11th UK Foundations of Physics Conference — Laws, Symmetries & Quantum Probabilities

0:00 Okay, so today's first speaker is Peter Allendan, who is at the University of South Carolina, and also has been visiting the Oxford for the last year. And he's going to talk about laws, serratrix, and quantum properties. I should first thank the organizers for giving me the opportunity to vote on giving this talk on Friday the 13th, which is appropriate because I'm going to argue in superstitions, not just Friday the 13th, but also some of the superstitions that we hold in physics. First, I should acknowledge my two institutions. And also, I should thank the Fulbright Foundation for the grant that enabled me to visit Oxford during this academic year. And this talk is based on this paper, which is in the archives. The first position that I want to deal with is what I call the paradigm of laws. And the feeling that many facelessness have towards loss summarized usually by the statement of Max Planck. But I want to emphasize that the construction of this paradigm was not at all self-evident or obvious. It took many years for philosophers to recognize that we could describe the world by means of loss. The early explanation of the world, in fact, on the initial conditions of the universe, such as what you would find in the book of Genesis, a description of how the universe was created in six days.

2:30 But there was a major breakthrough that happened in the 16th, 17th centuries, which is that some natural philosophers recognized that if they give up, trying to describe boundary conditions, which is a very ambitious thing to do, to describe everything that exists, But instead, look for universal regularities in phenomena, that is to predict what would happen if we are given some initial condition which we don't know exactly what it would But then we can predict what's going to happen as a consequence of those initial conditions. so this led to laws which describe these universal regularities and the initial conditions which are contingencies this led to a tremendous progress in our knowledge and it has been the paradigm of physics for almost four centuries there have been many people who contributed and some of the most prominent ones are given here Galileo, Descartes, Newton, Heidel, Faraday, Maxwell, Einstein, and Schrodinger. But after Schrodinger, something strange happened. As you all know, as you all know, the laws of classical physics did not apply to radiation and atomic phenomena. So people knew that the laws of classical physics are not valid. So what Pesce did, working within the paradigm of laws, is to do what is the most natural thing, which is to replace the laws of classical physics with a new law. That is called the quantum law. And that is described by Schrodinger's equation. Now Schrodinger's equation, like the laws that existed before, Schrodinger's law, the evolution of the state of a system, in this case given by a wave function, and it undergoes a unique evolution. And that is described by Schrodinger's equation, which you can solve and obtain this unique solution, given the initial condition, which is the

5:00 initial wave function. But then, if you try to verify this prediction, you need to make And then something strange happens. The wave function seems to undergo a sudden change. So there is a collapse of the wave function leading to the measurement problem which people have been working on ever since. Schrodinger created his theory. Now, there are two possible approaches one can take to it. First of all, you can say, well, it seems like Schrodinger's law doesn't tell you what is going on during the act of measurement. That is to say that this law breaks down when a measurement is made. There seems to be no law governing the measurement process. Or you could say, no, we want to work with the paradigm of law, so we have to do one of two things, rather reinterpret Scheringer equation in such a way that it could be a law that all physical processes, including what goes on during a measurement, or modify this law so that we get a new law that would then describe what goes on during a measurement. Now, there have been a lot of work that have been done, which have been done as the second approach, that is to work within the parallel laws, either by modifying Schrodinger's law, and there was so many so much work like you know, Gerard-Iramini and Weber and then there was this work by 10 laws trying to do the gravitational to modify Schrodinger's equation and there was a final work done by introducing a non-linear equation. On the other hand there have been a lot of good work that have been done which takes Schrodinger's equation as the law of quantum physics and the important ones, most prominent ones are the ever-interpretation where the wave function never undergoes a collapse but then you pay a price for it which is this cosmic schizophrenia of having so many different worlds and so you get replicated millions of times every time you interact with the quantum system or you can take the Bohm approach where you have a dual ontology

7:30 of the wave function and the particle and the wave function guides the particle So these are all approaches within the paradigm of laws. But I want to now explore the possibility that, in fact, there is no law governing the measurement process. Now, what happens during the measurement is what we actually observe. What is predicted by Schrodinger's equation is the evolution of the wave function is something that we do not observe. So I want to take seriously what we actually observe, that is that during this measurement that we perform on the quantum system, there seems to be no law governing the physical process. So I want to extend that to all physical processes, because after all, I want to treat the measurement process like any other physical process. And another reason why I'm going to consider this possibility that there is no law is that, which is a philosophical reason, which is that there's a certain metaphysical necessity that is associated with a law which tells you what things can happen or cannot happen. But this is not a logical necessity, like something like Pythagoras' theorem, which you know should be valid for any triangle, any rectangle triangle, but then that's because of the Euclidean axioms and it's tautological in that sense because it's something that cannot be refuted once you accept these axioms. But the law of physics is not like that. In order for it to carry information it must be refutable. And so it is not a logical seem to be one, but at the same time, it's an imperative, and it's not something intermediate between a tautology and a universal statement that is in agreement with the whole observation. Also, a law always comes with symmetries, and this is due to the reproducibility of experiment. If I do an experiment over here and then I translate my apparatus somewhere else and do the same experiment, I get the same result. Because that's translational

