- So coming back to the textbook definition of quantum mechanics, this idea that I don't think we talked about, can you, this one of the most interesting philosophical points, we talked at the human level, but at the physics level, that at least the textbook definition of quantum mechanics separates what is observed and what is real.

One, how does that make you feel? And two, what does it then mean to observe something and why is it different than what is real? - Yeah, you know, my personal feeling, such as it is, is that things like measurement and observers and stuff like that are not going to play a fundamental role in the ultimate laws of physics.

But my feeling that way is because so far, that's where all the evidence has been pointing. I could be wrong and there's certainly a sense in which it would be infinitely cool if somehow observation or mental cogitation did play a fundamental role in the nature of reality. But I don't think so and I don't see any evidence for it, so I'm not spending a lot of time worrying about that possibility.

So what do you do about the fact that in the textbook interpretation of quantum mechanics, this idea of measurement or looking at things seems to play an important role? Well, you come up with better interpretations of quantum mechanics and there are several alternatives. My favorite is the many worlds interpretation, which says two things.

Number one, you, the observer, are just a quantum system like anything else. There's nothing special about you. Don't get so proud of yourself. You know, you're just a bunch of atoms. You have a wave function. You obey the Schrodinger equation like everything else. And number two, when you think you're measuring something or observing something, what's really happening is you're becoming entangled with that thing.

So when you think that there's a wave function for the electron, it's all spread out, but you look at it and you only see it in one location. What's really happening is that there's still the wave function for the electron in all those locations, but now it's entangled with the wave function of you in the following way.

There's part of the wave function that says the electron was here and you think you saw it there. The electron was there and you think you saw it there. The electron was over there and you think you saw it there. Et cetera. So, and all of those different parts of the wave function, once they come into being, no longer talk to each other.

They no longer interact or influence each other. It's as if they are separate worlds. So this was the invention of Hugh Everett III, who was a graduate student at Princeton in the 1950s. And he said, basically, look, you don't need all these extra rules about looking at things. Just listen to what the Schrodinger equation is telling you.

It's telling you that you have a wave function, that you become entangled, and that the different versions of you no longer talk to each other. So just accept it. It's just, he did therapy more than anything else. He said, it's okay. You don't need all these extra rules. All you need to do is believe the Schrodinger equation.

The cost is there's a whole bunch of extra worlds out there. - So are the worlds being created whether there's an observer or not? - The worlds are created any time a quantum system that's in a superposition becomes entangled with the outside world. - What's the outside world? - It depends.

Let's back up. Whatever it really says, what his theory is, is there's a wave function of the universe, and it obeys the Schrodinger equation all the time. That's it. That's the full theory right there, okay? The question, all of the work, is how in the world do you map that theory onto reality, onto what we observe, right?

So part of it is carving up the wave function into these separate worlds, saying, look, it describes a whole bunch of things that don't interact with each other. Let's call them separate worlds. Another part is distinguishing between systems and their environments. And the environment is basically all the degrees of freedom, all the things going on in the world that you don't keep track of.

So again, in the bottle of water, I might keep track of the total amount of water and the volume. I don't keep track of the individual positions and velocities. I don't keep track of all the photons or the air molecules in this room. So that's the outside world. The outside world is all the parts of the universe that you're not keeping track of when you're asking about the behavior of some subsystem of it.

- So how many worlds are there? - Yeah, I don't know that one either. There could be an infinite number. There could be only a finite number, but it's a big number one way or the other. - It's just a very, very big number. In one of the talks, somebody asked, well, if it's finite, so actually I'm not sure exactly the logic you used to derive this, but is there going to be overlap, a duplicate world that you return to?

So you've mentioned, and I'd love if you can elaborate on, sort of idea that it's possible that there's some kind of equilibrium that these splitting worlds arrive at. And then maybe over time, maybe somehow connected to entropy, you get a large number of worlds that are very similar to each other.

- Yeah, so this question of whether or not Hilbert space is finite or infinite dimensional is actually secretly connected to gravity and cosmology. This is the part that we're still struggling to understand right now. But we discovered back in 1998 that our universe is accelerating. And what that means, if it continues, which we think it probably will, but we're not sure, but if it does, that means there's a horizon around us.

Because the universe is not only expanding, but expanding faster and faster, things can get so far away from us that from our perspective, it looks like they're moving away faster than the speed of light. We will never see them again. So there's literally a horizon around us, and that horizon approaches some fixed distance away from us.

And you can then argue that within that horizon, there's only a finite number of things that can possibly happen, the finite dimensional Hilbert space. In fact, we even have a guess for what the dimensionality is is 10 to the power of 10 to the power of 122. That's a very large number.

