 Yeah, hello everyone and welcome to the next edition of the theoretical sciences visiting program seminar series That's a second season our next speaker is a Physicist more precisely a mathematical physicist and it's a great pleasure to introduce Leon Loveridge Who's currently an associate professor at the University of southeastern Norway? so his research interests cover Broadly the foundations of quantum mechanics somewhat more precisely the mathematical foundations of quantum mechanics with a healthy input from operational and conceptual considerations and that has also brought him to interact much with some philosophers of science To give you a brief glimpse on his biography He has done his PhD at the University of York in the UK under the supervision of Paul Bush Who was a rather significant figure in in the mathematical and operational foundations of quantum mechanics in recent decades? he then moved on to do postdoc in Vancouver at the University of British Columbia in quantum computation in fact and then went on to the quantum group in Oxford Before spending some time in Utrecht in the Netherlands actually in the foundations of physics groups interacting with philosophers And then he took up a lecture or position at the University of York again And then about three years ago he moved to Norway to become an associate professor there so and yeah The talk will of course reflect his research interests and he will tell us all about what What the mechanics is is about and we expect of course? enlightening answers Okay, can everybody hear me okay microphones working perfect. Okay. Thanks for that introduction Philip And I want to start by just thanking Oist and and this program in particular for Allowing me to be here in this really amazing place So I just noticed that in the foreground we have the world's greatest blackboard chalk It's rumored that you can't write to false theorem with this chalk And in the background I have the sea and in between I have the of course the highlight of the visit Which is the the people that I can interact with so thanks to Jonas and to Philip and to everybody Um before I start I want to say a little bit about My background as Philip said I'm a mathematical physicist But I'm really motivated by conceptual foundations of physics and particularly quantum mechanics I like to Understand conceptual questions by by sort of proving a theorem and reflecting on the meaning so it really is somewhere in between Mathematics physics and philosophy and I think all of those communities probably regard me with a sort of healthy suspicion I'm not sure how you'll you'll feel after this talk And I want to say two things about the title so I retrospectively Realized well about five minutes ago that this is actually sort of ambiguous in a Serendipitous way so it can be read in two ways one In the sort of natural language Way, you know, what's quantum mechanics about and I I'd understood there would be a broad audience I know there's at least one philosopher here And some mathematicians who maybe have not been exposed to much quantum mechanics before So I hope to at least address to some extent this sort of This question there's sort of a naive question What's the theory about but then there's another meaning which is a sort of more literal translation of the question Which is what is the actual content of this theory? What are the sorts of objects that quantum mechanics is supposed to describe and it turns out there's not really a consensus So that's the second purpose of this talk. So I start with some history so Probably this will be quite boring for some of the physicists. It's a slightly hackneyed tale I hope to go slightly beyond the standard undergraduate sort of lecture course treatment of the history We go back to 1900 like I was really in two minds about whether to put this guy in the talk I just I literally just googled smug and about the first 400 hits Were variations on this. So I thought I had to do it And then I also thought that actually the history of quantum mechanics has some pretty questionable Figures. So why not add another one? It is yeah rendered in color So if we go back to 1900 is really when everything changed So the science of thermodynamics that's that's heat mechanics of celestial bodies Newton's theory of gravitation and all this stuff And electricity and magnetism were all functioning sort of reasonably well. There were sort of things in the water that made people believe that There may be There were some there was some tension But generally people were pretty pleased with themselves and thought that sort of physics was was nearly done Um, of course, we know that's not how things turned out. So We go from everything's mostly fine to everything's definitely not fine almost exactly 1900 Um, well, there was a known tension between thermodynamics That's the theory of heat and the theory of electromagnetism which is given by this black body radiation So a black body is a perfect emitter and absorber um and the theory and the Well, so the the theory said that the The energy at the short wavelengths is just far too high to be reasonable and of course, it also didn't match experiment so The father of quantum mechanics max plank introduced a new constant um And sort of solved this problem with some ad hoc fit of the experimental data that he was not completely satisfied with In the story that we tell ourselves plank sort of quantized the energy In a certain sense that is what he did But he didn't really see this as being what he'd done. So if you look at his Nobel Prize winning address in 1920 he attributed this idea that energy is somehow particulate to einstein So what he actually did was you had to sort of he had to Apportion