10:00 symmetry. Or I can do the same experiment tomorrow or yesterday and get the same results obtain, the style translation of symmetries. So, the law of physics, by its very nature, is associated with symmetries. However, just as much as we can have the same law for many initial conditions, as I mentioned earlier, we can have the same symmetries for many different laws. So, if you instead of trying to obtain laws, as being the fundamental concept of physics, we start with symmetry, then we have a greater economy of concept. Because the same symmetries can have many different laws. And also, as I mentioned earlier, there was this major breakthrough that was made when people gave up the initial conditions and started looking at laws. because there could be many different initial conditions with the same laws but then if you fix the initial condition then the law gives you a unique evolution so we end up with a unique universe so one could argue that it was not really such a big radical change from the view that existed before. However, if you take this point of view that symmetries are more fundamental than laws, then it is really not necessary for a system to undergo unique evolution. There could be many different evolutions of the same system that are consistent in the same symmetries. And this is a possibility that I will explore. Okay, one advantage of taking this point of view is that if you don't have laws, then, here by laws I mean causal or dynamical laws, then the world not necessarily be deterministic, okay, because not every physical system, for that matter, any physical system is going to be put in some cosmic realm for it to obey some evolution equation.

12:30 Okay, so different systems that start with the same initial condition can end up with different final conditions. And this is something that we actually observe in nature. It seems like nature has a certain capriciousness. That is, if you think in the paradigm of laws, which is that you can produce, for example, atoms, which are all in the same initially excited state, but they decay at different times. What quantum mechanics does is to predict the probabilities of decay. And this is why that physicists today believe that there are laws because the probabilistic predictions of quantum mechanics are extremely successful. So anybody who wants to do with causal or dynamical laws will have to provide an explanation for the probabilistic predictions of quantum mechanics which is what makes it the most successful theory that has ever been created and that is something that I will try to do in this lecture alright so what I am going to attack now is causality and before doing that I want to give you these two passionate quotations by Einstein in defense of causality which would seem to weaken my case but I hope to persuade you that in fact there is a certain causality in the metaphysical sense in physical processes although there is a certain physical causality which is what is exemplified by these positive predictions that I mentioned earlier. Okay, now, according to the laws of classical physics, a particle takes a unique effect rate from a given initial point to a final point. So let's take A to the initial point. And this is what I call the Cosmic Railroad.

15:00 So it's compared, for some strange reason, to follow this unique trajectory. But suppose we give up the notion that there are causal laws that compare the system to move along this trajectory. Then, we should say that all possible trajectories have a different problem. So I call this a maximal violation of the laws of classical foolishness. you can take any arbitrary trajectory joining A to B. So, if, for the universe to come to existence, we need to have probability amplitudes. Actually, you should disregard the central number, assuming now there is probability amplitudes are complex numbers. But, now, the set A of probability amplitudes It should form an algebra because I shouldn't be able to add problem temperature which is what gives rise to this cancellation that would be We need to say to multiply the probability of B, because when a system goes from A to C, it can go to B, and then the probability of it going from A to C is the product of the two probabilities, that is going from A to B and B to C. So we should have this A, a probability amplitude in algebra, but then we need it to have a norm from which we can construct the probabilities, and that norm should have this property for the reason I just mentioned, okay? So we have the amplitudes to go from A to B is xi, and from B to C is phi, and so xi phi is the amplitude for it to go from A to C, and then we should have

17:30 this property. Now there is a theorem of Hurwitz and Albert, which says then that A, should they be the same real complex numbers, quaternions or octonions. Now octonions are non-associative, and that makes it unreasonable to octonians as probably amplitudes to illustrate that let me consider a box like this and let's suppose that I have the other box with two holes in it So now, a particle here can go through this or through this. So let's say that the amplitudes are xi, phi, chi. We still don't know what these amplitudes are, but they're one of these four possibilities. and the real complex numbers are quaternions or octonions. Okay, so, and then let's suppose that there's another amplitude here which is called alpha. So the amplitude where it goes from A to B is alpha plus xi phi chi. But then now when you multiply xi phi chi, there's an ambiguity. You see, this is not equal to alpha plus what you get by first model time, y, phi, and then chi. So coordinates, coordinates are a little good. Do you have five minutes? I've got five minutes. I don't think I can finish it in five minutes. but I'm going to try and finish the case I can. Okay. Alright, so it leaves us with quaternions and complex numbers. The real numbers are not good because

20:00 if the log of the real number is the same for all the parts, then the real number can only differ by sign, and then when you add all those real numbers and furthermore what I'm going to lead up to is the Feynman path integral formulation of quantum mechanics Steve has shown that there is no Feynman path integral formulation of quantum mechanics ok so on that basis I want to exclude quantum mechanics as well so what we have is the sum of amplitudes and because these complex numbers have the same norm. They can be written as some non-negative number any time usually is gamma. And S-gamma is a real function of the parts. And this may explain why we have complex numbers in quantum mechanics, because the probability of two must be complex numbers. The second postulate I want to make is that the probability of under a group of symmetries. And these two postulates imply that this phase S gamma is any real function of the paths that is invariant under the symmetries. if you do this then because I don't have a law I should allow for SKMR to include all the terms that I love by symmetries and if you do that with the fields that we have in the standard model, then it turns out that for all the ultraviolet divergences, there are counterterms which cancel these divergences. So that you have a theory which is just as renormalizable as the renormalizable standard model. But then these higher-order terms will be seen only in when you go to higher energies. so in presently accessible energies we see only the Lagrangian of the standard model

