00:00:00.000 Hello everyone, thanks for turning out those of you who are not in physics coming here in the in the rain

00:00:05.760 It's my pleasure to introduce Professor David Deutsch who's going to speak to us today

00:00:11.480 Many of you will know David's name. It's not controversial to say he's one of the key individuals who really

00:00:18.560 kicked off the field that has become the field of quantum information and quantum information technology

00:00:24.440 Which as you know Oxford now has a very large and leading role in the UK and in the world

00:00:29.120 David's a really first paper that people recognized was the one that went on to be described as the Deutsch algorithm

00:00:36.360 And that was in 85 he's continued to contribute to the field over the intervening years in particular

00:00:42.280 Wrapped soon afterwards in 87. There was an important paper on quantum networks

00:00:46.360 And when I became interested in this build myself in the 90s David's work was one of the key inspirations for me

00:00:53.600 So David is based in heading turn in his kind of perpetual visiting professor here in physics

00:00:58.560 and in

00:01:00.560 2008 he became a fellow of the Royal Society recognized for his work in quantum information

00:01:07.280 2013

00:01:09.280 David

00:01:10.960 is now the lead researcher in a project on

00:01:14.560 Constructed theory, which I guess we're about to hear some more about

00:01:18.000 With the Kiara with that's Kiara

00:01:20.640 So Kiara has the postdoc and if you want to know more you can either talk to me or David or Kiara

00:01:25.720 So I think it without further. Thank you

00:01:34.320 Right, well

00:01:36.320 The ideas I'm going to talk about today are

00:01:39.400 part of Constructed theory which I've been working on with Kiara my letter and

00:01:46.600 Among other things Constructed theory uses a new mode of explanation of

00:01:54.040 physical reality

00:01:56.480 Through which we hope to eliminate a lot more than just probability a

00:02:02.200 whole load of explanatory

00:02:04.840 Dead weight and blind alleys from physics and from other sciences and even beyond science

00:02:14.000 What's a mode of explanation well?

00:02:17.000 At present the prevailing mode

00:02:20.080 Which is mistakenly thought to be the most fundamental is

00:02:26.200 like this

00:02:27.840 There are particles and there are fields

00:02:31.360 in space-time and

00:02:33.880 They obey laws of motion and initial conditions and once you know those you can predict the whole of the rest of their behavior

00:02:45.040 But there are other modes of explanation in

00:02:48.040 in common use in physics and elsewhere and

00:02:52.960 Here are some of them

00:02:56.360 No, yes good

00:03:01.600 Just for illustration I'm mainly going to talk about the probabilistic mode that I put in red there

00:03:09.280 But as I said Constructed theory seeks to

00:03:14.160 Unify and to underlie

00:03:16.080 All those

00:03:18.840 modes and others with a single mode of explanation the constructive theoretic mode which is

00:03:27.040 explanation via the dichotomy between

00:03:33.040 Transformations that it's possible to bring about accurately and ones that it's not possible to bring about accurately and those are possible in impossible tasks

00:03:42.720 Now the basic principle of constructive theory is

00:03:50.080 That

00:03:52.080 Just that all the laws of physics are expressible in that way

00:03:58.760 Since every task is supposed to be either

00:04:02.120 definitively possible or impossible to perform

00:04:06.680 There can't be such a thing as a task being

00:04:09.600 Possible with a given probability not not zero or one and

00:04:16.560 At the fundamental level such things might arise as approximations, but that that's not description of reality and therefore

00:04:23.880 There's no place for

00:04:26.320 Probability according to constructive theory. There's no place for probability or random processes at the foundations of physics

00:04:34.800 However, I'm not going to make the case against probability from

00:04:42.600 Constructed theory today. It's more like the other way around. This is a motivation for constructive theory because

00:04:50.600 Independently of constructive theory the world just is not probabilistic. It's an illusion and the probabilistic mode of explanation

00:05:00.280 Has about the same status as the flat earth theory

00:05:05.560 You namely

00:05:07.560 You might you might find it useful to use the predictions of the flat earth theory when you're planning out your garden

00:05:16.480 But when you're thinking about what the world is like and even more when you're thinking about what the laws of nature are

00:05:24.480 it would be hopeless

00:05:26.480 The the theory of the flat earth would just be an impediment to understanding what's out there

00:05:36.360 So same is true of probability and so let me explain

00:05:42.960 well

00:05:44.560 probability and

00:05:47.040 The associated concepts such as a stochastic process that that produces a random sequence of outcomes

00:05:58.480 These weren't originally invented for any purpose in physics or any fundamental purpose

00:06:05.600 the basic mathematical theory of probability

00:06:09.800 namely

00:06:11.000 Certain numbers attached to certain elements of a set which then obey axioms like they all add up to one and stuff

00:06:19.760 Was invented in the 16th century by people who only wanted to win at games of chance

00:06:29.960 This is one of them

00:06:32.640 Cardano

00:06:34.640 And that started off game theory and game theorists use the idea of a random sequence

00:06:45.440 as a

00:06:46.720 mathematical model of

00:06:49.280 Physical acts that are integral to games of chance such as shuffling a pack of cards or throwing dice and

00:06:56.080 And probability via the central concept of equally likely

00:07:04.800 Was a mathematical model for the intuitive idea of

00:07:09.960 Fair shuffling of cards a fair dice

00:07:14.280 Fair dice and fair throw the dice

00:07:17.520 so

00:07:19.200 When I when I say that we which is also essential to games of chance when I say that this was merely a mathematical model

00:07:30.480 Perhaps I should say more clearly what I mean

00:07:33.240 I mean that they didn't assume that anything in the physical world

00:07:41.640 Shuffling cards and so on was literally what we would today call a stochastic process

00:07:47.320 That it literally had properties such as probability

00:07:52.120 That's because first of all

00:07:55.440 The properties that they actually needed from shuffling cards were far weaker than full literal randomness

00:08:04.840 They were basically that the outcomes of shuffling

00:08:09.880 should be fair and equitable among the players and

00:08:13.080 Unpredictable to them

00:08:17.400 So that that meant that the the outcomes were not related in any simple way to any sequence or algorithm

