(bright music) ♪ Hey ♪ (bright music) - Welcome back to "Conversations at the Perimeter." Today, we're bringing you a conversation with Lucien Hardy. Lucien is a theorist here at the Perimeter Institute, and he works in quantum foundations and quantum gravity. - And Lucien was actually one of the very first researchers to come to Perimeter Institute about 20 years ago, when the institute itself was really just a theoretical idea from Mike Lazaridis, the founder and the creator of the Blackberry.
So I loved hearing Lucien tell stories about some of the early days working with the other original researchers here, like Lee Smolin and Rob Myers, who's now the director here at Perimeter. - I also really liked the part of the conversation where he told us that his perspectives on physics and specifically the operational approach that he uses to study quantum theory was significantly influenced by the time that he spent in an experimental lab.
He actually says that every theorist should have to spend time in a lab. (Colin laughs) - And Lucien is also, I'm pretty sure, the only person that I've ever interviewed who has a paradox named after him. Hardy's paradox is this thought experiment that he devised in the early 1990s, and he tells us about in this conversation. He also told us that Hardy's paradox paradoxically may not actually be a paradox. So try to get ready to wrap your mind around that, and let's step inside the Perimeter.
(light music) Lucien, thank you so much for joining us here today. - It's my pleasure. - You've been with Perimeter Institute, I looked, for 20 years. It's 2002, and we're coming up on- - Yeah, yeah- - Your 20-year anniversary- - Almost 20 years. - Can you tell us what does somebody do as a theoretical physicist at Perimeter for 20 years? - Well, I mean, lots of things.
(Lauren laughs) (Colin laughs) I guess one of the great things about being in an environment like this is it influences you, and you change your research direction. So when I came here, I had some interest in quantum gravity, but that's now increasingly the main thing I'm interested in, 'cause of people around it are thinking about this, too. So there's never a shortage of people to talk to, and ideas to think about, and so, yeah, I'm busy. I have lots of things to work on.
- You mentioned that right now you're really focused on quantum gravity. Can you tell us what that is?
- So I'd like to say that the, like there's a problem with quantum gravity, and this is that we have two less fundamental physical theories, so general relativity, Einstein's theory of gravity on the one hand developed in 1915, 1916, and then we have quantum theory on the other hand developed by a whole bunch of people, including Einstein, so Heisenberg, Schrodinger, many others, developed in the mid-1920s.
And those two theories are both very successful predictively where they apply, but they don't fit together. They don't fit together mathematically. They don't fit together conceptually. Really, it seems there ought to be a kind of unity in nature. We should really only have one theory that describes all of nature. So if we have two different theories describing different parts of nature, that isn't a satisfactory situation.
So the problem of quantum gravity is to find a new theory, and probably a deeper, more fundamental theory, which approximates to general relativity on the one hand in situations where that theory has been experimentally confirmed, and approximates to quantum theory on the other hand in situations where that theory has been experimentally confirmed.
- When I was preparing some notes for this conversation, I wrote down only one sentence that had a big box around it in big block letters, and it said, "The problem with quantum gravity," because it seems like that's a very big problem. Why is it so difficult to reconcile quantum mechanics with general relativity? - Yeah, I don't know. (group laughs) I mean, if I knew the answer to that question, I would have done it already. You know, it's 100 years or so now since the problem has been around.
- I'm not placing all the blame on you personally for not having done it- - I have not done it so far. (Lauren and Colin laugh) Yeah, I don't know. What I think is happening is that I think we're just not asking the right questions. We're not thinking in the right way.
You know, if you look at, you know, historically at other situations, like after Newton developed his theory of gravity, his theory, universal theory of gravity, he wrote down this equation, he didn't like it, because of it had instantaneous action, a distance, like I mentioned, and no substance mediating that force. And so, he did the natural thing.
He tried to invent a sort of mechanism by which gravity could act like that, so two masses that are far apart could influence each other, and not just him. Other people also tried to think of, they were called, you know, mechanical aether models, so mechanical models that you could use to explain how gravity worked. These models were, you know, amazing.
They were quite detailed, and you know, people spent a lot of time doing calculations, and sometimes successfully reproducing Newton's equation of gravity. You know, for example, Newton himself had this idea that the force that caused planets to be attracted to one another was the same as the force that causes aeroplanes to fly. So in some sense, he anticipated the work of Bernoulli, which came, you know, about 50 years later. You have an aeroplane wing.
Then the speed at which the air particles go underneath the wing is faster than at which they go over the wing, and if the speed is reduced, if the particles go faster, then they don't hit the wing as often, so there's a lower pressure. And so, that puts a force on the wing, and makes the plane go up. And Newton had this idea, you know, already back then, and he thought he could come up with some mechanism which explained gravity.
Rene Descartes had this idea about vortices, very detailed models. There were many, you know, interesting characters, and that seems to be a lot of what people were doing were trying to come up with mechanical models to explain gravity.
And then even later with electromagnetism, when Maxwell, Maxwell himself actually used a mechanical model to explain, to derive his equations of electromagnetism, people were just trying to explain things in terms of the concepts they understood, in terms of the concepts they were familiar with, and everyone was familiar with stuff, you know, stuff pushing on stuff. That was a, that's a familiar concept. And so, and I think that's where we are now.
We're bringing to bear on the problem of quantum gravity the ideas that we understand, and it's probably just not sufficient. We probably have to find a way to think beyond that, or to somehow get out of ourselves, and look at the problem from a different point of view. It turns out to be very difficult. - I think it's really a unique challenge in this field, right?