a certain amount of energy into a certain discrete number of of black bodies in the walls of this Sorry of harmonic oscillators in the walls of this black body and of course there's an infinite number of ways of doing this So he just cut it up into chunks. So it was essentially a sort of pragmatic move And so from here He derived his new his new law of the spectrum of the black body based on some new ideas that had been introduced by bardsman Here's plank And this is what he said quoted incline in 1972. It doesn't we don't need to go into it in detail But this is just a quote to sort of indicate that he knew that there was there was a lot more going on than what he suggested as the formal formal rule so So I'll just let you read that for a minute The interesting thing as well is at the end after a few weeks of the most strenuous work of my life And this sort of struck me because if one looks at the history of quantum mechanics What I'm struck by partly, maybe just because I'm extremely slow But it's just the absolute the rapid speed at which people got things done is is really unbelievable. So Um so plank plank really is the father of Of quantum mechanics or at least the sort of quantum mechanics that existed between 1900 and 1925 um And this is when things became began to really unravel so um Einstein understood the Planks maneuver in a slightly different way And saw the discretization of the energy not at the level of the black body But at the level of the electromagnetic field Okay, so and this is where the theory of although the name quanta comes from these sort of units of energy Um, this photon idea was widely rejected at the time. It was rejected by bohr even as late as 1925 Um, also 1905. So this is another example. Einstein wrote a paper explaining how Well, in a sense justifying atomic theory on the basis of brownian motion And he also constructed the special theory relativity. So this was his miraculous year unbelievable For me everything changed in 1913 when bohr Entered the scene very young and explained the Observed spectrum of the hydrogen atom So they knew from experiment that Hydrogen radiated energy and in certain sort of discreet spectral lines Bohr got the Nobel Prize in 1922 for this and the idea here is that somehow the electrons in this planetary model Orbiting the nucleus of an atom can absorb or reject atoms only in sort of finite units Interestingly, he didn't see these he didn't think of this in a photonic way. He was really talking about the the electrons only um So this is again a sort of quantization maneuver. He also introduced this correspondence principle that at high High orbits somehow the classical theory is recovered. So this is really the first idea that that relates quantum mechanics and classical mechanics as a sort of classical limit um And then it took de Broglie until 1924 to sort of explain the bohr model in terms of Uh, the sort of standing wave assumption of electrons orbiting a nucleus okay, so The point really is that physics was in total disarray at this point and this is when everything Changed for the second time and Schrodinger and Heisenberg into the scene um And for me it was Heisenberg that had really the most radical and important insight here So he wrote this paper. I will not attempt to pronounce it um Roughly speaking the translation will be something like on the quantum theoretical reinterpretation of the kinematical and mechanical Uh relations Would you agree? German speakers. Yeah, okay So this is the breakthrough paper for Heisenberg really He had he had a feeling that somehow Somehow physics was going wrong by trying to describe things that were not directly observable And this is where this so if you if you know about quantum mechanics, you know people could talk about observables all the time So this this was a sort of slightly positivistic move um And you know, he claimed very strongly that one must this is a direct quote One must specify definite experiments with whose help one plans to measure the eg position of the electron Otherwise the word has no meaning so The application of these concepts has to be done in a very specific operational way so Philip mentioned Paul bush in the introduction so um Paul bush's supervisor was Peter mittelstead and mittelstead supervisor was heisenberg So there's a direct line of this sort of operational thinking through that academic generational tree So these ideas are still going strong This this um do it and this reinterpretation is crucial So he thought that the position in the momentum that's x and p here I've got a horrible feeling it changes to q and p it does indeed Um, that's a typo. So I started with x's and changed to q's um They they both have their the same classical meaning So the position and the momentum x and p but they have they interact in a way The they don't in classical physics. So this is this reinterpretation again is a sort of first idea about Quantization of classical physics um And one can show actually it took kenard to prove that the uncertainty relation that's famously attributed to heisenberg can be derived directly from this equation Okay, so this is position momentum and on the right hand side we have h bar Which is planks constant divided by 2 pi and we have the imaginary unit, which is maybe surprising to some people Um, so we'll come back to heisenberg in a minute schrodinger went a different route. Um, so that so this heisenberg's Contribution has become known as matrix mechanics Interestingly so he writes in a memoir somewhere that he didn't know what a matrix was He talked about all these learned getting in mathematicians talking about matrices and he didn't know what they were But he's the father of matrix mechanics Strictly