Sean Carroll - Locating Yourself in a Large Universe

right there we are very pleased to have Sean Carroll from Caltech the water used in both numerical physics sorry this is a water h2o from the Walter Berkeley what if institute there yes and if working on the reco cosmology and the emergence of space like this today's talk is locating yourself in large universe thank you thanks Eddie thanks for having me over here two days ago I was at Columbia at a workshop organized by Justin Clark Duane about mathematics and morality I feel I started like I didn't give a presentation but you know chaired a session I started by saying you know I am I do not produce any mathematics or any morality but I do consume but I use that most every day right so I feel the same way and talk about the foundations of probability so I'm not going to pretend that I'm an expert in any sense on the foundations of probability but I use probability I've been forced to think about those foundations in my physics research and so I'm hoping that the talk will be at least as educational probably much more educational for me than for you I'll talk about some some foundational issues and and you folks can help me figure out how I should be thinking about them so this this specific issue is there are large universes that we contemplate as physicists and cosmologists where large has a very specific meaning not just very large which the universe undoubtedly is but you can imagine universes that are large enough that any local condition like you or this room or the existence of an intelligent observer happens many many many times so some of these the sort of the most famous example is the cosmological multiverse if you believe in inflationary cosmology it's very easy to make many many regions of space where conditions could be very similar or very different perhaps an infinite number of them and then you want to know the question the answer to the question where am I in that multiverse there's also the idea of Boltzmann brains in a randomly fluctuating universe if you just have a box of gas that randomly fluctuates what's inside and last forever that gas will come into every allowed configuration an infinite number of times and the universe can be like that so observers can pop into existence and we'll talk about that in some detail but just so you don't think it's completely speculative the same thing happens if you're just in a open universe that is to say a universe that is either spatially flat or negatively curved cosmologically that goes on forever while remaining more or less homogeneous so we live in universe where there is a horizon we can only see so far but between us and the horizon it looks quite smooth on large scales there are fluctuations on large scales but they're relatively small and so if the universe is infinitely big and has these small fluctuations everywhere then any particular configuration of stuff is going to occur an infinite number of times somewhere in the universe you don't need inflation or quantum fluctuations to make this happen so in these circumstances you want to know like how do I reason probabilistically about my place in such a large universe so there's two questions one I'm gonna claim I have an answer to and what I'm not so here's what we typically do we say well there's many observers don't ask you what an observer is that's a perfectly good question deserving of its own talk that I'm not going to give but imagine we've agreed on what an observer is and imagine we've partitioned the set of all possible observers into different groups so you might say like groups of DNA based observers and alternative biology based observers carbon based observers and silicon based observers observers on earth and observers not on earth whatever you want there's different ways of doing the partitioning and let's label our or by depending on how narrow you want to be subset you want okay so you can't stop me from doing that and here are the two questions one question is can we assign a probability to having been in u1 we know that we are in u1 by construction can we assign a probability to having been in that group and from that and the fact that we are in u1 draw conclusions about the nature of the universe beyond which what we can see now I phrased it both carefully and awkwardly because I think it's an awkward question to ask but it's one that is very very frequently asked this is basically the idea of can we think about the entropic principle can we imagine there are many many places in the universe with different observers different conditions and can we reason something along lines of saying well in this ensemble it would have been likely that we would see this thing we don't see that thing therefore we probably don't live in that ensemble is that a valid question to ask I don't know I used to think that I knew but my confidence is deteriorate over time so I think this is an interesting question I'm going to highlight but not answer there's a simpler question I think we can answer which is that given that we're in u1 given that we're in whatever group that we've decided to highlight can we assign probabilities within that group and can we draw conclusions from that so it it might be and in fact I will consider the case where the group u1 is as narrow as observers that have exactly my macroscopic configuration right now so by that I mean observers who are standing in rooms wearing these clothes with my mental state seeing people like you observers like that there could be a fair number of them in the large universe can I draw conclusions on the basis of some probability distribution so those are the questions let's start with the question I don't know the answer to number one here's what we should accept everyone except bayes's theorem it's a theorem right of course we can talk about what it means and there there are interpretational issues that get in there so I presume in a seminar called the foundations of probability you've seen bayes's theorem before I presume I haven't had a typo when I typed it but it's a way to draw conclusions about the probability two different theories being true given some new data that you got in terms of the likelihood function and the prior probabilities for those theories so this should apply to cosmology and the question is in this large universe context it seems that we could imagine the meaning of the likelihood function the probability of the data given the theory in different ways it could be given that so given that we are observers at all what is the probability because so if the data is the data that we have about us right we're observers we live on a planet we breathe air we're made of carbon etc is the probability of that data giving different cosmological models the probability that we would have ended up being the observers that we are in among all the observers we could possibly be or is it the probability that there exists observers like me that I see so one example that I gave in earlier talks but none this one but maybe it's clarifying given that this is not very clear I think imagine that the universe was a string of bits zeros and ones in some way right and there's two possible theories of the string of bits one is that the string of bits is 0 0 0 0 and it's nothing with zeroes the other cosmological model is the string of bits is randomly chosen ones and zeroes 1 0 1 1 1 0 0 1 1 etc right you wake up and you look around then you're an observer in this toy model of the universe and you see the to your left and to your right there's nothing with zeroes for 5000 direction so there's 101 zeroes in a row does that observation count as evidence against the theory that the zeros and ones are just randomly selected because in both cosmological models there would exist with probability 1 some string of 101 or any number of zeroes in a row so the fact that you're that observer should that give you new information or not that's the question it seems intuitively like that should count as evidence right against the idea that they're just random but it turns out to be a little bit more subtle than that so in particular there's many different applications of that question I'm going to focus in on this Boltzmann brain problem this is a particular case where we're going to really do exactly as I suggested focus in on the class of observers who are observers who have exactly my macroscopic data so this comes from cosmology I think that every foundations of philosophy probability talk should have data in it so these are data that this is the data from the supernova cosmology project and Heisey supernova team that taught us in 1998 that the universe is not only expanding but accelerating a fact that we attribute most likely although we're not completely sure - vacuum energy this is an artist's impression of vacuum energy this is just if you take a little cubic centimeter of space and you empty it out so it's completely empty and you ask yourself how much energy is contained in this completely empty cubic centimeter of space according to Albert Einstein the answer is not zero necessarily the answer is some constant of nature the inherent energy of the vacuum the vacuum energy and these data indicate that the answer isn't zero the answer is ten to the minus eight herbs per cubic centimeter and the action of this vacuum energy is to push galaxies apart that's what we seem to be observing in the data and the nice thing about this well nice or not the simplest model line Stein's cosmological constant implies that the vacuum energy is strictly constant it does not dilute away as the universe expands so not only is the vacuum energy making the university accelerate in the simplest model not necessarily the only possible model but in the simplest model it will do so forever the universe will continue to expand and accelerate for infinity years toward the future that's not necessary but it's a completely plausible straightforward cosmological model and there's various consequences of that in the 1970s Stephen Hawking taught us that if you have a black hole if you take into account quantum field theory around the black hole the black hole isn't completely black the horizon seems to be giving off blackbody radiation at a certain temperature in an accelerating universe which approaches a spacetime metric called de sitter space when it's empty except for this vacuum energy there's a cosmological horizon around us so rather than looking at the black hole horizon from outside we're looking at the cosmological horizon from the inside but the same phenomenon holds true there's radiation and it has a temperature and the temperature turns out for our real world universe we've about 10 to the minus 30 Kelvin remember that the actual cosmic microwave background radiation our universe today is about 2.7 Kelvin so this radiation is really really cold so we're not gonna ever see it but if the universe expands and empties out forever there's a feature called the cosmic no-hair theorem that in the universe with vacuum energy plus other stuff if the universe doesn't wreck elapsed the vacuum energy always wins in the end it pushes everything away smooths everything else out we will eventually be left with an empty universe that doesn't have a microwave background in anymore because every one of those microwave background photons in the current universe will be redshifted to a length scale larger than our horizon science and this will be what is left in the universe this thermal radiation that a thermometer would detect so there's a subtlety here they'll get to in a second but at but before we get to the subtlety let's just take this picture at face value so if you look if you have a particle detector outside a black hole you see a thermal spectrum of radiation coming out if you have a particle detector in an otherwise empty accelerating universe you see a thermal spectrum of radiation coming at you from all directions that has implications for the future of the universe you might think that if it cosmic no-hair theorem is true the universe just empties out and there's no more observer so we don't have to worry about them but look big Boltzmann figured out a long time ago that if you live in a universe which has random fluctuations usually it's in thermal equilibrium usually the entropy as a function of time which is this a toy model in the top box over here it's usually stuck at its maximum value that's why there seems to be an upper limit here this is the maximum entropy you can have in a box of gas but it will occasionally fluctuate downward right there's a standard undergraduate statistical mechanics calculation given the air in this room how long will you have to wait for all the air to fluctuate onto one side of the room the answer is very very long but in this picture you have infinity years to wait so Boltzmann pointed out that sorry he didn't he pointed what he pointed out strictly speaking was that if you waited long enough