Because you really, from what you're describing, you really need to find a way to think in a different way, and not rely too much on something that you already understand, whereas in other fields of research, we would be trying to build on things that we already understand, or look at consequences of things that we already understand, and whereas you have to probably keep reminding yourself don't think too much about those things that you already understand, try to think in a new way.
So how do you train yourself to be in a kind of state of mind where that new way of thinking is possible? - You could imagine developing a systematic approach to that sort of thing. You could perhaps follow sort of lateral thinking techniques, or some sort of meditative approach. I don't do that especially. I think I just, you know, sort of throw myself in every day and try to think of new ideas.
I don't have a good answer to that question, but I think it's a question that people should think about. What are the methodological tools you should bring to bear on physics? I've even asked philosophers. You know, philosophers spend a lot of time looking at physics, and often speak about the work after it's been done. But philosophers could position themselves in such a way as to attempt to provide working physicists with methodological tools.
You know, how do you go about, well, in this case, for example, finding a deeper, more fundamental theory when you have two less fundamental theories? That seems like a fantastic philosophical question. You know, even if you don't actually construct the theory, just what are the methodological approaches to solving that kind of problem? But philosophers haven't really worked on that as far as I'm aware. So yeah, it's a fantastic question.
I don't know the answer to it, but I think we should think about it. - That's great, yeah.
As a follow-up to that, I'm just curious if there was a satisfying solution of quantum gravity that was proposed in the near future, either by you, or someone else, so that you needed to go think about some research in another field, would you want to look at the consequences of this solution of quantum gravity, or would you wanna find a new area of physics where you need to find another more fundamental theory? Because that's kind of the way of thinking.
- Oh, right, so that's a good question, too.
If you look at, contrast Newton and Einstein, the two people I keep confusing, Newton spent a lot of time, you know, doing calculations, and being very careful about what, you know, what is theory really predicted, theory of gravity, and Einstein has been criticized for not doing enough of that in the case of general relativity, and there was kind of a lull in general relativity, and then some years later, people took up the cause again, and did all these amazing calculations.
So I hope in that particular case, I would be more following along this sort of Newton type approach. It's difficult to anticipate- - Of course. - In advance. - Yeah. - The challenge that you're working on, it seems like there's a parallel to 100 years ago, and how are you trying to build a model of, or a version of quantum gravity that overcomes some of these differences between quantum mechanics, relativity?
- So you mentioned that parallel with the problem 100 years ago that was solved by Einstein when he combined Newton's theory of gravity with his theory of a special relativity, which included Maxwell's equations. It's a sort of an example. So I take that parallel very seriously, and if you look at what Einstein did, how did Einstein go about solving that problem? How did he go about coming up with the theory of general relativity?
Well, he had to go through a number of steps, but his starting point was what he called the happiest thought of his life, which was when he came up with the principle of equivalence, and the principle of equivalence is really just this. If you imagine having a box, and it could be an elevator, and you have, you know, a person inside it and some objects, and that box could be falling, or it could be floating out in space, and imagine there's no windows.
So the person inside has no idea of which of the two situations they're in. So I suppose they'd be screaming. But aside from that, in the case where the box is falling, everything would be falling at the same rate. And so, it would feel like it was floating around. It would feel like they were floating out in space.
And so, Einstein said these two situations are equivalent, and that was the starting point, and then that idea gets turned into some beautiful mathematics, and he ends up incorporating geometric ideas that he learned from Minkowski, and also from his childhood friend Marcel Grossmann. Grossmann was a mathematician, who knew about the sort of field of differential geometry, which went back to the mid-1800s. So there was lots of steps.
It took him from 1907, when he had this happiest thought of his life about the elevator, until 1915, when he finally wrote down the correct field equations. - And how did he know in 1907 when he had this thought that it was definitely an important ingredient in formulating GR? You know, it still took him eight years to finish, so I'm just curious. - Yeah, it's a great question, and I'm not enough of a historian of science to know exactly what his thinking was around that.
But you can see looking at the idea that it has lots of promise. Suddenly, previously we thought of gravity as a force. So Newton's first law says that a body will continue, you know, at a state of rest, or in a constant speed in a straight line until it in essence is acted upon by an external force, and gravity was regarded as an external force. So under gravity, a body wouldn't go in a straight line.
It would go along a curve, and that was okay, because gravity was regarded as an external force. And suddenly, Einstein saw a way to stop thinking of gravity as a force at all, and think of it as, you know, more to do with geometry. So a particle would actually be going sort of in a straight line once you're in this falling frame of reference, I mean, for a while. The principle of equivalence only applies in small boxes over small periods of time.
He must have seen that, and realized he was onto something big. I can see that would have been the case. - Mmm-hmm. - In terms of your research into quantum gravity, what is the sort of parallel challenge, or the parallel path you're trying to take to make progress? - So Einstein, as I said, started with this equivalence principle.
And so, the idea is that perhaps there is a quantum equivalence principle that can play a similar role in constructing a theory of quantum gravity that the equivalence principle played in constructing the theory of general relativity. So I should try to explain the quantum equivalence principle, but to do that, I kind of need to back up a bit.
You're asking the question of how do I combine general relativity and quantum theory, where you should look at these two theories, and ask, you know, what kind of theories are they? They each have conservative and radical features. So general relativity is conservative in that it's deterministic. It's a classical theory. - By conservative, do you just mean that it's similar to other theories that came before it? - Similar to, yes, theories in the past, yeah, yeah, yeah.
