Instant Genius - Could 'counterfactuals' solve the biggest problems in physics?

Episode Date: May 17, 2021

Most laws of physics tell us what must happen. Throw a ball in the air and it will come back down. But physicist Chiara Marletto, a Research Fellow at the University of Oxford, says that laws like this only tell us part of the story. She believes that the rest lies in 'counterfactuals': things that could be. In her new book, The Science of Can and Can’t (£20, Allen Lane), she explains how these counterfactual properties could solve many of science’s biggest outstanding problems. Let us know what you think of the episode with a review or a comment wherever you listen to your podcasts. Subscribe to the Science Focus Podcast on these services: Acast, iTunes, Sticher, RSS, Overcast Listen to more episodes of the Science Focus Podcast: Prof Avi Loeb on what 'Oumuamua tells us about the problem with modern physics Marcus Chown: Does the Big Bang really explain our Universe? Dr Douglas Vakoch: Should we try to contact aliens? Katie Mack: How will the Universe end? Sonia Contera: How will nanotechnology revolutionise medicine? Everything You Wanted To Know About… Physics with Jim Al-Khalili Hosted on Acast. See acast.com/privacy for more information. Learn more about your ad choices. Visit podcastchoices.com/adchoices

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You're listening to the Science Focus podcast from the BBC Science Focus magazine team. With the UK's best-selling science and technology monthly, available in print and in several digital formats throughout the world. Find out more at sciencefocus.com or look out for us in your app store. Hello and welcome to the Science Focus podcast. I'm Sarah Rigby, online assistant at BBC Science Focus magazine. Most laws of physics tell us what must happen, throw a ball in the air and it will come back down. But physicist Kiara Marletto, a research fellow at the University of Oxford, says that laws like this only tell us part of the story.

She believes that the rest lies in counterfactuals, things that could be. In her new book, The Science of Canon Can't, she explains how these counterfactual properties could solve many of science's biggest outstretched. problems. First of all, could you please just give us a brief outline of what your book is about? Yes, so the book is about describing a new mode of explanation for physics, but not just physics, in fact, for science at large. And the key idea is to move away from the standard way in which physics has described the universe so far, which is basically in terms of laws of motions and trajectories of objects in space time with initial conditions and so on, and use instead statements about what transformations are possible

and what transformations are impossible and why as your fundamental building blocks. So that's the key idea in the book. And of course the book is about also a number of other things. There is a bit of epistemology in it, so the way in which science makes progress, and how is it connected with the fact that it's good from time to time to switch to new modes of explanation because it allows us to incorporate more things in the laws that we have in physics and in science in general.

And it's also a bit about storytelling. So you touched on this a little bit about the idea of what can and can't happen. So in the book, you talk about this in terms of an idea called counterfactuals. So could you just tell us a bit more about what a counterfactual is and why it's different from any other quantity that we would normally use in physics? Most of the fundamental laws of physics that we currently have are phrased in terms of factual statements about what happens to objects when you set them in motion in a sudden way. So, for example, you can describe how the ball moves in space with a given trajectory. Newton's laws are a good way to do that. However, there are other things you can say about the physical situation that are also important

in physics. And for example, thermodynamics is an example of a traditional field of physics where these other statements are central. And these other statements are the things I call counterfactuals. And they are statements about what can or cannot be made to happen on a given object. And so classic example is the conservation of energy, where we see. say that it is impossible to build a perpetual motion machine of the first kind. And this is a machine that creates, let's say, energy out of no energy.

Now, when we say that, we're not saying that this machine does not happen on a particular trajectory of the universe, let's say. That constraint in terms of what's impossible is much stronger than that because it says that it cannot happen at all, no matter what initial conditions are and no matter what the laws of motions are. So in that sense, these counterfactuals are deeper and more general than laws of motion. And the idea that I'm posing in the book is that there could be a much broader way of using them compared to just say thermodynamics or say information theory in a way to unlock a number of physical phenomena that are really based on counterfactuals rather than

factual statements that currently physics can't quite deal with. Right. So what sort of problems in could be sold by using counterfactuals? So one key problem is the problem of incorporated entities that have so far been regarded as as emergent and approximative, macroscopic and not really worthy in a way of being incorporated in physics. And one example of this is information. So when you think of what are the regularities in the physical world that allow for things that can process information to exist,