from the background thermal equilibrium in an eternal universe you would fluctuate something like what he called our world which by which he meant the Milky Way galaxy that's what they knew about they knew about a part of the Milky Way galaxy he didn't know about the whole galaxy in it everything other galaxies but there is a rate for these fluctuations there were fluctuations downward and entropy but very naturally small fluctuations are much more probable much more frequent than large fluctuations exponentially suppressed it will be the larger fluctuations so if you wait long enough in an eternal universe you're in an empty universe with radiation coming at you from the cosmological horizon it's not predictable when it comes it's it's quantum fluctuations in the truest sense so you can't predict exactly what will happen sometimes a slightly more energetic than average photon will come hit your detector sometimes a whole bunch of energetic photons will just by chance hit your detector at the same time sometimes enough energetic photons will hit your detector to create some matter and anti-matter right in reverse in pair production kind of things this might lead to all sorts of different things popping randomly into existence and you can run the numbers it's very unlikely but you can make a galaxy or a solar system where the whole universe if you're willing to wait long enough just out of these random fluctuations so you can ask yourself and you yeah you can ask yourself Boltzmann himself said maybe that's our universe he said maybe we come from a low entropy past because we live in a universe that's mostly in thermal equilibrium but if you wait long enough that will occasionally fluctuate downward to low entropy and then we're in the portion where it's relaxing backward point-x on that graph the problem with this was pointed out by Eddington a few decades later he says look you have a knowledge of how frequent these fluctuations are they're much more frequent when there's small fluctuations than when they're large fluctuations so the game you should play is you tell me what kind of fluctuation you want to wait for do you want to wait for a fluctuation into a galaxy or do you just want to wait for a fluctuation in to an observer right Eddington picked mathematical physicists as the thing you should wait for and he said if you want to wait until it's a fluctuation into a mathematical physicist then what you will see is a fluctuation that creates that mathematical physicist and nothing else the rest of the universe will still be in thermal equilibrium because that's the smallest possible fluctuation that would make that physicist albrecht and Sorbo more recently pointed out if you're doing the anthropic principle then you don't really need a mathematical physicist in fact you only need a whole person you just need a brain eat enough particles to assemble themselves into the form of a central nervous system that has the capabilities for looking around going hot thermal equilibrium and then it will die and this is called a Boltzmann brain and this is the minimal thing you could possibly make from random fluctuations that would qualify as a conscious intelligent observer if you personally have stronger conditions on what it means to be intelligent conscious observer then that's fine the point is you will satisfy those most frequently by waiting for the smallest possible fluctuation into them so that's a problem if you think that we live in this universe that is expanding and accelerating at face value it says that we live in the universe which toward the future will be eternal and will be thermal will be undergoing fluctuations randomly two different configurations so there'll be an infinite number of Boltzmann brains in our future there will also be recurrences of our universe in the future but the total number of observers will be by far dominated by these Boltzmann brains because they're the easiest ones to make that doesn't seem to be the universe we live in that's the usual problem so I'm going to talk about that problem but is everyone get the scenario the idea that Boltzmann brains fluctuate randomly into existence note that I didn't predict this on the basis of string theory or eternal inflation or anything like that this is the theory that we think correctly describes the actual world based on data right the theory that cosmologists call lambda-cdm cause module constant lambda and CBM called arc seems to predict this yeah well that's what we're here to discuss I will discuss exactly that yes that's right we don't seem to be Boltzmann brains let's put it that way but we'll discuss it okay okay yep yeah well well that's exactly why we're here to discuss that yes good here's there's a footnote that that I would say makes the Boltzmann brain problem in the real world considerably less pressing than it would otherwise be I tried to be precise but I'm not sure whether I was talking about these fluctuations into Boltzmann brains in a cosmological horizon there's a bit of a sloppiness here because in these cosmological settings quantum mechanics you need to be little bit more careful about your quantum mechanics than you would if you're in a laboratory with a Geiger counter okay I made statements about what a detector would observe in the sitter space with a horizon around it with a certain temperature but guess what there aren't any detectors doing any observing in de sitter space it's empty okay so what you actually evolve toward is a thermal state and there is a difference in quantum mechanics with thermal States versus classical mechanics classically when you have a thermal state of the gas in this room the thermal the thermal miss says that there is a temperature probability a probability distribution for the positions and velocities of the air molecules that depends on the temperature but there's also a microstate the macro state of air which is just constant density and a certain fixed temperature is static it's not changing over time but that's just because there's a microstate that is changing without affecting the macroscopic properties quantum mechanically a thermal state is a density operator that is a superposition of stationary energy eigenstates the individual microstates of which the thermal State is made don't themselves evolve with time and therefore if you don't have a detector there there isn't anything fluctuating in a thermal state in quantum mechanics there isn't anything changing over time when I speak all these words I you know I'd betray my Eveready and prejudices so if you have a different favorite interpretation of quantum mechanics you can reanalyze this issue but the point is this is an image of the wavefunction of an electron in a helium atom so in a certain energy eigenstate the point is that if you're never ready and this is what's real there's not really an electron fluctuating around in different parts of the way of the atom there's really a wavefunction and it's not changing at all so it's not fluctuating at all so there's no sense dynamically in an ever Eddy inversion of the universe where things fluctuate dynamically into existence even in de sitter space even with a cosmological horizon if it's true that dynamically you approach this thermal state yes yes Center fluctuation here it might not be quantum fluctuations but it could still be a thermal fluctuations of Hungary occurrence time so can prove a seminar by reversibility argument see what kind of you can't you can't because it's not a closed system and the recurrence theorem doesn't applying it is an open system without assuming it this is a real cosmology that we're doing things leave the horizon it is the expanding yeah that's right the horizon is a fixed-size physical particles and excitation x' leave it so this in in well yeah I will tell you the the point the point is that if the vacuum energy persist eternally end Hilbert space is finite dimensional the hilbert space of the whole of reality then there's a recurrence theorem then you really will get these fluctuations into Boltzmann brains etc but in quantum field theory or in the simplest extrapolation that you would have from inside our what what happens inside our horizon is described by a finite dimensional part of Hilbert space but what happened outside our horizon may or may not be so the claim is that if the outs if the rest of universe outside our observable horizon is described by an infinite dimensional hilbert space then we are described by a dissipative dynamics what happens inside our horizon does indeed settle down to a thermal state which is actually stationary and actually stays there recurrence theorems be damned so I don't know whether the hilbert space of the theory of everything is finite dimensional or infinite dimensional if it's infinite dimensional you get rid of the Boltzmann brains if it's finite dimensional they're still there that's right yeah and you would certainly the the existence of the detector would by construction say you were not in the thermal state right so in a true thermal state you would be stationary you will get to a thermal state if you have an infinite bath around you you would not get to it if there's only a finite dimensional over space for the whole world just to make sure so suppose I start them to zero the evolving if you're in a closed system you will not evolve into a thermal State ft if you don't start with one because thermal states are stationary just like you will never evolve into an energy eigenstate if you don't start in one you start yeah okay so this is all just a footnote to say that maybe we can get out of Boltzmann brain problem in the real world but maybe we don't so we should figure out what to do if we land ourselves in it ah know what to say okay so here's to fix our ideas here are two cosmological models a and B to simplify our lives a has no Boltzmann brains we just have ordinary observers I picked quasi randomly some large number of ordinary observers the point is that if you live in a universe with Boltzmann brains very typically the number of Boltzmann brains is enormous ly larger so the chance that there are some interesting competition between the number of ordinary observers and the number of Boltzmann brains is very very very low in the space of all possible cosmological models either you generally don't have them at all or you generally completely dominate Boltzmann brains okay so these are two very typical models a has no Boltzmann brains just ordinary observers B has the same number of ordinary observers and a huge number exponentially exponential of Boltzmann brains so the question is as we were getting to can we rule out cosmological model B on the basis of empirical information we look around and go in B there's a lot more Boltzmann brains I should probably be a Boltzmann brain I'm not and therefore we should rule that out this is a very common argument that is made by working cosmologists not all of them agree with it but it's an argument ok so here is what I would call the standard argument this is just a slight formalization of that argue of those words I just said remember what a and B are a is no Boltzmann brains B is with Boltzmann brains the standard argument says we look at bayes's theorem and with a probability that we're trying to figure out are we in theory a or Theory B so we calculate the likelihood function what are the probability of getting our data given the theory and the standard argument says the data is I'm not a Boltzmann brain I'm a person giving a talk I remember the past it's reliable etc I did not just fluctuate into existence you're all here etc and there's a probability that that was going to be true it's roughly speaking the number of ordinary observers by this divided by the total number of observers which is one in theory a and infinitely tiny in theory B therefore it's almost irrelevant what the prior was if you have roughly comparable priors for theory a and theory be the fact that I wake up every morning and see that I'm not a Boltzmann brain is evidence the theory a is true in theory B is false ok that's the usual argument that as working cosmologists we should try to construct models which do not have Boltzmann brain domination and this idea that in each theory we should sort of give a uniform probability to being any observer may be in some reference class but you tell me with reference class you want to choose and why should be randomly chosen from with inside that class has been called the cosmological Copernican principle principle of mediocrity typicality self sampling proportion and difference many people have suggested different things like this yes what the data is I wake up in another Boltzmann brain that's a good question yes I'm just giving you the standard argument that the scare quotes should let you know I do not believe the standard argument okay so that's that's what we need to think about a little bit yeah this is well this is what people say so