I think that's what I mean. Yeah, it's not surprising in some sense, and perhaps it's not surprising because of that similarity. - Mmm-hmm. - So it's conservative in that sense, that it's deterministic. But it's radical in that the causal structure is dynamically influenced by the distribution of matter. So the causal structure is the pattern of before and after, things, how things are, things, events are before other events.
It's this pattern of events that are before and after each other, and that pattern is influenced by the curvature of space-time. So if you, if matter affects the curvature of space-time, then matter affects the causal structure. And so, that's radically different from Newtonian physics, for example, where time was regarded as this absolute structure in the background. Time just evolved, unaffected by anything else. So dynamical causal structure is this radical element from general relativity.
And now, if you look at quantum theory, well, it also has radical and conservative elements. The conservative element is that the causal structure is fixed. Just like Newtonian causal structure, it's fixed. It's in the background. It doesn't change. And the radical element is it has this property, I would call it indefiniteness. So a particle, if it can go along one of two paths, it actually goes along both paths at once. It doesn't go along a definite path.
So it's indefinite as to which path it goes along. But I call that indefiniteness. So if you take those two radical properties together, and if you believe a theory of quantum gravity has to follow the radical path in both cases, then you expect a theory of quantum gravity to have indefinite causal structure. Causal structure will not just be something that varies, that changes, but also there will be two different causal structures at the same time, in some sense.
Same time is the wrong word, but two different causal structures will both, would both be, would both hold. So that's, I think, the sort of the central property we're likely to have in theory of quantum gravity. And that's a really strange idea, the idea that if you have two events, you know, usually you'd think, "Well, one event is before the other event."
You know, event A is before event B. But here, you could have it being true that event A is before event B, and also event A is after event B. Both of those things would be true, not just one of them. Yeah, so you'd have indefiniteness as to the causal structure. That is not something that we're used to, or it is not, that we're not used to thinking about the world in those terms. So the question is how do you make sense of that? How do you do physics still when you have something like that?
And so, the idea is to look at what Einstein did with the equivalence principle, and what he did was he said, well, you may have behavior, which is, let's see, like non-inertial, so it looks like things are moving in curved lines. It looks like things are behaving in a weird way.
But you can always transform into a frame of reference where you just have objects moving in straight lines, where Newton's laws apply, where things are just moving in straight lines, and that's called inertial behavior. So, and the way you do that is just by looking at it in a frame of reference that's falling. At least for short while locally things will be moving in a straight line.
So a different way of understanding what Einstein did with the equivalence principle is to say the equivalence principle says that there always exists a frame of reference with which, with respect to which the behavior is inertial in a small vicinity around any point. The question is can we take that principle forward to the problem of quantum gravity?
And the idea is to draw an analogy between inertial behavior and definite causal structure on the one hand, and non-inertial behavior and indefinite causal structure, 'cause in general relativity, non-inertial behavior is the sort of the weird thing that you're trying to tame by going to a falling frame of reference. In quantum gravity, indefinite causal structure is the weird thing that you're trying to tame. So that's the sort of background, and now, what would the principle say?
Well, the principle would say can you find a sort of frame of reference, where you get rid of indefinite causal structure, at least locally in a small region? Well, that's not quite enough. What you need to do is find what's called a quantum frame of reference, and this is a subject that was developed many years ago by Yakir Aharonov, and other people, quantum frames of reference. And it turns out you can do this.
So what you can do is you could find a quantum frame of reference, a quantum coordinate system to measure that frame of reference, where locally in the vicinity of a small point, you get rid of indefinite causal structure. The causal structure becomes definite. - So you know that A causes B?
- Yeah, you know that A causes B. Now, what you do when you impose that, you try to make it work in a small region, and then everywhere else it goes haywire, but that's okay, 'cause you can hope to use the tricks that Einstein used in general relativity. In his case, he knew he could locally make everything inertial, and if he did that, you know, far, far away from there, it would kind of go haywire. - Mmm-hmm.
- Crazy, non-inertial behavior, but that's okay, because he could write down some equations at that point that worked. And so, the hope is to be able to do the same trick in quantum gravity. - Is it especially difficult because you're dealing with these more radical, what's the other word? - Non-conservative? - Non-conservative element? Is there more uncertainty, or just probabilities, as opposed to certainties?
- A different approach would be to say, "Well, now, "I'm gonna take the more conservative path in each case. "I'm gonna look for a theory which is deterministic "and has fixed causal structure." It just seems unlikely to me that that would work. I mean, it's not completely impossible. It may be you could find some theory that was in some sense more classical, more like older theories, where that worked, and there are even ideas that I think fit into that category.
It seems to me to be the wrong idea. One should embrace the radical elements, and see what, how to go forward. - And is that what's really unique about your approach to quantum gravity? Is that what sets your approach apart from other approaches? - Definitely it's true that my approach is to put this indefinite causal structure front and central, I think. This is the central conceptual problem, and then we work out from that. Other approaches, in as far as I understand them, are not doing that.
But you know, everyone has their own take on this. So I think what's important when it comes to solving problems like the problem of quantum gravity is that there are many different approaches. So pluralism is essential in physics, as it is in other walks of life. And so, I'm hoping to bring, you know, a different kind of approach. I mean, there are other people now thinking about indefinite causal structure and quantum gravity, so I'm hoping there's starting to be a bit of a community.