then these regularities are really not about what happens to given systems when they are set in physical states or some kind, but they are about what you can do or cannot do with them. So the classic example, again, it's an example of a bit. If you want to try to explain why a given system can be used as a bit to encode information, it's not helpful to say the bit is in a particular state at this stage. time, zero or one, let's say. But what we have to stress is the fact that the bit can be put in either zero or one, and its state can be copied onto another bit when it's available. And you see,

these two statements are about possibilities and they're not about things that happen in a particular condition to the bit itself. So in that sense, the whole of this physics of information and the physics of computing devices is based on counterfactuals. And by switching to counterfactuals, we can state exact laws about these things within physics. And then there's the physics of life, which is of course connected to this, in the sense that the physics of life is based on information, but there are additional features such as, for example, Brazilians, the ability of life to survive and perpetuate itself and so on.

And then there's the physics of thermodynamics, not just in the traditional sense of heat engines, but in a sense that underlies both the heat engines. as we know them traditionally, but also other machines that can include things like programmable machines that we call constructors, that are generalizations of programmable computers, and so on. So I think these are the three main lines of inquiry that this approach can help with. And of course, in the long run, it could help also with understanding the mind, the way in which the mind works from a physics point of view. In your book, you mentioned an analogy, and an example of a counterfactual could be a writer has a pad of paper that he only uses in an emergency or something like that.

And the counterfactual is that the paper has the possibility of being written on that it is not guaranteed one way or the other. Could you give us some more sort of real-world examples of what a counterfactual might be? Yes. So there are features of objects. that we use in everyday life that are counterfactual and they explain why these objects are out there. And so in a way, if you want to tell a story about these objects, without mentioning counterfactuals, that's a good analogy to understand what physics is trying to do currently with this phenomenon I mentioned earlier in the sense that you just will not be able to explain why that particular object is there. So the piece of paper that you mentioned is an example. But of course,

you can also think of a lifeboat on a kind of cruise ship. In this situation, the reason why there is such a boat there is the fact that there could be a shipwreck. And it actually could be that the shipping question never actually undergoes a shipwreck and everything is fine. And so the boat, the lifeboat is never used for the purpose. It's there. If someone asks you, why is that boat there, it's no use to say, well, the boat is there and this is the current state of affairs of the boat in question in terms of its actual state, what you have to say is that the boat is there because it can be useful, it could be useful in case the shipwreck situation occurs. So that's a kind of nice example that shows that if you're trying to tell a story about the boat, why it's there,

without mentioning counterfactuals, you won't be able to tell the whole story. And another example that I can give is this one about the fact that, you know, when you, when you describe a computer program being run on a given, on a given computer, you know, there are different ways in which you can explain what's going on. So one way is to just list the sequence of states through which all the bits in the computers go as the program unfold. So for example, let's say the program is to factor as a number. You know, you start with certain bits in a certain state and then you see what they evolve to, et cetera, et cetera, and it's going to be a string of zeros and ones in an appropriate sequence. Now, this is a way of saying what's going on at a certain level of description, and it's about what happens. But for you to understand that the computer is really factoring the number, say, 15 and not a different number, you have to consider what values could the bits have assumed, have taken if you had inserted a different output. So you have to consider all the possible other inputs of the computer other than the ones that's currently factorizing to understand that the computer is really running a program for factorization.

And this is another example where you can understand how to describe, for example, functionalities of the computer, you really need to contemplate not just the specific input that is currently being given to the computer, but also all the other possibilities. the inputs that it could be given. And finally, I give this example in the book about chess. One way to explain why, for example, one gets to a situation like a stalemate is to notice that, you know, if you consider the current state of the board, you can see that there are no legal moves that allow you to do, you know, to move the king in a different place, let's say. But there is a deeper explanation for why that is. And this is really encoded in the possible and impossible transformations that you give to each of the pieces on the board. And that is basically the essence of the rules of the game on chess. They are only really about possibility and impossibility.

And ultimately, an explanation of a particular configuration like a stalemate or a draw is really reduced to statements about these counterfactuals that have to do with how the pieces could be moved or could not be moved, whether or not in that specific situation that can be moved in that way. There was something that you said in there that I think, for me, at least made it clearest about what the real purpose of these counterfactuals is. And you said, without the counterfactuals, you can't tell the whole story. In quantum physics, we would often talk about probabilities. We would talk about how a particle could be in one state or it could to be in another state and we won't know unless we measure it.

