Causally symmetric Bohm models / Probability time-neutral models of QM (contd.)

0:00 There are a lot of formalities for quantum physics at this time. You always put the initial values in the first place. But probably the weirdest thing when it comes to quantum mechanics is the interpretation of dimensional collapse. This is the only place in all of modern physics where you will find an asymmetry in not just the boundary conditions, but actually an asymmetry in the interpretation. There's no such thing as an un-collapse. There's no possibility in quantum mechanics. There was only a collapse in the forward time direction. So that, and if you jump to many worlds and say, I don't believe in collapse, you're only talking about universes branching off in the forward time direction. So there's a tiny asymmetry in the interpretation of quantum mechanics, and yet, when you check through all the numbers, you end up with our time-symmetric, or if you add span and charge, CPT-symmetric universe. And so you end up with all these symmetric results from this horribly asymmetric formalism. And so, to me, that in itself is a motivation to see, well, can we go back and redo the formalism in a time-symmetric manner or a time-neutral manner. Not too many people have done this. I started to make a list of people with an actual model that falls in this category. Rob is probably cringing to see his name on this list here, but I will throw his toy theory in with these other ones that sometimes explicitly use retrocausality. There's no retrocausality in Rob's model, but there's also no arrow of time either. There's no difference between what happens forward in time and backward in time. And so I'm going to throw them on this list. Okay, so, first of all, what do I mean by time-usual quantum mechanics? Well, here's an example of something I got from Hugh Price's book. You just take a photon going into a set of polarizers. And let's say you happen to know that it does come out. You measure that it comes out. And then your model's supposed to tell you, well, what happened in between? If you try to take a realist approach and say, well, something happened in between, I think most of us would take the intuitive position that, well, in here you have a zero-degree polarized photon. And then something weird happens and suddenly you have a 45-degree polarized photon and then that. Or maybe you think that, no, here you still have the superposition and it doesn't collapse until out here.

2:30 But regardless, you have this, you have this... There's some particular picture. If you try to reverse that picture, this is completely intuitive. But now, what if you just happen to know that the photon is coming in here and going out here? You just take the same, what you know and time reverse it. You end up with a different picture. When you apply your same intuitions, you apply this intuition, you have a 90 degree photon here and a 45 degree polarized photon here. Or if you apply the intuition that it doesn't collapse on the measurement device, then you have So, this is an example of what I see. It's a time asymmetric model. You have the exact same physical phenomenon, you time reverse it, and you end up with a different explanation of what's going on in the middle. A time-neutral model, what I want, is a model that when you do flip it around, you end up with a consistent picture of what's happening in the model. That's all I need by a time-neutral model. Quantum mechanics is not a time-neutral model because of that. Probability, the way we use it, is not timely. I mean, standard quantum mechanics, at least, can be manipulated into probabilities where you want to know the probability of some outcome at some time. And what you know, what this conditional lots on, is prior data. Now, actually, it's very difficult to get the predictions of quantum mechanics into this form as I'll talk about in a little bit, but an experimentalist is using probabilities of this form to compare the experiments. This is the only kind of correlated data you can really compare. And yet, there's a time asymmetry here, right? You're conditionalizing on the past information and you are asking for numbers that tell you the prediction of future information. So, does it even make sense to talk about time interprology? I'm going to argue, well, I can argue yes, but in any framework, in Rod's framework, my framework, any time neutral framework, the numbers that it spits out can't be these numbers because these numbers have a time asymmetry built into it. Now, if you have a time neutral framework, you can ask time asymmetric questions on that framework and get these numbers out eventually. But these numbers, the Born Probability Rule, things like that, cannot be fundamental to any time neutral framework. You have to end up deriving these from a time asymmetric assumption. Because these, there's this built-in time asymmetry in how we're asking the question. So how do we do it?

