2014-06-01 World Science Festival What Is Quantum Mechanics Really Telling Us
Duration: 01:23:13
Transcript
David Deutsch
If everything happens, what does probability mean? Right? If the electron will wind up here in one universe, there in another, there in another universe, and so forth, in what sense is there a probability for it to be at one location or another? Because in the multiverse, it will, in the God’s eye view, exist at every possible location. There is no such thing as probability at a fundamental level. The world is completely deterministic. We were wrong to want probability to exist at a fundamental level. We only want it for making decisions. And if we apply it with conventional decision theory, then we get the answer we want. Not all colleagues agree with this, to put it mildly, but the ones who understand it do.
Brian Greene
Hey everyone, thanks for joining us. Today’s conversation is in quantum mechanics, nature of reality, the kinds of topics that are near and dear to my heart and to the hearts of many in our core audience. And I’m pleased that the person that I’m going to be discussing these issues with is someone who has really had a profound impact on shaping the way we think about these things. And that is David Deutsch, who is one of the most influential thinkers of our time. He’s widely regarded as the father of quantum computing. He’s a pioneering theorist whose work has developed new ways of understanding computation, reality, and the deep laws that govern the universe. So David, thank you so much for joining us.
David Deutsch
Oh, thank you for having me. You know, it’s been, of course, I’ve known of your work for decades. I don’t think we’ve ever met before. I don’t think we have ever. I think we’re the victim of a very unlikely set of coincidences. Because we kind of move in the same circles or overlapping circles, but we’ve never met.
Brian Greene
Yeah, yeah. So good to finally do it, even though it’s virtual at a distance. So thank you again for joining. I wanted to begin with a, I don’t know, a pet peeve of mine that I think you also agree with. When it comes to quantum mechanics, unlike any other theory that we discuss, people use this word interpretation, the interpretations of quantum mechanics. And to me, as we’ll get into it, the interpretations are not interpretations. They’re different theories. And some of the interpretations don’t even qualify as a complete theory. And so that just seems to be a complete misnomer in the way we describe these things.
David Deutsch
I couldn’t agree more. And I got this view from Bryce DeWitt, who was my supervisor for a while. He was angry about this terminology as well. And I should throw in that my other boss, my main boss, Dennis Sciama, who was reluctant to enter into this debate in public too much. But he said to me on two occasions, the trouble is that when it comes to the interpretation of quantum mechanics, the standard of the argument drops to zero. Right.
Brian Greene
Meaning that if it doesn’t drop to zero, then we’re left with only the Everettian quantum theory. Right. So we’re definitely going to follow a trajectory that will shortly get us into the details there. But presumably, you know, if you were to talk to a standard average everyday next door physicist and ask them, why do you use this word interpretation? I presume the answer would be because I know how to use the theory to make predictions. And after that, it’s all just words. And so, I mean, I don’t agree with that at all. But what’s your response to that way of describing things?
David Deutsch
Well, for a start, I think that is giving up on the purpose of physics. The idea, the purpose of physics isn’t to track down the sixth and seventh decimal place of predictions. Nobody would follow a theory, a discipline with that purpose. Physics, like virtually the whole of the rest of science, is about understanding the world. And if I throw in engineering and so on as well, then it’s about understanding and controlling the world. And not in terms of its predictions or in terms of fine tuning, but about new ideas about how it, what is actually going on in the unseen that causes the seen. So the scientific explanation is always explaining the seen in terms of the unseen.
Brian Greene
And so when you talk about the unseen, of course, those are the very things that these words are meant to be articulating and bringing into some sort of visualizable or articulable description of the inner workings responsible for the things that we can see. And if you kind of go historically, look, I’m a semi-student of the history of physics. I’m not like a historian of science. I’ve done some reading and it does feel like Niels Bohr was one of the fulcrums around which this new way of talking emerged. I don’t know that he ever used the word interpretation himself, but it feels like historically he was interrogating this new description of the world, asking the kinds of questions that you and I would want to ask, what’s going on? What’s really happening? When he couldn’t extract an answer, he kind of shifted to a new view of you can’t ask those questions any longer. That’s the deep lesson, right? I mean, is that your take on sort of the beginning of this way of thinking about things?
David Deutsch
Yes, that was the beginning within physics. It was the beginning. Yes. Although in philosophy there was positivism and logical positivism and that kind of move had already been made by philosophers. And to some extent one can forgive Bohr for being mystified by what was happening and by saying, well, if physics demands that we give up cherished philosophical principles like reality, then I’m going to side with physics, not with philosophy. And that attitude is right. It’s just that he got it wrong on the facts and the logic and happened to be an extremely charismatic figure in the physics community. And so while he thought of himself as groping his way towards a new understanding, his colleagues hesitate to say acolytes, but his colleagues took that as the essence of the new view. And for example, Bohr, I think never talked about wave function collapse, that kind of thing, because he on the contrary, he insisted that quantum theory was the full, the fullest possible description of the world, which is also exactly what Everett said. But Bohr didn’t work it out to its logical conclusion.
Brian Greene
Right. Right. Now, I slightly wonder, too. And again, you know, this is all conjecture, but fun conjecture. You know, at the time that Bohr was struggling with these ideas, it was in like the zeitgeist where Einstein had completely rewritten the rules of space and time. You know, again, the philosophers like you’re describing, you know, you know, Wittgenstein talking about, well, it’s just sort of word games. And then you’ve got even in the art world, right, you’ve got modernism, you know, completely transforming the way we represent things on a canvas. I sort of get the feeling and maybe this is unfair that Bohr had an urge to kind of have that kind of a place in the history of ideas. And quantum mechanics in this guise that he ultimately was proselytizing about was ready made. We now are rewriting our rules of how we can even interrogate reality. Was that part of the driver?
David Deutsch
Maybe. Like you, I only know the sort of physicist’s history of this, not the actual history. And I don’t want to psychologize about Bohr, but it’s certainly true that many physicists were glad to adopt this theory, adopt this view of the world, adopt mysticism, positivism, instrumentalism, all these isms, because it took the edge off the necessity for what is called a hard realism, for taking the theory seriously. So they didn’t have to take the theory seriously. They could just use it to calculate results. And they were then not standing out as starkly against what you call the zeitgeist as they would have been if they had insisted on normal physics.