this leads to problems here's one of the problems the presumptuous philosopher problem and there's many other people have worked on this and I think I have the ideas right I don't always have the labels of the ideas right so this is my version of the presumptuous philosopher problem I think boström coined the title I think presumptuous physicist is just as accurate but the point is that the kind of reasoning we're doing here is to say to imagine that we are typical elements of some big set and that is to say within that big set we should give a uniform probability to being any element of that set and if we do that and we notice we're not exactly sure what is going on in that set in this case the set is all intelligent observers in the universe we're not exactly sure what properties the set as entirety has then by the fact that we have certain characteristics we can conclude that that's a typical thing for an observer an element of this set to have the presumptuous philosopher problem is that gives us enormous leverage over the state of the universe far beyond what we're actually warranted to have on the basis of any either reasoning or evidence so the example given by Harland Fred Mickey is you know imagine there's no intelligent life in the universe other than here in the solar system and for some reason I have really good reason to believe that there's a 50% chance that floating in the atmosphere of Jupiter there is a hundred trillion intelligent gasbags you know floating in the atmosphere like Carl Sagan imagined a long time ago maybe they're there maybe they're not those are the two theories everything else is exactly the same about the universe cardolan trade Nicky point out that by this reasoning if I use that model of the universe I would predict that I was intelligent gasbag in the atmosphere of Jupiter I observe that I am NOT and therefore I rule out that model to very good confidence so I'm able to say something about the existence of intelligent gasbags in the atmosphere of Jupiter without ever looking at the atmosphere of Jupiter that seems wrong right and if you believe that that's wrong then there are similar arguments the Doomsday argument says that we are a typical person in the history of humanity right and so humanity's been around for a certain number of years it is unlikely that we are in the first 1% of the lifetime of humanity right and therefore we can conclude there's probably not going to be any human beings alive in the far future because then we would be a typical then we'll be finding ourselves living right in the beginning so we're predicting the end of humanity just on the basis of our existence now that's right that is the assumption that is exactly the assumption yes that is this typicality assumption that these guys want to call into question but it's the same assumption that is being given in this standard version of the Boltzmann brain argument so we were typical observers in the universe typical observers are Boltzmann brains we don't seem to be therefore we rule out their existence the the reason why this should worry you is that it when you say I'm going to assume I am a typical observer in the universe it sounds kind of self effacing right it sounds kind of humble I'm just a typical guy right but in fact what you're assuming is that a typical observer in the universe is like you that is not humble at all that is extremely arrogant that it's extremely presumptuous it's like I said giving you enormous leverage over the state of the universe far beyond when you had collected any data abound so that is the presumptuous philosopher problem should we be able to reason in this way that lets us draw a sweeping conclusions about the rest of the universe without leaving our armchairs I agree with this I agree that this is a problem I agree that that standard argument just on this basis there are other criticisms of it but I think that it is true that reasoning on the basis that we should be chosen from a uniform distribution over all intelligent observers and we can use features that we already know about our current existence as evidence against different cosmological models that sounds wrong that sounds a little bit too presumptuous so how to fix it what can we do instead what Harlan Chad Nikki say is that when you have a theory that has some kind of distribution of observers then your theory is not simply specified by the physical state of reality your theory is also specified by different xerographic distributions which is to say different probability distributions that you were chosen randomly or you were chosen from this distribution on all possible observers in the universe that is part of the specification of a theory in their mind and they say I can test different xerographic distributions that I update just using bayes's theorem on my xerographic distributions just as I update on my physical model of reality so they say for example they could choose the xerographic distribution that says I simply have no probability for being a Boltzmann brain and I'm uniformly chosen from the ordinary observers in the cosmology so if you're if you grant yourself this ability then the fact that there are many many Boltzmann brains is irrelevant because you have defined your theory to say there are many many Boltzmann brains but I'm not one of them therefore the fact that I wake up and see I'm not a Boltzmann brain tells me nothing about anything in other words they're saying that it's not that there aren't Boltzmann brains is that whether or not there are is irrelevant to me because I see that I'm not one ok I don't buy this either I'm just telling you that this is a strategy so here's why I don't buy this because this xerographic distribution that they're choosing is not based on anything about the kind of observer you see yourself to be but rather some God's eye view on where you find yourself in the universe in other words this serie graphic distribution discriminates not on the basis of who you are but of where you are in the four-dimensional universe so to make this a little bit more vivid forget about Boltzmann brains forget about little disembodied pieces of protoplasm that come together just long enough to notice that they are conscious and then go away consider this room right now okay consider yourself and what you see and the macroscopic features maybe not necessarily the microstate of every atom but the macroscopic features that we believe are more or less accurately describing this room so that means the existence of all of us what we are seeing also our mental states the fact that our neurons are wired in certain ways okay that is a certain class of observers observers like me who see you right now okay and there should be an infinite number of them an infinitely big universe but if I mean the Boltzmann fluctuating universe if I'm in this finite dimensional de sitter space etc etc the overwhelming number of appearances of people like me in this room are minimal fluctuations given those conditions so there is no reason for there to be something called New Jersey Transit outside there's no reason for there to be New York the overwhelmingly strong prediction of this theory is that I walk outside it should be thermal equilibrium okay now harder lunch Fred Niki so these this is what I call Boltzmann you right and again you can tweak the exact definitions of what class your conditional izing over but the point is that fluctuations is exactly like this giving us much more comfortable and reasonable observers than a disembodied brain are still nevertheless way more likely than ordinary observers so all your knowledge if you're a Boltzmann you then all of your knowledge about the outside world randomly fluctuated into your brain there's no reason for it to have any strong correlation with reality outside ok just randomly fluctuating to your brain so Hartlage for Nicky says sure they agree with the counting but they say I'm gonna give a xerographic distribution that simply rules that out I give zero probability to being one of those newse I think that is completely unfair and it to be honest I tried to make this into like a science II philosophical argument but it really just bothers me that's what that's the best argument I can give you it seems like cheating to me okay it seems like in the universe that had both ordinary observers and Boltzmann use all these fluctuations I mean the Boltzmann used you know they live they have feelings they talk about things they're you know they have some beliefs about the external world and if you put a zero graphic distribution in this cosmology that excluded by Fiat the idea that I could be any one of them then all of them would be wrong right that seems unfair it seems like it's it you shouldn't be it makes sense if I bought into the xerographic distribution idea it seemed like it should be okay for observers who see different things to count as different parts of the distribution to be given different weights but not observers that see exactly the same thing just because they do or do not have pasts that are thermodynamically sensible I don't see why we should discriminate against the Boltzmann use in fact I think that we can do better than that let us narrow our reference class that we're looking at to as we said observers who are macroscopically identical so I'm here in this room talking to you let me consider the set of observers exactly like me up to whatever macroscopic precision I'm able to perceive okay and again in a big universe there might be an infinite number of such people so can I make statements about which one of them I am so this is the well-known problem in philosophy I think it's pretty well known of self locating uncertainty or indexical uncertainty under a large class of observers so we really I mean it's not that this is a better question to think about than the broader anthropic question but it should be the easier question to think about if we can't solve the puzzle of how to reason about identical observers then there's no way we're gonna solve the puzzle of how to reason about different observers so how do we figure out which one of the identical observers we are cartilage for Nicky would say I can make up a distribution and I should just test that distribution against the data so here's different attitudes one is indifference that is to say if I truly have macroscopically indistinguishable observers I should just give equal probability to being any of them that's a simple obvious thing to do David Albert and probably many other people have said I should just not do reasoning in this situation I should just say I have no clue what the distribution is you can't really make even a prediction in this particular situation it's sort of just a game you play without any point to it to make probabilistic predictions in this situation Harlan Chad Niki would say that they want to put some they want to attribute a xerographic distribution as part of their theory I want to basically argue in favor of indifference but I don't want to argue it as an assumption I think we can do better than that I think we can derive indifference under certain circumstances and you may or may not agree with the axioms that it takes me to derive it but that'll be the strategy that I take all right so there is a work done on this Adam Elga I know if he ever comes to these seminars but he wrote this paper so this is a what I'm going to tell you for the next couple slides is work that I did with chipsy Saban's Backlund chip was a graduate student studying philosophy physics he spent a summer at Caltech talking with me and other people and as a philosopher of physics you know he was skeptical about the Everett interpretation of quantum mechanics and I said that's too bad because Everett is clearly correct and he said well there's a good reason to doubt it because you can't get the probability right and we argued about and eventually we came up with a new derivation of getting the probability right so it started here with chips argument he says there's this paper by Elega that says that if there are two copies of you in the universe and they're identical you should give equal probability to being either one of them that's indifference and elegant simply just you know he doesn't he's not laplacian about it he doesn't say well what else could it be he purports to give an argument based on fairly reasonable assumptions that derives this and if that's true you would raise a problem with Eveready in quantum mechanics so here is the many world interpretation of quantum mechanics forever reading for those of you who are not experts it's a very simple theory in every theory of quantum mechanics you have quantum states which are vectors in something called Hilbert space and in every theory in quantum mechanics those states evolve usually according to the Schrodinger equation there's some Hamiltonian which gives you the time derivative of the state ok other theories of quantum