Our speaker today is Marie dot foo is the dean's distinguished professor of physics at Clemson University. Marie earned his PhD at Caltech, and he began his professional career as a theoretical physicist at Sandia National Laboratory in California. Very develop the piece of work he's probably best known for the embedded add a method, which is a widely used technique for computing the energetics of solids on the mechanical properties of materials. That's certainly how I first came into contact with them and use the metal myself. Murray is a fellow of the APS and also of the American Association for the Advancement of Science. About 25 years ago he moved to Clemson University. And as he tells me that not long after movie, Mary began to develop an interest in the foundations of quantum mechanics. And that is the subject of the colloquium today. Let me just make a note to all of the graduate students who are listening that immediately following the colloquium. There'll be it an opportunity at full hour, in fact, where you'll be able to chat with Dr. Duff. So please take the stage. Thank you. All right. Though. Yes. Thank you for coming. And and, and I am talking about the wave function collapse. And I think you'll find that an interesting subject I'm trying to provoke. So I'm interested in the topic which has been around, of course for a long time. And I think there are some new things going on in this often discussed subject. And, and I included on chat a link that will take you to the other links where you can download papers and things about that I'm going to mention in this talk. So it'll make it easy for you if you're interested in reading some more, you can follow the link that's in chat that will take you to other links that you can download stuff. And a lot of this work that I'm describing today is based on articles and a book by Anthony, who's a friend of mine. And we've, he's gotten to be very interested in this subject. And so I especially recommend those papers by Anthony Rizzi as well as the book. And so, so I'm reminded, when I'm giving this talk of, of this cartoon, maybe some of you know about this, where we have a couple of physicists writing on the blackboard. And then there's this interesting middle step here in the derivation about a miracle occurs. And the other guy is asking for a little bit more explanation here. The quantum version of this is the middle step. There is a measurement which is not very well explained. And a, as I kind of mysterious middle step, especially the collapsed, it's supposed to go along with this measurement. And so this is my talk in a nutshell. I'm asking for to being more explicit about this and trying to tease this out some more. And to make myself and others aware of what really goes on in a measurement. And so again here in some of the papers by Anthony Rizzi that I'm going to mention, and they're all available at those links. That link that I put in the chat. He's written a series of papers now and foundation of physics. And there's really nice been at the bottom there is a, a very pedagogy, pedagogical paper that talks about measurement in quantum mechanics. It's on the archive, so it's not published except on the archive now, but it will be published. I'm sure that's really excellent paper, but it's very good pedagogical paper so students can read and appreciate it very well. Undergraduates who've had some quantum mechanics. He's also got this book that I use here at Clemson, which I think is really good and has been out for about three years. And to give you a little bit more background on Rizzi, he was on the LIGO team. He was at sea Louisiana site. And to remind people, maybe who don't remember why Go team the leaders of the like OT, the three leaders were awarded the Nobel Prize four years ago, further out of the teams discovery of gravitational waves and the work that's coming out of the LIGO is still really fascinating. A lot of really interesting stuff coming becoming from LIGO and, and a similar sort of devices. So his main background is in GR, but he's a very solid, very broad, or a physics theorist, but he also has. Very good experimentalist as well. So what I'm going to talk about today then is the collapse hypothesis and discussion of the measurement problem in quantum mechanics. And I'm going to pay them of what I think is the barrier or the hypothesis. And in addition to that, I wanted to discuss what is, what is properly called the ensemble interpretation. And I, I think very few people know what this is, although I've run into maybe a couple of people today who maybe know better than I had expected about the ensemble interpretation. But it's very few people know exactly what the ensemble interpretation is, and it's not what you might think in spite of the familiar sounding word ensemble, it's not quite what you think perhaps. And discuss how the ensemble interpretation is the resolutions of this measurement problem that collapse hypothesis has kept with us for so long. So I'm going to start with the intuition of Albert Einstein and forgive me for reading this, but it's important. So I'm going to read through this. The attempt to conceive the quantum theoretical description is the complete description of individual systems leads to unnatural theoretical interpretations which become immediately unnecessary if one accepts the interpretation of the inscription refers to ensembles of systems, not individual. Okay, so that's that latter one. The interpretation, the inscription refers to ensemble of systems is what leads to the ensemble interpretation. So Einstein is, is hinting at this. He's got an intuition, but he doesn't really develop it any further than that. But another thing that he's doing in this sentence is to point out the unnatural theoretical interpretation, which is that's his way of describing the Copenhagen interpretation, which has especially this wave function collapses the part that he's objecting to. And the idea that the wavefunction is describing an individual system. Though he calls that the unnatural thing. And, and he, he did not develop the ensemble interpretation very well. He, he's got this kind of very tantalizing a sentence related to that. But he did not really work on the ensemble interpretation any further. And, and in spite of this objection of Einstein's, the Copenhagen interpretation was that wave function collapse becomes mainstream after the Soviet come from. And there's a nice book by James Cushing on, on how it is that the Copenhagen interpretation became mainstream even though it has these difficulties involved in it. So Einstein calls this the unnatural interpretation. And then this, the wavefunction describes the state of individual systems. And there are two processes that take place in the evolution of this, of the wavefunction. One is the ordinary Schrodinger equation. That just gives the evolution of the wave function except during a measurement. And then the measurement somehow causes the collapse or reduction of the wave function. And the system state becomes one of the eigenstates of an operator corresponding to the measurement. Though the, the state collapse was not fully explored, described, worked out by Bohr and Heisenberg. It really wasn't fun norm on and Dirac who developed it as part of a mathematical formalism. Its even part of the axioms now is often presented. And this is really what we've all been trained them