- Basically a 100-year-old problem more so in terms of marrying these theories. Is that challenging for a researcher to be working on a problem that has passed through other researchers' careers without being solved? - Yeah- - Do you foresee a day when you say, you, or a colleague says, "Oh, yes, that's quantum gravity, we've done it"? - I mean, I think we can do it.
I mean, there are, I don't know the particular approach that I'm taking is the right one, and you know, it may well not be the right one. There could be some young physicist at the moment who has the right idea, or somebody who's, you know, yet to even enter the field of physics. - Mmm-hmm. - Typically, big breakthroughs are made by young people in physics. And so, that's really where the hope lies.
- And what would it mean if it were, maybe you haven't even thought about that, but if there, these big questions had a solution, if the new theory, the unifying theory, was found, what would that mean for physics? Would physics be, done and we can all go home? - Yeah. (Lucien laughs) (Colin laughs) I mean, again, it really depends on what the answer is, doesn't it? I don't know.
You know, people were thinking about electricity and magnetism, and people started to become aware that there were these electric, started sending electricity through wires, and well, they had, you know, magnets forever. And I don't know if people before, before the subject was really completed by Maxwell, I don't know if people really understood what it would mean, what it would mean to have Maxwell's equations written out. Maxwell's equations have had a tremendous impact on humanity.
So much of our technology relies on understanding electricity and magnetism, and conceptually, you know, I'm not sure if people anticipated that this would lead to problems with relative motion. Problems come up when you get an answer, when you start to get a theory, and you can't really anticipate that in advance. Who knows? When someone comes up with a theory of quantum gravity, I think we'll be surprised by it.
It'll be interesting, and I think it will lead to questions that we can't possibly anticipate at at this stage. - I know that one thing that's important in your work, if I understand correctly, is that you have a set of axioms that you use as kind of the center of your work, and can you talk about why you use that kind of approach? - Yeah, so this is what happened. I mean, I should talk about my career. I started off in quantum foundations.
I did my PhD in, from 1989 to 1992, a time that the field of quantum foundations was very concerned with interpretations of quantum theory, you know, how do you make sense of quantum theory? And there was all these different interpretations, like the many worlds interpretation, where every time there is a quantum choice to be made, both things actually happen. The world splits into two copies with one thing happening in each copy of the world.
And by the world, I mean the universe, everything, and there's the de Broglie-Bohm model, where the quantum wave function guides actual particles that exist, and those particles are guided along a path by this wave, and many other interpretations. And so, that was what people were thinking about, and that's what I was thinking about. I became a bit unsatisfied with that way of thinking, because it didn't really seem to lead to any new ideas.
It didn't seem to lead to the possibility of real progress in fundamental physics. It was a lot like the aether theories, the mechanical aether theories. You know, people took Newton's theory, or Maxwell's theories and tried to make sense of those equations, and those ideas turned out not to be useful, and my feeling increasingly was that this wasn't a useful way of making progress in quantum foundations. And then I came under the influence of Chris Fuchs, and he was asking this question.
He was saying, "Well, can you derive quantum theory? "Can you derive quantum theory from some more basic ideas?" He wasn't the first person to ask that question, but it was the first time I'd encountered the question.
In his case in particular, he was working in this sort of new field of quantum information, and he was saying, "Well, can you give "an information theoretic reason "for the axioms of quantum theory, "for the structure of quantum theory as it was?" And so, I set about working on that. This was in 2000, 2001. And you know, eventually, I found a way to approach that problem. So the idea was to be very operational.
What I mean by operational is to just talk about what it is you do, the settings of knob settings, and so on, and what it is you see, like detectors clicking, lights flashing. So he- - Sorry to interrupt, though, but as a theorist, you are proposing the theories, but you're not the one actually turning the knobs, and watching the lights blink on and off? - Well, I mean, I, I mean, as an aside, I actually, I worked for two years in laboratories.
So I worked for one year in the laboratory of Anton Zeilinger in Innsbruck as it was then. I mean, I was a theorist, but I was allowed to look at the experiments. - You're allowed to touch the lasers? - No, that was- - Okay. - A step too far. - Yeah. - I was allowed to be in the same room as the experiments, and again with the same restrictions I worked in Rome in the research group of Francesco De Martini.
- Mmm-hmm. - So actually, he was more willing for me to get involved, but by that point, I was too cautious. And that was really interesting to actually see people doing experiments, you know, 'cause it's a remarkable skill. People, experimentalists have to solve problems that theorists can't even imagine. So for example, Rome, it's very hot, and the temperature goes up and down, and the air conditioning was broken.
So you'd have these beam splitters mounted on a metal base, but the metal would contract and expand, and that would mess the experiment up. They had to find a way to solve that problem. They had to buy this metal called Invar that has a very low expansion coefficient, and then the experiment was stable. I find that fascinating, you know? The real stuff of experiments is really interesting, and how do you get the information from here to here, the electronics attaching to it?
So I think every theorist should be forced to work in another laboratory for a while. - You think that informed your operational- - Absolutely, yeah- - Approach? - So I think, so that was probably in the back of my mind, and so, that's what pushed me towards this operational approach. So the operational approach is really just taking it seriously. Experimentalists have to do experiments.
They have to go into the world, and put things in different places, and set, you know, set knobs to different positions, and read off the data. So I set up a framework like that, and then furthermore, add in probabilities, because quantum theory is all about probabilities. You know, in the end, quantum theory, in some sense, quantum theory is a more natural descendant of classical probability theory than it is of Newton's theory. Quantum theory is a probabilistic theory. - Mmm-hmm.