Brian Greene
Yeah, it kind of reminds me of that famous quote attributed to Steven Weinberg. I think it’s actually accurate where he said something along the lines of it’s not that we take our mathematical theories. How do you say it? He’s basically saying, you know, we don’t take our mathematical theories seriously enough. It’s not that we take them too seriously, it’s that we don’t take them seriously enough. Right. So if you apply that to quantum mechanics, you know, it is basically saying if you take the math as the true description of reality, as we’ll describe, then it does naturally take it to the Everettian approach to quantum mechanics.
David Deutsch
Yes. Although I would perhaps phrase that a bit differently. It’s not a question of what you take it as. It’s a question of what does the theory say about reality first and then only then about predictions. So what does it say about reality? That’s that’s and I think I may slightly disagree with you and Weinberg on another issue, which is I think the mathematics has to be the servant of physical problem solving. You have a problem in physics. You know, how do you explain the photoelectric effect? How do you explain the energy levels of the hydrogen atom and in relativity? How do you reconcile gravity with special relativity? Those were problems and the answer was not an equation. The answer was an idea about how the world could be, which then required a very difficult climb up the mountain of finding the equations that express that physical solution.
Brian Greene
Then right, it’s only then is it necessary to take the mathematics seriously because the mathematics has then passed through the test of expressing a solution to a problem. Right. Yeah, in the best of all worlds, I agree with that perspective. I’ve also found in my own work in sort of the era that we’re in that sometimes it does have to be the reverse because we don’t have the data in the realms that we want to describe. And so, you know, it’s definitely an accurate accusation that sometimes we’re putting the math before the physics. You know, the horse we want to be in front of the cart. But what is the horse? Sometimes it feels like the horse is mathematics. But in any event, you know, one of the main issues in trying to come to grips with quantum mechanics is to come to a point of view on how you think about this thing that we call the wave function. So again, our audience is familiar, I think, with many of these ideas, but it’s good just to backtrack a little bit. You know, the data and the research in the early part of the 20th century convinced people like Bohr and others that there’s this probabilistic description of reality that comes to the fore. And there’s this mathematical gadget called the probability wave or more precisely the wave function that includes the probabilities for an electron being here or there or over there and so forth. And the big debate for a long time and really still till today is how should we think about this wave function? Is there a real thing in the world called the wave function, even though we can’t smell it or taste it or touch it? Or is it something that just describes our knowledge about the word sort of the ontology versus the epistemic approach to how we should think about the probability wave? Where do you think we should come down on that?
David Deutsch
So I have for many years now adopted a different view of how this stuff all fits together. I think that the Schrödinger picture, which is the one that uses the wave function and as a probability wave and the probability of one thing happening rather than another, that is, I think, a misleading way of expressing the theory. Though it does express the theory correctly and fully, but it’s misleading in that it doesn’t include an account of how the outcome comes about. So I favor using the Heisenberg picture, which is the other way around. It takes as fundamental the observables of a physical system exactly like classical physics does. And the state is a constant. Therefore, it doesn’t; you can take it to be anything you like, any convenient thing so long as it is something. And what really moves or changes what causes the outcome, what explains why the outcome happens is just the motion of the observables of a physical system exactly like in classical physics.
Brian Greene
So we don’t have to think, you know, what is the wave function of the universe? If I change it here, why does it change over there? That kind of that none of that happens in the Heisenberg picture. It’s slightly harder to use in many cases. But for understanding what the theory says, I think it is far clearer. But historically, it’s quite interesting because Heisenberg came up with his approach about a year before Schrödinger, if I’m not mistaken, driven by his conversations with Niels Bohr, where their basic approach was, let’s only ever talk about the things that we can observe, you know, and let’s just try to find the dynamics, the equations that govern those things. And Heisenberg comes up with this equation. But the way it’s framed mathematically is, at least in those early incarnations, is so complex looking because you have to talk about, you know, all possible outcomes of all possible experiments that you could undertake on a physical system. And so a year later, when Schrödinger comes up with the probability wave, the wave function approach, well, a wave we know about water waves, you know, about electromagnetic waves. It was so much closer in a way to the things that physicists were comfortable with that Schrödinger kind of won the day, at least in that historical period.
David Deutsch
Yes, there are several ironies about that period of about a year when everything happened. One of them is that the Heisenberg picture was originally called matrix mechanics because Heisenberg expressed it as matrices. But he had never heard of matrices. Matrices were not covered in the mathematics for physics class in his day. So other physicists had to tell him what you’ve just invented is matrices. And now I prefer to call them Q numbers because matrices are just a representation. And there are many other representations. And we should concentrate on the physics, which says that basically that variables in the real world that look like real numbers are actually Q numbers. They have a lot more structure than a real number does. And that gives rise to the whole of quantum mechanics. And in the Schrödinger picture, there is a ghost of this unfamiliar complexity in that the probabilities that are purportedly described by the Schrödinger wave function don’t obey the probability calculus. They only they only obey it in regard to the outcomes. But if you apply it all the way through, then you get violations of, you know, the probabilities of two mutually exclusive things add together. So that that’s no longer present. So but you don’t need that to calculate. You only need that to try to understand the theory. But for understanding the theory, that is fatal. Although I think Feynman once said, let’s allow negative probabilities.
