Theories of Everything with Curt Jaimungal - Chiara Marletto: Constructor Theory, Ghost Particles, and New Form of Science

Episode Date: January 9, 2024

Chiara Marletto, a theoretical physicist, discusses the innovative principles of Constructor Theory, a groundbreaking approach that shifts the focus of physics from traditional dynamics to the realm of possibilities and impossibilities. She explores its applications in information theory, thermodynamics, and the fundamental understanding of life, highlighting how this theory could revolutionize our perception of reality and quantum mechanics. Her insights blend deep scientific knowledge with a philosophical perspective on the nature of discovery and the endless pursuit of knowledge in physics.TIMESTAMPS: NOTE: The perspectives expressed by guests don't necessarily mirror my own. There's a versicolored arrangement of people on TOE, each harboring distinct viewpoints, as part of my endeavor to understand the perspectives that exist.THANK YOU: To Mike Duffey for your insight, help, and recommendations on this channel. Support TOE: - Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Crypto: https://tinyurl.com/cryptoTOE- PayPal: https://tinyurl.com/paypalTOE- TOE Merch: https://tinyurl.com/TOEmerchFollow TOE: - Instagram: https://www.instagram.com/theoriesofe...- TikTok: https://www.tiktok.com/@theoriesofeve...- Twitter: https://twitter.com/TOEwithCurt- Discord Invite: https://discord.com/invite/kBcnfNVwqs- iTunes: https://podcasts.apple.com/ca/podcast...- Pandora: https://pdora.co/33b9lfP- Spotify: https://open.spotify.com/show/4gL14b9...- Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeveryt...Join this channel to get access to perks: https://www.youtube.com/channel/UCdWI...

What is constructor theory and how is it different now than in its original formulation by David Deutsch? So, constructor theory is a new way of formulating the laws of physics. And this was originally proposed by David, I think back in 2011, something like that, I think back in 2011, something like that, as a new mode of explanation. So he wrote a paper that had a very strong philosophical component, which laid the foundations of the theory in the form of a program, in a sense. And the key idea there was to modify the way we formulate laws of physics and so the fundamental laws of physics. So instead of using things like dynamical equations, so laws of motion and initial conditions, which is what most fundamental theories do,

which is what most fundamental theories do. Switch to a different mode where the basic fundamental statements are constraints about which transformations can be performed and which transformations cannot be performed and why. So what is possible and what is impossible. And then consider dynamics and initial conditions as kind of emergent consequences of these principles. So it's really like a switch of perspective into thinking what is the fundamental element in a physical theory.

And this was there, I think that's the key idea, and David was really inspired to do this by the quantum theory of computation, which is a theory that he himself pioneered in the 80s when he, with other people, proposed the idea of a universal quantum computer. in that theory to think of what can be performed by a universal Turing machine and what cannot be performed by it under given laws of physics. So in the case of classical physics, you have a classical universal Turing machine that can do certain things and not others. And then you have a quantum universal Turing machine, which uses the laws of quantum theory, not classical physics.

And there you have new different modes of computation available. And this was a key insight in developing this idea of the universal quantum computer. And constructive theory, one way to see it, and this was already there in David's paper, is to think of it as a theory of a more general programmable machine that is even more general than a universal computer. And this is a universal constructor. So a constructor is an entity that can be programmed to perform a number of tasks that are not necessarily computations.

So you can think of a heat engine as a constructor if you like a 3d printer is a constructor anything that can be programmed to perform a given physical transformation you can think of it as a programmable constructor it just has to have this property of being able to do the transformation once and then keep its ability to do it again so that's the key feature of the constructor, which makes it different from a different system that can just simply perform the transformation once and then maybe be destroyed or whatever.

And a universal constructor is the most general programmable machine that we can think of. And this is what the physicist John von Neumann thought of when he was imagining the ultimate, you know, the most general programmable machine that could be built by humans in a sense. And constructed theory can be thought of as a way to generalize the quantum theory of computation to cover these machines that are more general than computers.

And this is somehow a completion of what von Neumann had in mind, because von Neumann had this idea of the universal constructor, but then never really delivered a physical theory of these machines. Whereas we are hoping with constructor theory that we will be able to deliver a theory of these machines. At the same time, also deepening our understanding of physical theories because when you understand what are the fundamental limits of the universal constructors, so what is it that it can or cannot perform, you've also expressed what are the possible and impossible tasks

according to the most fundamental laws of physics. So in a sense, studying the universal constructor and studying what is possible and impossible under the laws of physics is the same. And this is a key insight in David's paper. There are lots of other things in that paper, I think, different ways of thinking about constructed theory

as a way to expand on complexity theory and chemistry and thermodynamics and so on. But back then, and I, well, a few years after, I think later, something like 2012 or something, I was doing my PhD. Back then, we didn't have any specific application of the theory, so it was more like a program. And what happened between then and now, and let's say what I was really interested in

when I started working with David and then kind of developed various things on my own, was that I liked this idea, this new switch, this sort of switch of perspective, and I thought it was very promising. And then I wanted to find some specific problems that this approach could be applied to. So then I think in partly my thesis and then later on in my research work, I did a few things where I applied this theory to various problems. I did a few things where I applied this theory to various problems. So initially with David, we applied it to information theory.

And we found a very interesting way of expressing, with this language of constructive theory, the laws, the principles that underlie physical theories of information. So this theory that we developed together, David and I, was to express what are the regularities in nature that are needed for information to exist and uh also for quantum information to exist so these are ways of handling both quantum and classical information in the same theoretical framework and this is very important for, um, direction of research that I'm really keen on, um, nowadays, which is the direction where you're thinking of, uh, systems that are in interaction with, uh, objects that obey quantum theory, but may not themselves be a quantum.

Maybe they behave according to a new theory. Maybe they behave according to a post-quantum theory. For example, gravity is one of these objects because we don't know. We have various proposals for quantum gravity, but we don't know which particular quantum theory of gravity is the correct one yet. And so in that case, it's very important to have a framework, a theoretical framework to handle the situation where gravity, that may or may not be quantum, interacts with a quantum object. And a framework that can handle both quantum and classical things, let's say, in the same unified scenario.

And that's what the constructed theory of information can do for you, among other things. So it's one direction. Another direction where we made progress was thermodynamics. So there was an application of constructed theory to thermodynamics and to expanding on the current formulation of the second law, something that we can discuss later. Right. And then a third direction uh broad direction was the an application of constructive theory to the physics of life so there are these issues about how um what is you know what is the simplest entity that can occur in the universe which can be considered as um alive um what are, let's say, essential features of this entity?

So does it have to be programmable in some way? Is it a kind of programmable constructor? What's the minimal structure of this entity? And in that direction, I think I applied constructor theory to tell us under what are, let's say, the necessary and sufficient conditions for an entity to be capable of self-reproducing very accurately so just like living things do um so in a sense you know when we think of self-reproducing entities we think of

laws of biology but ultimately what we can do in biology is really set by the laws of physics that we have available. So it's interesting from the physics point of view, and especially from the constructors' point of view, to ask, considering the laws of physics as we know them, what are the minimal features that are both necessary and sufficient for a living system to be capable of self-reproducing accurately. And this is the kind of stuff that the constructor theory can deliver on. And I think I developed this branch of constructor theory with a view of applying this to the study of, for example, the origin of life

and possibly the study of life elsewhere in the universe. Um, so these are, let's say the three macro directions in which there's a lot of progress on. And then David has, uh, also worked independently on, on various other things to do with, um, the universal constructor itself. Um, and finally the, there are a few things in the pipeline with some collaborators of mine, Maria Violaris, who is a PhD student, a default student here in Oxford, who's developed some interesting results about irreversibility, so again about thermodynamics,

and then some work that David and I are doing on the constructed theory of time. So this is kind of forthcoming. And then some extra work on the applications of constructed theory to this area where we have a quantum system interacting with something that may or may not be quantum. And this is something I'm doing with Giuseppe Di Pietro, who is another PhD student here in Oxford. So there's been a lot of work. And finally, there's also been an interesting application of constructor theory to the problem of testing quantum effects in gravity, which is something I've developed with Vlatko Vedra, who's a physicist here in the physics department. So I think that's an overview of what's going on. Wonderful overview.

Thank you so much. Thank you. The audience should know that there's a book that you have called The Science of Can and Can't, which goes over these topics in an extremely introductory manner to people who don't know even what a Turing machine is. And so I have read your recent papers and that book as well. So I'd like to get into some of the technicalities soon, but I would like you to explain the difference between a Turing machine,

a universal Turing machine, and then a quantum Turing machine and a constructor and a universal constructor. So please. Yeah. So this is a great question because it goes, let's say at the heart of the matter. So a Turing machine is a programmable machine.

So it's an entity which you can program to do a number of tasks or transformations. And these transformations are computations. So they are a particular kind of transformations that involve, if you like, information variables. And a classical Turing machine is a Turing machine that operates according to the laws of physics that, if you like, um, Newton discovered, albeit, uh, a discretized version of, of those laws, but let's say, you know, it runs on that kind of physics, therefore does not have, uh, all the new, uh, and very interesting effects that quantum theory led us to discover about a century

ago when it was proposed. A quantum theory machine is a programmable computer, is a programmable machine that can perform computations that obeys the laws of quantum theory. So instead of having the laws of Newton or discretized version of those, we have quantum theory, which is, by the way, one of the best available explanations of the universe. And I think David told me an anecdote which was quite fun at some point where, you know, telling me about how he thought about this universal quantum computer idea initially about how he thought about this universal quantum computer idea initially, was that he was discussing with someone and I think it occurred to him that somehow the laws of

a standard Turing machine, a classical Turing machine, were running on the wrong physics in a sense because they were using an obsolete type of physics right newton's laws if you like um whereas uh somehow computer scientists should have looked into something that run on uh the actual uh laws of physics that are you know updated now and they they they obey the the sort of scheme of quantum. So somehow the idea was to update, upgrade the idea of a classical Turing machine with the right laws of physics, with the laws of physics that we know superseded Newton's laws at the beginning of the last century.