for the most part is this unnatural interpretation on it. And for the most part, this collapse I find is really hard to get rid of. It's in our thinking even when we're not realizing it. But there is present for us we have to work hard to do. I think we're going to have to get rid of. And so it's, I understand I'm, I'm challenging people to change their thinking. And and that's what's, I think I can be a challenge. And this Copenhagen wave function collapses. The Copenhagen interpretation is in virtually all textbooks, undergraduate and graduate textbooks that are there. Very few that don't do this. And so I'm inclined to say virtually all, but there's one or two exceptions that I'll talk about. And so there's a lot of these confusing statements. Breakfast is one that we use here at Clemson. And it's pretty popular. It's very good in many ways. But when it comes to measurement, It's very confused and very confusing. And it has these statements that I'm sure people will recognize, including that measurement causes the collapse of the wave function. And this is unhappy with these things. But he admits that he's unable to exercise this mysterious ghost of the wave function collapse from his thinking about quantum mechanics. Welcome back to this particular statement in this later. But here's a 0 at Clemson and other places it's, it's pretty good in some ways it, but it's actually very good in some ways. But when it comes to measurement, it's also very confused. And he has the typical things like the electrons don't have a position until they measure. The measurement collapses the wave function. And so one of the eigenstates, that kind of stuff. And that's what I'm challenging here, especially that last thing about the collapse of the state. So here's a diagram and Morrison. And it's not just doing the decomposition of a state into eigenstates. He's actually saying that the measurements box there, little box that describes a measurements, it actually does collapse the wave function. But one of these possibilities, and it's, it's mysterious thing, don't understand that. And in fact, the collapse elapses it to the Eigen, to the state associated with the measure, the value of the observable. Okay? So this of course is, has had a lot of resistance over the years. And it was Einstein originally who objected to it in Schroedinger, added to one of Einstein's objections to the bowl of the cat. And so it's called the Schrodinger cat. And really it was Einstein's objection and Schrodinger elaborated some on it. And it was intended to be a demonstration that the collapse of the wave function and the description that the Copenhagen School was giving to quantum mechanics was, was incorrect. So just to be sure that people know what I'm describing here, the Schrodinger cat is placed inside of a box that has a radioactive nucleus and there's a detector. There's some, the nucleus has a half-life of, let's say, a day or something to make it easy to do the experiment. And if the nucleus decays, the detector will break open a poisonous gas that will build a box. And then you set this up and you close it up and then you wait half-life. And though according to Bohr and Heisenberg, the individual cat is both alive and dead. Until then you open the box and that's when the collapse of the state occurs. And the cat, it seemed to be either alive or dead. But before observation it is both alive and dead. So this, this, using a macroscopic situation like this was supposed to demonstrate clearly that this wasn't tenable. This doesn't make any sense. Although this is now used in many textbooks to demonstrate that your, your own intuition is just wrong and you're going to have to trust the mathematics and the explanation, the poetry, the Copenhagen interpretation. And it's interesting, I think it's not just that the Copenhagen interpretation is self-contradictory. It's in fact, maybe because the Copenhagen interpretation is self-contradictory that became kind of mainstream. And it's a very strange thing. And, and it's, and it's, has provoked a lot of discussion over the years. Of course. I remember, especially John Bell's statement that I didn't put down here, that he'd thought professional physicist should be able to do better. And I think that is certainly true. And Schrodinger himself became disgusted with it and said famously that it was sorry, ever bought the subject? Vigor, thought up some other thing called the Wagner strand experiment where he has a, imagines now instead of a cat and the radioactive nucleus has got, say a spin will be common for us to use a spin system and he's going to make some measurements of friends, is going to make some measurements of friends is closed up inside of the lab. Wagner is observing all of this, but maybe he hasn't opened up the box yet. And so the friend is going to collapse the wave function of the spin when he observes that. But vigor is not going to collapse the wave function. And so that leads to this kind of contradictory statement here that the friend has collapsed. So there I have this bracket notation here, whereas in the then up and spin down and then friend sees the spin is up or the friend sees that the spin is down. And after this trend has made his observation, according to the collapsed hypothesis, it's one or the other. But Wagner has an open the box yet. So now the friend, the state consists of both being spent up and the friend sees the spin up and also the spin is down and the friend sees spends down. And so there's this preposition being with regards to Wagner. So thicknesses, this is a contradiction. And that this is a problem for the measurement theory. And he even wants to try to resolve that at 1 by invoking human consciousness is relating to the collapse of the wave function, but it gives up on that later. He just rejects that idea, later, rejects his own idea was to that. Okay, so now I, most recently, there is now a new thought experiment that I'm going to tell you about. I'm not going go into great detail on this. If you're interested in the subject, you should read the paper. But it's a very difficult paper to read those because it's just too complicated that a sequence, sequence of steps that takes place. But also, I just don't think it's written very well. Though it, it takes some work to make your way through this paper, but I think the point is, is correct. I think the conclusion is that this is another example of a contradiction that happens if you have wave function collapse in your theory. So they are there, they're set up properly. And Renner, I've set up an extended Wagner strand experiment. So now there are two spends and two friends in two different labs at two victors. And they can all see each other in some way. There's allowed to communicate in some way. The lower lab is held in some isolation, so we're held in suspense about the state of the overlap until eight or measurement is done. In the upper lab, the, the first friend, f bar, observes the spin C bar. And based on that, he prepares the state that goes into the lower left. So it's very convoluted set up here. But I think the conclusion is correct. Act that this produces a two different predictions based on which come about as a result of the, of the wave function collapse. Having the wave function collapse. Though the conclusion of that, and I have a link to that paper and also another paper by Rizzi where he explains this paper. I