The Quantum Conspiracy: What Popularizers Get Wrong

I'm Arthur Gleckler and I'm happy to introduce Dr. Ron Garrett here who is going to be speaking about quantum mechanics today. He's a former Googler from the very early days of the company around 2000. He was the lead engineer on the first release of AdWords and the original author of the Google Translation Console. He also wrote the first billing system that Google used. Also from many years he worked at the NASA Jet Propulsion Lab in Pasadena specializing in AI and robotics. I'm hoping to convince him to come back and talk about his experience as debugging spacecraft 250 million miles from Earth. Here's Ron. Thanks. So I'm told that my abstract caused a little bit of a kerfuffle. So let me start out with a couple of disclaimers up front to kind of manage expectations. The title of the talk was intended to be tongue-in-cheek. There is no actual conspiracy, at least as far as I know. But there is a fairly big disconnect between what you read about quantum mechanics in the popular press and what the actual underlying truth is and that's what this talk is about. I am not a physicist. Do we have any actual physicists in the crowd? Oh, boy. Okay. You can make sure you keep me honest. I'm a software engineer. I came upon this about actually 20 years ago when I read an article in Scientific American and I thought this can't possibly be right. And it took me 10 years to finally find a physicist at Caltech who could explain to me why in fact it wasn't right. And at that point everything just kind of clicked in quantum mechanics made a lot more sense to me than it did before. And that's what this talk is about. It's about a different way to think about QM that hasn't gotten very much attention. And dispels this idea that quantum mechanics is sort of intractably weird. Somebody said to me once that quantum mechanics obeys a lot of conservation of weirdness. And to a certain extent that is true, there is a certain amount of quantum mechanics extracts at all on your intuition. And some of that will never go away. But I don't think the quantum mechanics needs to be fundamentally any more incomprehensible than say relativity which most technical people seem to have no trouble wrapping their brains around nowadays. So with that sort of expectation management out of the way, I want to start out by inviting you to think about the question what does it mean to measure something. So imagine that we're sitting or doing some experiment. We have some system, let me grab a pointer, that we want to measure some property oven. So we have some sensor here like a camera. And gather some data and we feed it to a computer and that data pops up on the screen and we look at that with our eyes and we form some mental image in our head. And how do we know that this mental image that we form in our head actually corresponds to underlying physical reality? Well one indication that we have of this is that we can do experiments more than once and observe that we get consistent results. So for example, what color is this? Green, yes. So we can observe through our common everyday experience that the results of measurements are consistent across space and time. And this is really a very reliable aspect of our universe, but it's actually a very deep mystery why this is so. And Einstein famously said that the most incomprehensible thing about the universe is that it is comprehensible. We can't actually do experiments and get results that are consistent across space and time. And we don't really know why that any inherent reason why that should be the case. Now there's one very plausible sounding explanation of why this is the case and that is that the results of these measurements are actually an accurate reflection of some underlying metaphysical reality that reality that the really is a universe out there. And when we measure it, we're getting back actual information about that underlying physical reality. And that is the reason why these measurements are consistent because reality sees to it, that's the case. Well it turns out that we can demonstrate that that's not true. Now that's a lead you down a rabbit hole, but my purpose in leading you down this rabbit hole is to do it in such a way that you can find your way back out again. So I'm going to do it very carefully step by step and tell you in advance where we're going. I'm going to start out by reviewing the usual QM story. What you will read if you go to a popular account of quantum mechanics that you read, you know, pick up at Amazon or a bookstore or read about in Wired or whatever. And I'll then show you how that story can't possibly be true because if that story were true, it would lead to a violation of relativity, in particular it would lead to fast with the light communication. And it doesn't do this in the usual way that most people think that it leads to fast with the light communication. It does it in a more subtle way that really hasn't gotten a lot of attention. So you're a physicist in the room, bear with me. Then I'm going to walk you through somebody actual underlying mathematics or quantum mechanics in a way that is accessible to anyone who knows, can do basic algebra, knows what a logarithmic is. And finally, tell a new story based on our understanding of what the underlying mathematics actually says about what's really going on and hopefully will achieve enlightenment at the end of that. So is there anybody here who has not heard of the TOOSELIP experiment? Good, I will just blast through this very quickly. So this is, you have a laser that shines through to Slicts and you get an interference pattern that shows that light is a wave and can interfere with itself like any other wave. And there are two strange things about this. If you look at the results of this experiment with very low intensity light, what you find is, and this isn't showing up very well, but this top image here shows just some dots scattered randomly and the dots get denser and denser and denser until down here at the bottom, you have a dense enough pattern of dots that you can see this interference pattern and start to emerge. And this is an actual photograph of laser light going through a single slit and going through two slits and you can see this interference pattern here. This is an actual photograph of the same experiment. This particular one happened to be done with electron, but the underlying physics is the same. And the thing to notice here is that the total amount of light that you get in this pattern when there are two slits is brighter than the overall amount of light that you get with one slit, which is what you would expect. But that there are some places where you have these dark bands that were bright up here when you only had one slit. And this is the interesting part that you want to kind of focus your attention on because what this means is that there's a spot here where light was shining and then you open up an extra path to get to the screen and that spot