Now, a universal Turing machine is a computer, so a programmable machine that can perform computations, that's capable of performing all physically allowed computations. So not just one computation or two or whatever, but if you consider the set of all physically possible computations under a given law of physics, the universal Turing machine in that specific physics is capable of performing all of them. So, for example, you can think of a computation being, I don't know, an addition, you know, you can think of addition and multiplication. These are, I don't know, two possible computations.

You can imagine two specific entities entities one that can add things and another computer that can only multiply now a universal a more universal machine than either of those is one that is a computer that can be programmed to perform either multiplication or addition and now if you consider all the possible computations a universal computer

is one that can be programmed to perform all of these computations put together. So it's like a multi-functional entity. And so provided that you give it the right program, it will perform the right computation. Sorry to interrupt, but the computer that someone is listening to this on, their iPhone or their desktop, is that a universal computer? Yes, so that's a universal, it's an approximation of a universal classical Turing machine, yes. So I think that's what Turing gave us with his ideas was basically the model, the theory, let's say, that powered all of the information technology that we currently use. And the idea is that the quantum universal Turing machine will upgrade these machines when the universal quantum computer comes about

in ways that they can perform new algorithms that are based on quantum laws rather than the classical laws of physics. And now constructors are simply, if you are happy with this idea of programming something to perform a computation, which is what Turing machines are about, constructors bring this concept a level up in the sense that instead of just having computations as the transformations that you're considering in the repertoire of your machine, you have any physical transformation that is conceivable. So in the case of a constructor is a programmable machine that can perform a given task. The task can be a computation.

So computers, Turing machines are special cases of constructors, but constructors can be more general. And typically examples of constructors are things like catalysts, computers, as I said, heat engines, 3D printers, all sorts of machines that can be programmed to perform a transformation, a physical transformation, and also have the ability that they can perform it and stay unchanged in the capacity of performing the transformation again. This is very important. This is true for computers too.

There are special cases for constructors because they perform a computation and then you want them to be able to do it over and over again. And I think the ideal Turing machine should be able to do this indefinitely. Likewise, constructors have this feature of being able to perform a task

and then repeat this over and over again if given the right input. And so, again, programmable constructors are those that can be programmed to perform given tasks. And then a universal constructor is a constructor that has all of the possible tasks in its repertoire. So you can program it to perform any task that is physically allowed and there can be a quantum programmable constructor and the quantum universal

constructor and possibly a universal constructor that runs on better laws of physics than those we currently know so maybe post quantum uh constructors and um but so the idea is always the same uh different laws of physics give you different sets of tasks that can be performed, just like different laws of physics give you different computations being performable by a Turing machine. Um, and so the, the von Neumann's idea was really to extend the scheme of Turing's to other tasks that are not just computations. Um, so thermodynamics transformations are an example,

chemical reactions are another example, and for Neumann specifically he was concerned about emulating life. And so he noticed that the reason why he thought of this constructor idea was that he noticed that in the Turing machines model there was a gap in the sense that you are not, it's impossible to program a Turing machine, a universal Turing machine, whether it's quantum, classical or whatever, to self replicate. So you can program a computer to simulate a self-reproducing cell. But if you wanted to program your own computer to create a replica of itself, which would be very convenient, out of raw materials, that can't be done. Reason is that simply the scheme of Turing's doesn't accommodate for this

kind of stuff. It only accommodates for computations to be performed on a tape and doesn't have things like arms and things that can be assembled things and so on so you have to get out of the scheme of turing's uh turing's machines you you have to sort of think of something more general and that's where von neumann landed on the idea of the universal constructor okay great so how does one make a difference between what's extremely unlikely and what's impossible so it's my understanding from what you've just said and from the papers I've read is that the traditional way of doing physics is that you have some initial data set and you evolve it forward. That's like the dynamics. And the constructor way of looking at it is, okay, well, actually, let me go back. What you can do is then look at these laws as some causes that produce some effect. and one of those effects may be that entropy tends to

increase okay so in other words you can derive thermodynamics from statistical mechanics so it seems like constructor theory is working backward by looking at the effects and then stating those as laws rather than deriving them so when i hear you say look entropy doesn't or the heat engine entropy doesn't increase but well entropy is not likely to increase so at what point do we make a cut off between the likeliness and saying that something's impossible yeah that's a great question um so the so let's first consider the fact that when you say that something is possible or impossible, you're not directly referring to likelihood or probabilities for it to happen. So somehow probabilities are not there in the foundations of constructed theory and they come as, say, derivative statements, approximate things. But somehow they're not necessarily built.

In fact, they're not built at all in the foundations of the theory. And this is a plus in a sense. So when you say that something is, a task is impossible, what you mean is that there is a law that forbids the fact that this transformation, this physical transformation that's referred to by the task, is brought about to arbitrarily high accuracy by a constructor. So by this device that can operate in a cycle

by returning the substrate that you gave to the constructor in the right input state in the correct output state. And so if the laws of physics say there is some fundamental limit beyond which we can't go as far as this transformation is concerned, meaning there cannot be a full cycle that can operate this transformation and then return itself to the original state of affairs, just like a catalyst would do.

That's the case when the task is impossible. A very simple example is the task of changing the energy of a substrate. So if you want to change the energy of a battery, for example, so from low to high, you can't do it with a constructor without any other side effects because the constructor will have to give up some energy because of conservation of energy,

it would give up some energy to the battery. Yes, yes. Thereby not being able to return itself to the original state of being able to perform the task again to the same degree of accuracy. So that's an example of a transformation that's actually possible in the sense that it can happen, it can occur under laws of physics, because obviously we can use another source of energy to replenish the battery once it's on low. However, this other source will have to be depleted itself.

So it cannot be a constructor. So now if you're looking for a constructor that can give you energy without depleting itself, you will have to go to a physics where conservation of energy isn't true. itself, you will have to go to a physics where conservation of energy isn't true. And so it's not the kind of physics that we believe kind of describes our universe. Likewise, you can think of another example of an impossible transformation. That's the case of in quantum theory. We know that we cannot reliably copy any two states of a physical system. This is related to the Eisenberg's uncertainty principle,

the fact that you cannot measure reliably any two observables of a physical system. Typically, we say the velocity and the position of an electron cannot be both measured simultaneously with the same device. Indirectly, this is a constructors' static statement because it says we cannot have a constructor that can copy or measure accurately these two variables without changing itself in some way. And so it's no longer a constructor, right? So these are examples of impossible tasks.

And note that I haven't talked about probabilities there yet um and now if you have lots of physics that let's say tell you a number of things that are impossible but the rest they don't constrain then whatever is left is a possible task so if you you know if you think of a way of expressing a theory in constructors' theoretic terms, you will have a number of statements about tasks being impossible. And those that aren't impossible are possible in the sense that then somehow it's allowed to bring about a constructor that can perform these tasks. And there is where you can think of

somehow approximate constructors. So when you're thinking of a possible task being realized, performed, let's imagine a possible task is, for instance, to copy the two values of a bit. So, you know, zero and one can be copied. We know this is possible. We do it all the time, approximately in computers. Um, so, you know, you have zero and one and et cetera. Now, um, the fact that the task is possible is, um, a statement about an

idealized scenario where you're thinking, okay, that means that, um, there's a number, there are a number of ways of approximating arbitrarily well this behavior of an ideal constructor that can copy 0 and 1 when given them in input. Now, of course, if we look at each particular realization of a copier in any of the computers that we have, for example, they will be approximate. So they won't work perfectly in the sense that at some point they may break down, they may incur in errors, et cetera. But this is simply a feature of the fact that our, you know, we're using limited resources to implement each particular realization of a copier.

However, the laws of physics, as far as we know, don't put any limit on how well we can copy. So it means that for each of these imperfect constructors that are approximate, we can work a bit harder, put a bit more resources into the particular device that we have, make it better so we can meet a better accuracy target if we want to. And so the fact that the task is possible simply means there isn't a limitation beyond which we cannot go as far as accuracy is concerned for this task, as far as we know. So these are very different statements from the statement that something is unlikely.

So a transformation can be unlikely or more likely depending on the kind of statement you're looking at. But that would mean simply, for example, that in the standard way of thinking about physics, there is a bunch of possible trajectories that can be realized, as you were saying, and given the initial conditions and what we know about them, we can say that a given trajectory is more likely to occur than another. But that doesn't mean necessarily that there is a constructor that can operate the transformational correspondence to that trajectory, let's say, of the particle growth from A to B.

So that's a different statement. The fact that the trajectory is very likely, for example, just means that if we run the system and those are the initial conditions, if we run repeated experiments, we will see most of the times that trajectory occurring, but it doesn't mean that necessarily there's a constructor. So this device that can work in a cycle to bring this transformation about. So the fact that the trajectory is very likely doesn't necessarily mean that the task associated with it is possible. Likewise, the fact that the transformation is unlikely doesn't necessarily mean that the task is concerned.

Yeah. So, for example, you know, you could say in, you know, given the initial conditions we have, some transformations that are currently occurring really, you know, very reliably in some laboratories i don't know in cern or something um you know they're very unlikely uh you know compared to the standard processes physical processes occur natural you know they are naturally occurring in the universe however they are possible tasks because we can simply harness enough energy and enough sort of devices that compose the CERN's labs, if you like, and we can actually reliably bring those transformations about. So even though some trajectories are unlikely, they can correspond to possible tasks.

In fact, most of the things we do in laboratories, even in quantum computing laboratories, are very unlikely trajectories for certain entities, certain charges or whatever fields, and yet we can bring them about really accurately simply because we are following some sort of program to implement these things in the laboratory. So I guess this is a difference between something being likely and something being possible and likewise unlikely and impossible. I see. Okay, let me see if I have the terminology correct. There's something called resource theories.