00:08:26.000 That they could call to mind or or execute during playing the game

00:08:31.640 So most sooner random sequences would have done just as well if they'd had computers then and

00:08:37.560 And secondly more importantly

00:08:43.160 Don't think it would even have occurred to them to connect that their probability in their model with some real physical quantity

00:08:51.320 Because classical physics which was in its infancy at the time of Cardano, but a bit later when it was perfected

00:08:59.560 was deterministic and

00:09:01.560 therefore inconsistent with stochastic processes happening in nature so

00:09:09.480 Why did those game theorists blindly use

00:09:13.640 mathematical axioms

00:09:16.360 probability theory that were both far too strong and

00:09:20.600 Already ruled out by what was known about fundamental physics

00:09:24.440 Well simple by being too strong. That's harmless. They they set that meant that they certainly satisfied

00:09:30.920 They're conditions that that were necessary for analyzing games and

00:09:37.960 The real properties that they really wanted such as fairness and so on couldn't be expressed precisely mathematically

00:09:44.680 By the way, they can be precise express precisely in constructive theory, but that's another story

00:09:54.280 Consequently it didn't matter also that their model relied on impossible physics

00:09:58.840 because

00:10:01.560 The conclusions about game playing if

00:10:05.160 There had been that impossible physics

00:10:07.960 led to the same

00:10:10.200 conclusions about strategy and tactics as for the real physics, so it didn't matter for them

00:10:23.560 There's another reason

00:10:25.560 Why they might have been blase about the connection between their theory and physics

00:10:31.720 Certainly this was a move made

00:10:33.880 later in game theory and in probability theory up to the present day

00:10:38.040 They might have regarded

00:10:40.040 the probabilities not as attributes of the dice and the cards or the dealer

00:10:46.040 but as attributes of

00:10:49.000 Player receiving the cards

00:10:51.000 That's the subjective interpretation of probability

00:10:55.880 Now come back to it in a moment, but note already that

00:11:00.600 Whatever role the subjective state of mind of the player may play in this story

00:11:08.680 Fairness must depend on physical properties of the cards and dice and how they're treated during the game and therefore

00:11:16.360 Game theory must in principle be rooted in some sort of model of those objects and processes

00:11:26.440 anyway from that theory

00:11:29.480 Game theorists derived

00:11:31.720 Maxims for playing games of chance such as in poker never draw to an inside straight and

00:11:41.640 The important thing is that this was a narrow

00:11:44.840 Parochial

00:11:47.160 Application of a mathematical trick the theory of probability

00:11:52.360 Indeed

00:11:53.720 The reason that game theory was possible at all

00:11:57.480 Was that its conclusions don't depend on the detailed physics of any game playing processes

00:12:04.360 It didn't matter what the orbits of the planets are. It didn't matter what matter is made of

00:12:09.400 Or let alone anything deeper about the laws of physics the theory was directed specifically at

00:12:16.920 Modeling a particular human social behavior

00:12:21.560 Which even other animals don't do let alone

00:12:25.000 The physical world at large so it should be very surprising

00:12:30.360 That this little mathematical trick

00:12:32.920 The theory of probability has found further applications

00:12:37.240 in a very diverse fields in science and and beyond and

00:12:43.560 Even that it seems to be fundamental to some of those fields. So here are some of them

00:12:51.640 Roughly in a historical order of their invention

00:12:55.160 So we'd we'd be surprised if if say the seven of diamonds appeared in a law of physics

00:13:01.000 But probability which has the same provenance as the seven of diamonds

00:13:08.200 Seems to be central

00:13:10.200 To physics in particular and it seems to work

00:13:14.680 So why would anyone want to expunge it from physics and from every other fundamental theory

00:13:21.080 Well, of course, we don't need a reason physics likes to do without things

00:13:31.400 As we discover more and more about the world

00:13:35.160 We sometimes did find out that things that we thought existed don't exist and

00:13:41.000 such as

00:13:43.000 celestial spheres and and

00:13:45.560 the force of gravity

00:13:47.560 And the trajectories of particles and so on. They were all thought to exist and then

00:13:52.520 Discovering that they don't exist was a great advance in understanding

00:13:57.000 But before we can decide that something doesn't exist

00:14:00.520 We must explain what the world without that thing is like

00:14:05.480 and

00:14:06.520 Also preferably why thinking in terms of that thing

00:14:11.320 seemed to work

00:14:13.000 And why it was a useful fiction and why it may still be a useful fiction

00:14:18.680 So compare

00:14:21.400 These two statements

00:14:25.560 Yeah, the first statement specifies a factual observable

00:14:33.160 Property of the world it specifies what will happen when

00:14:36.920 Poker is played and and specified hands arise but the second one

00:14:44.280 Is not about physical facts. It is consistent with any

00:14:49.480 Sequence of cards arising in a poker game. It's in fact. It's consistent with with any physical events

00:14:58.360 Such as someone repeatedly drawing to an inside straight and repeatedly winning

00:15:03.000 Not inconsistent

00:15:06.840 Yes, it's true that it was risky the second statement is true all right

00:15:12.040 But it doesn't apparently

00:15:14.360 Refer to any physical events that actually happened in that case

00:15:21.800 One sometimes here's a sort of

00:15:24.360 desperate denial

00:15:26.760 of this

00:15:28.760 Along the following lines the statement it was too risky is about the physical world

00:15:36.120 It refers to all the other players

00:15:38.600 Who drew to an inside straight and lost and it refers to the fact that they're more of them

00:15:43.400 They outnumber the winners

00:15:46.840 Well, first of all, it doesn't

00:15:49.640 They have only been finitely many poker games in the world

00:15:53.800 Ignore for the moment the fact that there are parallel universes and in those

00:16:01.160 Particular player both wins and loses in different universe

00:16:04.680 Quantum theory does in fact solve some of these problems, but not by counting the number of players

00:16:11.480 So for the moment in a given universe or in classical physics

00:16:16.600 The proportion of players who drew to an inside straight and lost

00:16:20.360 Doesn't exactly equal the probability of losing

00:16:27.160 Just as repeated tosses of a fair coin

00:16:31.320 However, fair it is don't result in equal numbers of heads and tails in general

00:16:38.120 and anyway

00:16:39.800 Since when do gamblers care about whether other gamblers lose or win?