5:00 Is there a way to do a time distribution probability? There is. The first solution that the one I had to come down on the slide of is basically you, instead of doing conditional probabilities, you do something in probability theory called a joint probability distribution. And every time you see a little subscript W, that's the time I'll use weight to... To summarize this phrase here, every time you see this little W, I'm talking about the probability of, say, two events both happening. And then it's a very simple matter to generate conditional probabilities from these weights. For example, if I want to know the probability of some outcome B0 given A0, well, I say, well, what's that weight? And then you divide by, and you have to normalize it. You always have to normalize it. You consider all other possible outcomes. You don't sum over the A's, because that's given. You sum over the B's and presto, you have yourself your conditional problem. So if you had a time-neutral model that spit out numbers that looked like this, that would be okay, as long as these numbers that you switch A and B around don't change things. And that actually was what Bra did in his talk, whether you listen or not. So, just to give a little example, if you didn't follow that, say you have some initial data, you can assign weights to some models, say it tells you, you know, if A and Y happen, well, that's the weight of 2, if A and Z happen, that's the weight of 2, and so on, and then you can start to ask questions. For example, you can say, well, given data A, what's the odds that I'm going to get Y? And in that case, you would just look at these two numbers, right? You don't care about... Or you could say, well, given data B, what's the probability of getting the outcome? And you can generate that outcome as well. You can just see 1 in 3, you get 25% chance. And you end up with lots. You can get these conditional probabilities. You can also ask these sort of perverse questions. Given the final state, what was the probability of the initial state? And you can do that using this formalism too. For example, given, which one did I do here? Given Z, you just look here. This is 2 and this is 3. And so now you can figure out what the probability of where it came from. And these are the numbers you need to determine whether a theory is time neutral or not. Because if you're going to flip the theory around, you also, and you... All of these are examples of how you can use these numbers to figure out whether or not your model is time neutral.

7:30 So that's what I mean by these weights. Hopefully fairly intuitive. The question is, are a given set of weights going to be in a time neutral model? And if these weights don't change upon time reversal, if you time reverse this and PWAY still is 2, then you're automatically time neutral because you're going to have the same weight regardless of what direction you run time. Okay, there's another way to do it. The way we typically do all of our models in physics is you put the probability in the state. I don't know what this is called. It's so ubiquitous. Well, you have some initial data. So you have some initial data. You map it onto a state. How do you do that? Well, you have some part of your model that tells you the probability of some state given your data. So given some data A, what's the probability that you're in some state in your model? So every time you see this PSD, that's the probability of a state given some data. Now you have your state and you have some model that can time-evolve it and tell you what's going to happen at some later time. And then you have this mathematical state, but you have to map it back on the reality. And so now you need some other distribution, the probability that gives you some data based on your state. So now these are two different objects. And now you can combine all these and figure out if these probabilities are well-defined, This is basically what we do. We say, well, we know our initial state, so now, we know some data, so now we know how some mathematical state we're in, our distribution of states, we time of all those states, and then from that result, we figure out what's likely to happen. And pretty much every model in physics you can point to, with the exception of a couple of these time-neutral ones, work this way. Now, is this a time-neutral way of doing things? Well, it depends whether there's an is symmetry between PSD and PDS because if you flip this around, right, going from B to A, now you do PSD first and then PDS over here. And so the question is, is there an is symmetry between these two methods? For quantum mechanics, there is not an is symmetry. When you do state preparation, if you do a complete measurement, you assume you know the state. You assume there's no probability distribution, right? You can do a complete measurement on your state. I know. So these numbers are not fractions. They're either one or zero. There's one state that's picked up by your initial measurement.

