I have photographs on my computer. Here's one. This is a photograph of my cat Caliban, but it's a picture of what he looked like in the past. There are no pictures of what he looks like in the future. I have different epistemic access
1:08:25
to the past and the future. That's so blatantly built into our experience of reality that we take it for granted. But the fundamental laws of physics, whether they're Newton's or Schrödinger's or Einstein's, do not differentiate between the past and the future. Why do we have this manifest difference in the real world? The answer is something called the second law of thermodynamics. Entropy increases over time. Entropy is a measure of the disorderliness of the universe.
1:08:56
It is true that, we think that it's true, we hypothesize that it is true, that there's some fundamental law of physics that says how the state of the universe exactly specified evolves with time. But you and I don't observe the exact state of the universe. We observe some features of it. Here in this room, there are air molecules, they bump into each other, but we don't see the air molecules. We see some coarse grained features of temperature and density and so forth.
1:09:22
So given that incomplete knowledge of the state of the world, there's a feature that the universe started in a very orderly state, low entropy, and that entropy is increasing over time. And I wrote a whole nother book called "From Eternity to Here," which will explain to you why that increase of entropy over time accounts for why we can have photographs of the past but not the future.
1:09:49
Who's next?
1:09:55
- I wanted to ask a question about many world interpretation. So correct me if I'm wrong about understanding the interpretation. In many worlds, in each branch, the world seems to be classical to us. 'Cause every single moment, when the superposition splits.
1:10:15
So how do we measure the interference of electron in one world, one of the branches we are on? - Right. Good. This is a great question. It's actually crucially important to understand, but we do mostly understand it. Why is it that on the one hand, when we open the box, we see the cat awake or asleep? We never see a superposition. But on the other hand, when we look at electrons, we do see them in superposition. The rough answer is because cats are big. And what that means is,
1:10:48
you cannot shield the cat from becoming entangled with the environment. The photons and the air molecules in the box are continually banging into the cat because it's a large macroscopic object. And that is decoherence. That is exactly this process that we saw here. But a single electron, you can shield from interacting with the environment, you can keep it from bumping into air molecules. What we're trying to do in quantum computing is build larger and larger quantum systems
1:11:21
that you shield from decoherence. Very hard to do because every photon could mess you up, any warm object emits photons in the infrared. That's why your quantum computers have to be really, really super duper cold, to prevent them from decohering.
1:11:43
- Thanks for the great talk.
1:11:47
I wonder if I could take you back to the discussion of the arrow of time for a moment.
1:11:54
'Cause the remarkable thing about that to me or the one obvious thing about it, is that it's highly asymmetric in time. And based on your answer just a couple moments ago, you suggested that that's essentially to do with the second law of thermodynamics. But could you make that connection a little bit clearer with reference to this diagram. Are those branches psychological in nature?
1:12:15
I'm just asking to say a bit more about it. - Yeah, so it's a great question. There's absolutely, even though the Schrödinger equation has no arrow of time in it, this picture clearly does, even though I told you that the picture, that the whole theory was just the Schrödinger equation taken seriously. Well, the answer is you also need to have an initial condition for the universe. And for reasons that we truly do not understand right now,
1:12:39
the initial conditions of our universe were very special. They're very special in a way that can be quantified into saying that the entropy was very low. There's different definitions of entropy depending on whether you're talking quantum mechanical or classical, but in every way the universe was simple and very, very organized at early times. That's reflected in this picture by seeing that there's just one big quantum state at early times and many, many complicated things later on.
1:13:08
So we don't know why that's true, but you need it to make it work. Eventually, by the way, it will go away, right? We live in this world right now, in the middle of the evolution of the universe, where classical physics seems to be a pretty good approximation. This is a temporary condition, just like if you mix cream and coffee, they will eventually equilibrate and become maximally mixed. Eventually you'll branch the wave function of the universe as much as you can. And when that happens,
1:13:38
there will be no distinction between one branch and another. Classical reality will no longer be a useful approximation to talking about the world. In terms of psychology, that's not quite the right way to say it. There's an emergent pattern here. There is something that works about describing parts of the universe using a classical approximation that is not just psychological, that's a true real pattern in the universe. We're just taking advantage of it.
1:14:04
I think it's their turn.