Brian Greene
You know, what’s the harm? But I don’t know if he’s joking. Yeah, I mean, obviously, as we all know, having studied the mathematical innards of the theory, we know exactly what Feynman meant by that, you know, in terms of allow the probability amplitudes to combine in a manner that allows negative numbers and complex numbers. But you’re right when it comes to the actual probabilities. You know, we have to do something to those amplitudes. We have to take the norm squared for those in the audience familiar with the math. And that’s been an interesting puzzle since the early days as to why that is the way this probability calculus does work in quantum mechanics. So heading onward to attempts to turn this quantum idea into a full theory, you put your finger on what has long been a missing piece or the puzzle, which is how do you get to the outcomes? Right. So even Schrödinger, as you say, he writes down this equation for how this probability wave, if you allow me to use that language to describe it for a little bit. Now, how this probability wave varies in time. But then he doesn’t say go out and observe the probability wave as you would a water wave. He says, go out and measure where you find the electron on a whole slew of identically prepared versions of a given experiment. Work out the statistics of your observations and compare that to the probability wave properly turned into probabilities through this norm squared procedure. So this is weird moment where you don’t actually see the primary actor in the theory. You just see a glimmer of that actor in the actual data. And people have tried to figure out how to bridge that gap. Now, one bridge that you and I grew up with was to say, you know, it doesn’t sound very nice, but the shut up and calculate approach. I guess it was David Mermin, I think, who framed it this way, which simply says, don’t worry about what you’re doing at that step. Just assume that there’s something that bridges the gap and follow the rules. And for certainly when I was a student, that was it wasn’t even questioned. Like I was a student. I took quantum mechanics back in the 1980s. And yeah, that was just what you did. And you couldn’t ask. So it feels like Bohr’s shadow, you know, was cast over many, many decades post the 1920s, 1930s.
David Deutsch
Yeah, a very good way of putting it. And the result is a sort of induced. What do I call it? Induced cringe or something. The students, students of quantum mechanics are trained not to ask those questions. And if you’re trained not to ask certain questions, that has an effect on your worldview. It has an effect on the culture in physics because students think that they’re the only one who worries about this. And in fact, they all worry about this. They’re the ones that are studying physics in order to understand the world. Always worry about this. And they learn this language of substituting ideas about abstractions for ideas about reality. So you ask what actually happens? And the answer is, well, the wave function. And so that the wave function is a function. It’s a mathematical function. And what we would normally do, as you said earlier, is we would ask what thing in reality does this function refer to? And in Heisenberg picture, the equivalent question has an answer. It refers to the actual variables of the physical system. And if you ask what is the outcome of the measurement, let’s say, well, then primarily the outcome is another Q number, another the matrix which has lots of different values simultaneously. So, you know, that should lead you to Everett type thinking. But then you say, well, how come I don’t see many of them? Well, then you can ask within quantum mechanics, how many of them will I see? And the answer comes out one. Then you ask which one? Oh, all of them. So how do you reconcile that? And that is the sort of progress one can make by taking the theory seriously, which one can’t make by adopting one of these copes.
Brian Greene
But among those copes and we’re going to come to Everett in a moment. But among the copes, if you allow me to be a bit a historical in the temporal outline of our discussion. So there’s a very straightforward cope which came from three physicists whose initials are GR and W who came up with what’s called the GRW approach. And they said, look, you know, if you want to align with experience where you only ever see a single outcome in any given experiment and yet this probability wave speaks of many possible outcomes, how do you go from the many possibilities to one? They said, let’s change the equation so that there actually is an explicit procedure, an explicit effect in the physics that causes the probability wave over a very short period of time. When a macroscopic piece of equipment or observer is part of your system causes that probability wave to change its shape, to not be spread out and allow many possibilities, but rather to kind of spike or in the language of the field collapse, which is sort of a weird term because it’s not really collapsing. It’s collapsing and spiking, you know, to spike at one particular outcome. So they gave a cope that may not be aesthetic, but it seems to be the most straightforward or a pretty straightforward approach. Now, of course, it’s a new equation and you might say, well, you know, now you’ve sort of ruined the aesthetics of the theory. But what do you think about that cope?
David Deutsch
Well, I think it was applicable in practice at the time when it was proposed. But it is, in my view, destroyed by quantum computation because in this collapse or spike or whatever you call it has to take place at a certain speed or at a certain complexity or at a certain something. You need a parameter that says how fast it will do this and when. And if the bigger the quantum computer you’re contemplating and I accept that we don’t have one yet, that’s very big. But let’s take as a hypothesis that it will be made one day. Then if you’re going to set this parameter so that the collapse or the spiking happens too slowly, then it will extend into the human observers. And if you make it happen too quickly, then the quantum computer won’t work. And this dividing line where you’ve got to set the parameter is going to change every time somebody makes a better quantum computer. So it’s a bit like saying, as Lewis Carroll did, I was thinking of a plan to dye one’s whiskers green and always use so large a fan that they could not be seen.
Brian Greene
OK, you know, how green are you going to make your whiskers and how large a fan do you want?
David Deutsch
There’s got to be a theory of this. And I don’t think it can survive the practicality of quantum computers. Of course, if it turns out that for some reason they’re not practical, then something like GRW could be a candidate. Although you’d have to have, I think, a theory of why the parameter is what it is.
Brian Greene
So but I agree. There’s definitely tension, you know, that that can emerge there. The other approach that I wanted to quickly talk about, although you may want to talk about it post-Everettian, you know, back in 1927 or something, De Broglie introduced an approach to quantum mechanics, which was then rediscovered by David Bohm in the 50s. And it’s kind of a dark horse approach to quantum mechanics, the De Broglie-Bohm approach. People don’t in like I don’t know of a physics course where it’s taught like I teach it when I teach quantum mechanics. And I have to tell you, there were some in the department at Columbia who, when they heard that I was going to include that in the curriculum, I kind of felt they weren’t too happy that that I was doing that. And my view is that here’s an approach to quantum mechanics where particles have positions, particles have speeds. There’s this real wave that does something in this approach that kind of pushes the particles around. It feels to me that, yes, you have to go over to a probabilistic view of the world, but you don’t have to give up as much if you still have definite positions and speed. So it feels to me that this should have been given more attention historically. Now it has been in certain circles since then. What’s your view of that approach?