00:16:45.240 If probability refers to other players losing money, it doesn't refer to any

00:16:53.320 physical fact about the game as it actually was in the case that I cited

00:16:59.880 And the same holds for all probability statements

00:17:03.720 So that's meant to be in the second column. That's meant to be all probability statements. That's the dot dot dot

00:17:16.600 The blatant fact that is generally overlooked

00:17:20.760 Is that no statement from the second column can ever imply any statement from the first column?

00:17:26.280 In other words, assertions about probabilities do not refer to the physical world. They don't assert anything

00:17:36.760 about the physical world

00:17:39.000 Frequencies like the fraction of winners over losers historically are things that happen in real life and therefore they don't in general equal probabilities

00:17:50.760 It's no good saying that they equal them approximately

00:17:53.640 Because they don't they only probably equal them approximately and that's a statement from the second column

00:18:02.440 Similarly, you can't say that

00:18:04.440 Probability statements are about what will happen in the long run. No, they aren't all you can do is deduce from them

00:18:11.560 Our statements about what will probably happen in the long run

00:18:14.360 But frequencies in an infinite sequence of measurements of experiments

00:18:24.120 Do equal the probabilities exactly and this inspires yet another desperate denial

00:18:31.480 To the effect that the finite sequences are approximations to infinite ones

00:18:37.560 But nothing about a finite subsequence of an infinite sequence

00:18:41.800 Can possibly follow from a statement about relative frequencies in the infinite sequence

00:18:49.640 Unless the subsequence is a typical one and tip statement that is a typical one belongs firmly in the second column

00:19:00.280 Or you may take that subjective route that I mentioned you could imagine that

00:19:05.640 Probability statements are not assertions about the world at all. They are assertions about our minds

00:19:10.360 Probability being a measure of ignorance or of a degree of rational belief. There's a two different subjective theories

00:19:19.480 called credence

00:19:21.640 That's no good for present purposes because

00:19:24.760 Then you still need something to connect statements about our minds

00:19:30.440 Just statements about physical reality

00:19:33.000 So to this end

00:19:34.760 The philosopher David Lewis proposed his principle principle. That's a

00:19:41.960 principle principle

00:19:45.400 Which just asserts as an axiom

00:19:48.200 That rational agents have the same credences as the physical probabilities

00:19:53.400 But note that that gives no explanation about why

00:19:57.320 Those physical purportedly physical numbers should inform decisions in that way

00:20:03.080 You may as well propose an axiom that rational people avoid black cats or ladders

00:20:11.240 That's not physics

00:20:13.880 So

00:20:15.560 The upshot is that Cardano and the a game theorists never did succeed after all in their purpose of

00:20:23.240 Finding ways of winning a games of chance or of minimizing their losses

00:20:29.000 They only found ways of probably winning

00:20:34.920 And later people added these purported philosophical principles that say a rational person would do this or that

00:20:44.120 But actually a rational gambler

00:20:47.720 knows that

00:20:50.440 Having probably one

00:20:53.080 No matter how often one does it won't pay the rent

00:20:56.280 Physically

00:20:59.400 Physically it is most unlike actual winning

00:21:04.600 So in case there still appear to be any clothes on this emperor

00:21:09.080 because of the

00:21:11.080 Mass of cultural

00:21:13.080 Interpretation that that's been loaded onto it

00:21:18.120 Just replace all the probabilistic terms in the second column by magical terms

00:21:23.560 Why?

00:21:25.560 What physical reason is there to allow

00:21:31.000 Statements in the second column to inform decisions by fiat and not statements in the third

00:21:37.560 If you could equally well connect to reality by some fiat

00:21:40.920 Yeah

00:21:52.120 There that's the magical column. Thanks. Thanks a lot

00:21:58.040 So what I have called these desperate denials of the of the firewall between the first column and the other two

00:22:05.640 Are more commonly known as interpretations of the probability calculus

00:22:13.000 subjective interpretations

00:22:15.000 Frequency interpretation ensemble interpretations and all in many variants

00:22:20.760 Regarded as attempts to connect the second column with the first

00:22:26.120 They are all

00:22:27.720 Like the examples I've given either circular or meaningless or

00:22:31.640 Or conflict with the probability calculus or just don't do what they say they do

00:22:38.440 This discussion that I've just given about the defects in the theory of probability

00:22:44.280 Draws on the work of David Papano who's a philosopher of probability

00:22:49.000 He has called this situation

00:22:51.880 At the heart of his field a scandal

00:22:55.320 probability concepts and language and

00:22:58.200 And the whole theory simply form a closed system

00:23:05.320 Of statements and ideas that just refer to each other and can never yield a statement about the physical world

00:23:14.680 Now if we go back to the applications of probability we can see

00:23:20.760 That there is a common feature running through all of them

00:23:24.440 They are all in a certain sense and slightly different senses they're all

00:23:31.160 Normative that is to say they're about at root

00:23:36.600 How one should act if one were to believe that certain potential events have particular probabilities

00:23:43.080 Now how one should act is rather a strange thing for a scientific theory to talk about

00:23:50.040 You know you can't get an all from an is

00:23:52.040 In fact the firewall between

00:23:56.440 factual statements and moral statements exists for a very similar reason to the one

00:24:01.560 Separating factual statements from probability ones

00:24:06.440 So

00:24:07.640 Another way of papering over the divide or ignoring it is

00:24:13.720 By different kind of fiat

00:24:16.200 One

00:24:17.080 Simply puts a normative statement about probabilities into the physical theory

00:24:24.600 That's called a stochastic physical theory

00:24:28.040 Now in many ways of expressing that that fiat here's one

00:24:35.720 So

00:24:37.320 Contains a lot of hidden stuff it pretends only to contain that first first row

00:24:42.040 but

00:24:47.320 Actually

00:24:49.800 There are some

00:24:50.840 Reportedly factual statements about numbers that purportedly have something to do with physics and then there has to be a

00:24:58.120 Principle to give them some normative psychological meaning

00:25:02.200 Second row and then the third row actually you need another axiom from decision theory to say how one should actually behave

00:25:09.240 Rather than how one should think and this is weird

00:25:14.920 But luckily

00:25:17.320 It so happens

00:25:19.480 That the only

00:25:21.800 stochastic theory that has ever been proposed in the history of science

00:25:26.520 For as a fundamental description of the world is quantum theory

00:25:31.560 In its mid 20th century state vector collapse form

00:25:39.640 And in that form its probabilistic part is called the born rule

00:25:45.240 Which says that if and only if

00:25:49.960 An observable is measured then the probabilities of the various outcomes are the moduli squared of those coefficients

00:25:57.320 And the bottom line there by the way

00:26:02.360 Does anyone here actually believe that the state vector collapse occurs in physical reality?