goes dark. And that is the manifestation of interference. But the strange thing about it is that this is not a continuous phenomenon, it's an accumulation of all these particles. Now I can actually, I used to think that this was a fairly subtle experiment that you need as specialized equipment to conduct this experiment. And the turn-th<|pl|> is not sure you can actually do this experiment yourself. These are some pencil leds that I've taped together with Scotch tape and this is an ordinary laser pointer. And if I pass these, and there's a very narrow gaps between these leds. So you can actually see this happen if I pass the leds in front of this pointer, you can see the light start to spread out. And if you're close enough, you can actually see the interference bands. I don't think you can see it in the back, but if you're interested, after you'll talk them up, I'll give you a closer look at it. You can actually see the interference band. And the point here is that this is not a subtle phenomenon. And it's not something that you need expensive equipment to reproduce. This is an everyday experience for modern humans at least. Okay, so this is not yet intractably weird, because there are all kinds of explanations that we can postulate about how this might be happening. For example, photons and electrons might be real particles that have real locations in velocities like our intuitions about particles that might be pushed around by some kind of underlying wave. And oh, I forgot to mention, oops. The location where these particles accumulate is random. This is known, known way to predict other than statistically where these particles are going to end up on the screen. So the randomness might just be due to some underlying real physical property that we just don't know how to measure. By the turn that we can eliminate this possibility as well. And the way we do that is by asking by trying to track the path of a particle and ask, on its way to the screen, on its way to producing this interference pattern, which of these two slits did it go through. And we can do that. We can add detectors to the slits. And we can measure which of the two slits a particle went through. But it turns out that when we do that, the interference pattern goes away. And the phenomenon that we were trying to get a better grip on has changed. And it turns out that this is an inherent feature of quantum cancels, any modification that we make to this experiment that allows us to determine even in principle, which of these slits this particle went through. Destroys the interference. This is the famous wave particle duality. Any modification that allows the experiment even in principle. I've been asked to ask the people on the BC to mute their mics. Did I get that right? Anyway, so the conclusion from observation is that something has to be something, has to be at both slits in order to produce interference. And the reason we know that is because we don't actually need both of these detectors. One of them is enough because if we have one detector and it fails to register that we know the particle went through the other slit. Now the particle going through the other slit had never interacted with anything. The particle never interacted with anything. But because it allows us to know where the particle was even though we didn't actually measure it, that's enough to destroy the interference. And so this particle that's over here must somehow of know that we were looking over here even though the particle itself wasn't there. So something must have been there to be able to tell that we had a detector here. But we don't know what that is. Now it turns out this is again, it's a universal property of quantum mechanics. It holds for any kind of particle in practice that means photons and electrons because that's all there is in this universe unless you start getting into nuclear physics. And any kind of measurement that any kind of two-slith experiment, any experiment where you provide two different paths for the particle to potentially go down and bring it back together without knowing which way it actually went, will produce interference. And any modification that you make that lets you figure out where it went will destroy that interference. Now this is still not in track. Because we can still tell a reasonable story about why this might happen. So maybe measurement does something to the system. These are after all very small particles and very delicate systems. And so maybe it's just physically impossible to make a measurement without disturbing the system in a way that is the cause of the destruction of the interference. Maybe the wave function collapses and becomes a particle somehow. This is the famous Copenhagen interpretation of quantum mechanics. But it turns out that we can rule out that possibility as well. And the way we rule out that possibility is by asking how and when does this collapse, this purported collapse happen. It's a number of features that ought to make us very suspicious of it just a pre-order without even doing any experiments. It's a discontinuous and non-reversible phenomenon. But once you know that a particle has gone through one slither the other, you can't go roll back time and undo that. And if you look at the mathematics of quantum mechanics, which we'll get to later, there's nothing in the math that's discontinuous. And more than that, all of the math is actually time-reversible. So we can hypothesize that this collapse happens. But this is fundamentally at odds with the mathematics of what quantum mechanics, of how quantum mechanics says that our universe works. So we can actually do better than that. We can actually do an experiment to show that collapse, if it happens, is a much subtler phenomenon than it would have first appear. And this is the famous, this is quantum mystery number two, the famous quantum eraser. Now this is an, this is a two-slid experiment that I have now reduced to something more abstract. So we have some particle sources, this can be photons or electrons. We have some abstract way of splitting up that particle so that it has two different paths to go down. And some abstract way of recombining that particle so that both of those paths end up in the same place so that we get interference. And here, notionally, we have one detector at one of these dark fringes and another one at a bright fringe. So that if we introduce some kind of an abstract measurement on one of these branches, then the interference pattern fuzzes out and we now have the half the amount of light at each detector. So we don't have fringes anymore. We have the spread out pattern that we saw in the single slit version of the experiment. Like I said, there are lots of different ways that you can do this, actually let me go on to the next one. So it turns out that you can erase this. There are physical ways that if this measurement, certain kinds of proto-measurements that you can do here, you can then go back into race after the fact and restore the