think he does a better job of explaining paper than the original authors. But so there's a link to that if you're interested in pursuing, and I'm not going to go into more depth except point out that I think it's correct in the conclusion that the Copenhagen interpretation is inconsistent. And specifically it has to do with the collapse I've office. And remember back to the quote from Einstein, this, this contradiction which has been working with us for years is rooted in the assertion that quantum mechanics is not a statistical theory, that it applies to a single system. That's that unnatural interpretation. Then topical, I think it's really do very much with us. Those of us who are unhappy with some part of it. I still think it's definitely part of your training and we've become used to using wave function collapse in some way. And we need to, I think be much more clear, focused about and rigorous about this. And so the question is, why do we have this? Keep using this in our textbooks. We keep teaching the next generation using the collapse. And I think that it's time we did away with. So that brings us back to that, this quote from Einstein and the second clause in that sentence about the, that the unnatural interpretation is unnecessary if you understand that this quantum mechanics is statistical theory. So this is, brings us to the ensemble interpretation, what Einstein called the natural interpretation for quantum mechanics, the wavefunction. Then we can go into further depth about what the wave function is. But the most important part at this point is that it encodes probabilities relating to measurements done over an ensemble. So ensemble averages measurements. And the Schrodinger equation gives the evolution of the wave function even during the interaction with the measuring device. And so this is an important thing to recognize that measurement is itself a physical process that involves an interaction between the measuring, measurement device and the system being measured. And this is key. There is no collapse of the wave function. You understand that you use the Schrodinger equation throughout and there is no collapsing wave function. And then, then there is a, I think now a much more sensible understanding about what we've got in the theory of quantum mechanics. From that, a lot of us, I think it's present in our thinking. But with the ensemble interpretation, there's a clear and complete understanding of the measurement process that involves an interaction between the measuring device and the thing being measured. And that's all described by the Schrodinger equation. And no need for collapse. There is no collapse. Now does lee Valentine wrote a beautiful paper and read up on. Reviews about in physics and 970, he did a very good development of the theory of measurement based on the ensemble interpretation, which based on that point that I was making earlier, that's a measurement is itself a physical process involving an interaction between the measuring device and the system. Today I've run into a couple of people who have read that paper. And, but for the most part it's unknown. This work. And part of it may be because Valentine did not explicitly demonstrate the resolution of the Schrodinger cat experiment or Vignesh trend experiments using the ensemble interpretation. It's certainly there implicitly in his work. Have you understand what he's doing? You can carry that step out. But he didn't explicitly do it. And so that might have helped had he done that, I don't know. But the it's it's, it's kind of strange that this very good work has been more widely disseminated and, and worked its way into the textbooks. He did write a textbook and I'm going to talk about Valentine's texts, but here in a minute. But then more recently, Anthony Rizzi, this fellow that I mentioned working on the LIGO experiment, has filled out the ensemble interpretation. And that paper on the archive goes the resolution of the Schrodinger cat and the Wagner strand experiment. And also he's written other papers that tackle this extended fitness friend experiment that demonstrates how the ensemble interpretation for Africa and renters paper is. Doesn't. That is the ensemble interpretation passes their logos here. It isn't affected by their logos here. Though it avoids the problem entirely because there's no wave function. Okay, So I'm, I really high on this book. It's called Physics for realists, quantum mechanics. It's an excellent book and it really makes a lot of quantum mechanics very intelligible. And, and as, as some of the people I've had the opportunity to talk to you today, we're pointing out we have a lot of language that we've developed related to this. And in order to accomplish this, we have to make I think, conscious decision that we're going to be more rigorous, which means that we have to develop our language and our understanding to do all of that before we can really teach it well, then learning how to teach it. So there are a lot of steps, there's some work. But I think this remediation as necessary as I say here, there are problems out there that I think point to a problem with quantum mechanics and that is for example, gravity quantized and the technical problems that we've had and trying to quantize gravity. I think some of the problem lies in our misunderstanding of quantum mechanics. Though I think that it is possible that understanding things, understanding the content of quantum mechanics is going to help us make advances in areas that we don't understand today. So again, in the ensemble interpretation, the way function does give the probability density, which is itself, of course meaningful only in relation to an ensemble. That's certainly true. But in fact, it does give more information than just the particle probability density and the contents of the wavefunction. That physical information that can be mined from the wave function is part of what's filled out in this textbook. And I don't want to go into that today. I'm focusing more on, on the collapse part. But it's also true that the quantum mechanics is holistic. That the wave function includes the system being observed, the measuring device, and even the rate of the observer. These things are entangled by the interaction. This is all part of the natural way to understand quantum mechanics at 0, 0. And also the term criminology has made much more rigorous like preparation and filtering. Those things are part of understanding the contents of quantum mechanics that we eat to be careful about words and understand what they mean. Well. Okay, so going back a little bit to balance happening, he showed us really clearly how to do a good quantum theory of measurements, where he takes seriously the understanding that all measurements are themselves interactions. And so even during the measurement, the wave function is evolving according to the Schrodinger equation. Though there has to be a Hamiltonian that say, for example, measuring something about the position of the electron, for example, in the detector. There has to be an interaction term in the Hamiltonian that represents that interaction. And so we have a simple case. We might have the measuring, say the position of a particle like an electron. And then we have this. So we have the state of the particle. And then we have the state of the detector, which is written here in two different pieces. There's Alpha, which is