mechanics take that beautiful structure and mess with it they change the Schrodinger equation now and again or they add more variables or they deny the existence of an external reality or something like that ever it tries to say I don't need to add to that structure I can just believe that that's the world the world is a state vector evolving smoothly and deterministically according to Schrodinger's equation but what happens is here's an example this is a cat that is in a superposition of awake and asleep no reason to kill the cat I don't think so of course a real macroscopic cat would be interacting with environment and so forth so think of the cat as a stand-in for an electron and spin up and spin down okay cats cuter and here's an observer this is Hugh Everett before he actually probably after he got kicked out of physics for proposing the Everett interpretation and what happens according to Everett is that you just solved the Schrodinger equation here you start in an unentangled quantum state so the observer is in what's called the ready state hasn't yet looked at the cat the cat is in a superposition and the action of the Schrodinger equation is to say the observer looks at the cat and the wave function of the universe evolves the new superposition of the cat was awake in the observer saw the cat awake plus the cat was asleep and the observers hauled the cat was asleep and Everett's brilliant leap is more therapeutic than physical he says and that's okay he says you don't need to do anything more there are actually now two copies of you there was one person not two copies of you there are two people there's one person here it evolved smoothly into two people a person who has your memories in the past but now witnesses seeing in a way cat and a person who has your memories of the past but now witnesses seeing asleep cat as long as you're happy if you're this person you saw the cat asleep as long as you're willing to accept that there's somewhere else in reality a copy of you that's hold the cat away everything is fine and you match your experience for these different observers or at least you hope you do that's the not everyone agrees so here is a big problem here's a worry what if you read elgus paper and were convinced in this indifference principle if you were convinced that if you had a universe with different observers who are in locally identical States you should give them equal probability there's a rule in quantum mechanics the born rule that says that when I have a wavefunction I have these amplitudes outside the different parts of the quantum state and they add up the obey Pythagoras's theorem the sum of them is equal to 1 and each individual one has the feature that this number squared is the probability that I will end up observing that particular outcome when I do it so in this particular wave function if there's a 1 over root 3 outside the awake cat and that what square root of 2/3 outside the asleep cat before the measurement is made the observer would say I have a 1/3 probability of seeing the cat awake 2/3 seeing the cat asleep but an LJN would notice that these two observers are in identical local conditions they haven't looked at the cat yet the cats the observer and the cat are not yet entangled there's only one observer or if you like there are two observers but they haven't noticed yet which branch of the wave function they're on so if you bought elegans argument straightforwardly or naively you would say I would give a 50/50 chance to being either one of these two observers right that is not the born rule that's not what quantum mechanics predicts so this is what chip said seems to be a good objection to taking Everett seriously as a theory of the world well we eventually were able to do is to dig into elva's argument and notice that there was a hidden assumption wasn't very hidden but it wasn't you know underlined either and so rather than taking his conclusion at face value we took the assumption we generalized it to a case which included quantum mechanics and we found that when you took the Assumption seriously don't get indifference over different branches of the wavefunction in fact what you get is exactly the born rule for quantum probabilities so I'll show you that very quickly the assumption is something that we call the epistemic separable ax T principle or ESP which is not a principle of indifference the principle of indifference would say I have two things one of them is true one of them is not I can't tell which one they seem pretty similar I'll give them 50/50 credence okay the epistemic separable 'ti principle says something's going to happen there's a probability that different outcomes will happen I don't know what those probabilities are but whatever they are they don't depend on things going on elsewhere in the universe so it's a separable 'ti principle not an indifference principle I think it's a little bit more it seems to be assuming less but that's a in the eye of the observer yes yeah it does yeah that's right so I'll give you examples but yes they are yes it's an epistemic view of what the probabilities are that's right because it's self locating uncertainty yeah so here is the classical example of what we have in mind here are two observers locally identical in the world somewhere else so they're asking themselves which one of these mi they have different locations different indices somewhere else in the world something's going on there aliens somewhere else in the world okay so the ESP doesn't tell you what the probability being this or this does yet all it says is if there's another universe where there's also two identical people and they also want to know which one they probably are whatever answer these ones gave better be the same as these ones give even if the external environment is different even if there are mean aliens in the one universe and happy aliens and the other one okay that's what the ESP says the changing you know the color of the president's socks are changing the aliens out there shouldn't change what's your predictions are for the particular question you're asking about these identical observers again you're very this is an assumption it's not just automatic but it's a pretty straightforward simple assumption I think so we claim that algaas secretly yes oh sorry you were first what do you mean by identical whatever you want me to mean well you tell me what can mean identity then that statement is vacuum right you must be the same macroscopic situation same Mack like immediately nuttin knowable stuff about your situation so this thing yeah certainly distinct these are these are definitely different observers or in different parts of the universe right they don't know which part they're in but if they look around where they are and they ask people what they're thinking locally they get exactly the same answer that's right the little red disks are the same but the locations in the bigger universe are different yes this is a person this is you this is somebody else but you don't know whether you're this person or this person that's what you want to know by the time you saw them you would no longer be in identical local circumstances I mean you can go explore the universe and notice that there are aliens out there so this is not an eternal condition this is just for right now that's right you don't know yeah then you would know then that would be a difference between you and them so I think it'll make more sense you might be exactly alike yeah exactly but you might but there might be these two guys that's all there is they look at each other they look exactly alike mm-hmm so we just those circumstances the macroscopically exactly alike yeah that's that's that's true the three possibility that they're located in different places right but they might have to have any idea they don't well they would do is to say we're located different places might be true both that's right exactly so they would say the same things their conditions are identical that's I shouldn't I mean I think identical has is carrying connotations I don't want to have the same same local conditions stay with it and they would answer any questions you ask them right now with the same answer so I think this is this is sort of a cosmologist way of thinking about it let's just give you elgus way of thinking about it and maybe it will make more sense for some reason you can tell me why we're as cosmologists like to think about different people in the universe philosophers like to think about duplication and transportation machines right teleportation machines so here's Elvis thought experiment there's a person named owl you put out to sleep and you duplicate owl to make an exactly identical copy so there are now two people there is the original owl and there's a new person which we call dupe all right but they're in exactly the same state and you wake them up and you put them in rooms that look exactly the same so when you wake them up and you ask either one of them who do you think you are al was told before going to sleep that this is gonna happen so who do you think you are do you think you're the original owl or do you think your dupe and elegants to argue that the correct answer for both of them is I don't know as a 50/50 chance right that's what his argument is that's indifference what is the credence upon awakening that each would give to being owl or the duplicate so here's the argument the argument is it seems a little complicated but this is what it took to get there imagine you add to that experiment a coin toss okay so al is asleep well there's well he's asleep you toss an unfair coin that a 10% chance of coming up heads 90% chance to come up tails so then at the end of the day there's four possibilities you're a land the coin was heads you're the dupe and the coin was heads etc four tails right the claim which don't worry about I'm going to justify it in the next slide but the claim is that if someone said what is the probability that either you're the original owl and the coin was heads or you're the dupe and the coin was tails then the answer you should give is 10% no sorry I said that wrong sorry erase that if you are told you wake up and you're told either you are Al and the coin was heads or you're the dupe and coin is tails then what should you say the probability the coin being heads is okay I like I said is a little bit contrived but that's the question you're asked so you know for certainty you believe the person talking to you so you know that you're either this or this and you know there's a 10% chance of being heads and items and chance being tails you don't know whether you're a lord OOP so alga number one claims that the answer you should give to this question is ten percent and if the answer you give that is ten percent then you should give it a fifty-fifty credence there the first part is actually a little trickier than the second part so here's the first part imagine that for some reason for some cool reason you agreed that after you flip the coin if it were heads you would not wake up do you put him into a coma and he would stay dead forever and if it were tails you do the same thing to Al let's just assume that you agree that that was going to happen and let's assume that Al knew that was going to happen and the person wakes up Al were doop or whatever it is and then you're asked are you so you're asked about the coin do you think it was heads or do you think it was tails right so the problem the claim is the fact that they woke up didn't teach them anything about the coin whether the coin was going to be heads or tail they were gonna wake up someone was gonna wake up either our dupe right so when they wake up even if they know that these two conditions we're not going to wake up they learn nothing about the coin and therefore they should still give 10% chance to the coin being heads that's the secret tricky move if you believe that then you can easily get to I'm not gonna go through the steps but you can easily get to 50 50 needed to be the credence in the first place for being a lure being duped and it's a it's a subtle argument you have to go through it carefully because if you're willing to believe there is an answer obviously the answer is gonna have to be 50/50 right you were never gonna get it 75 percent 25 percent right so you might worry that it's too easy to trick yourself into thinking that you have the right answer when you land on some 5050 thing but I think that logically all it seems to hold together as far as I can tell the crucial step was assuming that the coin toss didn't change the probability of being either out or do fundamentally okay there was an independence or a separ ability between the self locating uncertainty of being al versus dupe and whatever the probability for the coin toss to come so that we claim is this is a manifestation or an example of this principle that we call the ESP that the environment doesn't matter in the environment