00:26:10.360 Show of hands

00:26:12.120 Okay, no good

00:26:16.920 So I'm so one person so you have my sympathy and

00:26:21.800 I hope you'll see in what follows that that help is at hand

00:26:28.120 closer than you think

00:26:31.960 So because

00:26:36.200 Well

00:26:39.160 Help is at hand because

00:26:42.120 Ordinary unitary non collapse quantum theory

00:26:46.040 provides in large part the way out of that whole probability scandal

00:26:52.120 It's called the decision theoretic approach

00:26:55.080 Sometimes called the decision theoretic approach to the born rule or to probability

00:26:59.320 But those are both misnomers because neither the born rule nor probability nor collapse of course

00:27:06.760 Ever appear in the decision theoretic argument and in its simplest form it goes like this

00:27:13.560 We imagine an array of gaming machines

00:27:20.520 One arm bandits

00:27:23.720 In a casino so there's a whole array of them

00:27:29.080 And you play by inserting one casino token and then when you pull the handle

00:27:35.720 The machine prepares a quantum system

00:27:37.720 System in inside itself in a state psi and then measures an observable x of that system

00:27:44.760 It then displays the result as shown in red on the middle panel

00:27:50.600 And that will therefore always be an eigenvalue of x

00:27:55.960 And then the machine delivers a payoff of that number of casino tokens

00:28:00.440 We need not be a whole number. We're allowing fractional tokens if if x has non integer eigenvalues

00:28:09.000 Different machines in this casino

00:28:11.880 identical except for the state psi which is constant for each machine but different for different machines

00:28:19.560 But the size not a secret. It's written on the front of the machine just like this

00:28:23.560 Conveniently expressed as a superposition of eigenstates of the observable x

00:28:33.080 Now four machines whose psi is a single eigenvalue of x

00:28:40.680 With eigenvalue little x then playing on that machine is not a game of chance

00:28:47.320 It's it's just a matter of putting in one token and receiving back little x tokens

00:28:52.200 Let's call that a classical machine

00:28:56.200 Because it could be implemented without quantum systems

00:29:00.680 Without quantum technology so

00:29:04.280 Other things being equal

00:29:06.840 A rational player would be willing to play on any classical machine

00:29:12.280 That has little x greater than one and unwilling to play when

00:29:16.440 It has little x less than one

00:29:23.080 What about cases when psi is not an eigenstate of x what then is the dividing line between being worth playing and not being worth playing

00:29:32.840 Well, let's call the dividing line

00:29:36.280 For for a state for a machine operating with state psi. Let's call that dividing line V of psi

00:29:42.120 and

00:29:46.440 This is perhaps a little bit of a wordy definition, but it's just the maximum amount of money that

00:29:53.080 The player would be willing to pay for the privilege of playing that with that machine

00:30:03.240 So for a classical machine

00:30:05.240 Um psi is an eigenstate of x and V of psi is just the eigenvalue. Well some other facts about V of psi in more general

00:30:15.000 psi are obvious to

00:30:17.800 We don't need probability or the ball rule or anything

00:30:20.920 For example, if the if the state is a superposition of eigenstates of x

00:30:26.840 All of you whose eigenvalues are greater than one

00:30:29.400 Then elementary rationality says that it's worth playing because whatever the outcome

00:30:36.040 The machine will give you more than the one token that you put in

00:30:40.760 And similarly for a superposition with all eigenvalues less than one

00:30:46.120 It's not worth playing that is it's not worth playing in the token winning sense of the game theorists

00:30:53.000 You might well play for fun

00:30:55.240 But then you're being paid partly in fun

00:30:58.120 So let's ignore that complication

00:31:01.640 But now what if

00:31:04.440 The hard case what if psi is a superposition of two eigenstates. Let's say one with eigenvalue below one and one with eigenvalue above one

00:31:14.920 Well in collapse quantum theory with the ball rule and everything

00:31:19.240 That tells us that for general states psi the probabilities of the respective outcomes are those coefficient squared

00:31:29.720 And then the principal principal tells us to adjust our credences

00:31:33.960 To match those numbers that doesn't say why and that probabilistic game theory tells us that a rational player

00:31:40.680 Should value playing such a machine the same as if it were guaranteed to produce that expectation value

00:31:47.000 Again, doesn't say why in general axioms of stochastic theories are not explanatory which alone should disqualify them from

00:31:59.960 being

00:32:01.960 the part of any

00:32:03.480 Scientific theory in fundamental

00:32:05.800 science

00:32:06.840 But I digress

00:32:11.560 Now what about without collapse

00:32:13.560 Well, let's take a simple case of an equal amplitude superposition

00:32:21.080 X with eigenvalues x1 and x2 each with amplitude one over root two so we're aiming to prove without collapse or anything

00:32:30.120 that

00:32:32.600 The

00:32:34.440 V of that equal amplitude state sorry

00:32:37.640 Will be the average of x1 and x2, so that's what we want to prove

00:32:44.680 So here's the proof a quick and dirty version of the proof the the devil is in the detail which are not going to talk about

00:32:52.280 the details of

00:32:55.720 Extensive but they lead to the same conclusion

00:32:58.760 So first of all we need to note

00:33:01.240 Two implications of elementary rationality

00:33:04.680 Not probabilistic in any way

00:33:08.760 Namely equations one and two

00:33:11.160 I'm stating them for a slightly

00:33:14.440 More general case, but it doesn't matter that the theta is going to be pi by four in the end