the pointer. This thing we can read and is initially set to 0, say. And then there are other internal quantum numbers relating to the detector which aren't important and the following analysis. But just admitting that they're there, there are kind of irrelevant for the discussion. Butter. We just acknowledge that their presence. Though. The point is that the Schrodinger equation gives you the evolution of the wave function. So the wave function starts off as a, as a combination of the electron is at some position of the pointer is set to 0 pointer and the measuring device to 600. The Hamiltonian gives the evolution of the wave function. So this is written in a unitary operator, which is written as formally as just the exponential of the Hamiltonian there over time, integration of the Hamiltonian over time. And so for this to be a measurements, for this interaction to be a measurement, the pointer has to end up relating, telling us where the particle was before the interaction was, has taken place. And so this unitary evolution of the initial state where the particle is at position you and the pointer is at 0 ends up being a superposition that in general, because of all the action. But the pointer to make this measurement to the key here is that the interaction has to be devised so that the pointer ends up indicating the position of where the electron was before the measurement took place. But you note here in this, in this general expression that the particle may well end up some other place as a result of the interaction. In fact, you generally expect it to end up in a different state, not in the same state that it was in before the interaction. And you also notice here in the sum that the, the state of the system is entangled, the NDA is the particle detector are entangled. And this is part of the holistic nature quantum mechanics. Okay? So it's key here that the pointer is going to end up pointing indicating where the particle was before the interaction. And then depending on the interaction, the particle may well be in a different state from where it started off. In fact, you generally expect it to be, this is in contradiction with statements like that I showed you earlier from Morrison, for example, that the particle ends up in this eigenstate corresponding to the pointer. This is not the case. And I'll show you some specific examples that you can understand that this understand the contents of this. Because what's in the textbooks is just wrong. And i've, I've given this talk enough times now and there's always somebody in the audience who remembers those statements from like Morrison or Griffiths. And they just say, well that's just, those are just, Let's put that in the textbook. It's true. And I'm going to prove to you that that's not correct. Let me interrupt, true. And then let me see That's crazy. I mean the audience now, the reason it's still true that if you trace over the measurement device, you are left with the same state. Finger measured. By a trace. You mean something like some kind of interaction with the environment, right? Well, I think the density matrix describing subsystem a, which is what I measure, a subsystem B, which is my measurement device. My measurement, these entangling a and B. Now I trace the piece. If we then see the matrix corresponding to the subsystem B, the measurements device to get a stage of what you mean trace or some kind of physical process. I mean, we have a coherent state here where this u matrix is complex and all the phases are important. And I'm not quite sure what you mean by the tracery because that's often done when you're trying to consider, for example, interaction with the environment. And is that what you're trying to bring up? I guess I want to take anymore if you find this weekend. Okay. Okay. I guess I'm not I'm sorry. I don't quite understand the question. But I think this is clear that the state will evolve according to the unitary operation of the Hamiltonian. And that's the, it's also true that the pointer, obviously for it to be a measurement, it has to be an interaction which leaves the pointer in the state indicating where the particle was to begin with, but the particle need not. And this is the step that seems to catch people. The particle need not end up in the state. Where it began, because it isn't an interaction. There is a special case of this where the particle may end up in the same state. That's, that is a possibility, but it's not generally true. And I'll give an example of both, both the special case and the, and the, and the, and something which for this is not true. So there's really no need for collapse. Notice that the measurement doesn't involve a collapse. All the physics is, is present in this entangled state and we can continue to use it and do calculations with it. So this is, this is at the point where people kind of asked this question about what they remember in textbooks. And so I went to Griffiths and I pulled out the sentence that the problematic sentence while are a lot of problems unfortunately, but, but this is, this is very succinct. He gets it down in one sense and some textbooks will go on for a page to stay the same one thing he says it in one sentence here, which is very helpful to account for the fact that and immediately repeated measurements always yields the same result. We're forced to assume that the act of measurement collapses the wave function. This is the statement that's in there. He doesn't give the reasoning behind this, nor does he give an example that shows that a, the whole tech that is, that is immediately repeated measurement always gives the same result. He doesn't have any examples behind this. And he doesn't actually demonstrate this conclusion. But I'm going to pick this apart. There is in fact, no experiment that compels us to use the collapse. And that's always been true. But I want to pick the, pick apart the statement from Griffith's. As an example. I don't want to pick on Griffiths, but he's not as her favorite here to put it all into one simple sentence. So it's a logical argument is a logical proposition. Iff and immediately repeated measurement always yields the same result, then measurement collapses the wave function. That's a logical argument. And so it has a structure to it like a logical argument. A good logical argument should have a simple structure to it. There's two pieces. The first part is the antecedent and immediately repeated measurement yields the same result. And then there's the consequent, the conclusion that measurement collapses the wave function. Solve for the argument to be valid. Both the antecedent must be true and the consequent must necessarily follow from the MC. I'm going to show you in fact that neither condition is satisfy. The antecedent is false and the consequent doesn't follow from the antecedents, so it's doubly wrong. The argument is completely wrong. Though. I'm going to take, I'm going to do both of these. I'm going to walk you through this. And I'm going to start with the second one, which is an immediately repeated measurement, yields the same result does not require us to conclude that the measurement collapses the waveform. And I'm going to demonstrate this by counterexample using both the Copenhagen interpretation and the ensemble interpretation. Though let's suppose we have a Stern-Gerlach apparatus, which is what a lot of people have in mind when they're