the thing going on outside your local conditions right now is this coin toss and we claim it didn't matter right so if you so we are agreeing with Elga but we're pointing out that the assumption that he needed to make his claim is basically what we're calling the ESP and elegantly derive indifference under this particular thought experiment but rather than applying indifference to everybody in quantum mechanics let's apply ESP the separable 'ti principle to Eveready in quantum mechanics so number one we claim there is self locating uncertainty in Eveready in quantum mechanics so what happens is there's an apparatus you can tell me if you're not super duper experts on quantum mechanics and we go into more details about this but basically there's an apparatus that observes your quantum system and Tron or whatever and very quickly what happens is the wave function branches and the reason why it's very quickly is because this macroscopic apparatus interacts with the environment and this procedure this process called decoherence happens with an incredibly fast timescale and only later do you the observer actually see the outcome of the experiment and if you want to say well I'm going to try to imagine setting up an experiment where I see the outcome of the experiment before decoherence happens you literally cannot do that you can think of the apparatus as just being your eyeballs okay and your eyeballs will decohere on a timescale less than zero second which is much longer than any of the timescales associated with sending the signal to your brain and telling you what is going on so as a matter of down-to-earth nitty-gritty empirical fact it is always true that the wave function branches because of decoherence before you know what the outcome is and because that's the case it is inevitable that there will be self locating uncertainty so let's consider here's a wave function with an observer a quantum system an apparatus and an environment the whole rest of the universe so what happens just through the Schrodinger equation is the first thing is that the apparatus looks at the system and it becomes entangled with it that's measurement according to the rules of quantum mechanics but almost right away the apparatus which after all has a big pointer saying the cat was awake or the cat was asleep or the electron was spin-up or spin-down becomes entangled with the environment okay that's when the wave function branches that's decoherence that's very fast I'm just finish this and then we'll you can ask and the point is that just mathematically all these arrows are time evolution but this is when the branching happened when the environment becomes entangled with the apparatus that branching happens so I can distribute that poor observer on both branches of the wavefunction when there are two copies of that observer and they're identical and therefore that self locating uncertainty and only later does the observer actually read the apparatus go the spin was up or so forth so our claim is that this period of self locating uncertainty is absolutely generic and real realistic quantum measurements yeah yes it might it might I mean I'm certainly not claiming that it wouldn't let's put it that way it does but my very humble project is only explaining all of human experience not the experience of much quicker animals I can do that I claim some something good happen right okay all right so let's go through how am i doing who I'm not doing very well but you know philosophers get let me talk forever right okay all right give me another 15 minutes to follow them finish my slides and then we'll finish maybe even less than that I'm not sure I think we're nearing the end so here is how this plays out when you're gonna do it right okay so what we said is we have the self locating uncertainty we would like to assign grievances to being this on this branch or being that branch two identical observers is it just 50/50 or is it something more subtle so we decompose as we already sort of implicitly did hilbert space into an observer a system and environment and the statement of ESP is a separable 'ti principle in this quantum context is that when you take the environment and you act on it so you change the environment from one thing to something else whatever probabilities you assign to different being on different branches don't change okay so it's not an indifference principle yet it doesn't say two probabilities are equal to each other it's just saying the probabilities don't change if we only change the environment whatever those probabilities are for some observer measuring some outcome s so let's give an example in this simple case okay here are two different universes two different quantum states there's an observer and there's two different quantum systems which represented here by a cat and an alien okay so in psy one there's an observer an awake cat in a hungry alien an observer at a sleep cat and a friendly alien and the aliens and the cats are switched inside - so here is the chain of logic that we have to chase down let's imagine we treat the cat as the system we're going to observe we haven't yet observed it but we're going to and we treat the alien as part of the environment okay then in that case you notice that if we just treat the alien as part of the environment this part of the quantum state is the same in slide one in situ and therefore whatever the probability is that I'm gonna see the cat awake it's the same inside one inside - that's applying ESP and ignoring the aliens but I could also choose to observe the alien so I could treat the cat as part of the environment in that case the same structure works except the things that are the same are this second branch of SCI one in this first branch of sight - so the probability of the alien is friendly inside one is the same as it would be inside - but then here's where the miracle occurs inside - the branch where the cat is awake in the branch where the alien are friendly is the same so therefore before looking at anything whatever number I assigned to be the probability that I'm that the cat is awake in state two has to be the same as the probability I assigned to the alien being friendly that's just one branch of the wave function therefore this equals this equals this therefore this equals this the probability that I'm awake inside 1 equals the pub the cat is awake equals the probability that the cat is asleep inside one and those are the only two probabilities and they add up to one so they're both equal to 1/2 sorry about the fonts that's computer change ok that's the board rule by itself it's not a very vivid version of the born rule because it's only in the case where the amplitudes were the same right it's the same as indifference the probabilities but you know it's in the right direction the good news is once you get this part of the born rule once you get the born rule when the amplitudes of the two different branch of the wavefunction are equal then there's a known procedure you can plug into for getting the born rule when the amplitudes are unequal the crucial thing is that the trick that we just did to get equal probabilities doesn't work when the amplitudes are unequal if the very first step if you ignore the cats okay now the branch of the wavefunction with the friendly alien is different because there's a different number outside the state is not the same when you ignore the cats as it was the states i1 in the states I 2 are not the same ignoring the cats so there's no reason to assign equal probabilities as we did before okay so far there's just nothing that you can really say they're not treated equally according to ESP what you can do there's a trick do to Zurich let's imagine that your state is this you know some part of the wave function is e1 its entangled with environment a 1 let's say there's a spin up there's another part where the spin down and tangle with e 2 and its amplitude is bigger than e 1 with a square root of 2 extra back turn then I can simply choose to decompose I didn't write it down here but I can choose to decompose this vector e 2 into a sum of two orthogonal pieces 1 over the square root of 2 e 2 hat and 1 over the square root of 2 e 3 hat that's just math I didn't do any physics there ok but the point is I can write the whole wave function as a sum of three terms with equal amplitudes this one that this one and this one in one of them the spin is up and in two of them the spin is down and then I could run my argument from the last couple slides again and get equal probabilities crevices for being on this branch this branch in this branch so what that means is if the amplitude is bigger on one branch to another by a certain number the probability of being on that branch is bigger by that number squared which is exactly the born rule that's the origin of the born rule so basically you have a bunch of components that are unequal amplitudes you slice them you decompose them into perpendicular components until all the amplitudes are equal and those are the things you apply equal credence --is to being it that is the origin of one rule it's really just counting it's counting equal length components with indistinguishable observers so our conclusion is that if you do the logic of Elga rather just applying his conclusion now that this logic applied to everybody in quantum mechanics doesn't give you indifference my eally it gives you the born rule because you the probability is equal to the amplitude squared so what does that mean about the nature of probability and I really should just not say this but you people know more about the nature probability than I do so I'll tell you my informal way of thinking about it sometimes there's an objection to ever it on the basis of the following fact what you want to say is when I observe some quantum system there is a probability that I will see an answer right that I will see the spin is up or I will see the spin is down that's how we talk in our quantum mechanics classes but ever it says there is deterministic evolution there's no probability probability is one that this person will evolve into two people one of which it's all the cat awake and one of which saw the cat asleep so where does probability come in and the answer we're giving is that it comes in precisely because of self locating uncertainty so the origin of probability in a deterministic theory in this case is because given the simple structure of the wave function of the universe at early times there is an inevitable evolution from knowing where you are to self locating uncertainty and the way to resolve that self locating uncertainty is to give born rule probabilities so you start with once again cat in a superposition this is an apparatus this is the observer and as we said before the apparatus entangles and there are two copies of the observer and then the observer sees what the apparatus said so here in our picture there is necessarily self locating uncertainty and therefore these two observers both use the born rule to assign probabilities to where they are in the wavefunction and so the suggestion is that even before that happened up here that single observer should use the born rule to assign probabilities to what their descendants will see so it's really a very tiny shift it's not what I will see when I do this quantum mechanical observation because there's not going to be a single eye there's gonna be two descendants that I have but since they're both identical and they're both going to use a born rule I will treat the born rule right now as a probability that is the way to think about probabilities it's very epistemic and Bayesian it is not really objective but it works it's the data we would clean ok so now we can finish up by coming back to the Boltzmann brain question let's ignore this this is boring I'm gonna ignore it ok there we go that's boring okay back to the Boltzmann brain question at the level of the classical physics the epistemic separable 'ti principle gets us elegans indifference principle for multiple identical observers in the classical universe and if you believe that you can't escape the Boltzmann brain problem with a xerographic distribution because you've given a rational argument that there is one right way to assign credence --is between Boltzmann use and ordinary observer use you don't have that freedom anymore now you could deny the ESP that's fine your life it's a free country you do whatever you want but if you accept the ESP and get our born rule derivation that way you also should treat every occurrence of your local data classically on each branch as equally likely and that means if you live in a universe that is randomly fluctuating it's overwhelmingly probable you're a Boltzmann fluctuation even when you conditional eyes on all that you see around you so does that mean that if if I think they give a non-trivial prior to such a fluctuating universe I should non-trivial expect to walk outside and see thermal