And I understand that constructor theory is not a resource theory. But resource theories also deal with tasks and then ingredients that you put together to make some input transformation, some output. Let's say we have this cup and we have a bucket of water, a full bucket of water, and I want to fill this cup. So then we can combine them to make the task full cup of water after the bucket has poured in some water into it. But it's my understanding that this bucket wouldn't be a constructor because this bucket runs out of water. It's not something you can keep repeating. Yes. Yeah. Okay. So then is this realistic then for a constructor to exist? There is no infinite

bucket of water that exists, for instance. Is that realistic? How do you think about this? Well, that simply means the transformations of changing the content of a battery or whatever. If you're talking about a concert quantity, I think in your example, if you like, you can substitute your example with the idea of energy and the battery, because then we can use the conservation of energy as the thing that puts a limit on what you can do. So in the case of the energy conservation and changing the energy value of a battery, there is a different task that is possible, which is the task of transferring some energy from one subsystem to another. So that is a possible task. Meaning there can be a constructed, you know, a thing that reliably, um, you know,

if you have a, if you have an iPhone or whatever smartphone that's run out of juice, uh, you can plug it in as power supply. And if you consider the joint system of the power supply and the smartphone, on that system, there is a possible task that can be performed. It simply means you're transferring some energy from one side to the other. So it's like, if you want to think about it, not in terms of batteries and charges, you can think of it in terms of a seesaw. So you have like a seesaw with two weights and they can move like this.

And the task of changing the relative positions of these two entities is possible. However, changing the position of one side is not a possible task by itself because you would have to use energy to do that. So you can still talk about the fact that a charger is possible or a seesaw is possible by considering the joint system of the thing that you want to recharge and the battery supply or, if you like, in the case of the seesaw, of both sides of the seesaw. So it's completely, I would say it's completely fine to talk about it in those terms. And in a way it's more insightful because it tells you somehow where is it that the the constraints are right so the reason why we need a power supply is because the you know the fact that we care about the fact that battery runs out of juice is simply because there isn't a um well we need to supply the energy from somewhere else once it's gone and the reason why we need to do that is the conservation of energy, after

all, the fact that overall in the universe, the energy is conserved. And so whenever you change energy in one subsystem, you have to change it somewhere else as well. And the interesting thing is that you can explain then some limitations of what you can do, for example, with a heat engine or, um, uh, like, uh, you know, any, any, any kind of engine that, that runs on the laws of thermodynamics as we know them in terms of the fact that energy is conserved. So that's the explanatory power of the law of conservation energy, which you can express in constructivistic terms by saying the energy, changing the energy of the substrate is impossible. Um, and so that's the content of the theory.

And in a sense, I think, unlike what you mentioned, resource theory, the difference between say what construct theory does and resource theory is simply that, well, there's some technical difference, but I think the most important difference is that resource theory is more like a framework where you can express existing dynamical laws with some symmetries in this language of transformations being allowed or disallowed. And then sometimes they also care about the fact that the transformations are performed reliably, and then they talk about the catalyst, which has some overlap with constructors, but the main difference is that they don't have principles of their own. So resource theory is not a physical theory. It's a framework to express physical theories. Whereas constructor theory has principles of its own.

So it's an attempt to have actual laws of physics, in addition to those we have currently, that can supplement the dynamical laws and tell us more about the universe. So the laws of information are an example. The new laws of thermodynamics that we formulated are another example. in the hope of having new predictions, ultimately, not explanations as well, but also ultimately informing some new tests that can be somehow... Testing in the laboratory has sort of changed. It can provide some sort of extra predictions, extra tests, compared to what we currently can do with the laws that we know.

When you're repeating a task, are you doing so using a constructor or the constructor? So in other words, are you reusing the same constructor or are you pulling from a different constructor every single time? No, so in the ideal case, it's the same.

So let's talk about the ideal case. It's a bit like a heat engine, it's the same constructor. So the idea is you've got the same constructor, like a fridge, and you want to cool the, I don't know, a cup of water of sorts. Sure. And so there's a fridge and the power supply. Yeah, exactly.

And, and, um, it should be, so once you do it with one, um, object, you would like to take it out, enjoy it cold, and then put a new one inside the same fridge. Ultimately, a particular fridge, simply because it's imperfect, will at some point break. But the point is that you can build a better one that lasts longer. And as far as we know, there is no limitation to how well you can approximate the perfect fridge, considering also the power supply that comes with it. Whereas for other things like copiers for quantum states, for states that are not orthogonal in quantum theory, so that

this perfect measure for, say, position and velocity of an electron, it's not that any actual instance of this measure is imperfect, it's really that you cannot construct a machine of that kind. So there is a limitation to the accuracy that this measure can work. And this accuracy simply cannot be increased beyond a certain value. And this is a law of physics that's built into quantum theory. So these are the two different statements. So one statement is any particular instance of a real constructor, a real approximate constructor will at some point break down,

but we can perform, we can build a better one. And that's the case when the task is possible. When the task is impossible, like in the case of measuring position and velocity of a particle, of a quantum particle, a measure for those two entities simply cannot exist, which means that you can build very poor measures of those two things that will be wrong most of the times when they're trying to measure both position of momentum, position of velocity, and they cannot improve beyond a certain accuracy. There's like a finite limit beyond which they can't go. And these are two very different situations. Do you think of constructor theory as a law of physics

or as a framework for explaining physics? Like, is it more general than just physics? Is it a paradigm in science rather than a theory of science? Is it a way of going about investigating? I'd say it's both in the sense that, so it has some laws of its own that are formulated in the way that I said. So stating what transformations are possible and impossible. the way that I said, so stating what transformations are possible and impossible. Um, but also because it's somehow phrased in this different way from the standard

traditional dynamical law plus initial condition type of approach is also a new paradigm, so it's not just, um, as a physical theory with new laws in it. It also has, uh, the value of being a new framework or a new language to express laws of physics. So it has both components. But the most important one to me is, I think, well, they're both important, but somehow the one that that intrigues me the most is the fact that it should ultimately allow us to say more than, if it pans out as we expect, more than what the current laws say. So it has a physical content of its own, which is non-trivial.

Otherwise, it would be just a framework to rephrase things that we already know, which could also be interesting, but somehow perhaps is less interesting than, say, this Boulder program that are hoping uh will pan out in this way you hope to have as an emergent theory quantum theory and general relativity yes so yeah so i so another aspect of constructive theory is that um perhaps this is a complement supplement to the previous question you asked, so the

way in which constructed theory works is that it doesn't pin down with its principles one specific dynamical theory. So we are hoping that, and I think we demonstrate this for quantum theory at least, and we're in the process of doing this for general relativity, that both quantum theory and general relativity are compatible with constructed theories principles. So for instance, if you take the principles about information, we know they are compatible with quantum theory, and we also have arguments to say

that they are compatible with general relativity. And in that sense, they are nice because even if you are maybe skeptical about the fact that these principles are really fundamental laws, so you can be agnostic about whether this is a better way to formulate the laws of physics, you can still find them useful because you can still find these principles of constructor theory very useful because if they are things that are obeyed by both quantum theory and general relativity, useful because you can still find these principles of constructive theory very useful because if they are things that are obeyed by both quantum theory and general relativity that we know don't go together as theories themselves because general relativity is a classical theory, it doesn't have quantum effects in it, whereas quantum theory is quantum, you

can appeal to these more general principles of constructed theories to provide explanations and make predictions in a context where both general relativity and quantum theory apply, but we don't know how to put the two theories together. But then we can appeal to these more general principles that do apply in that regime. And that's very much of interest for testing quantum gravity, because it's exactly the regime where we know that, you know, maybe one of the quantum theories of gravity that have been proposed may apply, but we don't know which one is the right one. And so having these principles that are more general is very useful because you can appeal to them. And the fact that they work both for GR, for general relativity and quantum theory is a plus. and quantum theory is a plus.

So I'm thinking of quantum theory also as a bridge. These principles could be useful to guess a theory that goes beyond quantum theory and GR, as well as to help us find predictions or experiments that can test the realm where this theory is relevant. So this realm where, for example, testing quantum gravity effects is one of the applications of these principles of constructor theory. And that's the stuff I was mentioning earlier

I've done with Vlatko. So thinking of constructor theory as some high-energy theory that in the low-energy limit reproduces the standard model or GR is the wrong way of thinking about it. Yes, I think, I think that's, um, that isn't, uh, cause that's the standard way of going about some tow, some theory of everything.

Yeah. That's, that's actually a great thing you said there because, um, that's the, that's the standard way to go about this thing of finding quantum gravity theories. Right. So you think, well, um, you know, I've got these two things, you know, I've got quantum theory, non-relativistic quantum theory, and then I have relativistic theories like either GR, general relativity, or special relativity. Then let's find a way to put them together mathematically, right?

That they kind of, and then there are proposals how to do that. right? And then there are proposals how to do that. We have quantum field theory. Then we have some quantum theories of gravity that can work in a low energy regime. Then there are those that actually work at higher energy, et cetera. And each of those will give you a prediction. Unfortunately, most of the predictions can be tested. The quantum gravity predictions are very difficult to test. What you do is that you say, okay, well, let's just look at some regimes that are experimentally accessible. That's the kind of logic that you have when you present those theories. You're hoping that one of them will be...