Just to compare it, the age of the universe is something like 10 to the 14 seconds, 10 to the 17 or 18 seconds maybe. The number of particles in the universe is 10 to the 88th. But the number of dimensions of Hilbert space is 10 to the 10 to the 122.

So that's just crazy big. If that story is right, that in our observable horizon, there's only a finite dimensional Hilbert space, then this idea of branching of the wave function of the universe into multiple distinct separate branches has to reach a limit at some time. Once you branch that many times, you've run out of room in Hilbert space.

And roughly speaking, that corresponds to the universe just expanding and emptying out and cooling off and entering a phase where it's just empty space, literally forever. - What's the difference between splitting and copying, do you think? Like in terms of, a lot of this is an interpretation that helps us sort of model the world.

So perhaps shouldn't be thought of as like, philosophically or metaphysically, but even at the physics level, do you see a difference between sort of generating new copies of the world or splitting? - I think it's better to think of in quantum mechanics, in many worlds, the universe splits rather than new copies, because people otherwise worry about things like energy conservation.

And no one who understands quantum mechanics worries about energy conservation 'cause the equation is perfectly clear. But if all you know is that someone told you the universe duplicates, then you have a reasonable worry about where all the energy for that came from. So a preexisting universe splitting into two skinnier universes is a better way of thinking about it.

And mathematically, it's just like, if you draw an X and Y axis, and you draw a vector of length one, 45 degree angle, you know that you can write that vector of length one as the sum of two vectors pointing along X and Y of length one over the square root of two.

So I write one arrow as the sum of two arrows, but there's a conservation of arrow-ness, right? Like there's now two arrows, but the length is the same. I just am describing it in a different way. And that's exactly what happens when the universe branches. The wave function of the universe is a big old vector.

- So to somebody who brings up a question of saying, doesn't this violate the conservation of energy? Can you give further elaboration? - Right, so let's just be super duper perfectly clear. There's zero question about whether or not many worlds violates conservation of energy. It does not. And I say this definitively because there are other questions that I think there's answers to, but they're legitimate questions, right?

About where does probability come from and things like that. This conservation of energy question, we know the answer to it, and the answer to it is that energy is conserved. All of the effort goes into how best to translate what the equation unambiguously says into plain English, right? So this idea that there's a universe that has, that the universe comes equipped with a thickness, and it sort of divides up into thinner pieces, but the total amount of universe is conserved over time is a reasonably good way of putting English words to the underlying mathematics.

- So one of my favorite things about many worlds is, I mean, I love that there's something controversial in science, and for some reason it makes people actually not like upset, but just get excited. Why do you think it is a controversial idea? So there's a lot of, it's actually one of the cleanest ways to think about quantum mechanics.

So why do you think there's a discomfort a little bit among certain people? - Well, I draw the distinction in my book between two different kinds of simplicity in a physical theory. There's simplicity in the theory itself, right? How we describe what's going on according to the theory by its own rights.

But then, you know, a theory is just some sort of abstract mathematical formalism. You have to map it onto the world somehow, right? And sometimes, like for Newtonian physics, it's pretty obvious, like, okay, here is a bottle, and it has a center of mass, and things like that. Sometimes it's a little bit harder, with general relativity, curvature of space-time is a little bit harder to grasp.

Quantum mechanics is very hard to map what the language you're talking in of wave functions and things like that onto reality. And many worlds is the version of quantum mechanics where it is hardest to map on the underlying formalism to reality. So that's where the lack of simplicity comes in, not in the theory, but in how we use the theory to map onto reality.

And in fact, all of the work in sort of elaborating many worlds quantum mechanics is in this effort to map it on to the world that we see. So it's perfectly legitimate to be bugged by that, right? To say like, well, no, that's just too far away from my experience.

I am therefore intrinsically skeptical of it. Of course, you should give up on that skepticism if there are no alternatives, and this theory always keeps working, then eventually you should overcome your skepticism. But right now, there are alternatives that are, that people work to make alternatives that are by their nature closer to what we observe directly.

- Can you describe the alternatives? I don't think we touched on it. So the Copenhagen interpretation and the many worlds, maybe there's a difference between the Everettian many worlds and many worlds as it is now, like has the idea sort of developed and so on. And just in general, what is the space of promising contenders?

We have democratic debates now, there's a bunch of candidates. - 12 candidates on stage. - 12 candidates on stage. What are the quantum mechanical candidates on stage for the debate? - So if you had a debate between quantum mechanical contenders, there'd be no problem getting 12 people up there on stage, but there would still be only three front runners.