equilibrium despite the fact that it was raining this morning so I I argued no I argue that's not the right way to think about it and the reason why is completely different than anything we've talked about yet it's causative instability remember we said that if you do if you are a Boltzmann you we could fluctuate exactly into this room but then with overwhelming probability there'd be no strong connections between our impressions of the outside world and the actual outside world so if that were the real world in which we lived everything that we know about physics and philosophy and logic would have randomly fluctuated into our brains so if we constructed a theory of the universe which was eternal and randomly fluctuating and concluded therefore that we were recent random fluctuations we would have no reason to trust that conclusion because all of our reasoning just randomly fluctuate to our brains so in case you are not familiar with the usual story about the past hypothesis etc if you live in a universe where there's some data you have about your current local macro state and you have that local data and the laws of physics there are many possible futures right there are many possible things that could happen compatible with the laws of physics in your current macro state there is an exactly equal number of possible pasts because the fundamental laws of physics are time reversal invariant and typically your current local macro state has an equal number of time reversed microstates as regular microstates in it but nevertheless we seem to have knowledge about the past that we don't have about the future we have photographs right we have memories if you have fossils why do we know more about what past we came from than about the future and the answer is we have this thing called the past hypothesis we believe that in the real world 14 billion years ago with the Big Bang the universe started with very very entropy so we don't just have our current local macro state we have our current local microstate and I pop this about the past which together picks out a relatively small number of possible reconstructions given a photograph in your wallet right now that you remember having taken the week ago it's extremely probable that whatever you took a picture of really existed a week ago given the low entropy past if you were really a fluctuation there'd be no reason to think of that photograph was an accurate reconstruction okay so random fluctuations can't make this assumption and therefore random fluctuations have no reason to trust their reasoning about anything at all and therefore my suggestion my strategy my coping strategy is to simply say that we should not take seriously cosmological theories in which there are a lot more Boltzmann observers Boltzmann brains and Boltzmann use than there are ordinary observers those are universes that are ruled out not because I look around then I see that I'm not a Boltzmann brain but because I can't live in that universe I can't do physics or philosophy or science or life you know or romance or poetry or anything everything just randomly fluctuating to existence they have no reason to believe anything and that even though that might be true it's no way to get on with your life therefore you should just assign a prior of essentially zero to universe is dominated by Boltzmann brains as a working cosmologists your job is to design empirically successful theories of the whole universe which are not dominated by these random fluctuations and these are just the same things I already said but let me just now say thank you all right so we have high-level questions that you in a book yes so the best thing is the thing you just said right yeah so are you really thinking about this as a prior it's hard I mean probably you know better than I do what should i what what meaning should I assigned to the word prior it I I don't make up priors before I existed right I mean I need to make up priors like before I thought about this problem I guess right and so I would say before knowing what my realistic choices of cosmological models were if I knew about the Boltzmann brain problem I would advocate assigning very very low priors to any of the ones that produce Boltzmann brains so I'm not using detailed empirical knowledge of my conditions my local environment I'm simply using the practical advice that I shouldn't contemplate these you know radically skeptical versions of reality that wouldn't make the universe intelligible if they were true I take this something relevant yeah okay I buy that again not an expert in foundations of probability there might be some well-known reason why this is either good or bad but I you know I think I could live in a simulation that could be a brain-in-a-vat I could be Boltzmann brain but it's no way to go through life until there's very very very strong evidence otherwise yeah what way do you catch down you say that you can have all my beliefs be to signify why's about you know yeah you'll be impossible to do serious physics without certain kind of hypothesis right shaking the clients but I was wondering whether the reasons you gave were so strong in terms of a priorities for example if you have a flush relation to the galaxy who is 500 years of history then we can still do a lot of physics yes observations and we have fond memories follow my words no to be veridical inaccurate no future to be Rolly okay that's right and that seems to be escaping the kind of a priori consideration say that you difference must be impossible or well do your pocket it could but what I am leaning on is the fact that the actual cosmological models I'm considering have the feature that when you can fluctuate into something just the size of our galaxy it remains true that with overwhelmingly larger probability will fluctuate just in this room plus thermal equilibrium well I mean I guess you don't like the traffic distribution right so I don't think it's fair and again this is an interesting question which I'm happy to change my mind about my current attitude is it's not fair to pick a xerographic distribution that treats different the different observers but with the same local conditions differently I see that's I think the policies you rule out that things after the first epoch before you wish people sorry have to say that again I just know I when you have the capital publicist you could have equilibrium yet what tuition in future we need a Daniel Kaffee publishing to say that we're near the past we ain't no range people yes it's basically brought by a distribution over certain times observers empires well right but I think that um in that my papi if I were Fayed so it's tricky if I were faced with three different cosmological models one of which had truly any fluctuation with probability e to the minus Delta s one of which was thermodynamically sensible so just a good past hypothesis and the other had no local fluctuations but big fluctuation so that in other words if the probability distribution on entropy fluctuations was not e to the minus Delta s in fact any Albrecht has tried to construct cosmological models of this form where when there's a fluctuation it's more likely to be a big fluctuation than a small one right I think that would be an interesting edge case where you could start asking yourself is there sort of competition between being fair about your xerographic distributions and ensuring that you have a reason to trust your conclusions based on the data you see but I think you'd have to be sort of go through it by case-by-case basis really the the I'm getting all my leverage from the fact that with overwhelming probability nothing that I believe about the world is reliable and this in this real thing that I'm trying to rule out if I understood that the cognitive instability wouldn't be a reason for rejecting objects account right today but there would be kind of other kind of epistemic mother though I think since olicity about it because the kind of reasoning that we use to back a certain number of years gonna be evidence we have all of a sudden those waxy yeah nice that seems desirable well that's right so there's here's a potential empirical question you know we see the Cosmic Microwave Background we tribute this to the cooling plasma after the Big Bang what if the Cosmic Microwave Background disappeared tomorrow right what would we say I mean it might be that the best explanation of that data would be that what we thought was radiation from the Big Bang was really just locally coming toward us and it's not and you know if we continue to accumulate data I think that basically the right thing to do would be the thing people would actually do which would be to say I have this crazy hypothesis that the microwave background was not associated with the Big Bang but maybe our telescope just broke left you know but as they accumulated more and more data about it to realize that what they thought was a fourteen billion year old past hypothesis was much more recent than you would switch to switch to that but all that is only possible if you're at least in the subset of environments that are thermodynamically sensible right that do have some reliability with respect to their local environment if someone else try yeah yeah question but the was the ESP yes so we said that it's the macroscopic indistinguishability is the criterion for identity right but that's not going to be the criterion of identity for subsystems of the environment and I say because we um well because we want to like say when this electron comes out clean up okay you know this electron comes out in that desert does it stink microscopically I mean I think I don't think if there is a condition on identity in the environment right I'm thinking you're gonna get one on it if you just say the environment is just take out the dirt then you'll have one automatically they have identical and by my environments if when you take out the observer to get back start please and in fact you kind of need some sort of identity conditional apartments right because all printables build about but it's built on the concept of like even if this environment if this environment is a different teacher for me so you need a concept of identity or not identity requirement I think I'm think I'm missing something this is what I need I need literally that I can do unitary transformation on the environment and that doesn't change the probability that I'm gonna the credence I'm gonna attach to being one branch or another so can i connect that with what you're trying to say yeah okay yeah there we actually list different versions of the principal in the paper a loosey-goosey version and this is what we actually need so to prove what we want to prove I'm the warrior that's in the background line is that the trance dynamic said if you as a principal are micro dynamic and that micro details of the like departments that are going to be relevant first application but the own way your individuating some set subsystems is macroscopically and so you get this is kind of this is a sort of mismatch between so just to set up the whole problem yeah I'm just one of this one or this one yeah I agree with you it's like a macro scopic it's a problem but the characterization has these microscopic I mean I think this is a kind of a typical I've already insane where you don't take microscopic and macroscopic to literally like and also don't take the environment and system to literally in the following sense like I can describe myself like I have Avogadro's number of particles more than that in me and each of them have spin and location momentum so this is huge dimensional hilbert space but when I describe myself when I say macroscopically identical I am imagining just as I do I derive Boltzmann's version of the second law and and chunk up microstates in the microstates that there is some tiny subset of that data that is accessible to me microscopically and the way that plays out quantum mechanically is I would describe myself as a living in a tensor product of some macro variables and some micro variables and I think all I need is that the macro variables are the two things I want to say are identical or the same regardless of what their micro variables are doing the micro variables could be identical or not it actually just doesn't matter and likewise for the environment I think that's actually quite a weak condition Eddy so I think in develop the diagram again we have two quantum states AEM facilities Sumer right honestly yeah this one so we do this equivalence in a coop you say this is cooking this when this is equal to this by ESG right and go for this - you are the same and similarly for what 32 think there is a similar objection to maybe this application as David Albers objection to Wallace okay so in that case while he was claiming that the following equivalence principle holds if you prefer a over B and C over D then sickness oddity Department he preferred a superposition