- And so, I set up this way to write down sort of just probabilistic theories that pertain to operational situations. So you have an operational situation. You have probabilities. You can write down a mathematical framework that applies to that situation. - Mmm-hmm. - And then once you have that mathematical framework, you can say, well, you know, maybe I can find some principles, or postulates, or I call them axioms, that constrain you.
And you know, so say, you know, initially you have all possible probabilistic theories, but now you want to specialize to particular probabilistic theories. And so, the axioms I wrote down, I wrote down enough axioms that would get you to quantum theory, and that was work I did in 2001. So that was a very interesting exercise, and I felt like that kind of work helped to make progress. I felt like I was understanding quantum theory in a new way that I hadn't previously understood it.
- You said you think all theorists should have to spend some time in the lab. Is that, is it a different part of the brain that activates to work in a experimental setting? - Absolutely, yeah. I mean, like I said, I've never actually sort of actually got my hands dirty, so to speak, and moved these things around, but really a laboratory looks nothing like a bunch of equations, like these equations here.
It's a completely different world from a laboratory, and you don't really understand physics until you understand that it is about the experimental world. It's about experiments in the end. - And would it be the same framework that you hope might give quantum gravity, but with a different set of axioms? - Yes, so what happens is I did that work in 2001, just before I came to Perimeter Institute, and then I came here, and people were thinking about quantum gravity.
You know, there was string theorists, Rob Myers and Lee Smolin working on loop quantum gravity. And so, quantum gravity was very much in the air at Perimeter Institute back then, as it is today. And I started thinking, "Well, perhaps we can take "this kind of general probabilistic technique "that I developed, and apply it "to the problem with quantum gravity." Otherwise, what is it good for? You know, it's a lot of fun to, it's called reconstruct quantum theory.
So you start off with some general framework, you write down some axioms, and you get quantum theory. But we already knew what quantum theory was, so it wasn't really pushing us forward. It was just providing a new way of understanding things. What would be a real test would be if we could start off with some general framework, apply some axioms, and get quantum gravity, a new physical theory. That would be a great test. So I started thinking about that.
One of the problems was that the operational framework I developed wasn't really hospitable to a theory of quantum gravity. I realized you'd have this property of indefinite causal structure I mentioned earlier. The order of events would be indefinite, and well, the operational framework had boxes with wires connecting them, and those wires were the direction of time. So a wire, a particle would leave one box and go into another box, and that would be happening forward in time.
So it wasn't the right framework to treat the problem of quantum gravity. So I set about building a framework that would be hospitable to quantum gravity, I hoped, and this was a frame, a probabilistic framework that was capable of admitting indefinite causal structure. I took a very general operational approach. I tried to really sit back and ask, you know, what is an experiment? You know, what do we do in an experiment? How can we translate that into a mathematical framework?
You know, so in an experiment, what you do basically is you make choices. Like I said, you know, you set knob settings, and you collect data. And so, I imagined a mathematical framework that was capable of analyzing that sort of situation probabilistically, but very generally, without assuming any definite causal structure.
So that was work I did in 2005, and I called it the causaloid framework, 'cause the central mathematical object in that framework was something I called the causaloid, and that's really driven all my research since then is the attempt to formulate quantum gravity in this kind of more general mathematical framework.
You know, if you think about it, Einstein, when he was developing general relativity, needed a mathematical framework to do that in, and he was lucky that Riemann 65 years earlier, or thereabouts, had developed Riemannian geometry. This is a framework of curved spaces, and Einstein was able to take that mathematical framework directly, and use it for general relativity.
And so, the question was, well, maybe we need some similar sort of mathematical framework, but for the problem of quantum gravity. So that was the idea. But that, you know, that was 2005, and I'm still working on it. So it's not clear to me that that's exactly the right framework, but at least it was an idea, and it's something that came out of my earlier work on axioms for quantum theory that you asked about. - Mmm-hmm. - I jotted down some of the places that you've been.
You've mentioned Ireland. You went to Tirol, Durham, and Rome, and Oxford, and then you came here. You mentioned to us how you were convinced to come here. Can you just share that briefly with (laughs)- - Yeah, I was in Oxford. I was happy in Oxford. I mean, I had a position that would've lasted for 10 years, and I was about halfway through that. I was very happy there, and I did seem, I just saw my life as continuing there.
But then at a certain point, a sort of curious character visited called Howard Burton, and you know, I chatted with him for a little while. He said he was working on this project to set up a new institute, and then he went away, and I kind of forgot about it. About a year later I was getting, you know, communications from him, emails, and he was trying to call me.
- And this is just when Perimeter Institute is starting at- - Yeah, so this was even before Perimeter Institute really existed, and he, I mean, I guess formally it existed perhaps at that point, and he was, you know, he was starting to try and recruit people, you know? So at that point, I don't know that he'd recruited anyone at that point. But then when he started to communicate with me later, the place actually existed. There were people here.
Lee Smolin was here, and Rob Myers were here already, and other people. And he was calling, and of course, I never answer the phone, and he was sending emails, and I never answer emails, and I was very busy at the time with just life generally. And so, I ignored all those communications. I mean, I meant to respond, but I never did. And then Mike Mosca was visiting Oxford, and Mike Mosca had done his PhD in Oxford, so I knew I knew him very well.