David Deutsch
I agree with you that it well, for a start, it is different from all the copes. I wouldn’t even call it a cope. It is it is a real realist theory of the world that tries to make the same predictions as quantum theory. It does have probability, but only at the beginning. So the objection that it doesn’t satisfy the probability calculus doesn’t apply to Bohm. So it’s okay in that respect, but it has this I think original sin in it has this fundamental flaw that there’s a difference between the wave, the de Broglie pilot wave and the particle, or if all the particles are clumped into one configuration-space particle, the particle or particles. And the theory only makes sense if you equivocate between saying which of those is real. So I once asked at the one time that I met Bohm was he was giving a talk. I was in the audience and I asked a question at the end, which was is the pilot wave physically real? And in my view, he just mumbled because his theory if you say that it’s real, then the particle does not if you measure the particle, it does not is not measured at the place where it really is. You in an interference experiment, it can appear to be at a different place to where it really is. And if you say it’s not real, then you have to accept that particles are moved by empty waves in the wave function.
Brian Greene
Yes. So an empty wave can move a real particle. And if you measure the real particle, it’s not necessarily you don’t necessarily measure it in the wave that it is in. Right. So when you say empty wave, you mean a location where the particle is not.
David Deutsch
Yes.
Brian Greene
And yet the wave there has an impact.
David Deutsch
Exactly.
Brian Greene
Yes, for sure. For sure. Exactly. Yeah. So that’s weird. I agree.
David Deutsch
Yes. Well, that is I think that takes away the whole motivation of the theory because you can you can have it if the waves if the empty waves are allowed to have physical effects, then you can just remove the particle and just have the wave function, just the waves. And then you get Everett. So I think the de Broglie-Bohm theory is the Everett theory with unnecessary complications. That makes it very different from all the other copes, all the copes.
Brian Greene
Right. Right. And so given that, why don’t we turn to Everett since that’s the interesting approach that you’ve spent a great deal of time developing. And so, you know, I think people are familiar with the rough idea, but I’ll allow you to give your own summary. But basically it is if the wave function in that language allows for a range of possible outcomes. It’s not that when you observe the electron, one of them happens rather. They all happen. The reality embraces every possible outcome. And Everett came to this in, I guess it was 1957 by just looking at the equations of quantum mechanics and saying what, you know, to back to what you said early on, what is this theory telling me about reality?
David Deutsch
Yes.
Brian Greene
Throw away my preconceived notions of how the world is meant to be and just let me absorb what this equation is telling me. And that’s where it took him. Is that sort of an accurate way of thinking about how this came?
David Deutsch
I guess Schrödinger even indicated some ideas about this. Schrödinger had come up with the idea before, four years earlier, but had not developed it at all. So Everett was the one who didn’t know about that and developed it fully. But both of them used the Schrödinger picture. Therefore, their description of it had this problem that you change the wave function here and something changes over there. And its description of, for example, entanglement is not intuitive because you move something at you have two entangled particles. You move a magnet near one of the entangled particles and it changes the wave function at the other one. Why does it do that? Well, the wave function is actually six dimensional and blah, blah, blah. But again, in the Heisenberg picture, all you have to give up is the idea that the physical quantities are real numbers or integers or logical values. They are Q numbers. And when you change a Q number on the left in the experiment, the Q number on the right doesn’t change at all. It’s because the Q number on the right already has all of the potential outcomes. It has. Yes. And when you do the experiment to find out whether they’re correlated, you have to bring them together and make them interact. And that’s the only way it ever becomes meaningful. For example, whether one of them is parallel to the other or not. What does parallel mean? Well, it means if you bring them together, certain experiments come out the same and some come out different. So that again, the phenomenon of entanglement is as weird as ever. But the explanation for it makes sense in my view.
Brian Greene
Right. Right. And so when it comes to understanding the nature of reality, as we said early on, is sort of the goal of physics.
David Deutsch
Yes.
Brian Greene
To think in terms of Q numbers is itself a radical leap in thinking about the nature of the world. So isn’t it basically hiding within it all of the weirdnesses that we sort of have a more blatant in our face description of in the Schrödinger approach?
David Deutsch
Well, the two approaches are equivalent. It’s just that one of them makes it easier to get the results of an experiment and the other one makes it easier to get how the result comes about. So in practice, I use both. I still use both in practice, even though I advocate only the Heisenberg picture for understanding quantum theory. One of the advantages of trying to find out how the observed phenomena come about is not only that we want to know that because that’s why we’re doing physics. It’s that it’s only if you think of the theory that way that you can possibly make progress towards the next theory. Quantum theory is not going to be the last word in physics. They’re going to have successors. Now, if your existing take on quantum theory is kind of mystical that you’re not allowed to ask certain questions, then you’re not going to make the progress that will come from asking those questions. And there are plenty of problems in quantum theory that become apparent in the Heisenberg picture and are just hidden in the general gunk in the Schrödinger picture. For example, what is time? Time is all of physical quantities depend on time in both pictures. But time is a C number. So time can’t change. A classical number. Yeah, it’s a classical number and its commutator with the Hamiltonian is zero. Therefore, it can’t change. Okay, time can’t change. But time flows. It moves. Everything that changes changes with respect to time. So how can we understand how time changes? Well, that problem, I think, is not yet solved entirely. But the only progress that’s been made has been made in the framework of quantum theory, such as the Page and Wootters construction and which has been expanded by my colleague, Sam Kuypers and by others. And you can see that the questions that you can ask in the Everett picture because it’s fully realistic, make sense and can in a conceivable way lead to an answer.
Brian Greene
So when you intuitively think about the Everettian many worlds approach, I mean, do you absorb it at an intuitive level where you think of it as you order your dinner at a restaurant and you’re choosing, you know, the spaghetti or the roast beef? I mean, do you at that level imagine other versions of you in these other realms doing the things that you chose not to do in this realm?
David Deutsch
Yes. I think that that’s the way we can understand things like free will and the existence of counterfactuals and so on. That’s not to me that that’s not the hard part. The hard part is the stuff that we don’t understand yet. So, for example, we speak about the multiverse as being the parallel universes and the Q numbers describe the whole set of universes and their relationships. And, you know, that’s fine. But there is no theory of what the multiverse is mathematically. I find this perhaps a little hard to explain to in general because people are so used to the usual way of speaking. But in relativity, we have Einstein’s equations. They tell us how the quantities in Einstein’s theory behave, how they affect each other and so on. But we have R mu nu and G mu nu and so on. And in relativity, we can say, what do those quantities refer to? What is the physical reality that those things are properties of? And the answer there we have is four dimensional pseudo Riemannian manifolds with metric and so on. So then we know that it’s a theory that has equations. The equations apply to this thing, space time, which is very counterintuitive. But that’s what physics tells us is there. And we can learn to understand that simultaneity is not the same here as on Alpha Centauri and so on. We can learn to think that way. In quantum theory, the equivalent structure is missing. We’ve talked about the multiverse, but there’s no mathematical object called the multiverse in the theory. The only mathematical objects are the equivalent of Einstein’s equations and so on. They are the observables and the equations of motion.