10:00 Then use the Schrodinger equation, time evolved it, and then use the Born rule to figure out what is likely to emerge. And this is a probabilistic rule, this is not always one or two. You break the symmetry here, so quantum mechanics is actually not time symmetric as they are. But it's still possible to have models like this that are time symmetric. For example, what if I just had a bunch of paths between these two states? Remember, I had a weight of 2 between A and Y before, so I put two paths there, and a weight of 2 between A and Z, so I put two paths. I can come up with a time neutral model. What if I just said, well, here's my map. One path is taken, and all allowed paths are equally likely. This is a time symmetric SPP model, right? What I do, I say, well, say I'm in state A. All these paths are equally likely. I've got 25% in each one. And then I figure out that, well, 50% of the time, the middle line is only the other. Or, you know, down here, you recover the old results. And, basically, you're mapping onto the state, you're time-evolving the state, and then mapping back using a nice symmetrical map. So here's an example of a time-neutral model that fits in this way. Another example is just crossing the field. However, let's do a little reality check here, because you can actually do this. You can actually construct a state where you think you know it as well as you can, and yet it can still go through multiple slips, and you can arrange it so that all these, for simplicity, let's get rid of interference, say all these paths have equal lengths, and ask yourself, well what really happens? And you can change the number of paths and confirm that this is what really happens. And what really happens is that the weight turns out not to be just the number of paths. It turns out to be the square of the number of paths. The amplitude turns out to be the number of paths. But then you have to square the amplitude to find out the probability. And so look what happens now. If you square the number of paths, instead of having 2, 2, and 3 here, you now have 4, 4, and 9, and you get totally different probability distribution. Actually, you don't get a different one for A, because both of these are still . So if you know A, it's still 50%. But now, if you know it started in B, 10% of the time you find out experimentally, you wind up in state Y, and 90% of the time you wind up in Y.

12:30 And again, because this is a time-neutral model, you can reverse it and figure out, given state Z here, 9 and 4, you can figure out the problem. Now, the question is, can you match what we know from physics? Which is this, to a time neutral SPP model. And I think the answer is no. Let's see if we can do this in an SPP model. What we need are these probability distributions. Now, so I know my initial state is B. I've got to map my initial data is B. I've got to map myself onto this state. Well, how do I do it? Well, to get this answer, 10% of the time I've got to go here, 90% of the time I've got to go here. All of these things seem like there's any obvious way to do it, especially given, remember this is all in the future, an experimenter could do a delayed choice experiment and switch one of these paths up here and whatever scheme you came up with to try to get these numbers, some devious experimenter in the middle here could mess up your system and give you the wrong result. The only way that you can really interpret this in an SPP framework is the all possible paths picture, where what you say is Okay, my map is that you take all possible paths, and then you get down here, and now you have your paths split up, and then you have some sort of collapse based on the square of the weights. And that, of course, is going to break the time symmetry. As soon as you have this collapse, there's no uncollapse, because if you go from B to Z via this, take all possible paths and then collapse, If you believe in the real collapse. And then you go back from Z to B, now you get a different picture, right? My criteria for a time-neutral model was that if you go forward and backward, you should have the same interior picture in the middle, and you wouldn't have that. You would start with Z, you would take all possible paths backwards, and then collapse over here, and you would have a different picture. So the argument is you can't fit what we know about physics with a time-neutral model if you try to use this SPP picture. You can do it by either breaking time symmetry or giving up on what we know about physics and just say, well, I don't know this. Or you can drop to the weight matrix.

15:00 Okay, so I'm arguing that SPP, this classical way that we do physics, is just not going to work. How can it not work? These things are all measurable, after all. And if both of these exist, it should work. The question is, do they exist? The first point I want to make is that they're not measurable because S, which is in both of them, is a mathematical state. The experimenter can't go in and find out what S is. All the experimenter can do is find out what the data is on the other side. So independently, you can't go through and prove that this is a well-defined thing or this is a well-defined thing. You can only bundle it all together and show that the experimenter can show this is well-defined. Okay, well, now we're not asking physics questions anymore because it's not measurable. Now we're asking philosophical questions. And I don't know if there's philosophical literature on whether or not these things exist. Thinking about it, it seems like there's some pretty darn good arguments of why this better exist, or else it's probably not a very good model. If your state doesn't tell you what the likelihood of your outcomes are, then what good is this model in the first place? You might be giving up on all sorts of fundamental things like reality. I won't try to go into since I'm not a philosopher. But it seems to me that they're pretty darn good arguments that this better exists. So the question now is... Does this thing have to exist? Is it true that from your initial data, it's possible to get enough initial data to have a well-defined probability distribution on some mathematical state? Now, Chris Fuchs was telling me about one interpretation of probability that's all based on betting, a Dutch book. And suppose you went to a bookie and said, I want to bet that this outcome mathematical state happens from this data. He wouldn't take the bet. Because he can't measure that state, all he can measure is B naught. There's no, just looking at this alone, there's no outcome that you can determine. Now, but it seems like that should exist, right? We're used to saying, well, I measure everything in the state, all this data, I know everything, so I should know what the state is. Well, why couldn't that be? Well, what if there are hidden variables? If they're hidden variables now, you don't know all the information, but of course you argue, well, I could know all the information, you just don't happen to know. So let's drop back to unknown hidden variables that are fundamentally unknown. Epistemically restricted hidden variables.