talking about measurements, I think, yeah, I think it's overly narrow view of measurement. But by focusing only on that is an example of a measurement. But any case it's, it's iconic. Though you have inside of a region and inhomogeneous magnetic field. You're passing a particle with spin, a neutral particle with spin through this inhomogeneous field. And the interaction between the particles spin and the field gives you a term in the Hamiltonian which is proportional to z, which is the direction of the field, inhomogeneous field, and the spin component in that direction, but with z times z. And you can see Insha'Allah through the Schrodinger equation that it was an impulse, will allow many non-state that the span S z. If it's a spin 1.5, for example, then you get either up the impulse or down impulse. They magnitude but opposite direction depending on the state system is in. Okay, So then if you put in, for example, state which is polarized, say in horizontally, then it would be a coherent superposition of spin up and spin down. And the spatial wave function is the plane waves. The particle is moving into the detector from the left. And then afterwards, after the interaction, the state, according to the collapse hypothesis, will involve either the spend is up and the, and the spatial part is now has a vertical momentum. So it's a plane wave with some vertical component of momentum or its down, that is, the spend is down and the wave function has a downward component. Facial part. That's the collapsed hypothesis. And then Griffiths is apparently arguing here that if you now have subsequent measurements, that we have now three Stern-Gerlach apparatus is we've got the first one that's going to take the incoming beam and then we're going to go on the outer two possible states coming out. We're going to place two more detectors. And then he's saying, okay, well, if it goes only up pass, the wavefunction is clamped and it goes on the path. And the second detection will also show up. And that if it goes down path than the subsequent bear garlic apparatus will also show down. And so this is an example of the second measurement confirming that first. Okay, Now the question is this is prove the wave function collapse. While it doesn't prove that wave function collapse because I'm going to work the same example using the ensemble interpretation which does not involve collapse. I'm just going to invoke the Schrodinger equation. Okay, so you have this initial incoming state with horizontal polarization. And that's a superposition of up and down after the first measuring device. Now you have two branches to the wavefunction. The ensemble has two parts to it. One part of the ensemble is taking the upper path because this particles are spin up. And the sharing airlock apparatuses is also interacted with the device. The second branch of the wavefunction, the second term and the wavefunction has articles with spin down, they have downward momentum and the Stern-Gerlach apparatus also is entangled with this because in general interactions entangled things. And so now let's follow up by a subsequent measurements. So that's this third line here. The same two detectors following the first one. And the very simply, we still have two branches. Excuse me. We still have two branches of the wavefunction. Corresponding to half of the ensemble is in 11 configuration with the spin up, the other half of the ensemble has configuration would spend down. And you'll notice that those two terms here, those two pieces to the ensemble. You have confirmation the second measurement confirms the first. And it's very easy to understand. You're just polarizing the sub ensembles. You just, you just filtered, you've polarized, gotten half of the ensembles than polarized pushed in one direction, the other one, depending on the spend, has been pushed in the other direction. They're both terms is still present in the state and the ensemble description. And you're confirming that the second detection the same result as the first. But there is no wave function collapse. Though it isn't true that the that the follow-on measurement, the agreement of a subsequent measurement with the first measurement. That does not prove the Copenhagen interpretation. That is that the wave function collapses. It just doesn't felt. Okay, so it's not true that and immediately repeated that if you have an immediately repeated measurements that always yield the same result, that's the case. Then. Then that proves that the measurement collapses the wave functions. Not, not correct conclusion doesn't necessarily follow. Okay, so that's the second one of these. So that's enough to disprove the elapse argument. They'll also, the first first part is also false. That is, the antecedent is false. I want to show you that one here. This, this claim, the end immediately repeated measurement always yields the same results. That's not true, and I'm going to prove it here, but it's a counterexample. And to help your thinking recall always that the measurements is a kind of interaction between the system. And so I'm going to invent a detector. And instead of SG for Stern-Gerlach, I'm going to call it AG for a free grace to name it after my granddaughter, since I'm the inventor of this detector, not going to tell you what's in the detector yet how it works. I'm going to tell you that in a minute, but first I'm just going to present it as a black box. And black box works in the following way. There's a pointer on the black box that's going to read up or down. And I'm going to interact to spend with this black box. And if the spin, spin 1.5 particle and the spin is up, then the pointer is going to end the up. And the spin, it starts off down before the interaction. The pointer is going to end up down. And so that qualifies as a measurement. But I'm going to show you in fact that this particular detector flips the spin of the thing it's interacting with. So if it starts, the particle coming in starts with spin up, the pointer is going to flip that up. But the spin 1.5 particles is going to flip it spend two down. And so it leaves the detection with the opposite spin on what the pointer is indicated. And the same is going to be true of the point of the particle started with spin down, it's going to interact with the detector. The pointer is going to flip that down from 0. And the Particle will spend 1.5 particle being observed, flips IT spend up, though it also ends up in the opposite state. So in other words, it's always going to give the opposite answer. So now let's do a follow on measurement. We have 2-AG devices and we, we first interacted with one particle and as a result flips the spin. Now when we measure it by the second measuring device that's been coming into that second device is the opposite. But it didn't actually restores this, restores it back to spin up, but the two detectors disagree. The subsequent measurement is, comes up with the opposite result and that's always true. So using this is an example of a, of a measurement where the subsequent measurement does not give, does not confirm the state. So here's how the AG detector works. It's, it's not complicated. It really, it has a spin one particle with an initial spin at 0. And after the interaction with the external particle that's going to come up to the, so this measurement device that spin one particle after it's interacted with the spent 1.5 is going to