Is this the same sort of idea as counterfactuals, or is it just a coincidence? No, it's not a coincidence, and this is very nice point you're making, that the essence of quantum theory is counterfactual, and that's one of the themes that powers the subfield of quantum theory, which is called the quantum theory of computation. So one of the main principles of quantum theory, which is the Heisenberg uncertainty principle, is basically counterfactual. It's a statement about counterfactuals because it says that it is impossible to have a number of properties of a given object all in focus at the same time. So, you know, for example, momentum or velocity of an electron end position can be both measured, observed with the same accuracy at the same time.

this is the thing about what you cannot do with the system. So it's a counterfactual there for you. And a number of other phenomena that are important for quantum theory are also about counterfactual's entanglement is one of them. And it's very interesting that this wasn't quite clear at the start of the, when the founding fathers of quantum theory invented the theory. But then in the 80s and 90s, I think the field of quantum information was proposed. and one of the key ideas there was to say, well, there are a set of core properties of quantum objects that are independent of their particular details. So it doesn't matter whether I'm looking at a photon or an electron or a neutron or something. All of these objects have something in common, and it's the fact that it can be described as qubits.

And the key properties of cubits are counterfactuals. And I think this is a revelation because usually in physics, when you see something that is in common to a set of objects, there you have the possibility of finding a deeper regularity in nature. You have the possibility of finding a unifying law. And I think that's what quantum information has done for us, in the sense it's allowed us to understand quantum theory in a deeper way. And if you look at quantum information,

you will see that not by coincidence, most of its central tenets are about counterfactuals in the sense that I said. So now can you tell us a bit about how this idea came about? Is this your theory or was someone working on it before you? So this is connected with what I said. So I think David Deutsch, who is a quantum computing pioneers. He was one of the people that proposed the idea of this universal quantum Turing machine, which is the next step beyond what Turing thought about, which was classical computers. So David, who works in Oxford and has been working on foundations of physics for quite a while, he proposed this philosophy of the, you know, of the science of Ken and Kant,

if you like, the technical term for it is constructor theory. And I'll explain in a moment why it's called like that. Back then, I think I was a student in, as a, you know, I was working on my PhD thesis in Oxford. And we started collaborating on this. And I thought that, But the promise of this approach was great. And I set myself to actually applying it to a number of open problems in physics. And I think together with David and later also with other collaborators, I think we're now trying to put this approach to the test with actual open problems within physics, within information theory.

And this is very exciting. And the reason why it's called Constructed Theory is because there is a sense in which the way in which David proposed it initially was precisely to, make the quantum theory of computation more general than it is. To make it more generally in the sense that it can describe and apply not just to computing machines, but also to more general programmable machines that we call constructors. And we call them constructors because they are programmable machines that can perform not just computations, but any kind of transformation. And the first person who introduced the idea of a constructor was for Neumann, John von Neumann,

this great mathematician and physicist, who was thinking about what was missing in Turing's universal computer for it to be equivalent to living systems. So to, for example, a cell that can self-reproduce. And specifically, if you think about it, a universal computer, even a classical one, like the one we are using at the moment, communicate, unfortunately, they cannot produce replicas of themselves. It's very inconvenient. It's kind of sad, but we can't program the computer to produce a copy of itself. And so for Noemann noticed this. And then he said, well, there could be a more general class of machines that is allowed by the laws of physics, and I want to call them constructors. And just like there is a universal computer, there's also

a universal constructor. And this universal constructor is a machine that can perform any task that is physically allowed, provided it is given the requisite knowledge, the requisite knowledge, the program the relevant software, let's say. And now this machine is just an idea that has been proposed at the time, but in the way in which David thought of this theory initially was that it could, the science of Ken and Kant is that it could also provide in the long run a theory underlying this new generation of machines to generalize, let's say, the quantum theory machines that we have now.

And this is one of the most ambitious goals of constructive theory. What areas of science are you most excited about constructive theory solving? Well, I think there are a number of different directions. So the closest to physics is this one that I was mentioning earlier. So we've learned with quantum information that there's a way of going at the foundations of quantum theory at the very core of the theory by considering the counterfactuals that, under light. And the hope is that it's possible to do a similar thing with using the sense of Ken and Kant to extract the very essence of the current most fundamental laws of motion that we have,

which are quantum theory on the one hand and general relativity on the other hand, and that this procedure allows us to go at a deeper level of explanation where actually the two theories happen to be compatible. So there is this huge problem in physics that is being currently tackled in very many different ways by theoreticians around the world. And it's a problem of merging quantum theory with general relativity in a way that all the conceptual problems are solved. And it appears that on the surface they look like two tiers that are incompatible.