00:33:19.560 So equation two

00:33:22.120 Says that V of side does not depend on the objective exchange value of casino tokens

00:33:28.440 As long as they're additive

00:33:30.440 If the casino suddenly declares that it's going to redeem tokens in pounds instead of dollars

00:33:37.240 The relative order in which a rational player values playing on different machines will not change

00:33:46.360 So that's one implication of rationality and and

00:33:50.520 The other is expressing equation one

00:33:54.360 If two machines use superpositions

00:33:57.480 where each eigenvalue in the

00:34:01.320 Expansion of one of them is differs by constant k from that in the other

00:34:06.760 Then the rational players valuation of the two machines also differs by that same constant k and that's just because

00:34:15.560 In that case the first all the first machine does is physically is the same as this what the second one does plus

00:34:23.960 additionally paying out

00:34:25.960 k tokens

00:34:29.560 Now we make those substitutions

00:34:32.280 there on

00:34:33.480 On the slide

00:34:35.080 And it follows with a bit of algebra that for the equal amplitude state

00:34:39.880 V of psi is indeed the expectation value of x in that state and we can prove the same for a general state

00:34:48.920 And that's QED

00:34:51.800 But look what we've done here

00:34:53.800 In in a deeper sense we've proved the same conclusion

00:35:01.480 About what rational players do

00:35:05.720 As we would have from classical

00:35:09.000 Collapse quantum theory

00:35:11.160 But without assuming that collapse happens

00:35:14.280 We've proved it without the born rule without those

00:35:17.400 axioms

00:35:19.080 And all that stuff

00:35:21.080 So we've done this on the

00:35:25.960 right-hand side

00:35:28.520 Whereas with collapse quantum theory we have to go through all that process on the left-hand side to get to the same conclusion

00:35:40.440 So on the right-hand side the only assumptions are

00:35:44.120 elementary rationality and

00:35:46.120 Unitary quantum theory without without collapse from the perspective of this talk

00:35:54.440 That means that we have dispensed with probability

00:35:58.040 both in nature in the quantum world and in our minds if we have any credences about the quantum world because

00:36:07.080 In nature as described by quantum theory there are no stochastic processes and

00:36:12.920 no

00:36:13.880 credences

00:36:15.880 In the sense of beliefs with numerical measures that obey the probability calculus no credences

00:36:21.880 affect

00:36:23.400 The decisions of any rational person making decisions about quantum systems

00:36:29.960 But it's even better than that

00:36:33.080 Those decisions now

00:36:36.040 in on the right-hand side

00:36:38.040 are not only derived but unlike in the collapse case they are explained

00:36:47.240 Because we don't have to introduce all those unexplained postulates

00:36:53.320 And that also explains why collapse theory despite its false assumptions

00:37:00.280 Was and is successful in a particular domain of application

00:37:04.200 So now let's look again at that list of fundamental applications of probability

00:37:11.800 We can strike out quantum theory from the list

00:37:15.560 And we can put a tentative mark there

00:37:18.200 About credences too since we now know that they're not needed in this particular application

00:37:24.360 We've also eliminated

00:37:27.160 probability from the theory of games of chance

00:37:31.240 that use

00:37:33.240 quantum processes

00:37:35.800 Where the chance element is generated by quantum indeterminacy

00:37:40.600 So what about games of chance in general

00:37:43.960 Well recall what I said at the beginning probability is a is a very large sledgehammer with which to

00:37:51.560 crack the egg of

00:37:53.560 Modeling things like fair dice

00:37:56.360 Now we see that the same job could be done by quantum theory as by the

00:38:01.880 Impossible physics that they assumed since a pseudo random sequence would have served the same purpose

00:38:10.520 So would a quantum generated sequence?

00:38:14.280 And for the same reason we can strike out

00:38:18.520 the use of probabilities in general decision theory which is just

00:38:25.000 Game theory writ large

00:38:27.000 And in actuarial science. I just put that in because it was historically a very early application of probability

00:38:42.680 It measures it prepares the system in a state sign and then it measures an observable X on that system

00:38:49.240 The result is the pale

00:39:03.320 Just as in game theory the theory of evolution

00:39:09.000 Doesn't depend in any way on true randomness in the mutations

00:39:13.160 All it matters is that the theory can explain how biological adaptations to an environment

00:39:20.360 Can evolve if the mutations aren't systematic if they don't depend systematically on the environment

00:39:26.440 Only the selection is supposed to be systematic. That's the essence of theory of evolution

00:39:31.240 And probability randomness is just a feature of the model convenience

00:39:36.760 So we can strike that out to from theory of evolution

00:39:40.920 Strike out theory of evolution

00:39:43.560 By the way

00:39:44.920 Chiara has just published a paper about the construct a theory of biology which among other things describes evolution

00:39:53.720 Without evoking randomness in any way

00:39:58.440 Of course by the by all these strikeouts

00:40:00.440 I don't mean that the mathematical formalism of quantum theory isn't sometimes useful

00:40:07.400 I'm saying that the

00:40:09.400 Quantities called probabilities in that formalism do not refer to any

00:40:17.320 stochastic

00:40:18.440 random processes in nature

00:40:20.680 Nor to anything in rational minds such as degrees of belief or credence nothing in physics or in

00:40:27.560 Minds thinking about physics

00:40:30.280 So in information theory probability was again

00:40:33.160 Originally used as as a model for an even simpler thing namely

00:40:39.320 This could be any message of n bits with the the our

00:40:44.520 Communication system needs to be able to cope with any message of

00:40:48.280 Enbits and we don't know which it's going to be and this was translated in the model

00:40:54.280 To all two to the n strings are equally likely

00:40:58.760 And this is caused also of confusion

00:41:00.760 Such as people saying that a state contains maximum information when it has maximum entropy

00:41:09.320 Which is nonsense and so on

00:41:12.520 But that's another story anyway, we can strike it out

00:41:21.960 I'll just say in passing that constructive theoretic information theory is also something that Chiara and I have