be sent through the Stern-Gerlach apparatus. And the result is going to be shown on a macroscopic pointer to the three components to this detector. So the spin 1.5 is brought up to proximity. And then there's just an ordinary spin-spin interaction between the spin 1.5 and spent one. And you can work out the Hamiltonian is very simple to work it out, but you can already see what's going to happen here. So I've written the spin, spin product S1, S2. I've written it out in terms of raising and lowering operators for spin. One is for the first particle and the second particle. And that first term, which is the product of the z components, doesn't do anything but the second term raises the spin, 1.5 lowers the spin one particle. The third term does the opposite. It lowers the spend 1.5 and raises to spend one. If the initial spin 1.5 starts in the upstate, they can't raise it. So there's only really the lowering which will happen. And so it's going to exchange spin with that one and that sense it's going to be lowered and it's been one is going to be raised. And the other way happens when you start off with spin down for the spin 1.5. That's basically it's very easy to see without working out the details. But the details are easier workout. But it's easy to just interact with this API to two flips, the spending part. So a subsequent apparatus is a special case that a follow on measurement agrees with the first, but that's a special case and that in fact, it's easy to come up with a situation where it's not generally not true. That's not true in general. That and immediately repeated measurement always yields the same result. It's just not, it's just not true. So going back to Griffith statement then it's clear that it's wrong. This logical proposition has failed on either one, Either one, which would have been sufficient, defeated. And so this this is all based on faulty reasoning. This statement just isn't correct in, and as I say, it's, it's very common to find this, this kind of reasoning in textbooks. It's just faulty. Though these things, these statements are just incorrect though, to help you help your thinking. Because I recognize that that habit is hits us into certain tracks. We go along certain tracks. We actually think about the system of mathematics, the formalism that we've learned rather than the physical thing itself that we really should be concerned with. And so it's difficult for us to see beyond this kind of pack that we've gotten in. And so one of these things then I suggest that you try to help your thinking is to remember that all measurements are interactions. And that this wave function collapse is not a helpful thing. And in fact, as it's faulty reasoning and that we can replace it with a better habit, which is this ensemble interpretation of quantum mechanics. And so by the way, I want to point out that you can understand this, this conclusion in general terms about frap quicker and Renner. When, when they collapse the wave function, when one of the friends measures the span, it's supposedly collapses the wave function. That what they've done is they've thrown away part of the term and the ensemble which should be present on that term, actually downstream becomes reenabled with the system in and interferes. And so this is, it should, it should interfere, but it does not because they'd be removed by this collapse. And this is the problem with the frog agar and Renner. This is the problem with the Copenhagen interpretation that's demonstrated by this rather elaborate setup. Okay, so this is an excellent paper alive, I'm sorry that, so this is, this is the explanation of how the ensemble interpretation of this problem, the frog occur and Renner demonstrate for the collapse. I, and I think as I said, there's actually a better explanation of the original Frauke rigor and Renner paper. He explains it better than they do. It's even a better explanation of their original paper. Though. Actually, this is a good place to go if you want to understand the original papers about. But in fact, we don't need to have gone to such an elaborate links as the extended vigor strand experiment. Because this contradiction is really presents implicitly in the Schrodinger cat experiments and in Victor's friendly experiments, the original thickness friend experiment. And, and we have to get away from, from this. And the ensemble interpretation allows us to start saying meaningful things. Because we say a lot of things that are meaningless in quantum mechanics when we have this problem with a wave function collapse. A statement like this, this statement is false, is self-contradictory in it and it's actually meaningless. It sounds like you ought to be saying something because you understand the words individually. But when you put them together like this, because it forms a self-contradiction, that sentence is actually meaningless. And same thing applies to the cat is both alive and dead. It's really a meaningless statement. It sounds like we're trying to say something. And it sounds like it ought to mean something. But it actually means nothing. And so the, the point of this is trying to restore us to being able to say meaningful things in quantum mechanics and really understanding what we're saying and to say, Hey, things that we can work from. So how to say clear and meaningful things. He also goes in this book very carefully to talk about the distinctions between preparations and filters, and measurements, and disturbance and ensembles. It's all very nicely laid out. That's not all, that's not all that good stuff that's in this book, but it, but it's the stuff that I'm introducing you to. It's, it's full of very good stuff. And it does fly in the face of a lot of things because I ran into a high school physics teacher who insisted that the Schrodinger equation says the cat is both alive and dead. Well, I wrote down the equation forum like this and I asked him to tell me where it says that the cat is both alive and dead. I didn't, didn't get that from them. Okay, So to show you how this ensemble interpretation solves the Schrodinger cat experiment and the big, extremely expert. You could write state of the cat in the box before the box is opened as being a superposition. This is the ensemble interpretation. The ensemble presents both possibilities, which means that some members of the ensemble will be decayed and some will not be decayed. That when Wagner opens the box and look, it looks inside, he is entangled with that. Oh, I guess you could say maybe put the friends here. Friend opens, opens the box, looks inside, the victors outside and so forth. What the interaction and tangles all of these actors. And that, that's, that's the inherent nature of quantum mechanics. So again, the wavefunction describes not a single physical system, but an ensemble of similarly prepared systems. You have to have implicitly, you have to be able to make many experiments, that is copies and make multiple measurements on multiple copies in order to be able to use the wavefunction and in general, the formalism of quantum mechanics. This is a paper that I think is very pedagogical. It's on the archive. And if you follow the link that's in chat, you can download this paper. So you don't have to write down the number 2. Anyway, it's very simple, very pedagogical explains how the ensemble interpretation makes its way through the Schrodinger cat, the vigorous