interference. And here's a concrete example of that. If we polarize light and I'm actually going to show you this in just a second. So bear with me if you don't understand what I'm about to say. If you use polarize light and you do the measurement by rotating that light 90 degrees and then erase it by filtering at 45 degrees, that is an actual concrete example of a quantum eraser. And I can't show you the interference part of it, but I can show you the eraser part. So what I have here is some polaroid film. This is the same stuff that you find in polarize sunglasses. And I first want to convince you, has anyone not played with this stuff before? Okay, so again real quick, if the if the axes film are aligned, then you can see through it, and everybody see through this. And if I rotate it at 90 degrees, then you can't see through it anymore. And that effect is independent of the absolute orientation of the film. So the light that's going through to your eyes starts out unpolarized over here. It gets passes through this film and becomes polarized, let's say, in this direction. And I can demonstrate then that it has become polarized in that direction by filtering it out using a filter at 90 degrees. And there's also this cool adjunct of the experiment that you can do by adding a filter at 45 degrees. If you put it in front or behind nothing happens, which is pretty much what you'd expect. But if you slide this in between, and suddenly you can see through it again. Pretty cool, huh? And the reason for that is because if you start out with polarized light and you filter it at 45 degrees, then some of it gets through and is now polarized in this direction. And now I can do the same operation. And now the relative orientation of these two or 45 degrees, so some of it gets through again. But that's what I want to show you. That's not the cool part. Cool part. This stuff. This is what they didn't tell you, but they didn't show you in high school. This film is actually a polarization rotator. If I stick this in here, I can actually take this light that's polarized in this direction. I can rotate 90 degrees that it's polarized in the same direction as this film. And the thing to notice here is that the apparent brightness here in the center is the same as it is up here. There's before if you did the high school version of the experiment. Whoops. You got quite a bit of loss. So, so I really can take, I can take light and I can polarize it, and I can take that polarize light and I can rotate it by 90 degrees. And so I can create two different paths that I can tell which way the light went through. I can tell where the light's going through here or where the light's going through here. Actually, we'd back up a step. My claim is, without this filter, it's a little hard to tell. My claim is that the light that's coming out of here is different than the light that's coming out of here, so I can tell which way it went. And the way that I can demonstrate that to you is with this measurement apparatus that lets me filter out this light and tell which way it went. So this is a measurement. This should collapse the wave function according to the Copenhagen interpretation. But I can undo this and the way I undo it is by filtering at 45 degrees. And now I have to ask you for a little bit of suspension to this belief because this is not high precision optical equipment and my angles are to line just right. And if you look very closely, you will actually be able to tell a difference between these two paths. But the difference is now much less than it was before. See that? Oh, I'm sorry. Didn't realize why the people are right here. I'll show you all this at close range afterwards. So there's a measurement. There's a ratio of that measurement. The light's going this way. So in time the ratio has to happen after the measurement. And if I actually had a laser to shine through this, I could demonstrate to you that the interference would go away and would come back. So again, these are not subtle effects and they're not effects that you necessarily need high precision equipment to reproduce. So every day, I expect this is $30 worth of polarizing film. So this leaves us with the full of soft alcohol conundrum that is embodied by Shradan Joe's cat. If there's no collapse, then if we set up a radio act of source that triggers some kind of a mechanism that will break a bottle of poison, it will kill a cat that's in a sealed box. Can this what happens? Quantum mechanics says that this cat is in a quantum superposition of being alive and dead, which is intuitively absurd. But as far as we can tell, that's really what happens. So if that's not intractably weird enough for you, this is the the third quantum mystery entanglement, which is usually described as sort of an ancillary phenomenon to all these other mysteries. Oh, yes, it's sort of old by the way. As everybody seen this picture, has anybody not seen this picture before? Okay, this is what what the production of quantum entangled photons really looks like. This is not an actual photograph, this is a drawing, but this is an actual photograph of the output of one of these gadgets. There's an ultraviolet laser that shines through a crystal of some material called the beta barium-bored, detailed don't matter. And this crystal has this interesting property that it will absorb photons of ultraviolet light and re-emit them in two and it'll kick an electron up to an excited state. And then that electron will drop back down to its ground state and it'll do it in two steps and in those sort of kick up in one step down and to it in the process of coming back down, it will emit two photons instead of one. So what comes out of this system is visible light. And the photons always come out in pairs and they come out in matched sets because of fundamental conservation laws. We have law conservation of energy and momentum. And so an electron, a photon that, say, comes out over here is a red photon. We'll be matched by one that comes out over here is a blue photon and the same thing over here and in the middle you get this band where you get photons that come out at the same wavelength and it just matched in position. So a photon over here will be matched by one over here and there'll also be matched in polarization as it turns out. So this is the way it's depicted conceptually. You have this ultraviolet laser, it's called a down converter, this crystal is called a down converter. And you send these photons off to opposite sides of the universe and what and then you measure some property of them, let's say, we split them according to polarization or position. And what does matter any quantum state variable as long as you can filter them that way? And what you find is that they're perfectly anti-correlated because of the conservation laws. So if you get a photon up here on the right side of the experiment at the upper detector, that will always be matched by a photon over here on the left side of the experiment that the down detector, some