Brian Greene
But why wouldn’t Hilbert space? Sorry for getting slightly technical. But why wouldn’t just Hilbert space be the right mathematical architecture for talking about this?
David Deutsch
Hilbert space is linear for a start and to combine that with. Well, I haven’t spoken about the problem of combining the two theories, but that’s a different issue. Yeah. So but OK, even if we don’t combine them, we need to have something in which there is a structure of universes. We want to be able to say the multiverse resolves itself approximately into these approximately autonomous things called, which we call universes. They’re not exactly autonomous, so they’re not really parallel universes. They’re almost parallel. And in an interference experiment, they affect each other strongly. And they are those are all approximations to the multiverse. But so we need to think that you can’t have an approximation where you don’t know what it’s an approximation to. That’s the thing that’s lacking in quantum theory.
Brian Greene
So help me help me fully understand. So, for instance, and again, I should full disclosure. I’m deeply intrigued by the Everettian approach, but I am not taking the step that you would hope all physicists do take and just say this is absolutely the right way to go. But if I was trying to describe the many worlds approach, say to my students, I would set up this mathematical thing which embraces the probability waves, which in technical language of the Hilbert space, I then introduce this idea so-called decoherence, which shows that when a system interacts with a sufficiently robust environment, it winds up in a quantum state where the interference effects that you’re describing are suppressed. So it’s as if these realms approximately are parallel to each other in the sense that the odds of them coming back together and affecting each other exponentially drops very close to zero. Wouldn’t that why would that what would that be lacking in your way of describing things right now?
David Deutsch
So it’s lacking the structure that you’ve introduced after saying what it is. You said you said it’s a Hilbert space and the state is a structure in that Hilbert space. And then and then everything you said after that is not derived from the fact that it’s a Hilbert space. It’s derived from the fact that the Hamiltonian takes a certain form. Why does it take a certain form? Because it’s local. It’s local in space. Space is an emergent property of the multiverse, not of Hilbert space.
Brian Greene
Good, good, good, good. Yeah. So yes, you’re talking that deeper level of question and as you probably know, you know, within string theory where, you know, again, I don’t know your views of string theory polarizes the community, of course, but some of the wondrous ideas of recent discovery is giving insight into how space can emerge from a quantum theory where you don’t inject ideas of space and well, time is there, but you don’t inject space from the get-go. So like I feel there’s progress along the directions that you’re indicating, but I fully agree that we’re not there yet. But if I backpedal just for a moment, one of the historical objections and one that people still talk a lot about today, if you’re involved in a conversation about quantum mechanics and Everett is the most straightforward issue that even those in our audience who aren’t familiar with Hilbert spaces and all the stuff that we just went off on a little technical diversion onto, if every outcome happens, which is sort of the basis of the Everett approach to things. And yet at the same time, the way we confirm quantum mechanics is by checking its probabilistic predictions. It raises the question, of course, if everything happens, what does probability mean? Right. If the electron will wind up here in one universe, there in another, there in another universe and so forth. In what sense is there a probability for it to be at one location or another? Because in the multiverse, it will in the God’s eye view exist at every possible location. And you, of course, have pushed this problem to a place which I believe you think is a solution. Can you just give a feel for how to resolve that conundrum?
David Deutsch
Yes. So in my view, as you said, and not all colleagues agree with this, to put it mildly, but the ones who understand it do. There is no such thing as probability at a fundamental level. The world, according to Everettian quantum theory, is completely deterministic. The equations governing the multiverse are deterministic. They’re the differential equations, just like in classical physics. When you make a measurement and you see a certain outcome, the question of probability then arises when you want to make inferences from that outcome. For example, if the quantum mechanics predicts 99 percent or the square of the amplitude for doing that is 99 percent, then you expect it to happen. And if it keeps not happening, you think there’s something wrong with the theory or with the experiment or with your conception of probability or whatever, but you think there’s something wrong. That already is to me the clue to the answer, because if the notion of probability is only ever needed when you make decisions, then the decision theory needs to be part of your theory of it. So fortunately, there is a decision theory in the world. It was largely pioneered by von Neumann, who also pioneered the wrong interpretation of quantum mechanics. It’s an axiomatic theory that says things like that if you prefer x to y and you prefer y to z, then you also prefer x to z. Those axioms make up the whole theory. Then it has an additional axiom that says each of these things, x, y and z, has a probability. And the probabilities have to add up to one and obey the probability calculus. He didn’t say, but he should have said, at the time when you make the decision. It doesn’t have to be true at any other time, and indeed it demonstrably isn’t true at any other time. So now, therefore, I thought, oh, and in quantum mechanics there’s an equivalent thing. There’s the structure of quantum mechanics, which is deterministic, and then there’s the so-called Born rule, which attaches a probability to each outcome according to a certain formula that he proposed. And this works. So then you have quantum mechanics with a pragmatically useful Born axiom, and decision theory with a pragmatically useful probability axiom. What happens if you smush them together? That’s what I did, and removed from each of them the probability axiom. And you ask, without the quantum mechanical probability axiom and without the decision theoretic probability axiom, how does the combined theories tell you how to bet when a quantum outcome can be two things at the same time? And lo and behold, it tells you to bet exactly as if there were stochastic processes with those probabilities. So I think that solves the problem. It tells us that we were wrong to want probability to exist at a fundamental level, or for there to be a theory of it that is compatible with fundamental physics.