And then he had come over here to, he's Canadian, he'd come to Waterloo, and was very involved in setting up Perimeter Institute. So Mike Mosca was visiting Oxford, and he came, and Howard sent a plane ticket with Mike Mosca for me to travel to Canada. - A plane ticket with your name on it- - With my name on it, yeah, yeah. - That's bold- - And so, so I guess I just agreed, I guess, at some point after he did, but I didn't- - And here we are, 20 minutes later. It wasn't a return ticket.
(Lucien laughs) (Lauren laughs) - Actually, it was a return. (Colin laughs) (Lauren laughs) I remember being, you know, impressed, because, you know, I was, I remember being impressed when I got to the airport and there was a limousine waiting to bring us to the institute. I'd never been in limousine like that before. So you know, he brought me here, and I met him, and I met Lee, and Rob, and I met Mike Lazaridis.
I met Mike Lazaridis and David Johnston, and who subsequently became the Governor General of Canada. At that point, he was the head of the university. I met them in Ethel's Diner, (Lauren laughs) which was the location just on University- - Still there. - Still, actually, no, it burned down, (Colin laughs) (Lauren laughs) and then they built a new one. - Yeah. - So the particular one that we met in burned down. - That one was on University- - Yeah, yeah- - That one, oh, I didn't know that.
- Yeah it did. - Okay. - So we met there, and I chatted, and you know, I realized that this was a really serious endeavor, and there was a lot of backing behind it. And so, I kind of, I caught the bug, and I agreed to come to Canada- - Did you agree on the spot? - So the way Howard did it back then was he would, you know, he would bring people over, and then he would have them visit lots of different people, and then he would take them to a restaurant.
It was just me and Howard, and he wrote a number on a piece of, on a napkin, which was the salary I was supposed to get, and he pushed it towards me. - Oh, no- - Like a movie! - Yeah! (group laughs) - Well, I think Mike had done the same thing on Howard when he recruited Howard. So, (Lauren laughs) and I didn't understand exactly what a Canadian dollar was worth, but it was, it seemed good, and so, I agreed at that point to come.
- Going back even further, was this, were you a born physicist, you were meant for this, and this was the path all along, or did you, did it take some time to find? Can you tell us a bit about when you first got interested in science? - I mean, of course, when I was five years old, I wasn't reading physics textbooks. There were no physics textbooks around. More likely to be astrology textbooks than the physics textbooks in my background.
But I think I was always interested in, you know, making things, hammering together pieces of wood. At a certain point, we moved to a house, and across the back from the house, there was an electrical repair shop. This shop had, you know, televisions, broken televisions. You know, the guy, when he couldn't fix something, he threw it out the back.
So there were broken televisions, and broken record players, and broken radios, all sorts of things, and I was allowed to just go and take that stuff, and look at it. So you know, I would take the stuff apart. There were, in those days, things had vacuum tubes, rather than integrated circuits, which made a very satisfying noise when you threw them down. (Colin and Lauren laugh) Bang.
And so, I would take those things, and I would, you know, like combine two broken record players to make one functioning record player. I can't claim that I really understood exactly what was happening, but I think it got me interested. And so, that was probably one of the earliest times I started to think, "Well, this is something I could do," and my mom said, "Well, you know, "this is a job you could have. "You could fix electrical objects," and that seemed to be exciting to me.
- So then how did becoming a theoretical physicist happen? - Well, and then at a certain point, they started teaching physics at school, and I was very interested in that, and I studied it really, really hard. And so, I think, I guess at that point it becomes a fairly, fairly standard sort of path. And the school I went to wasn't terribly academic, but the teachers were very good, and the physics teacher was great, Mr. Barnforth, and he got me interested in physics.
So I, of course, I passed all those exams, and got to university. But even before I got to university, there was a radio program on BBC Radio 3 that was made by Paul Davies, who's a physicist, but also a very good popularizer of physics, and it was called "The Ghost in the Atom." My dad recorded it on a tape cassette. Had the radio playing, and he put the tape recorder next to it, recorded it, and he gave that tape cassette to me.
So I had this tape cassette in my possession for a number of years, and I would listen to it over and over again, and there were lots of physicists, some of which I got to know later, but he had people like John Bell, David Deutsch, Alain Aspect, many other very interesting physicists who were thinking about the foundations of quantum theory, and they were speaking in a way I'd never heard anyone speak about physics before. This is a very weird subject, you know?
How did you interpret quantum theory? What does the wave function mean? All these- - Mmm-hmm. - All these questions were completely new to me, and I think that was when I got hooked on quantum theory- - And then- - Quantum foundations. - "The Ghost in the Atom," the radio series, it was collected as a book as well, I believe- - That's right, yeah, you can still buy that, I think. - And then there was a book called "Elegance and Enigma"- - Yup.
- "The Quantum Interviews," which in the introduction it says this book is in some ways sort of a spiritual successor to "The Ghost in the Atom," and you are throughout this book. How did you go from being inspired by "The Ghost in the Atom" to essentially contributing to its sequel- - To its successor, yeah. So I hadn't thought of it like that.
Well, it was a great idea that Max Schlosshauer had to put that book together, and he sort of interviewed, or he didn't interview us, you know, in an audio way. He got us to write little pieces, and answer to a bunch of questions he had. I guess he was asking questions to the kind of successors of the figures that appeared in "The Ghost in the Atom." It's a long story, 'cause I, (Lauren laughs) I did a degree in physics.