speaking there should be an identity So of course now we know that they're not matrices at all. They're they're Unbounded linear operators in helbert space, but we'll get we'll get to that um It's anything else. I wanted to say no, I think not so Um schrodinger went a different route. He wanted a wave equation So these waves of debroy should be accompanied by some wave equation And from here he he was able to write down the schrodinger equation. Apparently there's a there's a Scandalous history of where he was when he did this I won't repeat it But if anybody knows the anecdote and or we can maybe discuss it when I'm not on not being recorded Schrodinger was a was a bad man. Anyway, so He wanted a wave a wave equation and this is of course the famous schrodinger equation Which has again the imaginary unit I And the left-hand side is the Hamiltonian the total energy Okay, so Schrodinger understood this is a classical field this function Okay, and he spent a lot of time talking about cats and trying to Show the idiocy in a sense of the of the new interpretation of quantum mechanics when he really thought that This should be somehow an underlying classical description. So Schrodinger's cat, which I'm sure you've all heard about Brian Brian Cox or something Was Schrodinger's It was his way of producing an absurdity about about modern quantum mechanics And then we should also mention born so that somehow this This wave function Schrodinger has a probabilistic interpretation in terms of its modular squared In fact, I so I didn't have time to look at the original paper of born, but I gather this appears in a footnote So I think he might be the only person in history to get a Nobel Prize for a footnote Then okay, so I'm I'm jumping ahead of it. I'm not mentioning Dirac There's not enough time to mention everybody. He was of course extremely important too, but for me this contribution of von Neumann in 1932 was sort of world changing Here he introduced really the mathematical foundations of quantum mechanics Which is still alive today and actually if you look back at this book, it's really remarkable how In a sense how little we've we've done since his since his book in terms of the actual structure of the theory so people have made progress but It's still worth reading today, which I find remarkable. So if you read the papers of heisenberg Schrodinger bore They're a little hard to understand But von Neumann's book is is really easy to understand if you have a mathematical background So he realized that the Schrodinger's wave functions can be written As elements normalized elements of a of a Hilbert space so von Neumann created this object It's popular to sort of say that heisenberg and Schrodinger discovered equivalent versions of quantum mechanics I would say that heisenberg sort of found the observables and Schrodinger found the states and von Neumann put them together In this concept of a of a Hilbert space So the superposition principle the fact these waves can be added together Is encompassed in the the linear or vector space structure of this Hilbert space The observables introduced by heisenberg very heuristically can be given extremely precise meaning the self-adjoint Bounded or possibly unbounded operators in this Hilbert space called hypermaximal Hermitian in von Neumann's book He introduced mixed states he gave an abstract formulation of Born's rule In terms of the spectral projections of some observables. So this is getting slightly technical. We'll we'll come out of this again in a minute But the point the point is really to say that this is this is the birth of quantum logic Um, so with burkov he was able to to create a new logical foundation of quantum mechanics in a certain sense and that is still Still going on today So von Neumann is in a sense the hero of quantum mechanics. What's really remarkable is he's also a hero of computer science and Economics and game theory and various other things. So I think he only spent about six or seven years on quantum mechanics So less than me von Neumann algebra's part of quantum field theory Still the basis of that theory. So it's still There's a lot to learn from von Neumann So I thought To honor paul, uh, he died about four years ago. Um, I talk a little bit about his work on the uncertainty principle So I think this is one of the things in An undergraduate quantum mechanics is perhaps the least well explained um Or at least I didn't understand at the time So if you read heisenberg's 1927 paper, it's extremely wordy and and heuristic And you can really so in a paper Yeah, uh about 15 years old now Bush with with takeo heinanon who now heinousali he Got married and he's finished and apparently it's becoming reasonably normal for people to blend their names in this way and peccalati And Really prized apart three very different Notions that are in this this uncertainty relation. So these are not implied by this relation three But it is possible to phrase More modern versions of the uncertainty relation in these terms so statement one Which is the embodiment of equation three says it's impossible to prepare a state a quantum state a wave function uh Which is better localized in position and momentum than is given by equation three the uncertainty relation Okay, so That's the sort of standard ruling what you call a preparation uncertainty relation the second a second version Is that there are no joint measurements of q and p position momentum You can't measure them together people sometimes say simultaneous measurements, but really it's a joint measurement And the third is that if you measure position you disturb momentum in a certain way. Okay, and these are logically independent So you've probably heard jokes about