David Deutsch
We only want it for making decisions. And if we apply it with conventional decision theory, stripped of its probability axiom, then we get the answer we want. I would have accepted it if it hadn’t given the answer we want, because it makes sense. But as it happens, it gives the answer we want.
Brian Greene
And some of the objections, I mean you made humorous reference to those who don’t fully agree as yet. I mean, a number of objections people put forward. Is there a unique measure that can uniquely be linked to probability and the way that we use it to test these theories? David Albert had this fatness measure. What if your concern for a given branch was not just the measures that you’re describing, but also your mass in that universe? People have tried to do the self-locating uncertainty, imagining you’re doing an experiment, you close your eyes, and then that’s when probability comes in. You ask, when I open my eyes, which universe will I be in? And so on. Have any of these given you pause? Or you just think, no, people just don’t fully understand? And if they did, they would agree.
David Deutsch
I think David Albert would be an exception to the set of people who don’t understand it. He has got a way of objecting to the theory, but his objection is along the lines of, your axioms don’t cover all possible realities. Sorry, how should I put this? Your axioms don’t cover all the ways that probability could enter the world. For example, if you had nonlinear preferences about the probabilities themselves, then you would make different predictions. Well, you’d make different predictions, but then you’d find that your preferences didn’t conform to physics. So, yes, also David Wallace, for example, who does agree, but thinks that my formulation is inadequate, and it needs more mathematical structure. Yeah, I don’t mind that. The important thing is, the theory is deterministic, and it meets what we need of probability in order to do experiments. We need to say if something comes out, if something is predicted to be astronomically unlikely, then we should be surprised if it happens. Now, if you tweak that and make it slightly different, and then you want to test that, that’s all right with me. I mean, I don’t think that unmotivated changes in the theory are ever likely to be borne out in experiment, but that’s a legitimate thing to do.
Brian Greene
Right. Now, there have been people who’ve asked the question in a more serious way than the question I asked you before about being in a restaurant, and do you sort of imagine yourself having both outcomes. People have taken this way of thinking about the many-worlds approach, the Everettian theory of quantum mechanics, to what you might consider as a logical place, but a little bit dark. If you wanted to maximize the happiness of all David Deutsches, you know, I mean, there’s so many variations on it, but I guess the lottery version, you know, you play the lottery, and if you lose, you extinguish yourself, because you only want the David Deutsches that persist to be the ones that are billionaires. There is one way of ensuring that all the poor versions of you are excised from this grander reality, and just don’t do it, people watch, you know, this is insane. But like, how do you think about these ways of embracing these ideas?
David Deutsch
So I think that that is a fallacy. It comes from mixing the old conception of probability with the quantum conception of probability, which I outlined, which is deterministic and so on. In particular, it’s saying that, as it were, the real you is the surviving you, which makes sense in the frequency interpretation of probability, but not in the objective conception of probability that comes out of the Everett interpretation or decision theory. So it’s an unsupported claim, an additional claim, that I should care about the surviving copies of me and not care about the dead copies of me. Why should I stop caring about the dead copies of me? Well, it’s because you only care about the surviving copies. Well, that’s circular. I can’t be persuaded to not care about the dead copies of me by telling me that I should care only about the surviving copies. And the argument that makes sense of probability, in my view, tells you specifically that you should quote care. I mean, it’s not about caring anymore, it’s about being rational, according to decision theory and quantum theory. That tells you that you should weight the possible outcomes by the same weights you would use if it were a stochastic process.
Brian Greene
Right. And then another related question that even comes into the issue of free will that might be fun to spend a couple moments on thinking about it, but you know, I’ve taught these ideas to students, a not infrequent response among some of the more thoughtful is, then why should I do anything? Because not doing anything is presumably non-zero probability, and there’s going to be some universes in which that happens. And I’ll just leave all the grunt work, the hard work of living to the versions of me that are guaranteed to exist in other branches of the probability calculus. Similar, I presume you give a similar response to that, but how do you respond to that?
David Deutsch
It’s much the same argument the other way around. It’s saying I’m going to care about the other, the hard working versions of me, and no, which way around is it? Oh, no, it’s a hybrid. It’s saying I’m going to care about the hard working version of me when it comes to working out probabilities of what good is going to happen, and I’m going to care only about the minority of me who just sits on the couch in terms of deciding what to do. Well, to do that you’ve got to violate the axioms of decision theory. Good luck trying to set up a version of decision theory that doesn’t have that. By the way, this move of David Alberts and other people to say what if you cared about things other than the outcomes, basically? Well, that’s true of classical decision theory as well. Von Neumann and Morgenstern or whatever their names were, they laid down some axioms for decision theory that they thought were intuitively right. But if you lay down different ones, then you will get different answers. And the only way of, well, there are two ways of deciding. One is whether it’s, three ways, one is whether it’s internally consistent. One is whether it conforms to physics, and the other is whether it conforms to your experience or to experiment ultimately. So the, you can’t arbitrarily choose what decision theory to use in terms of what you care about. You could say, well, I hate von Neumann and I’m not going to use his theory. But that’s not an intellectually consistent position to take unless you have an alternative to it.
Brian Greene
Right. And so, when you think about experience and wanting to align these ideas with experience, the dominant feeling in human experience is that we do make our own decisions, we make our own choices, and we have a freedom of the will that is exerting itself in there. Normally when I think about free will, I find it useful to divide the question up into a kind of classical version and then a quantum version and try to first convince people in a classical world, I just don’t see any room for free will at all because according to classical physics, the motion of the particles is fully deterministic and everything that you do and you think is just the motion of particles in body and brain, so there’s just no room there. And then the move is, well, and in quantum mechanics, sure, it’s probabilistic, but since we don’t volitionally control the probabilities, we can basically port over the classical conclusion without any change. Where do you, I mean, you spoke of us having free will earlier, so obviously you disagree with what I’m describing here. Where does the disagreement happen?