22:30 ok so let me go through this quickly so for the universe to come into existence the self-consistent entity in the absence of cause and loss there should be property amplitudes that persist that are complex numbers But now the question is, how do we determine the probabilities from the probability amplitudes? Okay, for this, I consider the well-known double-street experiment where a particle can take one of two possible paths. So the amplitude, for it to go from, say, from the initial point to the final point, the sum of the two amplitudes, the two parts. Now, but on the other hand, if you observe through which slate the particle went through, then the properties of the properties are going through either slate. Okay, for example, if you use the relative frequency definition of probability that Lucien was using in his talk, then you will come to this conclusion. Now, the interaction by definition changes the phase of the property and this uncertain phase gives rise to decoherence and usually we are looking at decoherence if the system gets entangled with some other system it gets entangled with orthogonal states and so that's what is to decoherence but you could equivalently think of decoherence as being due to the influence of the environment on the system most particularly space of the system becomes uncertain as a result of the interaction and this is the result of the work done by these authors. And so I require that if you average the face of one of the amplitudes then you should get some of the two probabilities. And since the property is a non-negative function, I should assume it to be some absolute value of y raised to power n. And then, one can show, there is some algebra that one has to do, that this equation would be satisfied only if n is equal to 2.

25:00 because this integral reduces to this integral and there are two cases to consider where n is odd or even and when n is odd, this cannot be satisfied because it's a rational number where pi is irrational. So you have to make n even. So we'll use this integral here and then we this like integral I had over there reduces to this condition which is satisfied if and only if n is equal to 1 which means that n is equal to 2 so that gives us the Born rule in other words we cannot violate the Born rule actually I started a little bit late I'll take my go I'll take my go I'll take my go all right all right so the only way it can it's not possible to violate the Born rule from this approach because if you do then you're going to violate result that if you do a rich way experiment then you should have some of the two probabilities and I don't think it's sensitive to violate that condition alright but then the final question is how do we convert when do we convert aptitudes into probabilities and this is the quantum measurement problem and there was some work I did with Harvey in which we proposed a criterion for reality, which is that if two objects interact so it has to satisfy their action-reaction principle, then they exist. So I want to assume most strongly the action-reaction principle as a necessary and sufficient condition for reality. Okay, so this would give us a criterion for when we observe an object to be real when we can regard some state to be real. And if it is real, like in the case of the double-slip experiment that I considered, we are going to observe through which slit the particle went through. And then it becomes real. And so then we have to add the probability. We have to convert the probability amplitude to probabilities. And so this is the criteria that I'm going to be using for deciding

27:30 when we must convert this probability amplitude to probabilities. And this notion of relational reality, so this leads to a notion of relational reality. I mean, what people normally assume that an object exists by itself, and then when you bring it close to another object, then it interacts with this object. Whereas I'm saying that two objects come into existence when they interact with each other. Before that, they have some kind of a ghost-like existence. In fact, postulate that there's a problem with the amplitude. it's a multitude making that assumption. So, okay, I don't have time to elaborate on this, so I'll skip that. Okay, well, there was some example that I wanted to go through, but it looks like I won't have time for that. Okay, but if there are questions, you know, I can go through the example to illustrate. call this relational reality you see you know it's like position being relative you see you can only talk about the position of one object with respect to another object or for that if you take simultaneously you know it was because of the attribute until Einstein pointed out that you know you can only determine the simultaneously of an event with respect to another set of events alright so I'll stop with this and I'll answer any questions as I'm about to confine myself to just one issue, let me choose the following think there are arguments against probability and in favor of probability you get probability measure on parts because if you assign equal probabilities to different parts then the probability for one part would be zero now this is analogous to the rejection of the concept of the probability measure on let us say the space of this room on the grounds that all points

30:00 should have equal probability and therefore the probability I didn't explain that carefully but in my paper I've gone through this exact part you're raising let's consider a dark board and I'm throwing dots at it and let's suppose that all the points on the dark board are equally probable and there are infinite such points so the argument would then apply to that but you see the point is that we want our probability measure to be such that the volume is increasing. Then the probability density is going to be 0. Now in the case of the dark port, it has got a finite volume, a finite area in that case. So the only way you can have this situation you have mentioning is there's some fall-offs. So outside the dark port, we know that the probability density goes to 0. If you have a fall-off, suppose you've got an infinite plane. Let's take that to be our dartboard, an infinite plane. The number of points on the dartboard, as you say. The number of points, no, that's not the argument. I should have made it clearer. I'm saying that it's not possible to define a measure, okay? Unless that you have a finite volume when you integrate that measure. Yes, I know, but what I'm saying is the measure has to be such that the total volume has to be finite because that's obvious, because the probability is constant. Yeah, but what I'm saying is that when you have an infinite number of parts, you could, if you like, say that that's a finite volume for the measure that's one of the infinite number of parts. You could find the measure as mainly, for example. But to me, that means that you're imposing a law. If you want to make that law infinite, then that's the law. Okay, she can discuss that later. But I have thought about that point. We can discuss that later. There are lots of questions. I think maybe I'll type one more question. Yes, I am. Can I just carry one question? Are you saying that if you write down every possible term in an action so that it's a stable, and you use that as your action principle, are you saying that you then extract the

32:30 model energy limit standard model, that seems to be your claim? No, actually I don't have an explanation for the coupling constants that we need to put in, so I agree. We may need another principle to do that. Yeah, yeah, what's right? The thing is... Right, I'm putting that in. So I put in the symmetry to the standard model, okay? So then the claim is that the standard model can be looked upon as an effective field theory. That is to say that there are all these renormalizable terms, which are all the terms that are allowed by the symmetry. And they are needed because they give rise And you're saying that that fact is independent of the values of the coupling constants. Yeah, right. But the thing is, why the values of the coupling constants are what they are? I don't have the answer, but nobody is there. I mean, super-string theory, which claims to be a theory of evidence, has no explanation for the values of the coupling constants. Thank you. Thank you. Well, Ian began his talk yesterday by stating his prejudice. so I think that's actually a very good way to begin so I'm going to start by stating the prejudice that underlies what I'm saying today I've got a friend who said that he wouldn't want to be part of a universe he thought he could understand which kind of expresses my feelings I think I mean, I suppose it's possible that sometime in the next 10 or 20 or 30 years I'll find myself in the position of understanding the universe. And I suppose if that happens, I'd have to make the best of it.