unfortunate artifact of English language that the word left and lower both start with a letter L, so I'm going to switch back and forth between them. This is what Ice time famously called spooky action at a distance. If you take this phenomenon, it's uncontroverted, this is experimental, an undeniable experimental result is really does happen. Combine that with the fact that there is no collapse of the wave function and the inescapable conclusion seems to be that as it was put in wired is recently as last June, that when an aspect of one photons quantum state is measured, the other photon changes in response even when the two photons are separated by large distances. And this would seem to be impossible because it would seem to violate relativity because it's an instantaneous effect and you know that we can't communicate information faster than light because if we could do that, then we could communicate information backwards in time and that would cause all kinds of problems with causality and it would just be horrible mess. So these instantaneous effects are supposed to be impossible but there is one thing that comes to save us and that is this quantum randomness. We don't actually have any control over whether the photon on one side ends up at the upper detector or the lower detector. And so we can't actually send information here to there. We know that if we see the photon on the upper detector over here, then our counterpart across the universe must have seen it at the lower detector over there but we haven't transmitted any information from A to B. And you can actually prove this mathematically that it's impossible to transmit information using this phenomena but it turns out that the proof of the impossibility has a loophole. So that is the end of step one. I'm now going to on a step two and show you why the story that I just told you can't possibly be true. So let's summarize the take stock. A split combined experiment produces interference. Any which way measurement destroys that interference. There is some which way that a proto-measurements that we can go back into race after the fact and restore the interference. And measurements on entangled part of the pulls are perfectly anti-correlated. So the quantum sphericcy is that all of these things cannot possibly be true and here's why. So this is a thought experiment. This experiment has not actually been done. Again with tongue, slightly in cheek, I've dubbed the Einstein Piddlesky Rosengerat paradox. And it's two two-slid experiments that are fed by quantum entangled photons produced by one of these downcovers set ups in the middle. And I have to consider the question of if we measure on the left, do we destroy the interference on the right? So if the answer is yes, then we have faster than the like communication because this interference is a macroscopic effect. It's really easy to see if you have interference or not. You just look at it with your eyes. You don't need any kind of delicate detectors or anything. So you just measure over here. Take the measurement away, measure, take the measurement away, and over there on the other side of the universe, this interference pattern will come and go and you can send more code instantaneously. That's obviously impossible. So the answer must be no. But if the answer is no, then we know the position of one particle but we have interference regardless. And that contradicts the fundamental principle of quantum mechanics, which is that we can't know the position of the particle and still have it interfere. Now this is not yet an iron-clad argument. There is one other possibility that I have not mentioned here, and anybody think of what it is, any of the physicists in the crowd. Oh good. So there's one last possibility and that is that there was no interference to begin with. It might be that entanglement sort of counts as one of these subtle proto-measurements that destroys the interference. So we didn't have any interference to begin with. But it turns out that doesn't get us out of this fast of the like-conundrum because fine, if that's the case, then we can still produce faster- than-like communications by putting in a quantum eraser and destroying the entanglement. It's very delicate property. Businesses work very hard to produce it maintain it. It's very easy to destroy. So just to destroy the entanglement and produce interference where there was none before. And again, we have a faster-than-light signal mechanism. Now that is a very compelling argument that the story that I have told you, the usual quantum story, is wrong. That argument is in fact correct. The story that I have told you up until now is in fact wrong. And that's why. Because all physicists know what the outcome will be. And I'm about to tell you what the outcome will be. And by the time I finish telling you, you will be convinced enough that the outcome is what I tell you that it will be that you will not need to do the experiment either. I promise you. Oh, I'm sorry. The question was why hasn't this experiment been done? Yeah. So the internal moment is about polarization in which way it goes through a splitter? Is that that exact? Is that the same polarization? That's right. So I'm assuming here, like I said, there are lots of different ways that you can do this split combined experiments. You can do something called a mach-zender interferometer. You can use something called a stern Gerlach device. You can, you know, lots of different ways. When I talk about polarization, the way that the splitting is done is with the device called a polarizing beam splitter, which is exactly like one of these, except instead of just absorbing half the photons and letting half of them go through it reflects them. So it looks like a mirror and half silver mirror. And what comes out this direction is photon that are polarized one direction and what gets reflected in the other direction are photons that are polarized in the opposite direction. Okay, so we are now in the depths of the rabbit hole and now it's time to find our way back out. So I'm going to do some math. Don't panic. It will not be as bad as you think. This is the mathematics of quantum mechanics. Here, this is the famous Schrödinger wave equation. This is the free variable. Here's this thing called psi. psi is the quantum wave function and it obeys the dynamics of this partial differential equation, which those of you who are proficient in partial differential equations will recognize as a wave equation, like any other equation that describes waves. And that's why these particles seem to propagate like wave because this is the math that describes how they propagate. The point here is that this, the dynamics of this thing are continuous and time reversible. All wave equations have continuous time reversible dynamics. And the second part of quantum mechanics is that you take this quantum wave function, which is a function of position and time and is a complex number. You take the norm, the magnitude of that