But the hope is that by approaching the problem with this counterfactual, take. You could actually see a way of setting guidelines along which some of these proposals for quantum gravity can actually be threatened and some of their problems, the conceptual problems, also solved. So that's one direction that I find very promising. And the reason why I find it promising is that it's different from the standard way of going about this problem, which is usually the current way to address this problem is to say, well, I'm going to propose a specific theoretical new approach to quantum gravity. There are lots of them out there. But the approach we are talking about here isn't directed exactly to find a specific candidate for quantum gravity is more like

providing a set of guidelines, a set of guiding principles that can help guessing such a candidate. So I think in this sense is a complementary approach and it works at a different level of explanation. And I think it's great that we have more tools to address this problem because being a very a heart problem, it's very important to diversify our bets and diversify our tools. So that's very promising, in my view. And then there is the other problem that it has to do with the physics of life. So there are all of these phenomena that we usually consider as emergent and not really part of fundamental physics.

So life is an example. Even thermodynamics is actually another example. It's something that physicists would regard as pertaining to the macro world. you know, steam engines and so on. They're really things that are microscopic that exist, are a scale. But when we go down to the microscopic details, for example, the irreversibility of the second law disappears, and it seems like the laws of thermodynamics

are not really relevant for microscopic particles. So in a way, they're not really regarded as fundamental either. And then, of course, there's a chapter of the mind, so how the mind works, what is it that when we are thinking and inventing new ideas, what is it that we are producing? So these three problems are somewhat all connected because they are all dealing with macroscopic objects

that are usually considered as non-fundamental and therefore not really the subject of fundamental laws of physics. And with counterfactuals, the key thing that happens is that you can formulate laws that appear to be exact and scale independent about things that on the face of it are usually considered as macroscopic and emergent. And so in this sense, so for example, to give an example, we already have a working example with computers. Computers are objects that are really not considered as fundamental usually. But if you study the laws that rule the possible

and impossible tasks that completely characterize computers and the physics of information. These laws are exact. These laws are actually fundamental. And it turns out that if you, for example, look at quantum theory through those laws, you can actually understand its deepest secrets. So in that sense, I'm expecting that the counterfactual approach has a very strong chance of capturing some of the regularities that underlie life, the way we're going to be. which life develops, the way in which life actually evolves and so on, in a way that it's

steeper and stronger than what's been done so far, for example, in biology. And it's closer to the way in which physics actually formulates laws. So for example, it could be leading to a number of universal laws of life that hold not just for life, as we know it, on this planet, for example, but anywhere in the universe. And likewise for the mind. So this is, of course, it's very far in the future. But that's also a field where physics hasn't done enough, in my opinion, and that's partly because of this reason that we think that that kind of topic isn't really for physics, maybe. But I think we should really try harder and having more tools like the science of can and can't is really important. And I think it's specifically important and promising that we have these tools

because they have this capacity of capturing regularities that otherwise with laws of motion, you can't just capture in a kind of fundamental law. And finally, what do you hope people will take away from your book? I think that, you know, when I think of the way in which readers deal with my book, I'm really hoping that they have fun when they read it. So I think that's the main thing. I do have a hope of having conveyed this enthusiasm for physics and the fact that physics is really an open enterprise.

So in a sense, that's one of the strong messages in the book that, so I'm describing this new model explanation. Hopefully there will be others, and I'm really hoping that maybe young readers who read this book could think that they could in a few years, maybe make a new contribution to physics, perhaps in this field, perhaps in a different field, but in a way that makes physics an open-ended enterprise.

And this is really important because I think especially with young students in school, sometimes it's not really emphasised enough that science and physics specifically is always evolving and, you know, theories get overthrown and, you know, things that we thought worked really well like Newton's laws actually turned out with falls and so on and so forth. And this is what makes physics exciting. So I think in that sense, I'm really hoping this idea can reach the reader. And at the same time, I'm hoping that the idea of combining physics and thinking about physics with some sort of intellectual delight or fun, that's also a thing that I'm hoping the readers

will enjoy. Usually maybe physics doesn't have a great reputation in terms of being fun and delightful, but I think it really is. And I'm really hoping that this also can get to my readers. and in general I'm really hoping they will have fun with it. Thank you for listening to this episode of the Science Focus podcast. That was physicist Kiara Marletto. Her book, The Science of Canon Can't, is out now. If you have five minutes to spare and want the chance to win £100, please fill out our survey to let us know what you think of the podcast.

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