00:41:28.120 Recently developed and it does fulfill

00:41:32.920 All the hopes that we have for constructive theory in general

00:41:36.360 Including not being subject to the kind of confusion about information that I just mentioned

00:41:41.880 And it unifies classical and quantum information our paper on that is is was published a while ago

00:41:52.280 So what's left

00:41:54.280 Quantum statistical mechanics at least doesn't need probabilities since it has entanglement and and decoherence

00:42:02.920 And therefore it can avail itself of what I've just described

00:42:08.040 About quantum theory the decision theoretic approach

00:42:12.200 I should say why the universe is in such a state as to make the laws of thermodynamics hold

00:42:18.840 For example, that it's uniform that it's initially ordered and so on is a substantive question

00:42:26.600 But it's not a probabilistic question so we can strike that out too

00:42:33.000 So I'll leave striking out classical

00:42:37.320 Statistical mechanics as an exercise for the audience

00:42:40.280 Now experimental error that's an interesting case I

00:42:47.800 Think it was historically the earliest application of probability after games of chance

00:42:54.040 And it has some interesting misconceptions in it in addition to probability

00:42:58.600 Which which one of them is as follows? So

00:43:04.760 Is connected with probabilities error error processes

00:43:08.200 In experiments are traditionally categorized as random and systematic

00:43:16.760 But both of those are misleading terms

00:43:20.840 For simplicity just imagine a measurement of a constant of nature such as the speed of life

00:43:29.000 And

00:43:30.040 Suppose that we are asked

00:43:32.040 To give an estimate of the best error attainable with a given instrument like fizzo's wheel

00:43:42.440 Processes that were random with known probabilities

00:43:47.320 Would not be sources of error at all in such in such a case since they could be reduced without limit just by repeating the experiment

00:43:55.960 But experiments so the important

00:43:57.960 Errors are the ones that affect

00:44:02.600 Experiments through processes whose governing the laws are unknown

00:44:07.960 That is the laws may be known, but how they affect the experiment is unknown and those cause systematic errors

00:44:16.440 So ironically a systematic error is one that obeys no known system

00:44:22.760 So what does it mean to estimate an error caused by the unknown

00:44:34.440 Traditional to

00:44:36.120 Going to probability and subjective probability, but as I've said that's all nonsense. So what can it mean? Well

00:44:43.720 Suppose that a physical constant let's say call it chi is to be measured and

00:44:49.400 And

00:44:52.520 And that the bound for a given technology is claimed to be

00:44:58.440 Asylum

00:44:59.960 so if

00:45:01.640 Little x is the average of

00:45:04.520 measurements obtained with

00:45:08.040 A particular instrument. Well at the best the best result obtainable with a particular instrument

00:45:13.240 Then the first line x minus chi modulus of x minus chi is less than a asylum. We're saying and

00:45:21.480 For simplicity assume that the individual outcomes that we obtain when we do the experiment repeatedly we different copies of the apparatus and so on

00:45:31.000 Our x1 and x2

00:45:33.560 Then we have the both x1 and x2 both obey that equate but that inequality as well

00:45:38.600 And then just from some algebra it follows that the average of x1 and x2 just as in the

00:45:46.600 If they were random errors

00:45:49.240 Has a smaller error than either x1 or x2

00:45:53.400 Separately which is a contradiction because a asylum was supposed to be the best error obtainable with that apparatus

00:46:03.000 So

00:46:05.000 Sematic experimental errors cannot be bounded by any known bound

00:46:11.320 Therefore among other things they can't be described by probabilities

00:46:15.560 Nor can our knowledge about them

00:46:19.880 These unknown variables in in science are counterintuitive and often misunderstood

00:46:26.760 Because we have been accustomed by

00:46:28.760 Bayesianism and other subjective philosophies to replace

00:46:35.720 Real ignorance by fantasy probabilities

00:46:40.840 But we've just seen that neither physical probabilities nor

00:46:45.000 probability credences can enter the analysis of errors in a fundamental way

00:46:51.080 So what do we mean when we estimate the error in an experiment?

00:46:59.480 Well, that turns out to be a big question

00:47:02.200 With surprising answers that there's no time to go into here except I'll just briefly mention

00:47:08.040 I hope to complete a paper on that quite soon

00:47:11.880 But I'll just briefly mention that what what what an error estimate really means is

00:47:18.280 It's the error

00:47:20.280 Such that if the experimental result turned out to differ from the true value by more than that when the true value is later discovered by some other method

00:47:29.320 Then if it was more than that it would make the theory of the apparatus problematic

00:47:36.200 So that's in short what what an error means but for present purposes

00:47:41.720 We can just strike out error analysis

00:47:44.360 There

00:47:50.280 So Brownian motion

00:47:53.000 That doesn't actually purport to be

00:47:55.880 a fundamental theory

00:47:57.400 Since although it has a stochastic law of motion

00:48:00.600 That's assumed to be an approximation to a more microscopic cause such as impacts from molecules

00:48:07.560 That aren't explicitly treated by the theory of Brownian motion. So

00:48:11.640 That theory is also related to the theory of errors

00:48:16.520 but in the approximation that the so-called random errors are

00:48:22.600 Swomping the systematic errors

00:48:26.040 Although we've just seen that that's something that cannot be known in a particular case

00:48:32.120 But

00:48:34.120 The unknown systematic errors are too large

00:48:37.320 Then it's not Brownian motion. So we can strike that out

00:48:50.360 And with it we can also strike out the applications from high finance

00:48:56.200 That are directly analogous to the theory of Brownian motion

00:48:59.800 Finally since none of those other applications of probability now involves stochastic processes

00:49:10.120 They do not require credences either

00:49:13.400 Doesn't matter what scientists think

00:49:18.600 What scientists believe

00:49:21.080 About whether a theory is true or false

00:49:23.640 As long as they execute rationality

00:49:26.360 And so Bayesianism and the other subjective interpretations of probability have no remaining scientific function

00:49:34.760 And for these purposes they can be dropped too

00:49:40.040 Now I hope I have shown you that probability doesn't make sense as a description or explanation

00:49:47.240 Of what really happens

00:49:50.200 It can be a metaphor

00:49:52.200 It can be a technique for calculation or an approximation in a certain sense