You will find an experiment that corroborates one of those quantum theories of gravity and refutes effectively the classical theory of gravity which is general relativity so you would like ultimately some sign of the fact that gravity is quantum so it doesn't obey general relativity after all because general relativity

is a classical theory now in constructed theories we are taking a different approach we are considering the set of, if you like, symmetries or constraints that both quantum theory and general relativity satisfy together. So it's an exercise of saying, okay, I don't really look at the specific dynamical laws that these two theories have. saying okay i don't really look at the specific dynamical laws that these two theories have but i'm trying to extract some deeper symmetry that they both um agree on for instance the fact that both um for allow for things like observables there is a concept of an observable both in quantum theory as well as in general relativity or in special relativity. And these

observables obey certain laws of information theory and in constructed theory we can express those laws. And then by looking at this common area of, let's say, agreement of the two theories, you can consider this deeper structure where the two theories agree, which requires you to forget about most of the formal details of the two theories. So you will be throwing away various aspects of both quantum theory and general relativity. There are specific formalisms. But you're looking at this deeper structure where they do agree. And for example, the information theoretic structure that concerns observables is something

that the two theories agree on. So the fact that there are local observables that you can measure some of these observables and so on is something that the two theories agree on. Then, of course, general relativity is classical. Quantum theory isn't. But I think there is a fundamental structure of observables that they share. They also share things like locality, um, and other features of information theory that are, uh, in common.

And you use these things, these common, um, constraints to, um, make some prediction about these, uh, regimes where a quantum system is in interaction with gravity. And this actually is very powerful because it allows you to imagine experiments that are in the low energy regime, but they allow you to extract quantum features of gravity in a way that's easier than ways that somehow were proposed before to test a specific quantum theory of gravity. And this is very exciting because it tells us that quantum effects in gravity can actually be easier to capture than it was previously thought. And it's nice that these tests that I'm discussing as part of my work with Vlatko and other collaborators,

these tests are really somehow probing a regime where we're not going to very high energies, so it's easier to actually access those regimes. And they rest on these general principles of information theory. They're very robust and they are obeyed both by general relativity and by quantum theory. So that's maybe the way in which it's nice to think about constructive theory as being relevant to this problem that you mentioned. And you mentioned earlier post-quantum, the word post-quantum, which rings a bell to me with Jonathan Oppenheim's stochastic gravity. And I believe you're both in the same university. So maybe the same departments. Is that the case?

I think he's at UCL. We are in the same kind of, well, we are interested in the same topic to some degree. I guess quantum foundations, broadly speaking. I think he's in UCL and I'm in Oxford, but it doesn't matter really. Oh, my mistake, okay. No, no, no. It's true that we have some common interests. It was his British accent.

Yeah. Yeah, I think approximating British accents is very difficult for me, but I try my best to sort of, you know, blend in. Right, right, right. But, yeah, I think the thing that you mentioned is very relevant because, okay, that's an example of a theory that is specifically going to describe gravity and quantum systems in a way that gravity is classical. So that's, so, you know, broadly speaking,

we can divide physicists into two camps. One camp says that gravity is actually quantum and we only, you know, we just have to find the right set of conditions to show that it is quantum with an experiment. And also we have some ready theoretical proposals for quantum gravity which exist. Some of them have been developed in the past decades and they sort of have some predictions, etc. But let's say no matter

which particular proposal you favor, I think if you are in this camp, your heart is saying that gravity is quantum mechanical after all, whereas general relativity says it's classical. And then there is a different camp that says that gravity is actually classical. And when it couples to a quantum system, various things can occur, but ultimately it will cause the quantum system to derail and become somewhat less of a quantum system. So it will become more classical than it should be. In this camp, you will find not just Jonathan Oppenheim, but many people that have been

proposing for years, these dynamical collapse theories, Gerardi, Riemann, Weber, there are all sorts of big names there. Roger Penrose with his collapsed wave function due to gravity. So there are all sorts of great minds that have been sort of powering this camp in many different ways. Which one do you belong to? I belong to the former. Which one do you belong to? I belong to the former. So I think gravity is not just, I think gravity is quantum mechanical,

and I think we just have to wait for the right experiment to be performed. But the exciting thing is that this theory that you mentioned, that Jonathan Oppenheim has put forward, together with many other theories of classical gravity that have been proposed over the years, can be refuted by this experiment that I was mentioning earlier. And this is what makes this experiment very exciting because it can allow us to find a spot where we can at least tell whether gravity has some quantum features or not.

So the test would entail two quantum objects, two masses, being quantum correlated, entangled through gravity. So if gravity is capable of creating these correlations between two masses, then we can use this argument from constructor theory to conclude that gravity has to have some quantum features. And this is nice because it will allow us to rule out immediately all classical theories of gravity, not just general relativity but also other proposals like those I mentioned earlier, the collapse theories, quantum field theory in curved space-time, which is another theory where gravity is classical,

Jonathan Oppenheim's classical gravity theory, and many others. And I think this is very exciting because it's something that hasn't been done so far. And that's the reason why there are still these proposals to say that gravity is classical after all. And it's quite if you think about it, it's really a very important issue at the heart of physics because in order to find a good quantum

theory of gravity, you need to be motivated that gravity has to be quantum but if say part of the physics community is already even doubting that gravity is quantum, then there isn't much of an incentive to look into a quantum theory of gravity, so somehow it would really be important to do this experiment because it will allow us to at least say, okay, now we can give up on this idea that gravity is classical.

Let's really get on with it and try to find the right quantum theory of gravity. We don't even have that confirmation, experimentally speaking. So it's really nice to have this kind of experiment out there. And it's something that people are working on to actually implement these days. So it's really an exciting thing. How do we know when to take a limiting theorem, like a no-go theorem at one level?

So for instance, you said the no-cloning theorem before. And then apply that under constructor theory when we're already thinking that it may not be the case that the laws of quantum mechanics or quantum field theory are the final laws there may be something else that's underneath it why are we taking what's a no-go theorem up here and applying it to something that's more fundamental that is a great question and i think it's part of this, um, of this search for the more fundamental, the deeper structure of quantum theory.

So, so if you take quantum theory as it is, there are lots of features in it and they are all packaged into the same, into the formalism. So if you think for the, for those who are not maybe specialists the mathematics is a very powerful language and when you write an equation of motion like in quantum theory um it gives you lots of things in just condensing in in this equation uh without giving much depth into when you're looking at all of these features. Some of them are deeper than others. For example, you can have particular features of the mathematical formalism that you're using

to express the dynamical law of quantum theories, which may be parochial in the sense that they are, they happen to be relevant for quantum theory, but they're not really fundamental. And then there are some other features to do with the fact that the laws are local, that they are, for example, one-to-one. So they map, you know, a set of states. There are not two states that go into the same state. So, you know, you keep, a set of states. There are not two states that go into the same state.

So, you know, you keep different states into different states. That's an important, it's called logical reversibility. That's one thing that comes for free in the laws of quantum theory, but it's a deeper feature of them that also is shared by classical theories of physics and by general relativity, etc. And then there are things like what you just mentioned now, the no-cloning theorem, which is a thing that you can prove mathematically

from the laws of quantum theory, but have a deeper essence in the sense that they are part of the set of constraints of the set of constraints that power the information theoretic structure of, of quantum information or quantum systems. And so by using an information theoretic perspective, you can see that there's no cloning theorem. It's not just a mathematical feature that happens to be true of specifically

quantum theory, It's not just a mathematical feature that happens to be true of specifically quantum theory. But it's a thing that holds promise for being a general feature. Something that even if quantum theory turns out to be wrong, so you have to modify the formalism and so on. feature of not being able to copy, um, yeah, the different states that are not, uh, that don't belong to the same physical observable, um, is a feature that will stay. So whatever modification you do to the mathematics of quantum theory. It's very likely that it will be, or it's inevitable that it will be. Well, it's difficult to say it's inevitable because these things are a matter if

you like you know as a physicist you also have a matter of taste if you like you know you're thinking of things according to your own philosophy and and so on but i would say that there's there are lots of lots of good arguments to expect that this feature will stay uh Simply because it corresponds to the fact that some transformations are impossible. We know that they're impossible. We've even done a number of tests that actually indirectly test this feature. And so if you like,

it's to do with the operational information theoretic structure of quantum theory rather than with theoretic structure of quantum theory rather than with the specific law of quantum theory. And so it's very natural to imagine that the next theory will conserve these features and maybe have more that are even more exotic and exciting. Just like in the case of classical physics, the fact that, so if you think of classical physics and quantum theory, the information theoretic structure of classical physics has been maintained within quantum theory, but then there are extra features, as we know. So the fact that you can have an observable in classical physics is also true in quantum theory, it's just that now you have extra properties of these observables that are even more interesting or exotic. And so it's reasonable to expect, you can make some arguments,

that these features that have to do, for example, with no cloning, that is a constraint on what you cannot do with certain information theoretic variables, will stay in the next theory. And maybe more constraints will come along and perhaps more interesting properties will be there. But they won't undo this change from classical physics. So to me, it's very unnatural to think that we'll go back to the structure of classical physics where, say, you can clone any state. And so in a sense,

the, you know, this theory, the idea of taking some of these properties of quantum systems, their information theoretic versions as general guidelines to describe post-quantum systems is a guess, but I think it's a well-informed one. So somehow we are thinking this is how it's going to pan out. Yes, yes, understood. But I have to say, many people would disagree. So there's a lot of debate there. It's quite hot as a topic.

And that's maybe why we can't make progress in certain directions because there are two diametrically opposed you know ways of looking at things um in these in these um physics circles and that's usually where the fun part of science is yeah that's right yeah exactly i still want to get to some of your papers your recent ones you have a couple on ghost particles and how you can possibly even detect them, which I would love to know more about because it's my understanding that they're undetectable by their nature. So we're going to get to that. But I believe in one of those papers, you said that there were inequivalent representations of QFT and that that not only has some interpretive issues for philosophers, but also for the mathematicians working on curved spaces or curved space times. So can you please explain what you mean by that? And does this pose a problem to all theories of quantum gravity, even string theory? Right.