(both laughing) And right now the front runners would be Everett. Hidden variable theories are another one. So the hidden variable theories say that the wave function is real, but there's something in addition to the wave function. The wave function is not everything, it's part of reality, but it's not everything.

What else is there? We're not sure. But in the simplest version of the theory, there are literally particles. So many worlds says that quantum systems are sometimes are wave-like in some ways and particle-like in another because they really, really are waves, but under certain observational circumstances, they look like particles.

Whereas hidden variable says they look like waves and particles 'cause there are both waves and particles involved in the dynamics. And that's easy to do if your particles are just non-relativistic Newtonian particles moving around, they get pushed around by the wave function roughly. It becomes much harder when you take quantum field theory or quantum gravity into account.

The other big contender are spontaneous collapse theories. So in the conventional textbook interpretation, we say when you look at a quantum system, its wave function collapses and you see it in one location. A spontaneous collapse theory says that every particle has a chance per second of having its wave function spontaneously collapse.

The chance is very small. For a typical particle, it will take hundreds of millions of years before it happens even once, but in a table or some macroscopic object, there are way more than a hundred million particles and they're all entangled with each other. So when one of them collapses, it brings everything else along with it.

There's a slight variation of this, that's a spontaneous collapse theory. There are also induced collapse theories like Roger Penrose thinks that when the gravitational difference between two parts of the wave function becomes too large, the wave function collapses automatically. So those are basically in my mind, the three big alternatives.

Many worlds, which is just, there's a wave function and always obeys the Schrodinger equation. Hidden variables, there's a wave function that always obeys the Schrodinger equation, but there are also new variables or collapse theories, which the wave function sometimes obeys the Schrodinger equation and sometimes it collapses. So you can see that the alternatives are more complicated in their formalism than many worlds is, but they are closer to our experience.

- So just this moment of collapse, do you think of it as a, so is a wave function fundamentally sort of a probabilistic description of the world and is collapse sort of reducing that part of the world into something deterministic, where again, you can, and I'll describe the position and the velocity in this simple classical model.

- Well, there is-- - Is that how you think about collapse? - There is a fourth category, is a fourth contender. There's a Mayor Pete of quantum mechanical interpretations, which are called epistemic interpretations. And what they say is, all the wave function is, is a way of making predictions for experimental outcomes.

It's not mapping onto an element of reality in any real sense. And in fact, two different people might have two different wave functions for the same physical system because they know different things about it, right? The wave function is really just a prediction mechanism. And then the problem with those epistemic interpretations is if you say, okay, but it's predicting about what, like what is the thing that is being predicted?

And they say, no, no, no. That's not what we're here for. We're just here to tell you what the observational outcomes are gonna be. - But the other interpretations kind of think that the wave function is real. - Yes, that's right. So that's an ontic interpretation of the wave function, ontology being the study of what is real, what exists, as opposed to an epistemic interpretation of the wave function, epistemology being the study of what we know.

- I would actually just love to see that debate on stage. - There was a version of it on stage at the World Science Festival a few years ago that you can look up online. - On YouTube? - Yep, it's on YouTube. - Okay, awesome. I'll link it and watch it.

- Many words. - Who won? - I won. (laughing) I don't know, there was no vote. There was no vote. But Brian Green was the moderator and David Albert stood up for spontaneous collapse and Shelley Goldstein was there for hidden variables and Rüdiger Schock was there for epistemic approaches.

- Why do you, I think you mentioned it, but just to elaborate, why do you find many worlds so compelling? - Well, there's two reasons, actually. One is, like I said, it is the simplest, right? It's like the most bare bones, austere, pure version of quantum mechanics. And I am someone who is very willing to put a lot of work into mapping the formalism onto reality.

I'm less willing to complicate the formalism itself. But the other big reason is that there's something called modern physics with quantum fields and quantum gravity and holography and space-time, doing things like that. And when you take any of the other versions of quantum theory, they bring along classical baggage.

All of the other versions of quantum mechanics prejudice or privilege some version of classical reality like locations in space, okay? And I think that that's a barrier to doing better at understanding the theory of everything and understanding quantum gravity and the inversions of space-time. Whenever, if you change your theory from, here's a harmonic oscillator, oh, there's a spin, here's an electromagnetic field, in hidden variable theories or dynamical collapse theories, you have to start from scratch.

You have to say like, well, what are the hidden variables for this theory? Or how does it collapse or whatever? Whereas many worlds is plug and play. You tell me the theory and I can give you as many worlds version. So when we have a situation like we have with gravity and space-time, where the classical description seems to break down in a dramatic way, then I think you should start from the most quantum theory that you have, which is really many worlds.

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