with speed to see if the particulars do you know basic determinate preferences over crying the positions by we can practice is over single states okay and Albert offers projections that it does not okay emphasis over single world's single outcomes don't you need to determine preferences over joint outcomes when we have some position between this Plus this the similarly here I was thinking okay so he SP give me I prefer L and C sorry I mean differently sir I've seen critical path of ANC and BNC but does not give me the same credits when a is the same proposition wispy or C with D so you're rejecting the sympathy principle in the case of preference it's doesn't principally wireless uses doesn't seem that possible possible yeah because this branch is just one branch I was thinking before you are at site you up site while you are before you an experiment you're thinking watch my words my curry recipe so right but I'm I'm not superimposing preferences or anything right I'm really comparing at every step I'm only comparing individual branches I'm never comparing superpositions I'm saying probability this branch the same to this probably this branch is the same as this therefore this then just numerically this is a number it's equal to this number it's also equal that number there for arithmetic I like dark wanna consistency I should have the same criticism my descendants right yeah and at that stage before mention it I should have criticized about well I I will be probably most likely in the future and I could have different credenzas when there's single world or with multiple words so Mike Mike written says over a SCIF BFD could change if ANC and B are in position later and cfd that maybe but I don't need it well this is all I need to get the born rule out of the year this one yeah all right this one right which one you want this one with the with the words with the words okay Adela for you should use this knife over to the future yeah but what I need to get that is just comparing things at this time like you died that descendants that wouldn't go through about the argument I'm not sure what your denying your so I like I said this use the board yes I speak at night that the other I should use the point which is that going into the future I don't see why how you can deny that so I'm not saying that I'm not waiting you know utility functions or anything like that right I'm saying that I know that I'm gonna be duplicated there's gonna be many copies of me in the future I'm not gonna know which one I am but I know that after I'm duplicated every one of them has a very certain probability they will assign to being every one of them so I should assign that probability ahead of time no it's some reflection principle for this consistency I think it's we couldn't that but okay I mean yeah I would like diachronic consistency yes and that was this that was the last issue between the Albert was is when whether you can so I think the end well has proved the or music that wanted assistance and that's automatically tuition so elder staying with this is not exactly required well I would certainly I would and I think that I'm certainly happy to accept I chronic consistency is something that I would like in my in my unfortunately impedances but that's different than what he started saying because at no point do I ever superimpose probabilities or suits right right this way but it's saying that that Marcus's is where he is to connect did he said this criticism yeah I'm word yeah so there's certainly something going on here but so this was I claim I've already derived the born rule but this is sort of recovering our standard understanding of the born rule and then maybe that there's a version of normal I derived the version that I applied after decoherence right after the branching has happened that's right so that's a born rule right but I also want to be able to speak the language that I teach my undergraduates about making a measurement and I think this is what lets me do that that's what you really need probably yeah probably I mean it'd be a weird world where I didn't have it before I did the measurement but I did after so Edie's point is that you're making this other assumption yes I agree that if there's another assumption to do that to the same and diachronic consistency does assume that your degrees of belief greetings us of changing rationally and that's that I'm worried that is a kind of circularity because I didn't get your points at first but this is way too seriously yeah the circularity because you know it's where you don't have value panic consistency just in a non splitting case right is where you think that you might get drunk later and have you know some sort of but it believed so you shouldn't obey the reflection pencil but here if you're you're demanding diachronic consistency because you're assuming that it's rational to change your degrees of belief by the born rule when am i changing my degrees of belief here I'm saying either they're seen in these ten suppose I'm not changing them yes but it is that a subset of changing yes but its act relating it yes it would say an update yes okay right so I mean are you proposing you there is some other rational thing to do in this circumstance as always that I don't have a I don't think that yeah risk oh do you have no clue I think the thing to think about is whether and he pointed out of a an assumption in the argument which they involve a circularity so I think there's an assumption I don't I still don't see why would be a circularity I'm not assuming I mean there is another principle so there's a derivation of how we assign grievances in this particular case of self locating uncertainty then there's sort of a recommendation about how to think of our splitting cells at earlier times and that recommendation uses diachronic consistency but I don't see any circle where's the circle circulation recipe required to use that but it is not required that we don't have the boy rule but that's so number one I don't believe that but number two is slowness circularity it's just ear to saying I need another assumption circular you may not find convincing those comparing it it's a reflection principle which works perfectly right as long as you're updating vibration conditional ization so if you're not updating by patient conditional ization reflection isn't right so if somebody was arguing for Bayesian conditional ization by way of the reflection principle they would go okay they're gonna chip that's that's why that sounds particularly yes right but I'm not sure that this yeah I don't think it's way but okay I that's why I said it right that would be worried I get it yeah okay but I think you know there's you know I think the chip has more nuanced views of this than I do because he's read some of this these worries in the literature and we talked about it a lot and he's never convinced me there's an actual problem like the strongest that I've become convinced of is that someone could stubbornly refuse to think this way never there's a good way to think like this is like so the ESP itself is an assumption right and you could deny that if you want to and I think David we've even deny the ESP and so by attitude there is look that theory is trying to tell us something and the thing is telling us it's the data so just declare victory you can do other things right like you know that you could just stubbornly insist that there are other measures you could put on things other than the one that the theory told you to use and then you would get the experiments wrong so I mean it's not like there's some empirical puzzle that would be solved by choosing a different measure right this is the one that both the theory says and fits the data so why are you complaining about this I mean I agree this is the one that would do a job giving you this morning but the questions whether I mean whatever we can to prove is a very noble task Thanks one I think I really respect is to say that even if the world does not have probabilities rational agents but we have the formal policies about the branches drum and write to prove that have to show that I did a rational requirement not just the expression impermissible to do this the rest me required you have this criticism those measurements well I think sorry I think so what I would say is it's rationally required given some assumptions I'm admitting that it is logically possible to deny those assumptions but then all you're left with is I can say nothing yeah sure yes well you can reject Evert empirically but but I would still want to know wherever it true what would I predict no but right but I'm still left with the question I would want to know if this were the world is there some prediction I would make about experimental outcomes I think David would just say there isn't any right yet right reason to reject it this is what the world is like that's right the reason right but and I think that if so my attitude is that if there's some extremely mild on a actionable extra assumptions that gets a unique answer and there's no equally mild objectionable assumptions that get a different answer and that answer agrees with the data I go home it's a French count a very natural matter French coffee is some kind of well it's not a very natural measure really I think that I think that it's it's sort of less natural in the ESP and it's not by chronically consistent and Belova it's you know it's but I think I think that's exactly what I'll gonna help us understand that rather than positing and difference yeah yeah we derive it from even more fundamental things yeah so this works at let's say from probabilities in self locating situations what about probabilities as implied let's say two ordinary statistical mechanics in a finite universe uh-huh Justin there they seem to be objective probabilities connected to free process I totally independent so good this is a very very good question so my suspicion which I didn't quite work up the courage to say out loud because the room is full of people are more expert than I am is it that all the real probabilities are epistemic and Bayesian in the world in statistical mechanics I don't know what the microstate is and I have a sensible measure to use over the space microstates and I use that it gets me the right answer the argument no but it's still it's the spirit and the I another slide that I deleted just because I had too many slides the spirit underlying everything we're doing is if the dynamics of the theory keeps pointing you in the direction of a certain measure then just go there and in statistical mechanics there is the Leoville measure is the unique measure defined by the dynamics it is invariant under time pollution ticket it's okay you know well we don't want to pick it period you better pick it with surpassed hypothesis yeah yeah sure is that bothersome if we just followed what you just said we just picked a moving measure well then that would instantly lead to cognitive instability so yeah so that's right but suppose we get it we can imagine a world or every pacifically positive world in which the frequencies diverge right enormous Lee from what the probabilities mm-hmm in a world like that yeah those people are in bad luck right so that's a response that is just so I feel sorry for those people yes the probabilities are different yeah I mean you know if this is a classic anti Eveready an argument is there will be branches of the wavefunction where all sorts of weird unlikely things happen I feel bad for those people vital but appropriated the word unlikely but your probability measure yes these guys well they would get the theory of the world wrong right they would draw incorrect conclusions so in any of these multiverse models with as many different possibilities going on there's it's very generic that doing their best every observer you know comes up with a conclusion about what the universe is probably like and they won't agree right because some of them will be in the really unlikely tails so you think that they yeah we're stat mech right they would think the satin like was a very different theory I wouldn't make them up with the dynamics in that division bicycle dynamics and just a different probability distribution well okay that's what I'm counting stat mech with the usual probability distribution yeah right I mean if every time you put two blocks together of equal temperature one of them that hot air one of them got colder they would derive something but I wouldn't call it step back it would be you know based on some weird thing right so in the multiverse and Everett even that people like that exist they're really really really really really low measure if I were in the past and we're wondering whether it should think of myself as gonna evolve into them I would put a problem small probability on it one period but it's because the world has certain frequencies in it and that's what makes it the rash for different accounts of