17:30 Something about the system that just, there's no way to know. If there's no way to know enough information, then maybe that probability distribution may not have to exist. And that's something I definitely want. Regardless, I want to make the argument that the way to get these probabilities out is this way, through the weights, not through, not through encoding it in the, in the. I think this is clearly more consistent with known physics. Any time you do a path integral, you automatically get this weight. You put it in the initial state, the final state, you do the path integral. Even in quantum field theory, you do this. In fact, that's all you get in quantum field theory. All you get in quantum field theory are these scattering amplitudes that are basically these weights. You're not getting these things. Remember, this is the Born Rule here, so you're not getting the Born Rule, you're getting these scattering amplitudes. Also notice that when you set out to derive Bell's theorem, basically what Bell's theorem starts with is assuming this exists. You assume that there are hidden variables with a well-defined probability distribution given data in the past, right? Basically, the existence of this term is the start of Bell's theorem. And so if this thing isn't even well-defined in the first place, and that's why this procedure fails, now you almost expect to get violations of Bell's theorem, and I'll show you. Okay, so if I'm right about this and weights are the way to go, any time-neutral model should definitely use these weights or joint probability distributions. That should be the output of the model, not the Born Rule or any other state-based probability. You should be able to effectively derive the Born Rule from it. It shouldn't be a fundamental part of the model. Because you can't do this, the FPP framework fails for quantum systems. And the fact that Bell's theorem is violated. I think that all indications are pointing to this thing just not being a well-defined probabilities. So what does this imply? As I argued, the only way I can think of that this isn't well-defined is if there are fundamentally incomplete initial data. So I think that the type of models we should look at are not only time neutral for other reasons, but models that are epistemically restricted in variables.

20:00 Something that is in the system that you cannot know. Now, does this mean you have to give up on realism? Well, no. You can still end up with a real intermediate state, even from a weight picture, but only for both the initial and final data. You can only retrodict reality. You can't predict reality. So, as long as you're okay with the reality in between these two measurements, which can't be measured because it's between the measurements, depending on the next measurement, as Rod argued must be the case, or could be the case, You can still recover a realistic picture. Okay, let's see if we can get through some of these applications. I don't know how much time we might use. Those of you who aren't familiar with this toy theory should all go check out this page. Basically, the starting point is the following axiom. Basically, it says even if you know everything, you still have equal amount of information that you don't know that you know. So you can know at most half of the information. Those of you familiar with the ontic states in this model, the simplest system comes in these four possible states. I'm not going to use this notation. I'm going to use this notation because it's a two-bit system. Basically, given a generic system where these are Boolean variables, this axiom says you can either know x or you can know y, but you can't know both. I can pre-measure them, right? One of the two bits here, as long as I don't know the other one, as long as I don't know x, I can measure, say, w is 0. And this one down here, I can measure one of the two bits, say, I'll measure z is 1. And so we have two hidden variables. These are epistemically restricted hidden variables. Now I'm going to take these two systems and throw them into a black box with yet another hidden variable. If you want, this might be a third state coming in that is causing this hidden variable. But this can also be 0, 1. And these two states emerge unchanged. And the question is, where do they emerge? And it depends on this third hidden variable. If v is zero, then the top one comes out the top and the bottom one comes out the bottom. But if v is one, it's the other way around.