1:14:07
- Hi, my name is Yoshi and I have a question,
1:14:12
about kind of trying to understand the world from quantum perspective, I guess. Do you think that Bohmian mechanics could also be a kind of fundamental or an emergent interpretation
1:14:28
from just quantum mechanics? Or do you think there's too many assumptions with that as well? - Yeah, if you remember back when we talked about the reality problem, I forget where it was.
1:14:43
Is the wave function the only part of reality, or are there other variables or physical quantities in addition to the wave function? So there is an approach to quantum mechanics, the foundations of quantum mechanics, that says the wave function is real, it explains why electrons behave like waves when you're not looking at them, but there's another set of physical variables that are also real. The positions of particles in addition to the wave function. And the reason why you see particles
1:15:11
when you look at electrons is because you're seeing the particles. You're not seeing the wave function. And the role of the wave function in these theories is to guide the particles around, to push around the particles right and left. This is called Bohmian mechanics. I think that there's zero interest personally in it for me because I think that many worlds works really well. Why make it complicated? But other people disagree.
1:15:36
- Let's get this one, and I'm gonna try to help Case with the mic. - My name is Dmitri. So judging by the Einsteinian theory of gravity, we imagine the universe is a flat membrane, as a whole plane in which objects of mass weigh it down and that's how gravity works. But as we become more and more informed in this area, wouldn't it be more accurate to represent the space as more of a three-dimensional object? Such a cube or a sphere in which objects pull in?
1:16:10
- You are just 100% correct. What can I tell you? When we draw pictures to give people a feeling for general relativity, we often do this kind of thing, where there's this two-dimensional plane and this is supposed to be, I don't even know, I have no idea what this picture is of. It's the cover of my book, but I do not get a say in what's on the cover of my book. So I guess this is like a star or something? And it's pushing down the fabric of spacetime.
1:16:40
Of course, it should really be three-dimensional space, but in fact, of course, it should really be four-dimensional spacetime. The only problem is, I can't draw a picture of four-dimensional spacetime on the two-dimensional book cover. So we do the best we can, and we try to be generous with each other in interpreting what it's about.
1:17:02
- Thank you for both of your lectures. I had this question. So in one of my, when I was taking the general relativity course here, I learned about the holographic principle, which is the idea that if you have a four-dimensional spacetime, the information about the region in that spacetime can be encoded on a three-dimensional boundary.
1:17:25
When you try to derive general relativity from quantum mechanics, as you have said here, based off of entanglement, you get a similar idea where the entropy
1:17:38
would impose a constraint on the geometry.
1:17:43
- Well, we don't know, is the short answer. In the approach that I was talking about, in deriving spacetime from entanglement, this particular version only is worried, so far, about situations where gravity is very weak. Like here in the solar system, where you have planets and stars and things like that. When gravity becomes strong, when you have a black hole, or the whole universe all at once, different features kick in that can separately be described
1:18:12
using ideas like holography and complementarity. Those are not things we're worried about here, yet. We would like to get there some day.
1:18:22
- We have time for one or two more questions.
1:18:28
- Hi, my name is Matthew. I had a question about this actually, I was a little confused. What's the difference between the entanglement that gives rise to geometry and the entanglement between two distant particles? It sounded like there's two different kinds, but I thought entanglement is entanglement? - Entanglement is entanglement, but in quantum field theory, most of what is going on in any physical situation is the empty space part of it. So even when you have a particle,
1:18:59
that particle is surrounded by many other vibrations in quantum fields that are in their lowest energy state. So particles are little tiny annoyances built on top of this huge number of quantum mechanical fluctuations in empty space. Therefore, it's that much more numerous set of fluctuations that we consider here.
1:19:22
I think this is the last question. - Hi. I'd just like to ask for a clarification real quick. When you were talking about the idea of entanglement as a spectrum rather than a binary, is the idea that you're trying to get across that if we have something that is only, like two particles that are only partially entangled, and you measure one of the properties on one of those particles, you have a probability of knowing that equivalent property on the other particle. Is that the idea?
1:19:51
- That is exactly right. You got it right. We've learned something. I feel like I did my job.
1:19:58
Thank you very much. - All right, well. (audience applauding) - Thank you very much.
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