what acceptable yeah that's right so I'm just I mean ya know I'm with Vivid what the right yeah and so I'm I'm sort of tentatively not having thought deeply about the foundations of probability but I'm you know tentatively maximally Bayesian about these things and I think that you know let's put it this way what if drw were right what if there was some true quantum dynamics that seemed there was truly random right as an eternal list I would say really there is some definite answer to what the answer for every quantum measurements gonna be I just don't know what it's gonna be right but it's there in the future it's just not accessible to me by memory or experiment or anything like that so the right way to talk about probabilities is still not as frequencies it's just my lack of knowledge about what that future actually is no exactly I'm not denying the time you can be well I think here it only makes my brain only wraps around this if I think from a Bayesian perspective I haven't used the word Bayesian that because okay thank me for the way of making inferences in that sense sure should I say you have to semuc or what do you can really say yeah yes I think your probabilities here is epistemic so what is the frequency I think that's right ready yeah yeah I would totally rent that that was my reason not liking the already it okay yeah so I would give it anyone else a chance before I stay in this corner no okay oh yeah all right hurry yeah he's going to several times go ahead okay so I wanted to follow up on Betty's real question so um I wanted to meet I think I'm just even confused about what the propositions are that the probabilities are signing - uh-huh so in the second case is it take the person who sees the cat asleep is it that they made history differences like this is they like great insisted 2% that I'm in the tax leaving world mm-hmm grant okay yep and then the person before that at the top they say something like there's a 50% chance that I will be that is it that I am in the world that will be the cat sleeping world right so no that's not what you should say like the whole point of this really is as much to clean up our language as anything else but the upshot is act as if only one world becomes real with a certain probability right the super correct words to say are I'm going to become two people both of those people should assign born rule credence as to the outcomes of the experiments that's the correct thing to say okay so on most theories of personal identity that's not it yeah I think that the Missouri weird person most theories of personal identity need a little bit of improving in an everybody world I was gonna say if you were just more careful in the original about the semantics of the decks cause like I might be able to I wonder if you might not have to admit like I want to be much more radical with respect to personal identity since I'm so I'm in love with the physics and I could take or leave the theories of personal identity I think that first my identity is overrated it's a there's one person here and there are two people there but then there aren't two people there's one person no I will be this person and I will be different so there I will I will evolve into two people so in this way of thinking there's not even even classically there's not one person through time there's me now there's the thing that will evolve into one minute from now and two minutes from now etc the extra Eveready and feature is that I evolve in a more than one person in the future so biggie okay I was thinking you were saying the third of three options the first option was that everybody's everyday I am just the time slice right now so higher first just to make my life so I am not the person later because no time slices these are different times I see it's one answer in the yeah so I want to accept that thing that everyone rejects the second one no as you said everyone rejects it that's one of the standard answers right but that's what I want to accept I like that one you'd like the time place yeah I think that you should know you aren't personally according exactly that the best person that descends from me that's not me okay there's no objective reality - there's you it okay okay well it's odd to think that there's a rationality requirement on what one person so you then your random choice has doesn't mean it has this logic you're saying what a different person should believe on the basis of what I like yes these are the people that's right not Lehrer partners if it's not even a diachronic consistency requirement that's why I'm gonna beam on different persons right what different person should believe police of course appearances it is that is an unusual rationality I think that so I think it's one of them so if thinking of I'm not so convinced anymore than it seemed super simple sort of innocuous well it's you know I think that the right answer to the Ship of Theseus is that it's a different ship every second so it's not complicated to say then having this rationality so I would tell me there's give you have to separate people and there's no rational constraint on one person to believe generated by liquid another person simply you have two people were completely spatially completely separate it never interact you're denying it well but there it's not that they're completely separated and never interact one is the descendant of another yeah I mean so what I would say is that the you know the Everett makes frightening Lirio all of these weird philosophical thought experiments about duplication and teleportation machines and so forth which have always been used to call into questions issues a personal identity and the right thing to do is to start from scratch with personal identity and talk about different people at different times and how they relate to each other and I'm sure it's doable this is part of that project like this epsilon of that big project but I think that I I and again I could be wrong I'm very willing to give up on the intuitive notions of personal identity in favor of a better understanding of what happens in the wave function the universe adeno yeah earlier so I think you could say in quantum mechanics the state is a big step that's true they don't have distribution over we don't have probability I was just talking of language of classical statistical mechanics but that's all I was talking about when I said the level measures yeah right yeah no I mean the world is quantum you should use density operators yeah yes yeah together all right yeah yeah yeah I still I'm still stuck won't understand your reasoning in the regarding the ESP and how it plays with the cat so can I just so okay so am i right that the the things in the Kent are the states here are the what is the environment in the situation well I could have included in an extra environment but the environment is I'm imagining different circumstances under which I am deciding to look at different quantum systems so I'm imagining that there's an observer there's a cat there's an alien and also there's the whole rest of the environment that I'm not even looking at right now but if I choose to look at the cat that I'm treating the alien as part of the environment and vice versa so I have two boxes both were the spin in them I'm gonna choose to open one or the other if I choose to open one the other one as far as I'm concerned as the environment is part of the environment and if I do that if I do open it then of course there's time evolution which is not here but the time evolution would entangle whatever is in that box with the actual rest of the environment and the pictures I showed you before would apply that are being found equal or equivalent yeah so the two pairs of things everyone are they being found equal or equivalent to the same environment yes but of course depending on whether or not I the observer measured the cat or the alien the Hamiltonian would evolve the state in different ways but in either case there would be a moment of self locating uncertainty when the observer was in the same system and everything else was different yes to other things I went through that one is mentioned at the beginning that one of the places where at the center is in the inflationary multiverse scenario right so there you sometimes hear people say something like this that anything that can happen happens in some universe or other and so this is a problem of finding a measure right I don't see that anything you've said so far it's that yeah because that's the exactly the transparencies I slipped over so in principle you can apply the SP to that circumstance right in other words this is sort of a mixed quantum probabilities there's different branch of the wavefunction and on each branch there can be multiple observers so this mixed classical and quantum uncertainty so we have an equation the probability being so on each branch there's an amplitude you square that and you call that a weight so this weight is gets attached to every observer on that branch in your reference class and the probability of being any particular observer is that way - by the sum of all weights because the son need not add to one right okay so in principle this is a derived rather than postulated measure in some big multiverse in practice it might not be regular izybelle in any way in the universe with an infinite number of observers so we don't solve the measure problem in any good sense but at least we're not guessing it we're just pointing out that the the actual measure you should use has all the problems of the ordinary guesses you want it is some story of that place as biology which would make multiverses what would universes with the cosmic background fluctuations but my cars right away that's right so I did you know I briefly entertained exactly that hope that that branches that you could actually you know so usually when cosmologists all about the multiverse because they're fallible human beings who don't really take quantum mechanics seriously they draw these semi classical pictures of bubbles nucleating right and with a certain probability so what they really mean is that there is a wave function that evolves into a superposition of all these different possibilities so you could imagine that you get lucky and in a quasi realistic or at least a toy model version of that the branches where you make lots of observers somehow get their weights killed off by a and the probability gets squelch even though there's lots of observers there in the toy models I could construct that did not actually happen so yeah so I think that in I don't see why I would but you know you have a new equation you got try it out right like you know you got a you want you to be the discoverer that not someone else if it's true so yeah so I think that's a I have no strong opinions about how to resolve that problem but it's a good one yeah I have weak opinions but no you know one more question or an ethnic it was the thing I've brought up and still know exactly what to think of it if the fact there were some preachers who became conscious of a result right prior decoherence Oh baby that just doesn't make it I think it's possible does make any sense yes like there's no definition of consciousness that occurs faster than the decoherence time that would be weird but maybe like I'm granting that is possible but is to understand is that I don't know worried that we're possible same I think those creatures you know the standard you know at when you when you give the sales pitch forever it and what he's trying to solve you very often say you know if I open the box with Schrodinger's cat in it I never see a superposition I think your critters would see superpositions so maybe after that's right they would fade away or something like that yeah good thank you very much all right thanks

Channel: Harry Crane

Views: 125,772

Rating: 4.5683813 out of 5

Keywords: self-locating belief, sean carroll, harry crane, born rule, rutgers, foundations of probability

Id: 6kwcokUFaqo

Length: 113min 38sec (6818 seconds)

Published: Mon Apr 23 2018

Reddit Comments

[u/chefranden]

I'm right here.

[u/easilypersuadedsquid]

Modern physics frequently envisions scenarios in which the universe is very large indeed: large enough that any allowed local situation is likely to exist more than once, perhaps an infinite number of times. Multiple copies of you might exist elsewhere in space, in time, or on other branches of the wave function. I will argue for a unified strategy for dealing with self-locating uncertainty that recovers the Born Rule of quantum mechanics in ordinary situations, and suggests a cosmological measure in a multiverse. The approach is fundamentally Bayesian, treating probability talk as arising from credences in conditions of uncertainty. Such an approach doesn't work in cosmologies dominated by random fluctuations (Boltzmann Brains), so I will argue in favor of excluding such models on the basis of cognitive instability.