35:00 It would be like trying to go for a swim in water that's only one inch deep. now I don't of course mean that I don't want to understand the universe in some limited partial sense obviously I wouldn't be here but the idea of sort of seeing right through it, well it's ridiculous of course, but it's also I think to me sort of horrible actually I've got a distinct fear that it's going to sound as though I'm kind of saying the opposite in other words that I'm some sense that physics just reduces to phenomenology that you can never get below the surface at all and I would just like to say that that would be equally horrible and equally silly I think it seems obvious to me actually that physics in some sense is deep but not infinitely deep now that's all very vague and unclear it's a prejudice so that's what's driving it Okay, that's sort of vague thoughts I've had for years and years. What stimulated me into life was talking with Chris Fultz in particular a couple of months ago. Because he's aroused quite a lot of interest amongst a lot of people for various reasons. And the particular reason he got me interested was because he suggested that the big difference, really, between quantum mechanics is that it resists, because it is possible, of course, to look at it this way, but it resists looking at it in the way that classical pictures invite the feeling that you see them right through the universe to the bottom, you know its basic elements. And quantum mechanics, well, you can sort of twist it around like that if you want to, so you can have an ever-type interpretation or something of that sort. But it's certainly not, how shall I, you don't find yourself being strongly pushed in that direction to put it as weakly as possible. And he's kind of suggested that's a good thing. And I found that very, very interesting. So I've got lots of reasons, actually, for being interested in what he's been saying.

37:30 But that probably is the thing that really got me interested. Now, having said that, I also have a lot of difficulty with some of the things that Chris says. And in particular, I have the feeling that he's kind of going... Well, Mermin said that he feared that Chris was letting go of objectivity on too many fronts, I think was how he called it, or words to that effect. Harvey Brown attributed to it the statement that reality is ineffable. In other words, we can say nothing about it. And I guess I've got similar concerns. so what stimulated this talk was my attempt to just get a little bit clearer on it I actually think I've given it a bad title I regret calling it a prologanon that was a sort of sudden wheeze I had when I was sending the title off to Harvey last week I thought that's a good title but I'd originally been intending to call it preliminary remarks which would be much better It's very, very preliminary. It's just a few thoughts. And I'm trying to clarify, really, this question of, okay, so why do we need a concept of reality anyway? People talk about the reality a lot. What do they mean by it? And I suppose I have some sense that, and I guess most people would probably share this sense, that although the word reality is actually very vague and ill-defined and it can mean lots of different things, associated to that word is a concept we just can't really let go of. And what I wanted to try and do was to isolate that central core, or to make some attempt at isolating that central core and stating it in a way that seems clear, at least to me. So that's what I've been trying to do. Okay, now Chris describes himself these days as a neo-Copenhagenist I think. I think the qualification neo is needed because he's rather clearly not saying just the same things that were said by the

40:00 what shall I call them the classical Cove of Hagen, for example. Now, actually, a long-standing, my attitude for many years has been not to think very much of the Cove of Hagen interpretation in that way, basically because it seemed to me obscure. I think Bell described it as unprofessionally vague and ambiguous, and that would describe my feelings about it in the past entirely. And certainly on this question of reality, I mean I've just chosen a quote from Bohr which kind of sort of illustrates the sort of difficulties I have in understanding what on earth he is trying to say. I've put in red certain qualifications if you were to delete the qualifications you just say reality cannot be ascribed to the phenomena or to the agency of observation. In other words, nothing's real. And it's pretty obvious he doesn't want to say that. So what he's saying is that things do have some kind of reality which lacks one or more of the attributes of independence, ordinariness and physicality. What does it mean? He's got some sort of vague sense of holism about it, but not anything I can get very clear on so that would be my difficulty with the Copenhagen interpretation and I just wanted to say that because I'm not really going along with the, if I'm interested in by what Chris says I've got severe reservations about the Copenhagen element it has occurred to me that maybe one could try making sense of ideas begin with, however. On the other hand, on the other side, I've chosen de Broglie bone because I guess that was the first alternative to Copenhagen, and what I think I would say of this would apply to the others. I want to make this point because I think I was misunderstood or rather by Jeremy, that I was kind of wanting to rubbish Bohm in particular, and other interpretations I've come,