you know people being stopped By the police and they say, you know how fast you're going they say, oh, no, but I know exactly where I am This is you know, so the uncertainty relation has entered into the popular vocabulary to some extent This is still active but what I want to Move towards is is understanding the fundamental meaning of this in terms of The sort of ontology of quantum mechanics if you like so one could ask the question So if we look at two you can't measure q and p at the same time position momentum or in the same state is this Epistemological restriction. Is it that position and momentum Could potentially have jointly sharp values. It's just that we can't measure them or is it really a sort of fundamental blurring In the concepts. So is the is this vagueness that's introduced by the uncertainty relation It's sort of inherent in the concept of position and momentum So those are two opposing views And we'll try to sort of make this a little bit sharper as we go There's a nice quote of powley another hero in the foundations of quantum mechanics One can look at the world with a pi so that's momentum and one can look at it with a qi But if one wants to open both eyes at the same time one gets crazy And this is a sort of poetic Encapsulation I think of this this heisenberg's umdreutung idea that somehow As long as you only look at one the classical concepts still apply But if you try to apply both simultaneously you end up in a in difficulty Okay, so this can be largely ignored As I say, I tried to make everybody happy Maybe ends up making nobody happy, but that modern quantum mechanics has the following structure As we now know we can write down states observables. I'm not even going to read out what they are I want to say a little bit about the the algebraic point of view So these commutative or non commutative c-star and von Neumann algebras. So those obviously go back to von Neumann in some sense And the reason that I think that This algebraic perspective is powerful is because it allows one to talk about classical and quantum physics in exactly the same language Okay, so so the key the key thing on this sort of woefully overfilled slide is that quantum observables don't commute with each other What that means is that the order of application matters. So if we go back to the Equation one Here, so this is maybe surprising for people who haven't seen quantum mechanics before is the order of application of these These quantities Matters it depends which order we do things in Okay so So this is encapsulated by this idea of non commutativity and if one sort of throws everything one can measure together Well, one gets a non commutative algebra c-star algebra or whatever the born rule has a as a precise formulation And another key thing that I want to mention is that this theory at least at a structural level is irreducibly probabilistic, okay, so That one can make this precise mathematically, but it says that there's there's no setting. There's no state of the world Or the quantum world for which all things that you can measure Have sharp values. Okay. So some of them will be spread out. They'll have a non zero variance if you like And you can't do any better than that in quantum mechanics so One can say well, again, is this an epistemic or an ontic statement Does this is this really a statement about the world or is it a statement about our knowledge of the world? What do the probabilities refer to? are they Is it a lack of knowledge? Or is it a fundamental vagueness? Okay, so I really hope that nobody thinks I'm going to answer all of these questions But hopefully we can explore them a little bit. So in contrast to classical physics So all observables can be measured together. We have a commutative algebra Um, and I've written somewhere that the state spaces are simplex Uh, I can't see it on here. I don't know if I dreamt that I wrote that it might be on a different slide But the point is that in classical physics Um vagueness Measurement error if you like is due is really structurally due to a lack of knowledge So it's saying that well, there is a state of things. We just don't know exactly what it is So our probabilities reflect our lack of knowledge Um, and as I say structurally quantum mechanically one cannot maintain this view But one can ask whether there's something underlying it. Is there something deeper? In which where this is the case. This is a question about hidden variables So just to to move on quickly so von Neumann also clarified The active measurement in quantum mechanics. So this has a very very different status to in classical physics You've probably heard of the collapse of the wave function Um, so what it says is that you start off with some vagueness And after you do a measurement the state of the system is different and there is no longer any vagueness anymore Okay, so this is what's called collapse one can phrase it as a sort of transition from the possible to the actual Um, so there's a famous problem quantum mechanics called measurement problem and trying to explain this is essentially the core of that problem Um, and I say here observation in uh influences quantum systems So you can't it's a theorem in in the in the mathematical Description of quantum mechanics that you can't learn anything about a quantum system without changing it in some way. There is a It's just a strict impossibility result um and and von Neumann also stressed the The entanglement between the system and the apparatus Um, which also sort of from a philosophical point of view blurs the subject and object divide somehow um, I mentioned somewhere that The von Neumann. Ah, yeah, so let's go back. I just wanted to mention. So I was just looking Uh, I was looking