You know, if you want to become a physicist, probably the best way to do that is do a degree in physics, and then I did a PhD in quantum foundations. I mean, even that in itself was a difficult thing to do because there were very few people doing quantum foundations at the time. It was regarded rather unfavorably. It was not thought of as being a sort of subject you would do if you were serious. But I was too interested in it to care about that.
So I found somebody who was willing to supervise a PhD, which was my supervisor, Euan Squires. I did a PhD in it, and just kept going. You know, once you start doing research in physics, you just keep going, and it's endlessly fascinating. Quantum theory is endlessly fascinating. It's constantly surprising. You think you've understood everything there is to understand about quantum theory. You work on it for 20 years, 30 years, and then it surprises you yet again. So it's easy to keep going.
It's a really, really interesting subject. - Well, we have more questions, and they're not even from us. We collected some questions from students. So Lauren, do you want to- - Sure, yeah, we have some great questions from some graduate students here. So I think we're ready for the first one. - Matt Duschenes, a PhD student at Perimeter. I'm wondering do you feel axiomatic approaches allow for easier collaboration and mutual understanding, as everyone is coming from the same starting point?
- Let me think about that. I think that's right. What these axiomatic approaches do is they force you to clarify very basic concepts, so that you can talk to people, and you end up having to clarify these concepts outside the natural habitat of quantum physics. So an example would be, you know, in quantum theory you have Hilbert spaces. You don't need to know what a Hilbert space is, but it's an object that has a dimension, N. So N is an integer.
It can be one, two, three, four, et cetera, and that's just a number that appears in quantum theory. But if you want to understand what that concept really means, then you should think about it in operational terms. And what it really means in operational terms is what are the number of preparations that you can prepare for your system that can be perfectly distinguished?
So by thinking in operational terms, you're forced to clarify concepts that might have just been elements of an obscure mathematical framework, and I think that's true not just for that example, but there's many concepts like that. They help people make progress in physics, I think, yes. - The next question is from another student here at Perimeter Institute. It was sent in anonymously, so I'm gonna read it. The question is, "You've famously axiomatized quantum mechanics.
"Do you think that a part of trouble with quantum mechanics "is similar to the one we have "in the foundations of mathematics, "where we know that there are a lot of true statements "that are not provable from the axioms? "Similarly, in quantum mechanics, "even though we have a set of axioms, "there will always be statements in quantum mechanics "that are true, but we can't derive them, "or understand them starting from first principles "of quantum mechanics, such as axioms."
- So people have thought about this kind of question. I'm not among them. There's this very interesting work the question alludes to on the logic of mathematics, and whether that work has some corresponding element in physics, and people have definitely thought about that. I think it's a difficult question, and it makes my mind go blank every time I try to think about it. I don't know how to begin to answer that question, but perhaps somebody who doesn't have my blind spots can.
I really have no good things to say about, no good answers to provide to what is a very good question. - It maybe requires a new way of thinking like you said- - Yeah, I, maybe I'm too old now to think (Lauren laughs) like that, yeah- - Great, we have one more question, and it's from someone that you know quite well. - I'm Nitica Sakharwade, a PhD student of Lucien's at Perimeter Institute. I'm graduating soon.
I had a question for Lucien about, like a broad question about the field of quantum foundations as it has evolved the last couple of decades. So I was just wondering, I was, since I have been, I had been writing my thesis recently, I was also going through your thesis, and I was just wondering what it was like, right, talking about nonlocality of a single photon at that time, when quantum foundations wasn't recognized as a field in itself quite, and how you think it has evolved?
In the decades since, like there definitely has been a boom, and I was wondering, so with the rise of quantum information, and then now more recently quantum computing, quantum hardware, quantum software, all of these things that are coming up, I was wondering what quantum foundations has to offer to them, and what are the things that quantum computing can bring? What questions it can bring back to quantum foundations? - Good questions, Nitica.
So yeah, definitely, it was a very different situation back then. You know, you didn't go into quantum foundations if you wanted a job, you know? It was sort of, you know, a temporary state of affairs before you had to find employment elsewhere, at least that was the idea, and nobody was taking it seriously. It started to be taken more seriously, I think, with experiments, so experiments in quantum optics in particular.
So already, even before I started, Alain Aspect did this sort of test of Bell's theorem, and even earlier experiments have been done by John Clauser and Freedman. But in the 1990s, these experiments became more and more serious. Leonard Mandel in Rochester, not so far away from here, did all these beautiful quantum optical experiments.
You know, when people do experiments, the rest of the physics world starts to take you more seriously, and these experimentalists were hungry for ideas, things that they could test. So that was a very good collaboration between the field of quantum foundations and experimentalists.
And then as quantum information came along, and also quantum computing, in the early days, the fields of quantum information and quantum computing were really, it was really just a joining of the fields of quantum foundations and computer science.
So if you went to conferences in the subject of quantum information, then half the participants would be from a background in quantum foundations, people I knew, and half would be people from computer science, and it was just these two subjects talking to each other, trying to get a common language, you know, like for example, Ben Schumacher, who was the quantum foundations person, came up with the term qubit, you know, qubit sort of borrowing on the term bit, which is basic in computer science,
bits at one, or zero. Well, qubit is the quantum version of that. And then once you start thinking in that way, all sorts of questions come up that weren't there previously, and you know, I worked in the field of quantum information a little bit myself for a while. I have papers on quantum cryptography, for example.
So this is a very exciting new way of thinking, and people in quantum foundations were in a really great position to contribute to that, to the development, and just even the idea of what that field was. And more than that, what was happening in quantum information and quantum computing was that you were finding a way to use quantum weirdness. So previously, quantum weirdness was sort of an embarrassment.