friend experiment. I started to show you that though it's very good to be used very violent. And of course, excuse me, sorry. And so just to point out, the books that we've been using to reinforce this, these statements are just wrong that are in Griffith's Morrison. Statements just aren't not correct. But was it the state via experiments have confirmed decisively Copenhagen interpretation. Now, once you understand that this, It's really regrettable that statements like that are in the textbooks. So this whole thing about the wavefunction collapse, I'm almost done here. Mark and now had conversations with Voronoi month. And based on those conversations, he was convinced that Von Neumann viewed it as a convenience. Not actually a necessity, as Griffith's says, it's necessary to conclude this. But so that'll be a convenience that you could sometimes use. But actually I've read through ongoing minds book and I didn't find that. It's not in the book. Maybe Von Neumann, that, that later to market. Now maybe he had changed his mind on it, but it sure doesn't read like that in his, in his book. And in fact, Valentine says that it's not convenient at all. It has never been convenient because it's generated a lot of confusion. And the amount of theoretical effort expended trying to explain the reduction of the state vector has made it the reduction, the collapse hypothesis, much more of an inconvenience. That could mean. This was back in 1970, here we are 50 years later and we're still collapsing wavefunction and trying to explain them that collapse. So lesly Valentine wrote a book. I guess it's about 990, I think when this book came out, maybe not quite so. Maybe the eighties and eighties graduate textbook based entirely on the ensemble interpretation and ends. And there are some people who have seen this. I'm, I'm gratified to learn More than I expected. I do start running into people, at least read this book. And a lot of people liked it. I think if you if you understand and appreciate what Valentine did in this book, which should have been more widely used all of this time. Then you really enjoy and learn from resists. Most recent book, The Physics for realists, quantum mechanics, which fills out the ensemble interpretation. And it's a, it's a book that can be used at many different levels. So it could be used even for freshman introductory physics course because it really lays out principles very clearly. And the mathematics rose out of an understanding of the principles. And so it can be used at a lower mathematical level than for example, bowel time, but this could easily be used as a senior level undergraduate quant, it would be excellent for that. And he says in his book, he does say, property speaking. We can use the collapse as an approximation if you're very careful. And there's no chance that this part here, throwing draw from going away, it's going to come back. Does. But you have to be careful. He defines exactly what are the conditions for this in terms of preparation and filtering. And what actually a measurement. This though I highly recommend that book. Okay, Thank you for your time and I would welcome questions and discussion there, sir. Yeah. Thanks. Talk. Every week we vote. I mean, we've known for decades that measurement is entanglements with our observer. So I'll just theoretically like people have also for at least two decades, I think experiments with weak measurements. We measure means being a partial entanglement with the observer. That the measurement process, which is of course described by the Schrodinger equation. I mean that's known, we know how to control that both theoretically and even experimentally and do the measurement one bit, that, one little bit at a time with weak measurements. So I mean, my right, So, so far so good. Of course I agree with you like it's too bad. Griffiths doesn't stop either about weak measurements are about measurement as entanglement with the observer. But I'm, I'm, I mean, I'm kind of, I don't know of a historical Lake who deserve the credit historically decades ago for coming up with these notions. But I feel like I'm not totally clear what's being resolved to recently. There is still, even with measurement as entanglement with the observer. There is the puzzle of me as an observer. I only experience. Let's spin I measure as being up or down. Once I've finished doing a complete measurement. So there isn't a puzzle there and I'm not sure we think that that puzzle is resolved. Yes. Yeah. If you understand that the content of quantum theory, quantum mechanics, as you know, was the Schrodinger equation and the wave function. Contents is statistical in nature, always applies to ensemble averages. Which means that you have implicitly a system. Are you going to make copies of the system prepared identically? And then you carry that out. So you're dealing out what you're calculating from the Schrodinger theory. The Schrodinger equation is the probability. Well, I guess we're in agreement with how people do. I understand measurement as entanglement with the measurement device. And then how you, how you think about that, that state at the end. If I have a Schrodinger cat states that says a state of a macroscopic superposition. At the end of the day, I only experience one piece of that superposition. That's what I would call the the wave function collapse. Mr. even though I know how to describe the measurement process as entanglement with myself. So the proper way to think about it then is that the cat is both alive and dead before you answer, what do entanglement? But the superposition shows is that the ensemble consists of both alive and dead cat. So you have a million of these things. Half of them are going to be alive, half of them are dead. When you open the box, you find out which one, this one, It's this either alive or dead, but it hasn't collapsed. The wave function, Let's see, I seem to have lost its Lamar. Oh yeah, I'm I'm here. Yeah, yeah. Hopefully we can say that there is that. I mean, all the Bell inequalities show that we have to use the complex number quantum mechanics. Um, but I think what you're describing sounds maybe it's a little bit like what people call many worlds to understand why I experience only one piece when I become entangled with the system, I experience only one piece of that entanglement requires me to imagine that I could have experienced either entangled. But it gets all the process of describing weak measurements and entanglement with the observer. There's nothing new there. This incorrect? Yeah. Except that I think it's new in the sense that we get this inconsistency at the very last part there. What does it mean to make a measurement? And, and so I think that, you know, kind of what you were saying there at the end. This problem about what happens when you'll be on 11 of those things. That's exactly the contents of the, of the wavefunction I think is to represent an ensemble. And so it's no mystery that you open the box, you've revealed which one that cat is alive or dead. And you become entangled with it in that sense, but then you become a member. You don't have to imagine that you're doing this a million times and each time you do it, There's a different outcome. But the Yan's, the wave function represents the ensemble as a whole. Not in each individual instance. It is true that the many roles is an attempt to get rid of the collapse of the wave