at this book a long time ago and I realized that actually so for all those who know about povms On on about the third to last page of von Neumann's book in 1932 He could have discovered them if he'd just written one more page. I think and it took until the late 60s So there's some interesting history He wrote down a model of a position measurement interacting with an apparatus um And it was so close anyway so I want to talk about a famous theorem from 1967. I think I'm doing okay for time yeah So this question of hidden underlying realism so to recap we have these this probabilistic structure We want to know whether there's something underneath it something that Where everything is actual, but we just can't We can't exactly know it for some reason. We don't have good enough experimental apparatus or whatever So there's sort of mirrors the situation and one thinks about the Macroscopic quantities of a gas the pressure the volume and so on We know that all of the atoms in the gas have Classically well behaved values, but we can't we can't know 10 to the 30 or 25 or whatever degrees of freedom So we have to sort of average over all of these unknowns We end up with these these macroscopic quantities. So the question is whether Whether in quantum mechanics the same sort of thing is going on. So this is a sort of A bunch of theorems I've condensed into a single A single theorem one can make it precise More precise than this, but I want you to get the idea. So The observables in quantum mechanics are things you can measure are modeled as some object Called bounded operators on a Hilbert space But just think of them as quantities that you can measure Then we want to introduce some some map on these operators That does two things So for the self-adjoint Elements the ones that we can actually measure This map gives you an eigenvalue Of the operator, right? We know that eigenvalues are what we actually measure in experiments So that's one. So this is called the spec principle if you've read the the history of this and two for any real valued function The valuation sort of commutes with the With the function. Okay, so one has to be a little bit careful here about what we mean by f of a well There is a sort of notion of functional calculus that can make sense of The functions of elements of a von Neumann algebra and Braille functional calculus But anyway, so we want to say well if the energy has value three And we cube it by applying f it's the same As cubing the energy and then finding its value. Okay, so really What seems like an extremely minimal assumption? So we measure the position and double it or we double the position and measure it shouldn't make any difference Okay, so this is what people call the funk principle Um, and it turns out that if your Hilbert space has dimension greater than two you can't find Such a valuation. So the upshot The upshot is that quantum mechanical Quantities operators Cannot have values in this sense Okay, and this is not a quantum state. This is much more general so This introduced so people call this uh contextuality I don't like that name for this result, but it's become Sort of fixed For the mathematician, so I know there are some here. I'll talk about this in the next slide, but this can actually has a beautiful Way of writing this in terms of a certain pre-chief not having a section So this casts for me extremely strong doubt on the ideas that quantum states Uh, average over averages over some underlying reality, right? So, um I just want to have a little aside to slightly advertise some other work that I'm not doing but I think is is profound Um, this is boar one of the one of the heroes of quantum mechanics He's got sort of slightly bad reputation these days people like to To say that he was extremely vague and difficult to understand which is probably true But he was also extremely deep and I would really recommend reading some of his early Philosophical thought it's It's very interesting. Anyway, so so he writes well, however father phenomena transcend the scope of physical classical physical explanation So he's talking about quantum phenomena the account of all evidence must be expressed in classical terms So he's saying well, whatever you do in the lab. I should be able to tell my friend what happened Okay, so so for boar somehow classical physics is part of quantum physics It's you have to understand quantum phenomena through classical physics um So this has led to some very interesting mathematical work Due to Well isham and butterfield and andre's during but also class landsman So this is The only deep mathematics that i'm going to talk about um So landsman well really earlier chris isham suggested that If one takes this algebra of all quantum operators And look at that all of the commutative sub algebras. These are somehow classical viewpoints or perspectives on the quantum system And the collection of all of them Tells you essentially all you can know about that quantum system Okay, so if we take some classical commutative sub algebra Um and apply the gelfand Transform of the gelfand line mark theorem. We know that we can write this as the space of uh, or the algebra of Of continuous functions on this locally compact house dwarf space, which is called the gelfand spectrum of v So one recovers this classical phase space from this Classical algebra And one can look at this entire So these these algebras form a partially ordered set Uh landsman refers to this as borrification. He's written a 1000 page book on it um Quite readable in contrast to his first book um So understanding this post set is is very interesting So for example, if the Hilbert space is finite dimensional one can I'll try some morphism reconstruct the