complex number and square it, and that gives you the probability of measuring a particle at this position x at a time t. That's really all you need to know about the mathematics of quantum mechanics. So there's some things to note about this. There is this distinction between the underlying amplitudes, which are complex numbers and the probabilities, which are of where we find these particles, which is the only thing that we can measure, which are real numbers. And the reason that particles can interfere is because complex numbers with magnitude greater than 0 can add to 0. You can have a complex number that points off in this direction, another complex number that points off in that direction. They both have magnitude greater than 0, but they can add and destructively interfere. That dynamics are continuous time symmetric, fully deterministic and hence reversible. And so there's no place, there's no place you can find anything that resembles collapse in this math. And no randomness either by the way. Going from amplitudes to probabilities by taking this wave function and squaring it, has no physical justification whatsoever. It's purely hack, but it's a hack that works really, really well. So here's what the actual math looks like for the two-slit experiment. This is, if you go to actual papers on quantum physics, you want to find this in the popular press. This is what you will find in physics journals. This is, or physics texts. This is the state, the amplitude of the photon being at the upper detector. This is the amplitude of the photon being at the lower detector. And we have to divide by the square root of 2 in order to make the total probability come out to be 1. So to figure out the probability, we take this number, which is a complex number and take the modulus on square at the one. We do that. It's almost exactly the same as just squaring A plus B in A greater algebra class. You get A squared plus B squared plus A B plus B A. You have to take these complex conjugates because their complex number is in the square root of negative 1 pops in there to do some weird things. Those kinds of details don't matter. The point is, this is a complex number, psi u is a complex number. Its magnitude is a real number. And when you square it, it's a positive real number. So here we have a positive real number. Here we have another positive real number. The sum of those two has to be a positive real number. But over here we have two different complex numbers and two different complex numbers that we're multiplying together. So this sum can be negative. So this is the interference comes from. This is the mathematical manifestation of interference in quantum mechanics. That's what it looks like in terms of Greek symbols. So what happens when we add detects? Well, when we add detectives, the amplitude starts to look like this. We have the amplitude for the photon to be at the upper detector. Times the amplitude for the detector to be in the state where it shows that the particle is at the upper detector. And the same thing at the lower detector. So this is just the mathematical description of that. When you take the amplitude of that and square it, here's what you get. Same thing is before. Say u squared plus iL squared. And this, which looks at awful lot, like an interference term, right? Which is weird because I just got through telling you that if we have a detector that tells us which way the particle went, that destroys the interference. Well, there's this subtle difference here between what we have now what we have before. And that's this weird notation here, which is called Dirac bracket notation. Don't need to concern yourself with it. Just take my word for it when I tell you that this quantity here is the amplitude for the detector to spontaneously switch between indicating that the particle is at the upper slit and the lower slit. In other words, it's a measure of the reliability of the detector. That just comes out when you do the math. And if the detector is working properly, that value is to do, oops. This, this values the, the, the amplitude for spontaneously switch between u and l, and spontaneously switch between l and u, those are both zero. So this term goes away. That's the math of how measurement destroys probability. And the interesting thing about this is that measurement is a continuum. It's not a dichotomy. The math tells us that we can measure just a little bit, or we can measure mostly, but not quite. And we have very, it's a, it's a varying levels of interference that we get depending on whether the measurement that we're making is reliable or not. That's what the math says. So what about entanglement? This is, if you go to a physics paper that talks about entangled particles, this is what you will see as the mathematical description of a pair of entangled particles. What this means is that you have an amplitude for the, the particle on the left to be in the upstate, and the particle on the right to be in the downstate, superimposed with an amplitude for the particle on the left to be in the downstate, and the particle on the right to be in the upstate. Again divided by this grid of two. Now this looks like the, the unmeasured two slit description. But there's some notational slide of hand going on here, because this is short hand for this, and it's, it's an unfamiliar notation. This vertical bar followed by the bracket. This is a term. So you got, this is a quantum wave function here. This is another quantum wave function here. This is the wave function for the upper particle. This is a wave function for the lower particle. And another way to write that is, you don't have to use arrows. That's just a notational convenience. So I could call this the left upper particle, and the right downward particle, and the left downward particle on the right upper particle. And this is just another way of writing this psi, this quantum wave function. So this, and this are the same thing in different notations. And this should now look familiar. This is exactly the same. As, oops. As this, the, the two slit experiment with the detector, modular few labels. And so that is now the answer to the first part of the EPRG paradox. In fact, entanglement does count as a proto-measurement that destroys interference. But it's actually much deeper than that. According to the math, entanglement and measurement are the exact same phenomenon. The math is exactly the same. And that is why entanglement destroys interference, because entanglement is measurement. Now, a lot more to say about that later in the talk. So, okay. So there's no interference, but now what about this last, the idea of creating the interference using a quantum eraser? So let's take another look at our, running a little short time. So I was going to blast through this. This is what the state equation looks like for the quantum eraser after the so-called measurement, but before erasure. So you have an upper photon that's horizontally polarized, because we've, what's the soon we