David Deutsch
When we spoke about free will earlier, you were speaking about my theory about free will in the multiverse, but I no longer think that that’s decisive. So my current take on free will is that there definitely is such a thing as free will, and it’s very important, but it has little to do with the multiverse. Good. So it would work in an indeterministic universe or a deterministic universe or a quantum universe, so I think my new view is more robust, and it is this. The objection that you have just made to the existence of free will is, I think, in my terms, that when you make a decision, like whether to eat spaghetti or beef, it feels subjectively as though you’re bringing something new into the world, namely your decision to eat spaghetti or beef, but in fact that decision was itself determined by the previous state of the universe, and therefore your feeling that you brought that thing, that decision, that novelty into the world is just an illusion or a mistake, not even an illusion, it’s just a mistake that conflicts with our best theory of physics. Now, I think that the reason that’s wrong is that there really is something new that you’re bringing into the world when you make a decision. Not any decision. If you make a decision according to a rigid rule that you decided before, then the decision came at the time when you decided on the rigid rule. But we do sometimes bring something new into the world, new knowledge, basically, and I want to get away from the idea that Einstein didn’t invent his theories, the Big Bang invented them for him. That I don’t think that everything that is in the universe, everything that explains the universe, was already present in the set of all things that explain the Big Bang. So, knowledge and free will are explanatory ideas which speak about an emergent layer of physical events which obey laws of their own. So, I would say, when Einstein came up with the new idea, whatever was the new idea, so he came up with the new idea to solve the problem of how do you reconcile special relativity with gravity, he had an idea, then, and at that point, there was something new in the world. Nobody had ever thought of that idea before. The Big Bang hadn’t thought of it. His colleagues hadn’t thought of it. Previous physicists hadn’t thought of it. It was there, and it obeyed the laws of epistemology, for example. It was produced by conjecture and criticism, and religious belief couldn’t possibly have created it, and so on. So, it obeyed laws. It came into existence. And then, he had to do the grunt work, some of which was, again, creative because he had to decide what things to work out and what order to try ideas in, but when he was doing a calculation, he was then doing what ChatGPT does now for us, the grunt work. I always refer to Edison, who said that discovery is 99% perspiration and 1% inspiration.
David Deutsch
Well, the thing about perspiration is that it can be automated in ChatGPT. Inspiration can’t be automated. So, it’s inspiration that creates the novelty. And free will is the ability to create novelty.
Brian Greene
So, let me ask you a question then. So, imagine I’m an alien, and I have very unusual senses relative to human senses. When I look at Albert Einstein, or you, or anything, but let’s say I’m in the room in 1915 in Berlin with Einstein, trying to get the tensor calculus to work out and write down the field equations for general relativity. So, I’m in the room with Einstein, and I don’t actually see a human being an aggregate. My senses are such that I see right into the little particles that make up Einstein and his brain, his hand, the pencil, and so forth. And there I am, and I’m watching him write down R-mu-nu minus a half g-mu-nu R equals 8 pi G T-mu-nu over c to the fourth. But the way I see it is just this aggregate of particles moving around in such a way that other particles are moving over a flat set of particles and leaving a gray trace of particles that has Einstein’s equations on it. And so I articulate what I see totally at the particle level, totally described using, let’s just say the laws of classical physics. I said it doesn’t really matter which set of laws that we use. What am I missing? Where is there freedom of the will in Einstein’s 1% of inspiration? Why is this set of motions of atoms different from all other sets of motions of atoms?
David Deutsch
Yes. If you try to explain what is happening, if you get it right, I don’t know whether this alien you’re imagining is so powerful that you can also see the future of what this is going to be, but some deposition of atoms on, I don’t know if you used a pen or pencil, of carbon atoms on the page cause an atom bomb explosion in a few decades’ time, and some don’t. In order to link those two, you have to use explanatory theories unless you imagine an alien that can perform the exponentially large number of computations that would…
Brian Greene
But that is what I am imagining. It’s exactly what I’m imagining. So maybe you say to me, you know, from computational irreducibility, but I’m really talking more like theoretical. So if the alien can do that, then he will still…
David Deutsch
Well, does he need explanations? Because once you’re thinking of a world in which explanations make no difference, then you’re also thinking of a world where free will doesn’t make any difference and knowledge doesn’t make any difference.
Brian Greene
Which is where I am. Which is the dark place I live.
David Deutsch
But… So he would still say there are two possible sets of motions of all these atoms and the carbon atoms and so on. Some of them have very different futures from the others. I may not be interested because I can work out at a glance which is which, but it’s an objective fact that one of them has a qualitatively different set of outcomes from the others. In fact, one of them could blow him up. And most of them couldn’t. The existence of those and their properties and how they came about, again, I don’t know if you’re thinking of this alien as doing science, but if he’s curious about the world, he surely wants to know what is the difference between that configuration and the other configurations.
Brian Greene
Right. So what I would say is, and maybe this is what you’re saying in just different language, what I would say is that there are different levels of explanation. Yes. And the one that I just described is sort of the rock bottom undergirding of everything, but it’s not the most useful one, obviously. And at higher levels of explanation, yeah, we want insight. We want to have an understanding that we can actually wrap our minds around for why it is that this happens versus that happening. And at that emergent level, free will is a useful idea. And allowing the kinds of explanations of the sort that we’ve been talking about is very useful in order to have a deeper grasp. But I would say that in the back of our minds, we should always recognize that compatibility among the different explanatory levels is really important. And that compatibility does strongly suggest that our intuitive feeling that we are the originators of the actions is misguided.