It was something that people hoped would go away, you know, trying to find an interpretation to get rid of it. Suddenly, now quantum weirdness was a resource. It was something that you could use. This is a point that Charlie Bennett makes frequently that rather than people in quantum foundations being, well, an embarrassment to physics, suddenly, we were useful. We could contribute. That was a great- - 'Cause you knew all about the weird stuff? - We knew all about the weird stuff.
Yeah, that's right, yeah. (Lauren laughs) (Lucien laughs) Just for that reason. So, and it was a wonderful period, and when it really wasn't. It was just an idea that came from, you know, marrying these two fields together, and it was a very, very fruitful way of thinking, and so much was possible, you know? But in those days, you didn't have to think very hard to write a paper that was relatively significant in the field.
The field of quantum information has since become much more technical, and people will build their whole career in the field of quantum information, you know, without having worked separately in quantum foundations, or in quantum, or in computer science. - So the conferences nowadays are all quantum computing experts instead of computer scientists and quantum foundations? - I mean, that's the impression I have. I mean, not all, but they- - Right.
- That's definitely- - Primarily- - The predominant makeup of those conferences, I think, which is, you know, is great, because there's a lot of very technical questions, but I think it's important still to keep looking to people in those two more basic subjects, because there's new ideas. One question I think is really important, and I still think this is something that we need to understand is what is it that gives quantum computers their power?
Why are quantum computers more powerful than classical computers? And this is a question I remember when the field of quantum computing first started to be worked on that people in quantum foundations were very interested in. I went to conferences with people in quantum foundations, and philosophers who were very interested in this question. What is it that makes a quantum computer so powerful? And there's many possible answers. You might say, well, it's because of quantum parallelism.
You have, you know, different, in quantum theory, you can have different things happening at the same time, this indefiniteness I mentioned. - Mmm-hmm. - David Deutsch believed that it was, that quantum computing was proof of the many worlds interpretation, 'cause in the many worlds interpretation, you have all these different realities being true simultaneously. And other people thought, well, maybe, you know, maybe it's quantum nonlocality.
Maybe the fact that you have entanglement, and entanglement enables a kind of nonlocal influence between different distant systems, and maybe that's what powers quantum computing, and people have working on this to some extent. You know, recent work showing that actually the advantage of quantum computers, it does relate back to Bell's theorem, does relate back to this- - Foundational? - Yeah, that relate back to these foundational ideas of John Bell proving nonlocality.
Another thing that people have shown is that it relates to something called quantum noncontextuality. I'm not gonna explain what that is, but it's a very, a basic idea in quantum foundations, and there seems to be a connection to, it seems that you can prove that quantum computing is related to that, too. So Joe Emerson at the at University of Waterloo nearby has worked on that, and there was a paper on the archive today talking about that.
So people are thinking about that, but I think there's still a lot more scope for that kind of interaction between quantum foundations and quantum information. - We're running out of time, but I have to ask, 'cause I've interviewed a lot of people, but I've never interviewed anybody with a paradox named after them. What is Hardy's paradox, and what's it like to have a paradox? - My wife asked me this question, you know, "How can you have a paradox?" And I said, "Well, you can't.
"There isn't really any such thing as a paradox. "So you can't really have a paradox "in physics, or mathematics. "It's always the case of you're not thinking "about the situation right. "So it looks like a paradox, but it's not really a paradox." And she said, "Okay, so I'm gonna call, "invent Hardy's paradox, "which is that there's no such thing as a paradox." And in that case, the Hardy is her, you know? So she called that Hardy's first paradox. - Right- - Zivy Hardy's paradox.
And so, then my paradox became Hardy's second paradox, and my paradox, which has to do with quantum theory- - I had a feeling it would. (group laughs) - Yeah, it has to do with quantum theory. So it goes back to work I did during my PhD, and it's really a situation where you have quantum entanglement, and you have two systems, and you can make measurements on each of them.
I don't want to explain all the details, but one way of thinking of it, it's not the way I originally thought of it, but other various people did, is that you can see it as a breakdown of logical transitivity. So if you have A implies B, that's a true statement, and then if B implies C, and C implies D, so if all those things are true, then you would expect from normal logic to have that A implies D, and there's a situation where that's not the case.
So you can have A implies B, B implies C, C implies D, but A does not imply D. - Sounds like a paradox. - So it seems like a paradox. Now, it's only an apparent paradox because what's happening is as you go from each of those statements one to the next you're changing other things, not the things that the statement is concerned with, but other stuff is being changed, and so, we can't actually make those logical inferences. It's only an apparent paradox.
I mean, I didn't call it a paradox myself, but I was quite happy to have a paradox. - Second paradox. (Lauren laughs) Yeah, your wife gets the first paradox- - Yeah, the first paradox, yes, yeah. - Well, I think we're out of time, but thank you so much for joining us. I'm sure we could ask a thousand more questions, but we won't. Maybe another time? - Yeah, well, thank you. It's been a pleasure. (upbeat music) - Thanks so much for listening.
Be sure to subscribe, so you don't miss any of our conversations. We've interviewed so many brilliant scientists whose research spans from the quantum to the cosmos, and we can't wait for you to hear more. And if you like what you hear, please rate and review our show on your preferred podcast platform. Great science is for everyone, so please help us spread the word, and thanks for being part of the equation. (upbeat music)