42:30 which is very far from my intentions. I can very much accept Bohm as a speculative scientific theory. So, for instance, Anthony Valentini's ideas are very interesting. I think it's very interesting in lots of other ways. I mean, I've actually spent a year working on the Bohm interpretation and publishing a couple of papers. that at all. So I'm not trying to rubbish it. But on this question as to whether it really provides a solution to this problem of sort of reality, I don't think it does. And I think the proof of that really is what I'm interested in is this concept that you can't really let go of, that you just can't let go of. And you obviously can let go of the Bohm interpretation. I mean, the Bohm theory is a pair of spectacles that you can look at the world through, but you can always take them off. And it doesn't have any dire intellectual consequences. So I don't think the sort of reality that you get in the bone interpretation actually captures this core concept that I would like to try and characterise. And I don't really regard it as a solution to the interpretation. It's interesting, but it's not, to me, a solution. Okay, so that's the introduction. I've got a quote here from Einstein. Seems relevant. Einstein has this idea which he gets from Mack, who in turn got it from Hume. that what, he's interested in what you're immediately presented with in consciousness, I suppose you could put it, and there are these basic elementary sense impressions, which would be coloured blobs in your visual field, I suppose, I'm not aware that he's ever that specific, but I think that's the kind of thing he has in mind, and that's kind of the data, that's what you've given to begin with and out of that the idea is you reconstruct or construct the whole of science of course it seems obvious to Einstein that you can't really do it which is why later on

45:00 in this quote he says that the concept of a physical body is a free creation of the human mind he elsewhere described it as logically arbitrary and of course If something as basic as that is logically arbitrary, it kind of follows that the rest is two. So actually, it's not a very satisfactory way of going about it, I don't think. That's kind of slightly archaic, that language and that picture. I'd just like to point out that I think you still get something very similar in quite a few people who are active now, amongst them, Chris Fuchs, who inspired my interest in all of this. I mean, Chris Fuchs wants to get the same sort of central role to what he calls detector clicks. That's quite a widespread idea, actually. And there's an ambiguity, actually, in the way he uses this. A lot of the time you think he's just talking about something physical, a little thing there going click or the sound waves coming off it. But I think a great deal of the time what he's really thinking of is its registration in consciousness. So it's actually the same sort of picture as Einstein, except the starting point is even more impoverished. I mean, it's not even lots of different colours and everything else, it's just hearing a click. something very very basic so that idea actually of trying to find some basic elementary starting point in your awareness is very much like that, I don't think it's particularly unusual in this, I've seen that idea elsewhere and what I want yeah, I mean the idea is to try and reconstruct the whole of knowledge out of some basic elementary starting point It's very like atomism. It's different, of course. The Greek atomists were trying to construct the whole universe out of little physical objects. This is trying to construct knowledge out of elementary sensations of some kind. It's a similar idea. And I think it's a very bad way of looking at it. I just want to give a quote.

47:30 from a book which was quite well known. It's a book by Oliver Sacks called The Man Who Mistook His Wife for a Hat. And I think this is rather a good passage because actually this is a man who is in something like the position Einstein imagined. He's got these basic... He's given a rose. Sacks is a doctor. I should explain that the Dr. P in this passage is somebody who has an actually rather horrible brain disease, which kills him. And the brain disease says, you might, okay, you really did mistake his wife, perhaps, you might just think, well, okay, you're rather short-sighted, but that isn't the point at all. His visual acuity was very good. The problem of having that passive describes his reaction when he was given a rose. And he says, about six inches in length, that on the moon is red or with a linear green attack. It's a very, very precise description of the basic elementary sensation. But what he actually can't do is see that it's a road. Eventually, he gets there, but only as a result of smelling it. Now, I wouldn't put that passage up because it actually brings home to you what I think is a rather obvious point, which is, I'm not quite sure in consciousness. It's a very nebulous, difficult idea. I think there's some sort of validity to the idea of being conscious of things. I'm not sure what. But what I think must be true is there's no grounds for thinking that one's perceptions of colours are any more basic than one's perceptions of physical objects. They're just as immediate. And a lot of other things, too. I mean, if I'm given a rose, I will handle it in a very different way than the way I handle a knife, and that's, of course, because I'm aware of the fact it's fragile. So I don't have to think, I don't have to run over my past experience of handling roses and finding them sort of damaged if I'm clumsy with them, and then perform an inductive argument. I just know it without actually having to think about it. in contrast

50:00 to that picture that you get in Einstein and Fultz and many, many other people, I think. I would like to just stress something. I'm almost embarrassed to say it, actually, because it seems so obvious. It's as far as I can see people are overlooking it quite a lot. What I'd like to say is there's an enormous amount that is, in some sense, immediate. it. We do, of course, perform conscious inferences and arguments, and they're very important in science. But, I mean, if you consider the problem, for example, a piece of experimental apparatus, okay, it's got a magnet there. How do I know it's a magnet? Well, I can check, I can check that there's a piece of iron with some copper wire wrapped around it. And I can get an ammeter and I can check the current is flowing and it's whatever it is. But at a certain point, I just think, right, that's it, it's a magnet. I'm relying on my ability to recognize copper wire when I see it. Now, of course, actually, if I really want to, I can send the copper wire along to the lab to be analysed to check that it really is copper. But if you do that, then of course you're relying on other judgements. In any sort of scientific argument, or any argument at all, you keep coming back to things you just know. And we absolutely rely on this. Now, what I would like to suggest is that we stand in relation to the operations of our own brains rather in the way that the average user stands in relation to Mathematica. In other words, you've got this very, very complicated code. I don't know, perhaps some of you have actually been through it and know it works in detail. I certainly don't. I mean, if I want to do a calculation, I put it in the, tell it what I want it to do, and it does it. And I don't actually know how. It's not blind trust that I place in mathematics. There are all sorts of consistency checks I can and do perform. And if I really wanted to, I could have a more detailed knowledge of it.