start with, with vertically polarized, like going in here, and we measure by rotating 90 degrees. So we have now the upper photon rotated from vertical to horizontal, and the lower photon still vertical. And this you will now should recognize as a measured and therefore non-interfeering state. And it turns out that if you filter an out 45 degrees, this is the state function, the quantum wave function that you end up with, you now have a photon that's either in the upper or lower slit, and that's either horizontally or vertically polarized, and this kind of makes sense, because if you think of these as vectors, and you have a horizontal polarization plus a vertical polarization, that's a 45 degree polarization, which is exactly what you would expect to see if we're filtering it 45 degrees, right? But remember this square root of two term here that I told you was there in order to make the total probability come out to be one. Now that's a two root blue, and if you run the math on this, you find out that the total probability is not one, it's one half. So either we've made a mistake or half our photons have gone missing. Well, in fact half our photons have gone missing, which is also shouldn't be too surprising, because we've filtered, we put this 45 degree, we put the filter in place. This filter is filtering out half the photons that go through it. If they come in a 45 degrees and half of them come out polarized this way and the other half get blocked. So it turns out that the other half the half that didn't get through have a different wave function that has a negative sign over here, which again makes intuitive sense, because the filter lets these, the filter is at 45 degrees, so it lets this axis through and this axis, which is the H-V axis at blocks. And these photons interfere with themselves, and these photons also interfere with themselves. So the photons that pass through the filter display interference fringes, and the photons that don't pass also display interference, but it turns out that they're anti-fringes. They're exactly lined the bright spots in the interference fringes for the photons that got filtered out. Exactly lined up with the dark spots of the fringes for the photons that were let through. And they sum together to produce what we perceive when we look at it as non-interference. So this quantum eraser doesn't actually erase anything and it doesn't produce interference. It just filters out interference that was actually already there all along. And it turns out that we can actually do this in the EPR experiment too, and the way that we, but in order to do it, we have to transmit classical information from one side the other in order to do the filtering. So the way it works is you make a record of all the photons that you collected over here, and keep an order. So you have this record of first photon. Was it the upper detector, the second photon, was at the down detector and so on and so forth, and over here you keep track of which photons ended up where on your screen. And then you take this record and you transmit it over here by some classical slower than light channel. And you look at all the up photons and sure enough there's an interference pattern. And you look at all the down photons and sure enough there's an interference pattern. But the only way to see that is to take classical information and move it from here to here. And that is the last nail in the coffin. So I very disappointed when I learned this 10 years ago because I was really counting on winning a Nobel Prize and taking over the world. But oh well, this is the next best thing. So that the take home message to this point is measurement and entanglement for the same phenomenon. And what you will find in many, many accounts and even some professional accounts is that they're completely different. That measurement is this common everyday thing that we can sort of intuitively grasp. And entanglement is the quintessential quantum mystery. And in fact, they're really the exact same thing. And having come to that realization, we can now tell a different story about quantum mechanics that to my software engineers' mind is much more intuitively pleasing than any of the other competing alternatives. So the Copenhagen is the most popular, but as we've seen, it's scientifically untenable. There just is no collapse. The next most popular interpretation is the so-called many worlds interpretation. Where it says that any time that a particle can go multiple ways, the entire universe splits. And the math actually supports that, but I personally find that that takes a heavier toll on my intuition than I'm really willing to concede. There's all the things that nobody's ever heard of called the transactional interpretation by a fellow named Kramer at the University of Washington. Actually, if you're really interested in this stuff, I encourage you to take a look at it because it is kind of interesting. It postulates that the backwards-in-time solutions to Maxwell's equations are physically real. And if you make that assumption, then you can explain a lot of stuff, but I don't have time to get into that. But what I want to talk about here is the quantum information theory which I have dubbed the zero worlds interpretation of quantum mechanics. It's an extension of classical information theory with complex numbers. And if you run through that math, you get some very interesting results. So here is a lightning introduction to classical information theory. It's the study of this quantity called the Shannon entropy of a system A, which can be in any one of a number of classical states. And it's defined as the sum of the probability that the system is in some state A times the log of that probability. And then you take a negative sign. And intuitively, it's a measure of the amount of randomness that's in the system A. So just to simplify things for the purpose of this talk, if a system has an equal probability of being in one of N states, then the entropy is just log of N. So when N is one, and the system is definitely in one state, then the entropy is zero. And if it can be in one of two states with equal probability, and we take this log base two, we measure information content in bits, then it has one bit of randomness in it. So you can define all kinds of other derived quantities like the joint entropy of multiple systems and the conditional entropy. And this quantity here, which is called the information entropy, which is a measure of how much information a system A contains about a system B. And the interesting thing to note about it is that it's the sum of some of these other quantities that have been defined up here. And the information entropy ranges between zero and one, where zero B is that this system has no information about system B, they're completely uncorrelated. And one means that they're perfectly correlated. So for example, because there are sums, we can describe these quantities as venn diagrams. So this circle here on the left is a system A, and