22:30 And you don't know which it's going to be because v is epistemically restricted. But there's a similar rationale I want to look at. So one of these two outcomes are going to occur. You just don't know which one. So you can see right away that there are eight ontic states in the system. We don't know x, we don't know y, we don't know v, so there are eight. So you can go through and work out, and you know w is zero, and you know z is one, but these three, w, y, and z, you get three possibilities, and you plug, you can do this on a napkin, it's very simple. You figure out what comes out of the top hole and what comes out of the bottom hole in each of the object states. Okay, now, if you are going to go for the SPP style approach, the state-based probability, you want the probability to be encoded in each of these states. So right from the start, you need to be able to say, well, this state has, say, 12.5% probability, and that state has 12.5% probability, or any distribution you want. Any distribution you want, you can say, you know, this one, and whatever, and if you do that, you get, well... And you get interesting results in the sense that you recover almost all of quantum mechanics, but you don't get Bell-type violation. You don't get any weird Bell-local effects if you do it this way, and this is basically what Rob did. You see, you make a measurement of w is zero, and you have 50% chance that x is one, and 50% chance that x is zero. You don't know the other one, so you put a probability distribution on it right from the start. Well, what if we don't do that? What if we try weights instead? Using the path integral as inspiration, let's try weight like, let's set the weight equal to the number of consistent ontic states, squared. So that's the inspiration for why we might try this. Okay, so now, here are our two outputs again. This is the top output and the bottom output. And now I'm going to measure these outputs. Let's see what happens. Let's say I measure the first bit on the top, so I'm on the top, there's somebody on top. State that comes out the top, somebody measures the first bit, and somebody measures the first bit in the state that comes out the bottom. Now, there are four possible combinations, obviously, and you can just go through here. I'm not going to give you the time to do it, but you can do it on a napkin very easily. There are four of these that have zero in the first two cases. So that's the number of logic states, and if you square that, you get this result. But you might do a different measurement. Let's say the bottom measure. No, I don't want to measure the first bit. I want to measure the second bit.

25:00 Again, there are four cases. And now, if you look at it, the ontic states are distributed differently. Now, if you think that the probability is proportional to the number of ontic states, nothing weird happens. Everything looks fine. The probability you get a zero in the top measurement is 6 out of 8, or 75%. The probability you get a zero in the top measurement here is also 6 out of 8. Everything looks normal. And say these are the probabilities. Weird stuff results. The probability that the first bit is a zero in both of these cases is different. The probability that the first bit is a zero here is 20 twenty-fourths and here is 26 twenty-eighths. These are not the same. This implies that this other experimenter, by choosing to measure a different bit here, is going to change the probability distribution of what happens to the other experimenter. This is even weirder than what happened with quantum mechanics, but it just popped out just by trying a different type. So, as I mentioned, you don't get Bell-violating effects in these Beckham's toy theory with that SPB type. But all of a sudden now, I didn't change anything. All the interactions are local. All I did was change the rules that generate the probability. And presto, I have suddenly not only non-local correlations, I have non-local signaling. Now, this is too strong. I don't want to go all the way to 9-1-1 signaling, but it's cool all the same. Now, why? What did I do that allowed this to happen? If I didn't, the dynamics of this model were all local, I have local hidden variables, how can I suddenly have non-local signaling? And basically it's because if you're going to go back and figure out what ontic state you really had, you need to consider, well, what final measurement was really made? And so if you are a realist and you say, well, there was a montic state, which I am, I believe there was a montic state, then in order to figure out the probability of that state, you need a symmetric... Okay, so that, I think, is one application. If we apply a different kind of probability to this non-local model, or to this local model, we might be able to recover some of these missing features of quantum mechanics that don't quite come out of it.