So I don't think that this is necessary. So just starting from the last bit of the question, I don't think this is necessarily necessarily so just starting from the last bit of the question I don't think this is necessarily a problem for quantum gravity theories so the way this is some work I've done with Vladko the way we wrote this this paper this couple of papers

was to investigate some foundations of quantum field theory and also of the theory of gravity that's called linear quantum gravity, which is a low energy approximation on which all of the quantum gravity proposals we know converge. So string theory, loop quantum gravity, et cetera,

agree with this theory that is basically a quantum field theory for gravity in the low energy regime. And all of this was informed by this experiment that I mentioned earlier and by also some more constructors theoretic questions that have to do with what counts as an observable in field theory, both in quantum field theory for electromagnetism, so for the theory of light and for the theory of gravity in this low energy regime. And there was some surprising answers to this question. And this fits into a more into a, agenda, if you like, or a

broader philosophical, uh, take that I have on, on things and that, uh, I think Vladko also resonates with me on as far as Amaspis are concerned, which is that. So quantum field theory is a theory that a theory that has lots of issues. So it's a problematic theory. And in fact, it was proposed by those who invented it, more like as a sort of recipe for making calculations as an approximation while waiting for a better theory. Exactly, yeah.

However, what happened during the years is that while the initial, you know, the founding fathers of quantum field theory did know that this was a sort of collection of tricks to make calculations, but didn't have strong foundations, philosophically and theoretically, the next generation of physicists, which includes many, and finally also myself, we've somehow forgotten about this fact. And so we are using it to calculate all sorts of things successfully, but somehow we've lost sight of the fact that the foundations are shaky.

So this is an attempt to look into the foundations, go back to look into the foundations. And I think there are many other people who are doing this. So not everyone has this view. But I think the prevailing view is the quantum field theory is all right as it is. And I think that isn't so. And these papers were making the point that we should actually look a bit more carefully into what quantum field theory itself means. Just as a quick point, when you say the foundations, some people who say, I work on the foundations of quantum theory, they mean the foundations of quantum mechanics most of the time. They don't mean, I work on the foundations of quantum field theory, which is different.

Correct. Yeah, that's right yeah that's that that is true uh and and um so the so quantum mechanics isn't um explicitly relativistic so um if you want to put it together at least with special relativity you need to modify it and i think uh quantum field theory is exactly what, you know, it's an attempt to do that. And the interesting thing is that even though quantum, non-relativistic quantum mechanics is, from the information theory point of view, is more or less equivalent to quantum field theory, and also it's also local, doesn't violate, doesn't allow you to signal faster than light and all of these things,

local, doesn't allow you to signal faster than light and all of these things. It still doesn't have all the features that are satisfactory as far as special relativity at least is concerned. So that's why you have to upgrade the theory to quantum field theory. However, when you do that, there are lots more problems that come in that occur. And these problems are maybe not so important for, say, making predictions about particle physics and that kind of enterprise, which is going well and everyone is happy with what's going on there to some degree. But they are still important for the foundations because they inform the way we think of the next theory, of quantum gravity itself, etc. And so that's why

we are dissatisfied with it and we would like to draw attention to the fact that there is a problem. Those two papers specifically were looking at both gravity and the electromagnetic case, but we focused on the electromagnetic case as an example, both because it's mathematically simpler and also it allows you to make the case in a more transparent way. And to cut a long story short, the way we think about this is that when you try to construct a quantum field theory for the electromagnetic field, the usual procedure is that you start

from the classical theory of Maxwell's equations, if you like, and then you apply what in jargon is called a quantization procedure. So you can think of it as a sort of machine that you just got to handle, put in a theory that's classical, and out comes something that's quantum.

So it's a procedure that's been put together by various people in a few decades ago. And the problem with that is that you can follow different paths to perform this quantization. And even though they all agree on certain observable effects, so experimental outcomes, they are not equivalent physically speaking. So, for example, they have, for the electromagnetic field, different ways of describing the quantized electromagnetic field

have different numbers of subsystems. So the photons are the quantized element of the electromagnetic fields and different ways of quantizing it lead to different kinds of photons being there. And there is one way of doing this quantization, which is, uh, explicitly compatible with relativity. And this is, um, in jargon is known as choosing a given gauge, which is called the Lorentz gauge.

And when you do this, you have, um have basically four kinds of photons that behave quantum mechanically, and they are part of your electromagnetic field that is quantized according to this procedure. And the typical way of thinking about these things is that two of these four kinds of photons are only there as mathematical entities, but they're not really measurable. So they can't really do much. So you can't observe them. They are just tricks, mathematical tricks, that are useful to do your calculations. But you shouldn't be able to, not only to detect them directly,

so to have a click from these photons, but also they shouldn't be detectable otherwise. So they're deemed as ghosts because they are there mathematically to help you make calculations. But they are not essential. In fact, there are different ways of quantizing the field, the electromagnetic field that only have, let's say, two kinds of photons, not four.

And so these two ghost modes or two ghost photons are not there. Yes. In those other ways. And why is it okay? Simply because given that they're not observables, no one cares and we are all happy that in some other ways of quantizing the field, they're not there. Now, if you... So this is the usual story.

But the problem is that if you look at the particular kind of experiment that I mentioned earlier, where you have now two charges, not two masses, they interact with the standard electrostatic, the standard electrostatic, quasi-static sort of Coulombian force potential, if you like. And they get entangled through this interaction. So it's a very simple problem. You've got two charges, they're interacting with one another,

and they get entangled through this interaction. If you want a local description of what's going on, meaning a description that satisfies locality at each point of the description, you're forced into using this mode of quantization that uses four kinds of photons. quantization that uses four, four kinds of photons. And particularly the ghost photons are very important in the, in the local dynamical description of how the entanglement comes about. So in the papers, in both papers, we make a point that, um, there is a way to indirectly detect these ghost photons by looking at the phases that you can create on these, uh these charge probes.

And this is a thing that hasn't been thought about by people who usually deal with quantum field theory, because they usually think in terms of input-output scattering amplitudes. This is one kind of bit of jargon to just look at. They look at certain physical processes that are very natural to look at in certain contexts, specifically in particle and, you know, particle physics and quantum field theory in the sort of traditional way.

But if you look at quantum theory from the quantum information point of view, where the emphasis is on phases and on things that you can extract out of charges once they interact with the field. It's very, if you draw, if you use this principle of locality

and various other principles to sort of guide your analysis, you will see that measuring features of the two charges among which there is the entanglement between them that's caused by this electrostatic interaction is equivalent to measuring accessing these ghost photons as dynamical degrees of freedom. And this is something that it's very interesting

because somehow it seems to at least contradict the standard way of thinking about these ghost photons. And it can also be the same argument you can carry it out in the gravitational field case in the linear quantum gravity regime. It's just it's more complicated. So instead of photons, you have gravitons and there are more kinds of gravitons involved. But the idea is the same. So the idea basically is this, that if you insist on having a local

account of what's going on in a very simple quantum information experiment that involves two charges or two masses or even just one charge in the field you have to somehow come to terms with the fact that these ghost modes are indirectly observable so you cannot measure a ghost photon in the same way that you can get a click out of a photon. Yes, yes, yes. But they are important. They are degrees of freedom that can be indirectly uncovered by measuring features of the charges

once they interact through the field. It's as if the charges got clouded with the field and then by measuring the charges, you're extracting features of the field. Yeah. And unfortunately, you're extracting these ghost features and not the ones that are supposed to be measurable. And this is very interesting.

I think this is a sort of, we're hoping this will cause some disruption in the field also because we have some proposal for an experimental test. So the theory that we have can be tested and it will be interesting to see what happens when this test can be performed. And you can do it both with gravity but also with electromagnetism which is probably easier to do considering you know what we can do experimentally

at present man a fantastic name for a theory would be ghost gravity you could write a book on that that's true yeah yeah yeah it's a great it's it's very yeah it's very exciting yeah that's true. Yeah. Yeah. Yeah. It's a great, it's very, yeah, it's very exciting. Yeah, that's true. Okay. So what is the physical interpretation then? Because ghosts come about from gauge fixing, which is just something you do to make the math easier, akin to if you care about the derivative of a function only, then your regular function can have plus any constant. It'll just go away when you take the derivative and you can set the constant to be whatever you like for whatever reasons, calculation reasons, but the constant go away when you take the derivative and you could set the constant to be whatever you like for whatever reasons calculation reasons but the constant goes away when you take the derivative that's a great point you're making there um so the gauge uh fix so the gauge fixing

is exactly what you said so gauge is corresponds to if you like these different ways of um okay let me let me let me make a step back and try to explain this a bit more clearly. Okay. Gauges are simply different ways of describing the electromagnetic field, even classically. So even classically, you have different gauges. field even classically so even classically you have different gauges so and as you said it's um they mathematically they correspond to um switching to different variables for your max for max's equation so max's equations can be written in terms of fields electromagnetic

fields and they have some classically speaking but you can also change the variables to express the equations and so instead of the fields you can use these things called potentials right vector and scalar potentials and the potentials are basically just a different you know mathematically speaking they're just even variables um however there are many different changes of variables that you can make and they're all equivalent. They all collapse to the same Maxwell's equations in terms of fields. And each of these different change of variables that may be useful for computational purposes is called a different gauge.