this circle on the right is the system B. And the total entropy is contained inside these circles, the total entropy for each system. And the information entropy is here in their intersection, and that leads the conditional entropy out here, because the information entropy is the systems individual entropy minus the conditional entropy, just simple addition. This is the important part. If we flip two coins, so that's a completely independent of each other, this is what the numbers end up looking like. The conditional entropy, the coin A has one bit of randomness, and coin B has one bit of randomness. So the total entropy in the system is two bits of randomness. The system is a whole of these two coins can be in one of four states, log four is two, and there's no information that one coin contains about the other. By the way of contrast, if we have a coin with a sensor, this looking at that coin telling us whether it's landed tensored heads or tails, then the sensor is working properly. Then we have one bit of information entropy, because the sensor gives us perfect information about the coin, and vice versa by the way. The coin gives us perfect information about the sensor. There's no directionality here, and the total entropy in the system is one bit, which will only be in one of two states. Heads and sensors has heads or tails and sensors has tails. If we extend do the same math again, except losing complex numbers instead of real numbers. Then you end up with something called the Von Neumann entropy, which is called S, and this hairy looking equation over here, which I don't have time to go into. But the intuition is kind of the same as it was before when we talked about how interference was produced, because we're now dealing with complex numbers rather than real numbers. The information entropy is no longer restricted to the range 0 and 1, and in fact, entropy is no longer restricted to be positive real numbers. They can be negative. And this turns out to be, if you do the math, the entropy diagram for a pair of entangled particles. You get a negative bit of entropy over here, and the information entropy, the amount of information that one particle quantum information now, that one particle contains about the other is two bits. So you can think about two entangled particles. The math is telling us that these particles are now somehow better than perfectly correlated. They've become super correlated, and the total entropy of this system. Some of all these numbers is zero. There's no randomness. That's not yet the cool part. What happens when we take a measurement? When we take a measurement, we have a particle that becomes entangled with a macroscopic system of particles. So what happens if we have three mutually entangled particles? You end up with a venn diagram that looks like this. And if we assume a two state system, then the actual numbers come out looking like this. You've got one bit of information entropy between a and c, one bit between a and b, and you've got these negative, these weird, negative entropy's over here. And it's all kind of mind-boggling. But let's imagine that this particle down here is the one that we're measuring, and this is these two particles here are our measurement apparatus. Let's look just at the measurement apparatus and ignore the fact that we're actually measuring a particle here. So we're going to take this particle c, and we're just going to throw it out for a minute, and it turns out that ignoring c is exactly what is represented by this trace operator here that ends up showing up in the math. Look what happens. This one bit of information entropy, we lose this boundary. So this one, and negative one, cancel out and become a zero, same thing over here. And what we have is that if we ignore this, is exactly the same system from an information theoretical point of view as a coin with a sensor. We have two classical particles that are perfectly correlated with each other in a classical sense. I should remind you of the experiment that we did at the beginning of the talk. Where everybody agreed that something was green, and we can get that from quantum accounts. We get these two systems that are in classical correlation. But we did that not by actually not by having an objective physical reality that we reflect by actually by ignoring the thing that we're measuring, or that we think we're measuring. As it turns out that this extends to any macroscopic system, if you add an arbitrary number of particles, the entropy diagram ends up looking exactly the same. So this is now the mathematical description of a quantum measurement. You have the system that you're measuring. It's particle q. It interacts and gets entangled with a particle which in the parlance of the theory called an encella, which is why they label it a. And that encella then gets entangled with a macroscopic measurement apparatus. Some system of 10 to the 23 particles on the entropy diagram ends up looking exactly the same where this entire system has the same quantum information theoretical information content as the third particle in a three particle entangled system. So that is now a description of what measurement looks like purely in terms of quantum mechanics. And the interesting thing about that is it describes all of the macroscopic phenomena that we see that we've now even observed about classical measurements, but it's purely in terms of quantum mechanics, which means that it's reversible. So somehow we ought to be able to undo an actual physical classical measurement. But in practice we can't seem to, and the reason for that is because in order to do that, in theory it's possible, but in practice we would have to undo all of the entanglements in this macroscopic system. So for me to now go back and back in time, you don't really going back in time. But for me to erase all of your memories of having seen this green thing on the screen and agreed that it was green at the beginning of the screen. I would have to undo this enormous web of entanglement that has since proliferated at the speed of light, and have to bring all those particles back together and recombine them. And in principle that's possible and practice obviously it's not, which is why classical measurement seemed to be irreversible. Despite the fact that the physics of the universe say that everything is reversible. So this has some philosophical implications. I called it the zero universe interpretation of quantum mechanics. If you buy this as a description of what the physics of the universe is really like, then it tells you unambiguierously that it is not the case, that the reason that measurements are consistent across space and time is because there's a real underlying metaphysical reality out there. It tells you in fact the exact opposite that what we really are is as David Merman puts at correlations without correlata. We are not made of atoms, we are actually made of bits, we are our thoughts. And these thoughts actually reside, forgive stretching a