algebra There's a c-star algebra just from this post set. So there's some extremely powerful mathematics going on here um If one wants to go even further one can view the category of pre-sheves on this post set As a topos, um, this goes back to chris isham So these are set valued pre-sheves and from here one gets um A multi-valued logic in which the law of the excluded middle fails and all sorts of other interesting things happen And the the key idea really is to view the the logical values as probabilities or the other way around view the probability The probability assignments and quantum mechanics to view them as as truth values in a multi-valued logic and they talk about a neo-realist Interpretation of quantum theory. This has sort of pitted out. It's a really complicated object to understand Um, but I think they made some some serious progress in understanding At least some aspects of the foundations of quantum theory And again for the mathematicians, this is really saying this spectral pre-chief So the pre-chief that assigns to each algebra. It's a gelfand spectrum has no global sections There's no natural transformation from the terminal object to this Um, this probably is not that interesting to most people, but maybe very interesting to one or two people So I'll move on Finally, I want to talk about uh Heidegger so in 1967 Which is the same year The kosher and specker wrote their their paper Uh, Heidegger wrote a book called what is a thing? This is not a picture of Heidegger. This is the hut in the black forest that he did his work in Really some of it. Um, I said there would be some questionable characters in this talk So he writes a thing is always something A thing is something that has such and such properties Something that is constituted in such and such a way. So it has such and such properties in Heidegger's view Um, it's interesting that this was published in the same year that kosher and specker published their paper Where they really proved that quantum objects don't have properties. Okay, so, um There's something else I wanted to say about Heidegger comment what it was Ah, what is a thing so so i'm really sort of Thieving some of this from chris isham. He gave some talks about this when I was an undergraduate Imperial college where he was working and apparently the previous year in the foundations of quantum mechanics exam He had asked this question. What is a thing in a physics department? So i'm not sure if that's heroic or not, but it's uh I'm not sure you get away with it anymore So let's uh return to the main the main question. So what is quantum mechanics about after all of this? Um, there are various sort of axes on which one can ask this question so One can think about it in classical terms or in terms of the relationship between classical and quantum physics So one can take two opposing views or maybe somewhere in between Quantum theory is the fundamental theory of the world The classical world is emergent somehow um, or apparent it just appears by happenstance in some some way And we experience the world in the way that we do but really everything is fundamentally quantum mechanical So heisenberg, I think thought this Decoherence theorists think this I think consistent Histories people probably too or one can take the exact opposite view. Okay. The classical physics is fundamental Uh, so this is really a hidden variables hidden state description and the quantum mechanics Somehow is approximate. Okay in the way that we've discussed. So Einstein thought this I would say I'm always a bit nervous about putting words in the mouths of Of the greats, but I think he spent a lot of his time really trying to sort of Show the incompleteness of the quantum description of the world Schrodinger to later bell berm and the spontaneous collapse theorists Okay, so that's about the sort of relationship between classical and quantum on the actual topic of quantum mechanics One can find a really bewildering array of views out there still so the obvious one I think But the obvious but maybe not the most popular is that quantum mechanics is a theory of individual quantum objects. Okay electrons protons and so on Microscopic entities if you want to call it that I didn't want to say things after the previous slide Um, one could take In a sense the opposite view that the quantum mechanical the structure of quantum mechanics the objects of the theory Sorry, the the elements of the theory. So the the operators and the the vectors and so on are really Referring to classical measuring apparatus. All right, so this would be an empiricist view So if one there's a book by de monc where he really claims this He's not saying that there is no underlying physical reality, but that's not what quantum mechanics is talking about. It's about classical preparations Um, one could even take the view that it's really a sort of psychological theory. It's about the beliefs of rational agents Gamblers who behave in a certain way Um These are all sort of somehow orthogonal to each other and of course one can keep going. What is the wave function? Well, it's it's a property. It's a says something directly about a physical system Or it could be just a way of keeping track of probabilities in our brains It could be a tool for making the right bets in a gambling game and so on so this goes on and on so There was an interesting experiment Based on an earlier experiment. So in in something like 1997 max tag mark Quizzed people at a foundations of physics conference on their beliefs about quantum mechanics. This experiment was redone by These three Schlossauer Koffler and Zeilinger in 2013. So this was another Conference on the foundations of quantum mechanics mostly physicists A few