So each of them, each of each gauge has their own, have their own name. So there is like Coulomb gauge, Lorenz gauge, Scala gauge. So they have names according to how they were discovered. Right. Now, classically speaking, this is irrelevant, meaning physically irrelevant in the sense that you can solve the equations with fields or with potentials in one gauge or another and no one particularly cares about what you're doing. cares about what you're doing. However, when you, um, when you quantize the field, things become different because each gauge corresponds to a different quantization procedure, if you like. And so the Lorentz gauge, which is the one that is, um, local and explicitly

Lorentz compatible, so it's explicitly compatible with, uh, special relativity so it's explicitly compatible with special relativity, leads to these four modes that four ghosts, sorry, four kinds of photons, which in jargon are called modes. And two of them are ghosts, because if you follow different quantizations, which start from different gauges, not the Lorentz gauge, but something, some other gauges, for example, Coulomb gauge, there are only two such modes or kinds of photons. And so they are ghosts because they ultimately are somehow usually thought of as being unphysical because they are not present in all gauges. Okay. So gauge fixing means you pick a particular gauge and that corresponds to some mathematical

constraint being there. Usually this constraint is supposed to be irrelevant physically because, as I said, from the classical point of view, all you care about is just Maxwell's equations. And for Maxwell's equations, the potentials may not even exist. And, you know, they're just expressed in terms of fields. Now, the significance of what we discussed, which, by the way, I think was discussed by other people. There's Bernard Kay, who's a researcher at York that has also made similar comments recently. And in the past, other people are some kinds of experiments that you can

perform on the charges, which are the things that you interact with, that you use to somehow extract features out of the field. There are some experiments that you can perform on the charges, if you think that they're quantum, which are not there in the classical case, obviously, because in classical physics, charges are also classical. And once you go along with this fact, and if you quantize the field and you want the whole description to be nicely local, et cetera, you are forced to see that the charges get in some situations, they simply get to depend on the degrees of freedom that are supposed

to be Gauss in the Lorentz gauge. And by then measuring the charges in certain situations that are possible now to measure because we have quantum metrology facilities that allow us to do that, you are indirectly accessing these Gauss. Yes. So in a sense, this idea of gauge invariance, which is very important for classical electromagnetism, is also relevant for quantum electromagnetism or quantum electrodynamics, but it doesn't forbid us from, it doesn't impede the realization of these experiments that we discuss in the

papers. And so it forces us to revisit the idea that the ghosts are not measurable. They are not measurable in the sense that they may not be measurable in the standard sense of being measurable. So usually standard sense means to detect a click. So, you know, you have a photon, it's emitted and you detect it. This is one way of measuring features of the quantum electromagnetic field. But there are other ways of probing it with quantum charges,

which don't necessarily amount to detecting a photon of the ghost kind, but they amount to some kind of detection. It's not a direct detection of these photons, but they are detecting some quantum features of these ghost modes. So in a way, we are suggesting that the idea of measurability and what counts as measurable should be revisited in light of the fact that we can actually perform these experiments. So would an analogy be like the Aronoff-Bohm effect,

where before that, the electromagnetic potential was thought to be something that was just mathematical, a convenience. And then afterward, you still don't detect the electromagnetic field directly, but you see its effect on the phases of the electrons that go through a soliton or the outside of a soliton. And that, by the way, was revolutionary. So this paper with you and Vidral, is that correct? Yeah. Let me read its title. Interference in quantum field theory detecting ghosts with phases, and I'll put a link to that in the description. So this paper, is it suggesting something physical? We think that there's something physical about the electromagnetic field, with one of the major pieces of evidence

historically being the Ernhardff-Bohm effect. So with your proposal to detect ghosts, are you saying that something else exists, like something that's choosing a gauge? Is there something else, some other field that is actually in existence that we thought was a mathematical trick? Yes. I think this is one way of thinking about what we do. In fact, it's very related to the Arnold-Bohm effect in the following sense. We've also actually thought about the Arnold-Bohm

effect and somehow this was part of the way in which we landed on this idea. I see, I see. Because even in the case of the Arnold-Bohm effect, the interaction between the electron and the solenoid is mediated. That's the right word, it's a soliton by accident. No, I thought you meant solenoid, yeah, yeah. Yeah, they're very similar words, somehow different things. the solenoid being this thing that generates an electromagnetic field only somehow ideally along a line and zero field elsewhere. And in the AB effect, you have this interesting fact that if

you have an electron that goes exactly in the region where the field doesn't appear to be there, it can still be affected by the solenoid. Because when the solenoid is switched on, the electron has a different phase when it interferes compared to the case when the solenoid is off. So this shows that the electron is actually picking up some signal from the solenoid, even though there is no direct field that's acting on it. Okay, there the issue was how does the solenoid and the electron

communicate even though classically speaking if we describe the whole thing classically, sorry if you describe the field classically it looks like there's no field at the point of the electron and the key to answer that is that even though classically that's true, if you consider a quantum description of the field, you will notice that first, there is a back action of the electron on the solenoid. This is something that was already pointed out by Lev Weidman, who anyway used still a classical model for it. And second, more importantly, I think there's the fact that even though the

field is zero classically outside of the solenoid, a quantum field can never be zero in the strict sense. And so, some aspects of the field can be zero, but there is still a quantum feature of the field that's there and some of the photons that are so there are photons coming in a sense going back and forth from the solenoid to the electron and vice versa and these photons happen to be also of the same kind as those that we referred to earlier so i think the mechanism in all of these experiments is the same. There's a quantum field that somehow allows the one system to communicate with the other.

And in some of these cases, the modes that are involved in this, uh, back and forth communication, if you want to call it like that, are ghost, uh, photons. And, um, and this is only, the fact that everything happens locally and nicely can only be accounted for as far as we know in a particular gauge. So somehow this set of results that we mentioned show us, on the one hand, as you said, that some gauges are better than others the Lorenz gauge is

more accurate in the description of what's going on because it's explicitly local and also Lorenz covariant but also there's the fact that in order to have

a complete description of what's going on you have to quantize the field so you have to have a quantum description of the field otherwise as it happened in

the case of Aharnov and Bohm, if you stick to a completely classical description of the field and you want the charges and the solenoid to... sorry, the solenoid is classical, the field is classical, but the charge is quantum, you will incur into some issues of the description. And Arnold and Baum somehow were concerned that this effect, as they described it in the semi-classical theory, appeared non-local. And this can be cured by the fact that you quantize the field. So the lesson in the two, in this set of experiments is both that some gauges are more accurate than others physically speaking,

they're more realistic, they make more sense, so they tell a more coherent story because they're all explicitly local, etc. Lorenz gauge is one of them. The second lesson is that in order to have a local description, you always need to quantize everything in your systems. Otherwise, if you insist on one of the systems being classical and the others not, you will incur some issues, typically with locality. And finally, the third lesson is that if we quantize the field and you look at some of these effects in specific gauges, like the RANS gauge, and you consider all the experiments that you can perform on the charges, not just these input-output scattering amplitudes, things that people usually look at in particle physics, for example, you will notice that it's inevitable to have to modify your notion of

measurability because even though you cannot detect, as far as we know, directly these ghost photons by, say, having a click in a photo detector, you can indirectly detect their degrees of freedom by making measurements on the charges. And that's an inescapable conclusion of how you analyze the analysis that you can make of the situation in the Lorentz gauge. And so this requires us to just simply enlarge the set of things that we can call observables compared to the way we usually think of observables in quantum field theory. So this to me sounds like a departure from constructor theory, but you see it as tied or you see there being implications. constructor theory, but you see it as tied or you see there being implications.

Oh yeah, absolutely. Yeah. This, yeah, I think, um, in my head, all of these things. So if you like, you know, if you, if you look at, I'm being very, um, now I'm sort of telling you somehow that, that, uh, things to do with the way I think about stuff, so I don't know if it's really relevant, but the way, the way I think of this is really, you know, you can look at these papers, they look different from each other, but I think it's really me trying to understand how to apply this notion of observable that's more general,

that you have in Constructed Theory of Information, so this paper I wrote with David a while ago, where anything that is copyable, any set of attributes that is copyable can be considered as an observable, whether or not it has some formal features that quantum theory requires, such as being her mission operator, et cetera, et cetera. Uh, so it's my way of understanding how this concept of an observable can illuminate different parts of, uh, quantum field theory field theory or quantum theory more generally, especially those cases where we don't have an understanding of what we can really observe. So quantum field theory is an example of a case like that because, as I said,

even though it's a quantum theory of fields, it has issues with various foundational aspects. And so what counts as an observable there is very confused. And I think the foundations of quantum field theory also are not so clear about what is an observable and what isn't. Yeah. And so this is a way to, in a way, show the power of... Yeah. And so this is a way to, in a way, show the power of, well, I don't know if it shows the power, but let's say it's a way of, um, applying these constructor theory notions of observables that are more general than particular notions in

quantum theory or quantum field theory to help us find new ways of probing fields compared to what we used to know before. This is a bit technical, but when I was looking up the categorical approach to constructor theory, I saw that what you want to do is you want to divide your space into what's impossible and what's possible. And your space is then, or tasks, I believe tasks are the morphisms in a symmetric monoidal category.

And I believe when you divide your space into what's possible, it becomes a subcategory. Do the impossible states also form a subcategory or no um i actually don't know because the the so i think the categorical so category theory can be applied i'm not an expert at all but i think it can be applied to a number of things. In fact, it's so flexible, it can be applied to a very broad set of theories in a way, right? And I'm not sure about the specific answer to this question. I think what is promising there, and I was very happy that some people who are interested in category theory actually decided to do this work, some people who are interested in category theory actually decided to do this work, is that it could be that by casting

constructed theory in these terms that are, if you like, more modern from the mathematic point of view as well, compared to set theory, which was what we were using to express our results so far. I think there's a chance that some of the theorems we have could be condensed

in a very elegant short proof. And as well, you could also see unifications between things that we think may be distant and not related. So I'm really hoping that that continues and that perhaps more people may come along and have more results in that kind of direction. But as far as your question, I'm not so sure. The only thing is that if I can, I mean, if I sort of understand correctly what you were saying, what allows you to conclude that is the fact that in constructed theory we have this principle that's called the composition law that says when you compose two possible tasks you still should obtain a possible task

whereas this isn't true for impossible tasks. Oh, okay. So then it wouldn't form a subcategory. Yeah, they wouldn't right so so the idea is that somehow this composition law only holds for possible tasks and um it doesn't for impossible tasks so in fact you can have two impossible tasks that compose together give you a possible task a typical example is the so imagine again the task of first raising the energy of a system and then lowering by, and then the second task is lowering the energy by the same amount. You can compose the two tasks joint, right?