metaphor to the breaking point. We are a simulation running on a quantum computer. I'm going to skip that. So that take home message is going back to design sign code that the most incomprehensible thing about the universe is that it's comprehensible. Here is an explanation in terms of physical theory of why the universe is comprehensible. Quantum mechanics actually predicts a comprehensible universe, but at the cost of forcing you to believe that what you perceive as physical reality is not actually real, it's actually an illusion. And the motto here is that spooky action at this point is no more and no less mysterious than the spooky action across time that lets us perceive the universe as consistent from one moment to the next. They are both produced by the exact same physical phenomenon namely entanglement. And I'll leave you with this quote from an ancient Japanese Zen master and open the floor of questions. Oh the physicists are walking out. Yeah. So you have the three particles and you will move to the show with a maybe two and look like and they work a little bit to the core of the sensor. Why not leave the paper? What happens to you leave the paper part? If you're taking a doubt as a matter of the thought of experience, you can say, well this is equivalent to. Yeah. Well this is all just math, right? So these are all mathematical manipulations. The results of which we interpret in order to tell stories about what our world is like. And if you leave it in then what you have is a description of the unadultrated underlying physical reality which is quantum. And the reason that's hard to wrap your brain around is because your brain is classical. Everything that you are is classical. You're made of classical bits that are ones of your atering machine. You're not a quantum computer. But you're made out of a quantum computer. And that's why there's this fundamental disconnect that will always take a total inner intuitions. I will never go away because they're really fundamentally different. The difference between real numbers and complex numbers. The underlying reality is complex but the thing that is processing the information that lets you think about these things is real is made of real numbers. That's really the underlying the pithiest way I know of summarizing this. So it just depends on what point of view you want to take. I'd like to make a short pitch for the multiple universes and hear your response. The multiple universes, the well-internality is that's really very equation. It allows for because it's linear. You can have things occurring that live in the same equation and sometimes say with the dead and the live cat, you can see that you can actually sort of separate them. Each goes its own way. They don't interact much for a very good approximation. It's to consider them one at a time. However, when real quantum effects go, then you cannot do it this way. So there are some things that you can separate and some not. So now you're saying that you have an interpretation of the one universe. No, no, no, no. Zero. Zero. All right. Very important distinction. One universe. One classical universe really is untenable. Well, you can, that's Copenhagen. You can, yes, so the question was what do I think about multiple universes? Multiple universes are just as tenable according to the math as zero universes. The only thing that's not tenable is one classical universe. That's the only thing that the math tells you unambiguously does not exist. And it's a matter of taste. I personally, so one of the things that the math tells you if you think about it in terms of multiple universes is that once you get beyond a certain level of separation, these universes are forever inaccessible to us, even to any reasonable degree of approximation, and then as this philosophical question of this, the thing actually real. And the analogy that the best analogy that I've heard is imagine a photon that leaves the back of the sun and goes away from us and so it's forever outside our light cone. Is that photon real? And my reply to that is there's a difference between the photon that leaves the back of the sun and travels away from us, because there's always the possibility that somewhere out there there's a mirror that's going to reflect that photon back to us. And we won't know that until that mirror actually reflects it and it comes back and we can see. But in the case of multiple universes, we know that it would be math tells us so that once another universe splits off, it's never coming back. There's no way to bring it back. I'll have to put on correct timing to wheel. Is kidding? I'll have to put on correct timing to wheel. In any amount of time that we have any practical reason to care about this. So yes, if you're thinking cosmologically, multiple universes is a is a is a tenable interpretation. If you're thinking in terms, if you want a story that you can help you to understand how the universe works in terms of your everyday life and what your fundamental nature is, I personally find that I gravitate more towards the information theoretic point of view and believing that I, the universe that I exist in is a very good high quality simulation. But that's a matter of taste. I don't know. I have to defer that to the physicists. That's a very good question. I actually don't know the answer to that. Could you answer that? Could you answer that? Could you answer that? I think this is, oh, by the way, the question back here was do multiple universes serve mass energy. It's a very good question because, and I don't know the answer. I should ask, I need to ask a physicist. Who? Okay, so somebody in the audience is saying that when universe is split, the total amount of mass in the universe gets evenly divided between the two universes. And I'm guessing that the math works out in such a way that if you reduce the amount of mass in a classical universe uniformly by one half, at everything ends up working out the same as it did before. But I'm going to have to think about that. Yeah, so we are now beyond the limits of my knowledge of this stuff. Yeah, those of us who are intrigued and teased, work me learn more. So I have a paper about this on the web. I highly recommend David Merman's book, Bouges all the way through, where he doesn't actually talk about this, but he talks about the bell inequality in a very accessible way, which is also, I didn't have time to talk about that, but it's very worthwhile knowing about or send me an email. I can actually put you in touch with the guys who's research this talk is based on their data caltech, I think. Yeah. So this is an entirely local theory that all interactions can be developed with the human life. Well, so the question was, is this a local purely local theory? It's quantum mechanics and whether quantum mechanics is purely local is the subject of debate. It depends on what you mean by purely local. Classically, it's not. And quantum, it is. This shed is no extra light on that question. Okay, guess that's it.