mathematicians and philosophers Only 33 people. So I'd like to see this Repeated in a larger more scientific way But they asked just sort of various Purposefully, I think ill-defined questions Um So this one. Do you believe that physical objects have their properties well defined prior to an independent measurement? So three percent. So that's obviously one person um This isn't so surprising. I think yes in some cases or no. I mean Yeah, I think one could probably Defend either of those Uh, depending on how one interpreted the question, but it gets in a sense worse So there's a question about the observer. So I talked earlier about measurement and observation. So There's an idea that somehow This collapse of the wave function is is due to actual observation rather than some physical interaction So it makes you think is the observer Is it a person? Is it a Mitochondria? Is it a computer? Is it any other system? So they asked Let's just try and see what people think about this. So is the observer complex quantum system Of course, these numbers don't add up to 100 but yeah about 40 percent Should play no fundamental role 21 percent does play a fundamental role But no distinguished physical role. I'm not sure if I even really understand the question But 55 percent of people agree Um, and does play a single uh, does play a distinguished physical role So e.g Consciousness collapses the wave function. So two people thought that Um So I think this one's very interesting So the the famous measurement problem the collapse of the wave function the transition from possible to actual Uh, some people think it's a pseudo problem. It's not really a problem Some people think it's solved by decoherence. This is a measurement. This is a mechanism by which interaction with the environment Does the the job of collapsing the wave function? um Requires another solution Or has been solved in some different way other than decoherence Only 24 percent of people thought it was a severe difficulty And 24 27 again. So about a quarter Just didn't want to answer So I'd be interested to know what people think about this. My view is that it's a severe difficulty I I really believe that we don't understand quantum mechanics Uh, let's have one more. I think we have one more Uh quantum states. So these epistemic and ontic are really orthogonal, I would say um So that really singled out two separate camps Some sort of mix. I guess that could be mixed states um Only one person went for ensemble So, I mean the the reason that I I mentioned all these is just to highlight that I think there's a lot of Deep issues or at least conflict in the Deeply hidden conflict in the community about really what quantum mechanics is about I'm not saying that all physicists should take all of their time thinking about these things But I think it's sort of fascinating that That we still Don't understand our best theory in some sense So I promise that I would answer the question. That's a lie. Um, I promise that I would say some vague and biased Final closing things about where I think we should we should go. Um, so I didn't really talk about my research in this talk Um, so the the final slide will touch on what I've been doing recently. I want to go back to Mac hero of relationalism Um, I'm not sure. I don't think I should read this out. I think I'll just sort of Take a moment silence for you to read it and then we can think about it a little bit So this is in the context of course of classical physical bodies interacting So So this is just one statement from this really amazing book that mac wrote that I would really recommend reading He was a very deep thinker. Um, and it it points to me sort of Towards a number of really important ideas in physics Partly it's this operational idea So mac was a sort of in a sense a a pre-founding father of the vienna circle and the sort of logical positivism movement um But it's it's this idea that well, we need other bodies to be present to say that anything's happened to body a if you like so it's a sort of I would say that in bodies a certain sense of operationalism But also a relationalism so it's saying that Yeah, so we can't really say anything unless there are other bodies present with reference to which the motion of the body k has been estimated So my research currently One of the reasons i've come to talk to philip is in a subject called quantum reference frames. So this is in my view Really the development of this idea But taking bodies a b and c and k and so on to be quantum objects quantum systems so in my view the the way to Or at least a Direction we should look in to understand the difficulties of quantum mechanics is into a sort of relational Ontology if you like i don't want to use that word too strongly, but Trying to understand what quantum mechanics is about well, I think it's about a sort of relational picture So there are various flavors of relational quantum mechanics to the first To be called that is due to carlo rivelli um I don't understand relational quantum mechanics from carlo But I think it's a very interesting idea and very inspiring So he claims that quantum mechanics as it is Is a theory about the relationship between physical systems and it's a complete theory. That's all we have So quantum mechanics needs no modification at all. It's it's complete So I don't agree with that but I do agree that the Sort of the moral of the relationalism is is right There's the perspec- perspectival quantum mechanics of bene and dikes and so on i'm not going to say much about that And then there's this subject called quantum reference frames. Um, which goes back to the 60s really There are various incarnations I've been working on this on and off for about 10 years So i'm not