52:30 And the same thing applies here, actually. I'm not just saying you have to take what your brain does on trust totally blind. but the fact is you keep coming back to the fact you have to trust on something you don't understand very well and we really don't have a choice about that because I think it must be at least 100 years before psychology and neurophysiology get anywhere near to giving a detailed understanding of higher cognitive processes well that's a yes about 100 years but certainly remote as of now so what I'm trying to say is that in place of Einstein's picture of sense impressions or Fultz's picture of detector clips one should think instead of the sort of starting point of scientific reasoning as being a much larger more ill defined entity I can't define it but that doesn't mean it isn't there it's know without being able to quite say how in the way that I can recognise people and tell that they're not hats in the way that Dr. P can't and I really can't say how I did that, I don't know. Right. Okay. Now what I'd like to say is that this mass of knowledge that's taken for granted has got quite a lot of theoretical structure built into it. I don't think geometry or mechanics or something like that is wholly unprecedented in human cognition. There are kind of precursors in the sort of pre-scientific background that people had before science even got going. And I would like to call that something like the primitive theory. And what I'd like to say is that to some extent this is actually built into our forms of perception. It affects the way we things. So, for instance, if I look at an object, I can't help seeing this but as a bored rubber. It's really not in my part to see it as anything else. So, I think that when you're testing a theory and using a theory, you're always relying on these primitive underlying theory that structures one's orbit's cognitive processes. And I'd like to suggest

55:00 that yes, I may hear a point I think that it's very closely related to Paul's point about the indispensability of common language it's just that it's not a matter of language it's common thought, not common language and common perception common language too but I think one shouldn't I think he's wrong to keep talking about language in this connection now, I'm just going to get to the final point interpretation is the way the theory relates to the underlying formal scientific theory relates to the primitive theory. It's making connections between the two. Now, coming to this question of reality, at various times in the development of science, you've taken some commonplace intuitive idea like, for instance, the Earth is at rest and just dropped it. and I think the attitude of somebody like Chris books actually is, you know, well we can just drop common sense assumptions about reality. I'd like to say there's an important sense in which I don't think that's possible because I think it plays an important logical role the crucial meaning that I would like to draw attention to is the meaning of the word if it comes out in a sentence like this Napoleon was a real historical character whereas Prince Andre was a fictional very closely related to the concept of fact and truth. And I think it's obvious you absolutely need this. Have I sort of run out of time now? No, you need to talk a few minutes. Okay. Now, it's just one final point, and it's kind of subtle. If you look at the logic of the words fact and belief then it's a striking fact that whatever you've got in your head is always a belief it doesn't matter how strongly you believe it there's always the possibility the facts would be different so I believe that's Harvey sitting over there but perhaps in fact it's a cat I don't know very unlikely I don't believe it at all so I think Fook's along with a lot of other people think well we don't need this idea of fact at all, I would just like to point out that the crucial role it's playing in our already

57:30 thought process is it's connected with the concept of error, if you don't have the concept of the facts being different from your belief, you don't have the idea of a belief possibly being wrong and therefore you don't have the possibility beliefs, and revising them in the course of subsequent information. And it seems to me that if you destroy that concept, you're actually destroying the foundations of science and a lot else besides. I think it's not really odd. Okay. Thank you. I think what you're saying, in time was just very little lesser degrees of things that a number of philosophers have been saying particularly about I was very pleased for you to say you think real gets its meaning from its contrasted views that's a point made by Austin in Sense and Sensibilia which is a wonderful book all about these sorts of things and provides also sustained attacking the idea of sense dating theories which will also appeal to you and that's what you seem to be disagreeing with also so that's one point I was reading, you didn't actually get to the bit on the slide, but you had a quick written sign modified from the first proposition of a fact-tasus. The problem with making the world out of facts is that there's no criteria of individuation for facts. If I'd had more time, I would have said I'd probably sit to preservation about that, it was just good. So you probably don't need to go that way, you could probably get into the real world. I definitely don't want to I was just trying to give a flavour I was going to qualify And finally when you're talking about Einstein why his position seemed unsatisfactory a stronger argument can be given there for instance the Swarton gives in his book Individuals explaining how the concept of material body and a particular person is crucial to our use of being able to talk about the world at all so it's a transcendental argument of existence of these categories of our thought I don't think that Chris wants to talk about the tactic that's being in a consciousness I don't think he's the sense-based and theorist in that way No, but I think there are shades of it I agree, but it's much more in Wheeler

1:00:00 Wheeler is differently, I think, going down those lines I think I would quote Cassidy's rather clear it's admiguous it's not just physical what you might want to say it's a fact that it's clicked and however you then want to explain that it's going to be easier he doesn't want to say it's a fact that it's clicked well he doesn't want to draw that many influences from the fact that it's clicked for me a major element of reality has been the refusal of the universe to understand me rather than the other way I can say that I mean what role do you ascribe of consensus in the scientists' use of terms like reality, truth, validity, and so on? Well, enormous, of course. Absolutely. No, it's not just a matter of an individual sitting there on his own. I'm not quite sure how it works. I mean, it's very complicated. And I don't know, but obviously the social... Well, I mean, you don't have to know how a I'd absolutely agree, it's absolutely essential it's not just a sort of no, I probably agree more the notion of a primitive theory seems quite a touchstone in what you've been saying that perhaps it's comparable to this sort of position it sort of obtains in logic and positivism by an observational language but at the same time it seems to me that logic and positivism its power from the formality of the observation language which you're denying and I wonder where you can go unless you do give some formal structure to the idea of a primitive theory I don't think I can give a formal structure to it because I'm thinking in terms of psychological and neurophysiological structures that exist and that I don't know about than that science has yet to describe.