function. But I think it's, again, it's a meaningless statement to say that there are an infinite number of universes spawning off all the, spawning the same time. Those are contradictions in terms. So you're saying actually something meaningless to talk about multiverse because it's a contradiction in terms. And so again, it's not necessary to invoke contradictions to explain this. And that's why I think the ensemble interpretations, this really allows us to say meaningful things about the, about the world that we know to be the case. Route. Accurate. Eight other questions, please. I have a question. Hello, Edward? Yes. Yes. Okay. So can you tell us just took a one sentence, what is the main problem of having a collapse of the wave function? What is it? Well, I guess, I guess I would, I'm not sure I can do it in one sentence. How about to go well, let's let's be honest. I'm sorry, say that I'm under classical probability. Let's say we have a classical distributions. There's no quantum mechanics. So we don't know the states of the system initially. So there's a lot of uncertainty and entities described by certain distribution. And then I perform a measurement, and then I see one of the outcomes. Isn't that also go into a collapse? Because I have changes the distribution to a single outcome even in classical physics. Why is there no issue in classical mechanics that, because clearly we have collapses of the probability distribution in classical physics, the why is this not discussed much more seriously of classical physics is such an important issue in quantum mechanics. Partly because I guess people are unclear about what this quantum state means and the wave function. And that's not an issue in statistical, classical statistical mechanics. But the problem is that for the quantum system, when you have the collapses demonstrated that frog that are in red are demonstrated. If you want, not want, the friend observes the spin and it collapses the state, then you actually get a contradiction. So the, the theory with collapse is self-contradictory. It has, as they demonstrated multiple predictions that are inconsistent with each other. And so it's just an invalid theory. It's not even doesn't even follow, doesn't even meet the rudimentary require that the theory at least produce self-consistent results. His yoke is this ensemble theory. We said this is actually how I learned quantum mechanics. When I was learning it too, caught in college. It was always an ensemble interpretation of these, relate this to me. This is nothing new. So how does this compare with Zurich theory of measurement? Which is, seems to be now the accepted view off what I said. I don't know you personally, so I can't really, but I do want to say that, that it is the dominant mainstream addition to talk. Ensembles like MRSA talk about ensembles. But as soon as there's a, they're discussing measurement, there's a wave function collapse. That's not the ensemble interpretation. The ensemble interpretation is to use ensembles consistently throughout without a wave function collapse. And so I know people will say, Oh yeah, I know the ensemble interpretation, but I can't, I don't know in individual cases, but I just think generally speaking, it's, we've used ensembles, but that's not what is meant by the ensemble interpretation. Okay? And so if you have, if you have collapsed in mind, then I think you're not there yet. So Zurek, yeah, so he's ease involved as I understand, discussion, concerned about the decoherence because of interaction with the environment. And so to be really good, I think this is I mean, there may be more to it than that, but that's the part of his work that I'm familiar with. So again, the quantum mechanics is holistic. You should treat the environment as part of the system that's being entangled. But then you can talk about kind of what might be random phase approximation. I don't know if I can use that word. But, but you know that there are other contributions from the environment that can have the effect of, for example, altering the state from being a coherent superposition to a mixed day. But that all can be understood as being as the result of interactions among the pieces of the system. Thank you. Other questions? Yeah, so I have a question about the wave function itself. So in the ensemble interpretation, what is the physical or maybe even a metaphysical state of the wave function? Would you describe it as a complete description of reality or maybe modify to say it's a complete description of all realities are all possible realities are. But what is your take? Well, it's obviously incomplete because preparation involves different members of the ensemble have to have something different. Or you would need a statistical theory. There has to be something else that is not, the preparation does not fully control what's going on. Though it's incomplete in that sense. The other the other aspect is that, that there's more than one entity involved. It's not simply a particle and decisively a wave that there's, in fact, I think more than, than to think of one entity that is the electron as being both particle and wave is part of the problem. In fact, the wavefunction is describing the interaction of the particle with some, with some kind of wave structure that's present. This. So the wave function contains a statistical description of, of that and the influence of this wave like nature on the particle. Okay. So you say that the wave function is incomplete, but you don't invoke hidden variables, or do you? Well, I guess it depends on, I mean, that term is kind of a loaded. But but I think that and I don't, I don't want to specify, I like hidden variables theory. But I think it's generically true that there is both a particle and wave nature at work. And it's not one entity which is both particle and wave. And so they get more specific. I think you have to learn more. But if you're concerned, for example, that the Bell's inequality and the EPR experiments and things like that. That's another talk. And then there is something we can learn from those experiments and their results are real, does not violate the ensemble interpretation. That is, the ensemble interpretation is completely consistent with those experiments, but the information that the conclusion that is to be reached, It's not something I can state and one simple sentence. But maybe that's a later talk. It is in Chapter seven or eight of resist textbook, and I don't recommend that you jump to Chapter seven or eight. Having read the earlier material live because he very carefully lays out the foundations of quantum mechanics. You really need to understand that part before you go to multiple article entangle systems and separating them space-like intervals, doing experiment. Perhaps very clever. One more question before we turn things over to other graduate students for their private chat with our speaker. Anyone else? All right, great. So let's thank our speaker again. Thank you very much for a very stimulating thank you for the question. I invite e-mail if you're interested in discussing further. I very much enjoyed hearing your feedback, right? Terrific. And I'll ask the graduate students interested to please hold on. And the rest of us will drop off. And thanks again, murray. Oh, yeah. You're welcome. I see there's some things in the chat. I'll try to answer those things after the fact. Wonderful.