sure everybody would agree but for me So the main theorem in some of the work that I was involved in Is to take the or you can take the ordinary quantum mechanical description of the world um And you can sort of relativize it in a certain way by introducing a second system also Described fully by quantum mechanics when that system becomes sort of large in a certain sense Sort of classical in a certain sense Um, you can't tell the difference between these two theories So that they are probabilistically identical Uh subject to some some technical conditions So my view So this is a very very personal take Is that quantum theory is really a theory about the relation between individual quantum objects And other quantum systems which have some sort of classical behavior I don't want to say classical systems But those that can be released approximately described in some scenarios by the laws of classical mechanics There's a small caveat in that I don't want to get into the details here, but sometimes the theory does indeed Uh describe ordinary quantum objects as they are So there's a confusion about the the reference the actual objects that are being described Sometimes it's individual quantum systems. Sometimes it's the relation between a quantum system and a classical system And I sort of have a feeling um That this is at least at least some of the mysteries of quantum mechanics can be resolved by thinking in this way Um, I'd be happy to talk more about that with people if they want to discuss Uh, there's obviously a lot of work to be done. So I'm not presenting a complete picture I'm just sort of hinting at where I think we should go. Okay. So that I think is that Thanks for listening Yeah, thank you very much for the nice overview and uh inspiring talk. So are there any questions? Yeah Um, why do you think the measurement problem is not solved by decoherence? Very good question. Um So the measurement problem Really is trying to understand the nature of the mixed state that you get when you trace out the apparatus right, so my view is that If it's not solved by just tracing out of the apparatus and and So that mixed state doesn't have an ignorance interpretation in my view um because of the the geometry of the state space And decoherence to me is just a whole bunch of measurement interactions essentially with the environment So the mixed state that you end up with has the same nature You know the same conceptual status as the mixed state you get out from tracing out the apparatus So you just have instead of one measurement problem 10 for 23 measurement problems in my in my view Any other questions Yeah, that's a very good question. I don't know the answer. So I didn't I mean high digger was also a bad man So I didn't pinpoint all of the bad people Yeah, I think probably yes. I think the body of evidence is moving towards thinking that Heisenberg was up to no good at least some of the time I'll ask a really vague naive question. Um, is there any room for experiment in this? Yes, absolutely. Um, well certainly in terms of For example, these spontaneous collapse models people are really looking into this. Um Regarding this relational idea That's that's a very interesting question. I'm not sure. Um It's something I should think about more. Um Yeah, I don't That's a very good question. I don't know the answer about trying to how one would distinguish this quantum reference frames based perspective Uh from ordinary quantum mechanics. I'm not sure because my view is that ordinary quantum mechanics as it is is already a theory of relations So the experiments that we've done um I'm probing that if you saw I mean But it's yeah, I should I should think about that more Any other questions? Uh, yeah, you're slide with the word top us on it Yep, you had classical viewpoints as commutative subalgebras. Yeah, I was just wondering if you had If there's a extension of this to approximately commutative subalgebras if you would Good question semi classical Yeah, that's a good question. So That so landsman has two ideas about glorification one is this sort of exact thing and one he calls I can't remember exactly what he calls it, but it's Yeah, it's asymptotic or something. Um, I don't know so much about that one. I'm not sure exactly How one would construct Approximately commutative algebra what that means in this setting, but it's an interesting question. I mean it's a one thing he does is creates A rigorous notion of classical limit Through these continuous bundles of c-star algebras. So you take the sort of h-bar goes to zero limit Um, so you take the interval, you know zero to one with h-bar living in it You have a bundle and the h-bar goes to zero limit one recovers a sort of classical algebra So I think in that sense one can one can talk about sort of approximate Approximately classical maybe if one sort of gets close to the limit in some sense, but Yeah, I'm not I'm not I'm not sure Thanks for the very nice talk Leon and so you you referenced the black body radiation problem So we know that thermal physics was was quite central to to the discovery of quantum theory Do you think that could still be the case for modern foundations of quantum theory? Yeah, I think so Good question. So I'm not an expert in this I think you're maybe you should answer actually because I know I think you know more about this than me, but yeah, I think that's the direction I'd like to start thinking in so people don't know sort of quantum thermodynamics Is a it's gained a lot of attention But yeah, I think Yeah, the answer is yes, but I can't say anything intelligent about it Any further question or comment intervention? So if not, uh, then let's thank leon again for the nice talk And he's gonna be around