1:02:30 I mean, the detailed workings of our brains at the level of higher-level cognitive functions are very, very... There's not much known. So, I mean, there is something going on that I certainly don't know. I'm not a psychologist. And I'm pretty sure that no psychologist really knows. don't see the possibility of describing it. I just think it's going to be there. I'm thinking of the things that are really almost built into the visual system. I mean, one's visual perception helps with built-in spatial structure, and therefore I would think built-in geometrical structure. But I don't know how to describe it. I haven't had my yearly conversation with you yet, Marcus, so I'm looking forward to this. Thank you. and the progressive discovery of dynamic unity in nature. What has happened since Newton is that we've developed theories that have enormously increased in the scope and accuracy of their predictions and at the same time have progressively led to a unification of this level of theory. And just a few highlights, Newton unifies Galileo and Kephthah, much else besides. Maxwell unifies electricity, magnetism, and life, much else besides. Special relativity brings greater unity to Maxwell. It partially unifies space and time, the form of constant space-time, and it brings unity to energy and mass, the most famous great physics, the meters and C-squared. And general relativity unifies space-time and gravitation by increasing the gravitation of the manifestation of the curvature of space-time.

1:05:00 Quantum theory and atomic theory unify a mass of phenomena having to do with the structure and constant of matter. QED unifies quantum theory of actual and spectral relativity the standard model unifies to the similar extent all phenomena associated with fundamental particles and the forces between them and the particle of gravity string theory or end theory or policy they use to be able to one day use by everything three comments it isn't just that we've sort of in my view stumbled across this we were doing we had an open mind and this is what emerged what actually happens in physics is that we're persistently seeking unity, and given that all the theories that we have accepted always have endlessly many rival theories that could be formulated, that would be even more empirically successful than the ones we accept that lack, that are horribly disunified. So we're actually accepting unified theories in a sense against empirical evidence. There are always these two requirements empirical considerations and requirements of unity. Unity is necessary for explanation. Other things being equal, more unified a theory, so the greater its expiratory power. And then, in the central mark of reputation of Kuhn, Kuhn has this idea that we have successive revolutions, theoretical revolutions, and nothing survives, nothing theoretically survives through a revolution. view these great unified theories that are the revolutions in corrective physics and there is in fact this persisting feed of the progressive discovery of unity in nature and this is a quotation from one of my books from obliterating the idea far from obliterating the idea that there is a persistent theoretical idea in physics, revolutions are just the opposite and let's assume that they all themselves actually exemplify the so that's all preliminaries now two problems first of all problem one

1:07:30 the fundamental problem of theoretical physics to discover the theory of my theory of everything and problem two I found a much rather more modest problem of the philosophy of physics to discover what unity and what physical theory means There is also, of course, the problem of justifying the precedent of the unified theory against the evidence. Well, and look into the same thing about problem one, and then we can not solve problem two. Could you just leave that one second? what do we mean by saying that a theory is unified or brings greater unity to direct or different the main problem I think is that whether in some sense whether a theory is unified or disunified seems horribly dependent on the way it's formulated you can always given a horribly complex theory turn it into, by changing our formulation into something that looks unified and vice versa. It seems a horribly slippery sort of thing, unity. How do we assess degrees of unity? How can justice be done to evolving conceptions of unity? We have different views about these things that say Newton did, although it's no four. Three of these four is up different degrees that have to do with simplicity. what is the relationship between unity and symmetry unity and simplicity and how come under justice and the ambiguity of justice and what implications are the solution to the problem so, well I'm really it's really problem one that I'm going to try to say something about I just want to give a rather delightful illustration of the technological problem which is to be found in Feynman's Lectures on Physics. It's in Volume 2, the one on Electrodynamics. And he considers a horribly, undeniably horribly disunified universe

1:10:00 with 10 to the 10 distinct laws, and here they all are, and peoples are made to this, and so on. and then we let A1 and A2 equal this and so on and then we let A equal the sum of all this and then we have this wonderful supreme equation that sums it all up with A to 0 and what could be a small you should be using A to 0 and then A to 0 and then A to 0 and we can turn a horribly complicated theory to a beautifully unified theory and vice versa What on earth do we mean? People have been thinking about this for quite some time. I mean, in a sense, we're talking not just about unity, but about the non-epirical consideration of the theory. By the way, I'd say the problem of simplicity is of central importance to the epistemology of that result, which is absolutely correct. Einstein, in his autobiographical notes in the Schilt volume, which, if you haven't read, read, but it's absolutely wonderful, discusses what he calls inner perfection, but it's clear that he needs unity, and he's talking about theories of everything that's the right thing to do. And he says that he's not sure, without more ado, and perhaps not at all, able to solve the problem, but he says that he thinks it should be possible to solve. Geoffrey of Rich some time ago 1920 I think about suggested that simplicity could be identical with positive adjustable constants in an equation something to say for it, but actually you can always change the number by changing your concepts properly the logic of scientific discovery suggested that simplicity can force liability and other people There's a book by Wesley Salmon called, I think, Four Decades of Scientific Explanations, which is a long account of various attempts at philosophy to science to solve this problem and argues that that would do.