27:30 The work I've been doing is the Klein-Gordon equation. I'll try not to wax on about this too much, but unlike, Ron said he wanted to make a minimal change to quantum mechanics. I have the opposite opinion. And I want to go all the way back, right to the beginning, and look and say, well, what do we know of pre-Schroding? And if you look and say, well, there are these waves and there's this correlation between the energy and the frequency and the momentum and the wave number, Schrodinger himself started by just saying, well, what wave-dispersion relation would correspond to our known relationship between energy, momentum, and mass? And he came up with the Klein-Gordon equation. This was the first thing that Schrodinger did. Now, this is a great equation. It's relatively covariant. You can even put it in curved space. It's a classical wave equation. And notice there are two time derivatives here, so it's nice and time symmetric. The solutions to it probably look familiar if you ignore half these terms. These terms look like solutions to the Schrodinger equation, except that you have the rest mass term in there, but other than that, that's just an overall phase. But now you have these other solutions, the so-called negative energy or negative frequency solution. So what did Schrodinger do? He effectively dropped half these terms. And saying, I want a first-order differential equation. And a lot of people think, well, it's just a non-relativistic limit. That is nonsense. There is no limit in which a second-order differential equation in time is going to give you a first-order differential equation. What he does is he literally drops half the solutions. The Klein-Gordon equation needs more initial data than the Schrodinger equation. To solve this equation, knowing the wave function is not enough, knowing this field is not enough, you also have to know the first-time derivative. So you can solve it. When you drop half the equations and you drop down to a first-order differential equation, I left the potential off here, not only do you have to pick a sign for i here, so you have to pick an asymmetry in the time, but you need fewer initial conditions to solve this thing, right? If you know psi, you plug it in here and you solve for psi. Here, you can't do that because psi is not... So, and then this propagates throughout the rest of quantum mechanics, the rest of quantum field theory. And when people try to go into general relativistic quantum field theory, this is a problem because we have these negative energy and positive energy solutions that have been picked out by this whole formalism, but you can't separate them out in curved space time. In one reference frame they look like positive energy and in another reference frame they look like negative energy. So this is actually a problem for quantum mechanics.

30:00 So, the story here is that, the summary here is that the Klein-Gordon equation has twice the three parameters of the Schrodinger equation solution. Can we get those extra parameters? Well, experimenters, experiments seem to imply no. Because if we could, we would have more information than classical quantum mechanics would tell us, standard quantum mechanics would tell us. We can't seem to make any better predictions. So, what if we say that we can't get any more information than what can be encoded by psi or, remember I said, just exactly half the information. Hopefully this looks familiar. So, therefore, if you start with a relativistic equation, out pops the axiomatic foundation of Speckens' y-model, where you only know half of the information in the system and the rest is epistemically restricted. It's epistemically restricted hidden variables in the form of this more complicated way of learning. So, my idea is that we can't solve it until we get the rest of the equations. Break time symmetry into the mix as well, and make everything time symmetric, put a final boundary condition as well as an initial boundary condition, and now we have the missing information to go back and retrodate. Basically what I'm talking about is you have to put a boundary condition, which is a mathematical thing of course. It has to correspond somehow to an external physical constraint of a measurement. And so you can use the ordinary measurement theory if you like. So here is time going up. Here's t equals zero. Let's say I make an initial measurement here. I can't figure out the wave function because I would need, as I mentioned, more information than I can measure here on this field. But then, at some later time, I can make another measurement and impose a second boundary condition here, an overall space at t equals t naught, and now I actually do have enough information to go back and say what really happened. Even better, if this boundary condition corresponds to your measurement, say I make a position measurement on a CCD and it's this pixel here,

32:30 the solution here must conform to that boundary condition, right? That's what boundary conditions do. It takes the interior solution and they conform to that boundary, and so what would the wave do in here? It would converge onto that pixel. You now could have a wave ontology where you naturally could get what looks like a collapse, although it's actually not discontinuous. It's a continuous effect. So the question is, can you recover ordinary probabilities from it? And I recently showed you can, with a couple caveats. You put an initial bound to condition here, a final bound to condition here. This is a, basically this goes out to infinity, where the weight function is zero. And so you can have this closed boundary. In more general, I'll talk about closed bound. Second, you put a hypersurface boundary condition, a single hypersurface boundary condition in time and space, and this thing has some unit normal here that is well defined by the boundary. Then, it turns out, you can write this in a generally coherent way, if you find this parameter w here, which is basically just feel along, you do an integral all over this closed boundary. Of the field times the normal derivative of the field, complex conjugate, you take the imaginary part of that, and then you see, well, how much does w vary, how many possible values of w are there, given all of my constraints, and then square that number of paths, or number of possibilities, I'm getting the right probability weight that matches up with standard quantum mechanics with, if you're interested in the details... There are a couple of caveats here. One is that this only works in the non-relativistic limit, which is OK. That's all I'm preparing it to. There's an additional restriction that the math only works out if there's an additional time, energy, uncertainty restriction that happens to be the same as the time, energy, uncertainty principle. And I've also only done it for zero potential, the non-zero potential. But that is the result. And of course, this is the probability weight that I'm matching up with. I've stopped in eight minutes. Well, let me just mention that probability doesn't make sense much when you try to think about the whole universe. For example, it's the probability of what? The probability of measurement.