So they're both impossible, right? As we said earlier. Yes, yes. By themselves. But if you compose them, you basically have the task of the impossible, right? As we said earlier. Yes, yes. By themselves. But if you compose them, you basically have the task of the identity, right? So you stay in the same place. So you go, you know, one task goes up,

the other goes down by the same amount. It's basically the task, the resulting composition gives you the task of staying in the same place, which is a possible task by somehow axiomatic, by assumption. So that's an example of two impossible tasks giving you a possible task by somehow axiomatic, by assumption. So that's an example of two impossible tasks giving you a possible task. So I'm guessing because there isn't this closure property, presumably the answer to your question

is that the impossible tasks should not have that property. But as I said, I'm not sure. Sure. And the principle of locality, that's super important to constructor theory. Is that different than locality in the regular physics sense? No, I think it's... Okay, locality is a very subtle concept and has lots of different meanings in physics. People often are... Well, they mean different things, but there is one,

one, so the principle of locality, the way that we understand it is the principle of Einsteinian locality, if you like, sometimes called like that, which says that there shouldn't be any action at a distance. So in other words, if you have a way to describe your, you know, you have a system that's made of subsystems and you have a transformation that only involves one of these subsystems, it should only be able to change the subsystem in question and not the others. And this applies both to the directly observable things on the other systems

and those that are not directly locally observable and this is a property that is true for quantum theory non-relativistic quantum theory for quantum field theory is true for general relativity and is true for some forms of I would say well it depends what you're saying, but I think somehow this is true for all the theories that we think are reasonable,

even in relativistic quantum field theory that somehow is not necessarily the final correct theory because it's not relativistic. Now, this is different from the concept of locality that's sometimes referred to as Bell locality, which is a notion that's very important in quantum foundations because it's the property that a theory can be described by a local hidden variable model that uses real-value stochastic theories. And John Bell had this very interesting result, which was a mathematical theorem that says that if you violate with some statistics certain inequalities,

which are called Bell inequalities, you can conclude that your statistics are coming from a theory that is not Bell local, so it cannot be reduced to a local hidden variable model. And quantum theory is not Bell local, so it's not describable as a local hidden variable theory that uses real-valued stochastic theories. So in that sense, it's often confused. It's often said that quantum theory is non-local, but what one means there is

Bell non-local, so it's the fact that quantum systems can violate Bell inequalities. But the locality we're talking about is really more basic or fundamental. So it's to do with the fact that there is no action at a distance. And even quantum systems that are entangled, that violate Bell inequalities, do not allow you to action, you know, to perform this action at a distance.

And so that's the feature that constructive theory cares about. And I think this theory, this locality is really built in in the foundations of the theory. It's a very important result. Sorry, it's a very important axiom, if you like, or principle. And it's also very important in the context of these experiments that I mentioned earlier,

the ones to test quantum gravity and also the electromagnetic discussion we had earlier with the ghosts and also the gravity version of those results. So yeah, it's a very important principle. Chiara, what's a no-design law? A quote-unquote no-design law. A no-design law is a law that is very important for understanding this is in the origin of life problem, frame of mind, so we're thinking in that camp.

So the problem of biology is to one of the problems of evolutionary biology is to explain how uh living systems can have come about without um there being a designer. So typically I think, you know, Darwin's was battling with the idea that somehow, uh, there was a belief that you had to appeal to a creation, uh, sort of,

you know, to, to God being there to design, to a designer, to create, uh, entities are highly complex out of simple beginnings. And,

uh, so if you don't want to go that way because you don't want to make that step to believe in such an entity, you're in luck because Darwin and all the great biologists who came after him and kind of refined his idea showed us that it's possible to have a complex entity to come

out of simple beginnings, simple initial conditions that don't include complexity, simply by waiting for long enough and allowing for these natural selection and basically mutations that are not specific to what you want to get in the end. So you need the mechanism of natural selection to be there and you need the possibility of there being things that can replicate, which you can call genes in a broad sense, a bit like with the Dawkins terminology. So they're not just genetic, they're pieces of strings of information that can replicate in a stable manner. And then you need the possibility of having errors in these

replications that introduce variations that can then be selected by the natural selection occurring in a given environment. Now this concept is very, this description is usually in biology is given at a high level, so no one really thinks of what about the laws of physics? You know, people just think, okay, the laws of physics are in the background. We don't care in biology. That's fine. But somehow when you are trying to imagine a way to reproduce this thing in a laboratory

or in a simulator or in a computer or in some sort of dynamical system, you have to have a very good understanding of what dynamical interactions you are happy to allow in your simulator to mimic the fact that, like in physics, these laws, these dynamical interactions, don't have the design of the life that you want to emerge out of your process of evolution. And this is a very tricky concept.

It's tricky even in physics itself and in simulation is even more tricky. But the point of no design laws, the definition of it is really to highlight the importance of the fact that when you're running an argument like Darwin's, you want to make sure that you haven't snuck in some assumptions about the laws that govern the interaction between microscopic entities

in your biological system, which ultimately contain the design of the living system that you create at the end of the natural selection process. So a non-designed law is a law that isn't specifically designed or crafted to bring about a specific complex entity or a set of specific complex entities. And we know that the laws of physics says we believe, the laws of physics we know kind of govern the universe. Our current guesses are no design laws in this way because they don't specifically contain symmetries that are especially suited for the emergence of a specific form of life. suited for the emergence of a specific form of life. And that's very important to know because that gives strength to Darwin's argument,

if you like. And so if you are concerned with the possibility that there could be a skeptic that might not believe in Darwin's explanation, it's good to remind ourselves that the laws of physics that Darwin presupposes for his own reasoning and neo-Darwinism in general presupposes are no-design laws. So nothing is assumed of the dynamical interactions that are used in the Darwin's theory of evolution. And when you then try to, if you're thinking of a way to reproduce this thing in a laboratory, so you think of having, or in a computer,

it's very important that when you, if you start with simple beginnings and you get complex entities at the end in your simulation, you want to have a criterion and a test or a check, a way to check that the dynamical interactions that you use in order to show this progression do not already contain the design of what you're getting at the end. So, you know, you start with something simple and out comes something like an elephant,

let's say in a simulation in a computer. You want to make sure that the computer doesn't have some rules of interaction between elementary cells that somehow contains the design of this entity that comes at the end. So you don't want to assume what you're trying to prove. That's right. You don't want there to be circularity. I see. Yeah, that's right.

So if you were to assume that, then you would be circular because it would be like saying, okay, well, I gave you an elephant, but actually I snuck in the program you know the design of it so that's not very surprising what's surprising and what's cool in in what happened in the biosphere on earth and perhaps elsewhere in the universe we don't know is that as far as we can tell um because given that the laws are not designed specifically for life, life came about and we have lots of complexity now going around the earth. And that's very interesting. And somehow that's important to...

So the no design concept is very important, not just in the foundations of theoretical biology, but also in the context of the emulation of this process, which we want to do it in the lab. Okay, great, great, great. Now that we've talked about design law or no design law, what is superinformation? So superinformation is a particular kind of... In fact, I should talk about superinformation media. That's the thing. So it's a generalization of the concept of quantum systems.

So it's in the context of the constructed theory of information. And the super-informational media are physical systems that obey the laws of constructed theory and have extra properties compared to physical systems like a bit that can only contain classical information. And these extra properties have to do with the fact that not all of the states are copyable just like quantum systems and in our paper with David

we proved that these systems these super information media have all the qualitative properties of quantum systems so they are if you like you can think of the theories that describe these super information media as a generalization of quantum theory um and a super information medium could be a medium a physical system that can perform quantum computation but may not obey fully quantum theory and so they are

they are like post-quantum their systems can be described like post-quantum, they are systems can be described by post-quantum theories that obey principles like locality and the interoperability of information. So all of these principles are constructed theory. And these super information media are very useful. The theory of these things is very useful in the context that I mentioned earlier, where you have a quantum system interacting with something that, like gravity, that may or may not be quantum.

Because a quantum theory of gravity may describe objects like super-information media, exactly. I see, I see. Does constructor theory have anything to say about dark energy or dark matter? Okay, this is very speculative. I think we've remarked a number of times, this is, like I said, the speculative level that, so these systems are things that may or may not obey quantum theory as we know it, and also may require some upgrade of the theories that we currently have in general, even at the kind of mathematical level.

And because of that, I think it's very useful to apply to them this theory of super-information media and or the constructed theory of information more generally because they may still obey the principles of information and also the principles of information theory that we laid out in our paper put constraints on them so for example the principle of interoperability of information which says that any system that can contain information should also be able to interact with another system that can likewise contain information and you should be able to set up some interactions

between them that allow for copying various states. I think this is the thing that can be... so this principle could be applied to dark matter, for example, and it may turn out that this principle rules out some of the theories about dark matter simply because they somehow have um they they somehow violate the principle and they say that some copy like operations between the dark sector and the non-dark sector are impossible so in a sense i think constructively i can say a lot about that and and maybe this is something for future application but it's definitely something that

is on the you know we something that we may at some point address now given that you're working on what is like a theory of everything or maybe it's a framework for a toe rather than a toe but regardless do you believe a toe to be possible there are two respects in which i mean that like does it exist so that's one question and then even if it exists, is it knowable to us? So I think, I don't think a constructive theory is a theory of everything for the reason that, as I said, it has the ambition to express. So as I said, it has a principle, it has a number of principles that can express some aspects of physics, ideally all of them.

Uh, but also it, um, it may not have the features of a dynamical theory. So, so it may not actually, um, directly respond to the standard paradigm of the theory of everything. Um, I think a theory of everything perhaps is not the most fruitful way of thinking about stuff in the sense that it is my philosophical position that, um, we, you know, in any theory, no matter how complete it looks, uh, we may be able to find problems and so these problems will lead to something else. And so the way I think about stuff is more like,

I like to think of there being different levels of explanations. Maybe there are infinitely many, and we just keep going from one to another by understanding things more and more. So in that sense, I like this more open-ended way of thinking about science, physics specifically, where we, we just keep digging. And sometimes when we dig deeper, we find a different level of explanation that brings some more unification along and we go from one level to another.