00:49:58.520 But approximation to make sense has to be an approximation to something

00:50:05.400 So if probabilities are to inform decisions in some approximate way

00:50:11.880 There has to be an explanation

00:50:14.600 rooted in a

00:50:16.600 Description of an actual physical world in which events and processes happen

00:50:22.840 Not probably happen and not justify some ad hoc

00:50:27.800 axioms

00:50:28.600 So I hope I've also persuaded you

00:50:31.480 that it's right and proper

00:50:33.720 to try to

00:50:35.720 expunge every trace of

00:50:38.360 probability and randomness

00:50:40.600 from

00:50:41.720 our

00:50:42.680 From the laws of physics and from our conception of the world and from the methodology of science

00:50:48.280 So that we may fully restore realism

00:50:52.920 as well as rationality

00:50:55.240 It's a

00:50:56.440 simplification

00:50:58.200 a unification

00:51:00.680 And an elimination of nonsense

00:51:03.960 And it's true

00:51:06.360 Now

00:51:06.600 I bet there are hard-headed instrumentalists in the audience who might be thinking

00:51:15.000 Okay, so this simplification is all very nice and elegant

00:51:20.440 But since the principle uses

00:51:23.480 Of of the mathematics of probability are largely unaffected

00:51:29.480 What really is the benefit of eliminating it at the fundamental level either

00:51:34.120 Well, it's true fundamental falsehoods

00:51:39.080 Don't always rear up and bite you

00:51:43.160 You could believe in a flat earth

00:51:45.480 As many people did for a long time and and that falsehood may never have affected

00:51:51.960 Your life or your thinking

00:51:54.360 On the other hand, it might have destroyed the entire human species

00:51:59.480 Because belief in a flat earth theory

00:52:04.600 As a description of reality

00:52:07.240 Is incompatible with developing say technology to avert asteroid strikes

00:52:15.240 Similarly a belief in probability

00:52:19.960 in quantum theory

00:52:21.960 may not prevent you from developing quantum computers quantum algorithms

00:52:28.920 In practice

00:52:30.440 But because

00:52:32.040 probability and the born rule

00:52:34.360 entail

00:52:35.640 fundamental misconceptions about the physical world

00:52:39.320 They could very well prevent you from developing the successes of quantum theory

00:52:45.720 And in particular

00:52:47.720 Constructive theory is the framework in which I suspect

00:52:51.960 Successes to quantum theory will be developed

00:52:55.640 As I said

00:52:57.160 Constructive theory is incompatible with physical probabilities

00:53:02.680 So that is my case

00:53:04.840 Thank you

00:53:06.840 Thank you very much David

00:53:17.080 Just before we take questions, let me mention that there's a website very easy to remember

00:53:20.680 Constructive theory the one word dot org where you'll find many of the things that they alluded to

00:53:26.280 papers and so forth

00:53:28.680 Okay, I saw one hand to go up

00:53:30.520 So I'm sorry with the slot machine. I'm pretty. I'm so far walking out of here with no

00:53:39.320 Understanding of how to modify the way of thinking about a single machine and it coming in so

00:53:44.920 If someone asked me how to

00:53:46.920 What are the funny numbers in this wherever it's mean in front of I can see it's in the slot machine

00:53:52.280 I would say well

00:53:53.800 With this funny numbers means I pull the handle lots of times then you know limit that I do it forever one

00:54:00.840 They're at the time we get this

00:54:03.560 This one result

00:54:05.080 Yeah, another two thirds of the time we get this other result and say well we

00:54:10.120 Which we'll be getting next

00:54:14.360 I don't I'm not I didn't understand how to modify

00:54:16.840 I'm the way of thinking about that based on our step you talked about

00:54:19.640 Um, well the idea is that

00:54:24.360 I'm not sure which version of quantity you're thinking in terms of possibly collapse theory in which there are such a thing

00:54:32.680 Right, yeah, I want to know. Well. Okay. The way you think about is not in terms of the outcomes

00:54:39.480 the outcomes are

00:54:41.480 an emergent property

00:54:43.480 In some complicated way what those coefficients are they're just a descriptive descriptors of the state the state that the thing is is prepared

00:54:52.600 So for example, if it was a spin system, it would be prepared by rotating it in some way

00:54:58.760 With magnetic fields and and those coefficients would depend on the angles through which it's been rotated

00:55:05.800 That's what it actually means

00:55:08.120 Now what that causes in our subjective experience

00:55:12.280 Do you need an interpretation of quantum theory to that?

00:55:16.920 and

00:55:18.280 interestingly all we need

00:55:20.600 Trus and the right interpretation is the many universe interpretation, but we don't really need to

00:55:26.120 Draw on that for these results. We just have to say that the motion is

00:55:32.120 unitary that's all the

00:55:35.480 State exists physically and its motion is unitary

00:55:38.040 Other questions?

00:55:44.760 I might just find out more about what you think about

00:55:47.400 We insist

00:55:49.400 Go along the idea that it's very weird to happen in a fundamental micro-physical theory

00:55:54.440 And even future we find it's a better which is a deterministic. We have to wrestle with what that means

00:56:00.280 Yeah, yeah

00:56:02.280 But there's a high level concept. There seems to be useful in some kind of vision philosophy of science. It doesn't

00:56:10.280 It's not trying to talk about the mental visits itself

00:56:13.160 so in observer

00:56:15.160 People would say has a credence. Maybe if they don't know exactly what the micro state of the real world is and they have some

00:56:22.040 They have some idea that I don't think it's all there in this region

00:56:24.920 But I've got no reasons to differentiate between actual micro states. Awesome. So having no reason is

00:56:30.920 It says so these are two slightly different ways of doing a subjective interpretation

00:56:36.600 the first one where you

00:56:40.040 Guess what the probabilities are

00:56:42.680 In some theory and it's going to be

00:56:46.280 An approximation to some microscopic state that you don't know that's a legitimate way of approximating something

00:56:52.360 You you have guessed what the probabilities are and then then you can test if theory says that there's something you can test whether that's so

00:57:04.360 When you say you don't know which of the way what the micro states are then you're trying to derive