David Deutsch
I think not, because there’s nothing intrinsic to that lowest level that you’re talking about that says that everything else has got to be expressed in terms of it. What if we just took, instead of taking level zero, we took levels two, three, four, 17, 19. If we took enough levels, maybe we could deduce the laws of zero level from those. So which level is the most fundamental level of explanation is not given to us by our theories. It’s a thing that we impose in addition to our theories. Moreover, this now you’ll have to stop me speaking because this takes us to constructor theory. But let me tell you quickly what constructor theory is about. It’s a theory that tries to express the whole of physics in terms of what processes, what transformations can be brought about and what cannot be brought about. So it’s not which will happen and which won’t happen. That’s the laws of motion view. I propose that we abandon laws of motion view and speak entirely in terms of what can and can’t be brought about. And then you see that the existing view, which is that the world, all the explanations in the world are basically initial conditions plus all the motion, which is why I had to talk about the big bang knowing about Einstein’s theory. If I talk in the by the way, doesn’t have to be the big bang and can be the big crunch. It can be the state of the world next Tuesday that everything reduces to people who deny the existence of free will. Never say I’m thinking what I’m thinking because of the way the world will be next Tuesday. But it makes exactly the same sense as with the OK. But although we have extremely good laws of motion and extremely deep and powerful theories about what the laws of motion are and what the things in motion are like we don’t have for the multiverse. But we don’t have very good theories for the initial conditions. In fact, we have really only hand waving because we’d like to say the initial conditions are homogeneous. Space time is homogeneous. It obviously isn’t homogeneous. Otherwise, it would be homogeneous now if it was. So it’s homogeneous, modulo quantum fluctuations. Well, what do quantum fluctuations mean? They’re not really fluctuations. They’re just differences between different universes. So what’s the initial condition in the multiverse? So we don’t have that. But in constructor theory, we might hope and I’m not saying we have this yet, but we might hope that a full theory of what can and can’t be brought about will imply at an emergent level. Because then both the laws of motion and the initial conditions would be emergent properties of these statements about what can and can’t be brought about. That the initial conditions will have to obey such and such a regularity if the possible and impossible tasks, as we call them, are as we say they are. And my favorite example of this is we think that in the world there is computational universality. That is, the computers that we’re using here to communicate cover that they can perform any computation that can be performed within the limits of their memory and speed. And that if we wanted more memory and more speed, we could arrange for that by adding more memory and going to a faster speed. So that fact that this can be pursued without limit is an emergent property, in a normal way of thinking of it, it’s an emergent property of the laws of physics. In constructor theory, you can instead say, you can instead postulate a law of computational universality, that the physical world can instantiate computers of arbitrary memory and so on.
David Deutsch
If that is so, that rules out certain initial conditions of the Big Bang, including the completely homogeneous one, but including lots of them, including almost all conditions of the Big Bang, are ruled out by the equivalent of the dynamical law or the constructor theoretic equivalent of the dynamical law, that there’s computational universality in the universe. So that’s how…
Brian Greene
When you say ruled out, what dynamics are you, I mean, how are you connecting the overarching principles of computational universality with a temporal moment that is so different from today?
David Deutsch
Well, I use an extreme example because to do that, you don’t need dynamics. You need to only have symmetry. You need to only say, if the initial conditions are homogeneous, then they’ll be homogeneous now, so they won’t be…
Brian Greene
Got it, sure, sure, sure, sure. Absolutely.
David Deutsch
But I expect more, I hope, more detail is possible.
Brian Greene
Right, right. Yeah, no, that’s a fascinating turn, which I’m not as familiar with. I should probably do some reading on constructor theory, which I have another conversation at some point. In terms of what level I preference, yeah, I definitely do think in a temporal sense, so I think back to the fundamental ingredients and I think of the higher levels coming as higher level aggregates form over time, of course. And that’s where my bias or preference there comes from. One final question, David, and then, yeah, if you’re willing, I’d love to do this again at some point as I become more educated on the ideas that you were just describing. But, you know, Einstein had this dream that one day physics would return to a more familiar place, the kind of physics that he grew up on, where, you know, there’s a definite state of the world. It’s unique. There’s these definite laws of progression. It’s a dream that I think Gerard ‘t Hooft, you know, Nobel laureate, shares with Einstein and he’s been working for a while and I’ve been at a distance following his progress on trying to come up with an underlying theory that would yield quantum mechanics as an effective theory at higher scales. But down deep would have features more familiar to Isaac Newton, you know, than the usual way of thinking about things. Do you think that is possibly in our future or is it time that we just bite the bullet and recognize that, you know, physics changes as we learn more and we have to give up certain cherished ways of thinking about things?
David Deutsch
Yes, though I would put it in what I hope is a more comforting way than that. By the way, Bryce DeWitt said that he was sure that if Einstein had lived another few years, he would have come to like the Everett interpretation because it is fully realistic. He died just before.
Brian Greene
Two years before?
David Deutsch
Yeah. Well, two years before the publication, but Everett was already, you know, they were both at Princeton.
Brian Greene
Right, that’s true.
David Deutsch
Yeah. So, you know, it’s something that might have been. But in ancient Greek times, people hoped, some people hoped, Pythagoreans hoped, that the world was fundamentally integers, that all the relationships in the world were relationships between rational numbers, ratios between integers. And at some point, not even before Pythagoras, they realized that the square root of two is irrational. And it took like another 2000 odd years before people had a satisfactory theory of real numbers that included the rational numbers and the algebraic numbers and the irrational numbers and the transcendental numbers. And now we think that describing the world in terms of real numbers is the standard thing. It is the thing that was always true and that’s the thing we want to come back to. And that’s not true. It is a radical new idea about the physical world. By the way, a single real number has as much information in it as the whole multiverse. Yeah. So if you really want to understand the present day view of conventional physics, it must include real numbers. And it must take this fact into account that real numbers are very counterintuitive if you start from the beginning. Now, I think that the step from real numbers to Q numbers is not very great conceptually. Because it doesn’t involve any violence to how everyday experience matches with the underlying reality. That step was already taken when the move to real numbers. That’s the thing that Zeno couldn’t get his head around. That there’s an infinite amount of complexity in the smallest thing. And quantum mechanics, well, Heisenberg just had a real matrix, well, complex matrix, but complex numbers are just a pair of real numbers. So he wasn’t making such a big step as the ancient Greeks or the 19th century mathematicians, depending on who you want to. So just a factor of two is all that Heisenberg did, in essence. Yeah. So we do have to conform our intuitions to our best theories. But I don’t think it’s such a wrench as you make out.
Brian Greene
Right. Well, look, whether or not those in our audience find that comforting, I can’t say, but certainly is a fascinating way of looking at the history of the subject. So David Deutsch, thank you so much for the conversation. We’ll get back to it at some point. And I’d love to continue on in the future. So thanks so much.
David Deutsch
Thank you.
Brian Greene
Thank you.
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