35:00 Well, now when you're talking about external measurement, what does that even mean for the universe as a whole? And basically, the picture here, I got to do this perspective. Here's our overall perspective on measurement. You have a preparation. This is time and space. You have a preparation that's sort of like a boundary, that is a boundary condition. It's treated like a boundary condition. And then, as time evolution goes, we have other boundary conditions. We have spatial boundary conditions on our system that are imposed differently from the measurement and differently from the preparation. You impose that on the time evolution of the equation. And then, at the end, you have a measurement which is effectively no boundary at all, and then you collapse and see what happens. I'm arguing that from a space-time perspective, it's far more natural to treat this as a single measurement with an external device, external to your system in time and space, making these measurements, or if you like, spatial boundary conditions, or if you like, preparations. But it's all basically the same thing. All together, the boundary will tell you the wave function of the universe, not just the initial condition. You need to know the whole thing. And from that, you can generate the probability weight and determine which universes are more likely than others, basically, if you have the right field equations. And so that is sort of what I'm calling block universe quantum cosmology, where you can make sense of quantum mechanics even in this. Why do you want your state to encode all possible outcomes that don't even happen? Why not just have a state that encodes the outcome that really happens?

37:30 I guess I was going to ask Rob the question, why do you want a continuity equation if you can't even measure what's going on there? There's no reason to have a continuity equation. There's no reason to put constraints on the system that must make sense if something else happens, if that something else never happens. So I think you get a simpler picture by having it depend. But you can consider any one experiment. Any one experiment. That's the lesson from the toy model. Different experiments give different probability distributions. And were those distributions encoded in the state? No. They were encoded in the solution space to the state.

40:00 So they were encoded in the solution space, not in the state itself. The probabilities come out of how many solutions are possible rather than being in the state itself. And then there's the interpretation. And the interpretation most people use is this one where it takes all possible paths and then there's some reduction. Now, that's one interpretation of the math. The same math, the exact same math, can be used in a weight picture instead. That same math, instead of being assigned to a picture of what happens, you assign that the prime of half integral spits out, you find the amplitude, you square it, and it spits out a number. That's the weight. So, now this is a discrete example. But you can do the same thing. You can have two different interpretations. Does it take all possible paths, or does it take all paths that go to that particular result, or does it take one of the paths that go to that particular result? You can't think of those last two in the previous formulas, but in this case you can. You can imagine that it took just one path, and the weight of that path was determined by this procedure. So let's go to this the way I would have calculated it.

42:30 Because it's the same here, it's all the same length. These are assuming all of these are the same. There's no interference here, but you could do the same for interference. I read Feynman's QE. He tried to boil it down to the simplest. You could derive a lot of karma just from basically counting how many paths. In reality, you don't do that. You're right. You have to go to the computer. But you're right. You have to do it. But if you do it this way, you don't need to take the all possible paths interpretation of the math. The math has a different interpretation. Could be viewed as, I want to mention this, this idea is sort of current in the research. Oh, Ockel, the Bose Boundary. Yeah, well, here, I saw that. My book will probably be. Thanks for letting me know. We come back at 3 o'clock. Yeah.

45:00 This is awesome. Thanks for giving me a probability of one-third. We're coming to the time. See, if it were zero, I would never have a chance of updating to probability one. But with one-third, there is some chance that I have to conditionalize it. The posterior will be what? Thank you.