00:57:10.520 knowledge from ignorance and

00:57:12.760 That is simply logic logically not valid and it's also inconsistent with the probability calculus

00:57:18.280 It's only by sort of hand-woven ignoring that fact that one can apply

00:57:24.920 Bayesian philosophy in words to things like we don't know what the state is if we don't know what something is we don't know what it is

00:57:32.600 so you know there's the standard reputation of that

00:57:39.400 Kind of subjective interpretation is if there are three possibilities

00:57:42.920 A B and C you don't know anything about which state it's in then you might say well bet on whether it's a or

00:57:51.400 Either B or C and then if that had if you if you say that because you don't know

00:57:57.320 Which of those true possibilities is right that you must give them equal probabilities then the same is true for the

00:58:03.400 Permuted versions and that's inconsistent

00:58:06.680 It's logically inconsistent, so it can't be used for that, but it has a

00:58:10.680 The situation is very analogous to the flatter theory

00:58:14.760 When you use the the when you assume that your garden is a plain surface

00:58:20.440 You're not assuming the flatter theory. You're just assuming the mathematics of the flatter theory applied to this process

00:58:27.000 But there's no way in which you are

00:58:29.000 Assuming that the true thing is an approximation to the flatter. It isn't

00:58:41.960 Decision-theoristic argument which is used to to bypass the principle principle. Yes, and the amount is arrived or normal you invoke this function of the

00:58:54.200 valuation

00:58:58.280 However, you also assertive that it had some

00:59:02.760 Obviously

00:59:04.760 And you also assertive that the rational entity would

00:59:18.840 Assuming a rational entity who has linear valuation. So this same issue arises in a classical game

00:59:25.240 As I said a person a real game player is not the same as the idealized game player of of

00:59:36.040 Game theory a real game players all sorts of other motivations

00:59:41.480 Otherwise a real game player would never play a game of chance sections in red where the expectation value of your winnings is negative

00:59:50.120 so

00:59:52.120 And we assume this idealized game player the classical game theory and we assume exactly the same player

00:59:59.560 In the decision theory approach the quantum theory. So it's not because we want to

1:00:05.480 Say what

1:00:07.480 Why people play games? It's just this one particular aspect of gameplay that has probability

1:00:13.400 And it's that it's it's knowledge is between between between between the two basically so you sort of made a search about

1:00:24.600 So

1:00:32.600 The search about how the player behaves is the same in both cases. We're analyzing how a player who believes a particular thing

1:00:39.400 Will behave. We're not saying that any real player actually behaves like that. There's no real player does exactly

1:00:49.720 Take another question

1:00:55.880 You're saying is you're eliminating the distinction between the epistemological chance and ontological chance

1:01:02.440 I'm saying that the epistemological chance well, well, yes, I am I'm saying that neither of them exist

1:01:11.560 But ontological chance can be a good approximation in some situations and epistemological chance

1:01:18.280 Really should be dispensed with all together

1:01:21.160 Okay

1:01:31.080 The outcome yes

1:01:41.160 Probably

1:01:44.040 Yes

1:01:46.040 Well, no that's a particular situation again in which the

1:01:53.640 Probability calculus may be a good approximation

1:01:58.280 Rather like

1:02:00.600 If we think about the distribution of the digits of pi

1:02:04.280 Then it's a meaningful approximation to say well, they're going to be random. They're not really random

1:02:09.320 That the mathematics of them has enough in common with the mathematics of truly random sequences for it to be a good approximation

1:02:17.640 For some purposes, but obviously not for all purposes

1:02:21.000 Yes, unpredictability can be modeled by randomness sometimes

1:02:51.000 You seem to be wanting to expunge probability

1:03:03.720 Replacing it with the decision of the arachic arguments in which

1:03:10.040 Made with respect to some admittedly non-existent

1:03:13.400 Play-up or some game that is probably also not being played. Yes, so I'm really struggling to see how that is any more desirable

1:03:25.560 Than any of the other approaches to the admittedly philosophically problematic probability

1:03:32.280 Yes, so

1:03:35.560 The main advantage is it doesn't assert anything false about reality

1:03:40.120 Well, it's it's asserting the some reality

1:03:45.800 No, no, it's just saying that if so it's taking an idealized

1:03:52.360 Game with idealized

1:03:55.320 Processes happen you quote the randomizing hand to the place

1:03:59.720 And it's analyzing how those players should or would behave if they believed

1:04:04.280 Some rashes if they if they conform to some elements of rationality that have nothing to do with probability

1:04:11.320 But just the pattern tie a rod in the discount factor

1:04:15.880 Yes, it's counterfactual, but then you need an argument to say that a real situation

1:04:21.720 resembles that idealized situation in particular works

1:04:25.160 So if if I go into a casino to play roulette

1:04:30.200 Obviously, I'm not satisfying the

1:04:34.520 Accidents of games theory because I'm playing a game which has an expectation values negative

1:04:39.080 when on the other hand

1:04:41.640 If I play poker and I'm good at it and then I wonder whether

1:04:47.720 Whether to

1:04:49.400 Draw or not or how much to how much to bet

1:04:53.560 Then I can use game theory because and only because

1:04:57.480 I guess

1:04:59.480 That my real situation resembles the idealized situation in the relevant ways

1:05:05.640 But it's only as good as that. It's not a theory of reality

1:05:09.240 But it's so it's based

1:05:11.240 You said on that I guess

1:05:13.240 On your correspondence between what you might be doing certain situations to something that you count back. Yes

1:05:20.920 Exactly

1:05:22.920 Inside me right now

1:05:24.920 But there are carbon 14 atoms decaying

1:05:30.280 That there is no one's doing that game with chance

1:05:34.760 There's no sensible way in which you prepare it to an ideal

1:05:38.440 Making that game jump talking about does make the title take a bit more

1:05:42.760 I think we'll just let data replace that

1:05:46.040 Okay, well, you can if you want to work out the half life

1:05:48.920 Then you simply have to imagine the situation in which these game players bet on how long it will take and

1:05:55.320 What the rational thing for them to do is and you'll find that the rational thing for them to do is to bet on an exponential cake