And I think the reason ultimately, so there isn't really a very strong, I think it's very difficult to convince someone who thinks otherwise that this is the case. But I think I can say that the reason why I like this view is that ultimately it's very hopeful. I think it gives you really, as a physicist or as a scientist, it gives you the idea that there'll always be something

to work on. And I think that's a fun thing to, to entertain in your head. Um, and in a sense, the theory of everything somehow suggests this sense of closure that you might achieve at some point. Uh, and, um, I think, um, given that we can never know whether what we know is true, it seems to me to clash with this epistemological stance that I have, that I think it's impossible to actually know whether what you know is really true. All you can hope for is somehow to be able to find problems in what you know and somehow

change your view accordingly. and somehow change your view accordingly. So in a way, you know, I think I kind of like this stance on things, I think this is very- I see. If you like, and I sort of subscribe to that, I really like this approach and it's very scientific. I think that's how scientists behave more or less, even though when they, you know,

even though sometimes they don't acknowledge that, but it seems to me that's a kind of very natural way of thinking of things. What would be the difference between information and knowledge? So knowledge is a kind of information that has extra properties. So information is really some set of states that can be copied to arbitrary high accuracy, whereas knowledge has this extra feature of being information, so a set of states that can be copied, which also are capable of causing transformations

to occur on physical systems and to stay embodied in these systems. So it's got this resilient feature, the fact that it can last given physical support, as opposed to standard information, which may or may not have this feature. So in a sense, knowledge is a kind of constructor for, it's information that's also a constructor, broadly speaking. Is it possible for there to be information that isn't physically realizable, like that isn't instantiated in something physically? be information that isn't physically realizable like that isn't instantiated in something physically no uh i mean that's at least the way we think about stuff um that's that's very much

in line with with uh i think there's a long tradition of people physicists have realized this i think charlie bennett being one of them um and i think the you know most of the founding fathers of quantum information had this bias of thinking that computers are physical entities, they run on physical laws, and therefore they have properties that matter for physics. And David, somehow the idea of a quantum theory machine came exactly from this conviction. And I think the idea of information as being an abstract entity that's not embodied in physical systems is really something that somehow doesn't belong to the sort of philosophical viewpoint that we are following.

philosophical viewpoint that we are following. And ultimately, the constructed theory of information precisely says that. So it gives you a handle on information that's physical. It says it's a set of states that can be copied. And so that's, you know, when you talk about the set of states of a physical system, indirectly you're saying that everything that can, you know, information is actually physical

okay now kiara before we go i just want to know what's one mistake what's the best mistake that you've made that has turned out well um well i think i think i've made lots of mistakes, but perhaps the one that comes to mind now is this fact that I, so I think I didn't know, I thought for a long time that I wouldn't be interested in necessarily in science or physics. So I think my love for physics came in late in my life. So later, let's say, than say teenage years, right? So I think I initially thought I would be a writer. So around about 10 or something, I had this idea that I would love being a writer.

And I loved languages. I loved literature, poems, everything that had to do with language just fascinated me. And so I ended up sort of working a lot on these things. And my own choice in school in back in italy i think where you can choose between it's a bit different from the anglosphere but i think you have a choice between two kinds of um um sort of main parts and one of them is more science inspired the other one is more classics and literature inspired so i chose that okay, you could think of that as a mistake in a sense that later on, I realized actually I really did want to study science. So that happened at the

end of the five years of secondary school. But so on the one hand, this meant that I managed to actually just satisfy this love for literature and literature and and classics and and languages and then it also meant that when i switched to science at university when i switched to to physics i actually fell in love in the second second time in a sense and that was very exciting so unlike maybe my other colleagues that somehow had read mostly, uh, you know, they already had, had this school mostly within science. So they had being exposed more to say physics and calculus, et cetera. I really just found it then when I was 18 and I just, I just found that it was mind

blowing and very beautiful. And somehow the fact that I had all of this baggage from the classics side of things made it even more exciting for me to see these things uh because I it's like seeing them with with different eyes and I so in a sense that was maybe you could classify it as a sort of mistake initially uh maybe I could have immediately started on the path of physics already back in the teenage years but I didn't and I'm very happy that I didn't because I somehow it's really nice to be able to see maybe similarities also between different you know between humanities and science and physics and the way I think physics is really a storytelling so I ultimately satisfied my life for my love for storytelling

which is actually what I really loved as a child, by ending up in this field that is really about telling stories about the universe. And it's the most accurate, most complete way of telling stories because it really has, you know, you have reality as a checkpoint and you have to sort of make stories that are compelling and clear and precise. And that's just what makes me fascinated about physics itself. Yeah, an aspect of your book to bring this back that I enjoyed is that, and again, the book is The Science of Can and Can't, and it's on screen, it's in the description, is that you get the sense of a love of writing. Something I'm curious about is many

scientists see their expositionosition they're explaining to the audience as some necessary evil they have to do at the end in order to get grants because they need to drum up some fervor in the public sphere but they don't see it as something that they want to do they like to do the research and speak technically when you were writing your book did you find that the writing actually helped you develop your more technical ideas? Absolutely, I think so. I do find it challenging. So in a sense, maybe if I followed my least resistance path, I would also sort of tend to just do my own technical bits of writing and research, but the, the task of explaining

it to someone who doesn't maybe have the same mathematical tools and, uh, doesn't maybe even have an interest in, in this stuff and making it interesting to them is a very, um, humbling and at the same time exciting enterprise. And I think I really enjoyed it because it clarified in my head also my own understanding of things. So it didn't perhaps lead to new discoveries in the sense, in a strict sense, but I think it's true. I agree with, I think many physicists have said this before,

that somehow if you only know a formula and maybe you understand the mathematics, but you can't explain it in simple terms, it means that something is escaping you and you don't understand it yourself. So somehow trying to explain it to someone in simple terms is really a great exercise for everyone to do. Data for teaching, I think teaching is a similar thing. It's a very nice activity because it allows you to to really try to sort of break down your understanding of something very complex

into simple uh steps that you can then explain to people who haven't seen this before so yeah definitely i i really enjoyed it and i really enjoyed writing anyway so because that's as i said this is part of my passions. And my last question, I know you got to get going. Where do you get your best ideas? When and where do you get your best ideas? Oh, that's very, uh, it varies. Um, I think it's, uh, really like, it's really true that you have to be, it's, it's really

a creative act. I think it's something that this probably is true for everyone who's doing some creative work. You have to be relaxed. You have to be free of worries if possible. So somehow you have to be able to bring yourself to a subspace where you're not concerned about, you know, daily problems. And you have to be, at least as far as I'm concerned, you have to feel free to explore things without constraints. So I was very lucky in my PhD or DPhil because all my supervisors, I mean, David was a collaborator. He's great at this, but I think also Arthur Eckert was my supervisor at the time. collaborator he is great at this but i think also arthur eckert who was my supervisor at the time they are masters of this uh freedom seeking um attitude so i think i was really inspired to be

just so i was let let you know left on my own and um to just think and i think that's the best state you can be in so you're not forced by someone to say, okay, you have to work on this problem or this other problem. You have to be free to let your mind roam, um, and, and,

and, uh, explore things like you are, you know, um, as Newton used to say, right, that you're on a seashore and you're sort of looking at pebbles and,

um, you're like a child playing with things. You have to be in this fun-seeking free state to have your best ideas. That's as far as I can tell. And this is, as I said, a constant also. Actually, my mentor, Mario Rossetti, who was the person, by the way,

who introduced me to quantum information back in my master's in Torino. I think all of them, all of my mentors had this feature and they all said that they're on mentors were like that. So I think somehow it must be a constant. It's true of, I would say it's true of most creative activities that you need to be in that state to be inspired and you have to be able to sit quietly somewhere to be inspired.

So it could be that you are on a journey. So sometimes I enjoy thinking when I'm traveling, it doesn't have to be able to sit quietly somewhere to be inspired so it could be that you are on a journey so sometimes I enjoy thinking when I'm traveling it doesn't have to be that you're in a super quiet place but somehow you're tranquil and and so you know you're in your own zone and then you can think and and so the place can vary it could be on a walk it could be on a swim it could be while I'm traveling or I'm sitting at the desk but there has to be a moment where you're sitting there in this space and waiting for inspiration and sometimes it doesn't come you just have to be patient and wait for it but when it comes then it's really nice to follow it and and yeah it's it's really very much like an artist that's that's I think the way I work and presumably all my colleagues also do.

You mentioned you're waiting for the inspiration or just the inspiration occurs to you? Like, are you sitting here like, come on, inspiration, come on. Yeah, I think sometimes you have to be patient and wait. It's a bit like when you're sitting to, you know, if you're outside walking and you want to see some rare animal in the wood. You just have to be patient but you've got to go there and i think that's the thought that's maybe the hard thing to do you have to cultivate these things especially if you're not you know there are also things that go in the way i think of researchers these days not just daily problems with the you know everyday

life but i think also you know grant applications as you said, and admin duties, etc. They're all enemies of creativity. I think they are not optimizing research-oriented ideas. So I think you really have to find some way to guard your time and say also no to things and find, you know, some free time to wait for inspiration. And you've got to be somewhere for it, for it to visit. Um, so in that sense, yeah, I think I very much think of me myself as sort of being one of those explorers that are waiting for, you know, to, to, to see a rare animal

in the forest. Um, I think that's how, how I think of myself. Thank you, Chiara. Thank you for spending so much time with me. And the audience thanks you. Yeah, it was great being here. And thank you very much for the questions and for listening. Yeah, thank you.

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