1:12:30 So it really is a serious problem, at least in the philosophy of science. I say that because I think that the solution is so horribly obvious and simple that you may wonder what's it all about what was the problem in the first place well I think that the crucial thing is to make is to appreciate the importance of distinction in context and form and unity has to do with content and not this form. In other words, what we have to look at in assessing the unity of a theory is not anything about the theory itself in a sense but what it is asserting about the world. I think what the difficulty is that you think that unity is some sort of feature of a theory and then you start to take the theory to see what sort of feature of the theory itself you can get at to see what this unity is, and it's the wrong thing to look at. What we need to be looking at is not the theory itself, but what the theory is asserting about the world. And at once the terminological problem becomes completely irrelevant, because if we have a theory that can be reformulated in many, many, many different ways, all of which are saying the same thing, formulations are beautifully unified and simple and others are horribly, horribly complicated, so 10 to the 10 axioms or whatever. The fact that you can do this is completely irrelevant. If they're saying the same thing, then it's what is being assertive that you need to attend I've been thinking about this problem for decades and it took me about 20 years of thinking of that. I appreciate this point. and this is a terrible suggestion that one could be so slow. So my suggestion is, a bit more specific here, that supposing we consider the space of all possible physical systems, all possible universes, if you like, to which the theory T applies, and I'm sort of thinking of T as a candidate theory of everything, that T might be a conjunction. and supposing that this space divides up into n regions

1:15:00 R1 for Rn such that T specifies the same dynamic laws for each R i that specifies different dynamic laws for any two R i R j and I'm assuming here that we would always pare down the theory to the minimal content that is required to predict that the way these systems evolved. Then the theory is disunified to the degree n, and the unity means three and five, n equals one, so the unity doesn't mean one. And that's basically it. So you can, I mean, you would want to agree with this and disagree with this. But one can sort of nevertheless consider variety in this theory. And there are eight of them that I've thought of, and they get, they begin with the most, what seem to be the most serious, and then you start to apply degrees to the kinds of this unit here that seem to be increasingly less serious. and in each case one is appealing to this idea essentially that you think of the space of all possible systems and the question is do the same laws apply throughout the space of systems so imagine that T has different and of course it isn't the form one can always play around with the way the theory is formulating what matters is what is being served so what first is that T has different content in n different space-time regions which is sort of as I say in the form of induction but one imagines that suddenly it's horrible and that seems to me that it's all the most serious kind of but close to it one could imagine that T postulates the distinct ranges of physical variables other than space such as mass or relative velocity in distinct regions of the space of all possible phenomena, distinct dynamics and laws attain, which would be a pretty serious kind of disability, or that T postulates n minus 1 distinct, unique, spatially and or temporally restricted objects, each with its own distinct, unique

1:17:30 dynamic properties. And if there were such objects, then if they came into our region, it would do all sorts of horrendous things. Or, T postulates physical entities interacting by means of endless state forces, different forces affecting different entities and being specified by different force laws. So, in the space of all possible systems, there will be some regions where only one force operates, and so one type of law operates, and then another region, another force, another region, another force. in each case the theory is disunified to degree n but in a different way or one could imagine less seriously that there are n different kinds of entities differing with respect to some dynamic properties such as the value of mass or charge but otherwise interacting by means of just one force which seems to be a lesser series kind of disunity T postulates S distinct kinds of entities which can be regarded as arising because T exhibits some symmetry as the electric and magnetic fields of classical electrodynamics can be regarded as arising because of the symmetry of Lorentz and Barriens or the 8 gluons of chromodynamics can be regarded as arising because of the local game symmetry of F3. If the symmetry direct product of subgroups, T is unified. If G is a product of subgroups, T lacks all unity, and if there is no symmetry, T is missing time. And then, again, as in 6, except one imagines it makes constant, spontaneous symmetry-breaking events have broken the relevant symmetry, they're being manifest unity before these occur, and then finally, So 8, and the least serious kind of disunity of all, for full unity, one requires that, well, T is disunified if it fails to unify particles before space. So for the full unity of each case, we require n equals 1.

1:20:00 And 8 doesn't really... 8 just introduces a new way of counting. In regards to space and walking in classes, there are two entities for a full unit. a remark about this I think that one can distinguish two kinds of unification which I'm calling unification by annihilation and unification by synthesis by unification by annihilation I mean that at some stage in physics you have two entities or two kinds of entities and then you develop your theory of A a bit, and you suddenly discover that you don't need B, that B is just an aspect of A, and B is an independent entity, so if you disappear. And examples are the electromagnetic theory of light. You don't need light as an independent entity, it's just an aspect of the electromagnetic field, where it's going to be a field. The discovery of elements enormously decreases in the sense that number of independent substances, and quantum theory of quantum structure or possibly general relativity annihilating gravitation. as a force in addition to the property of space and time. And then on the other hand, and much more problematic here, there's the unification by synthesis, where it isn't the case that you get rid of an entity, but rather you show that these two entities, A and B, are aspects of one entity. So let's call the synthesizer for one entity. And examples of this are Maxwell's unification fields and the electrolyte partial unification of electromagnetic forces. And in the unification by synthesis, symmetry plays a crucial role as I've already indicated. Because if you think of the electromagnetic field, the way you divide up the electromagnetic field into the electric field and the magnetic field depends on your reference

1:22:30 So some comments now. The kind of disunity involved as one goes from one to eight become roughly less and less severe. there is however no obvious sharp dividing line between one and another I think this has actually profound implications for the problem of induction because one of the extraordinary things about this endless discussion of this problem in the philosophy of science is that it tends just to stick to in a sense to water our grounds for rejecting disunified theories of type 1 and five minutes And then five minutes for discussion. So it's time, I think, that the discussion of the problem is actually recognised that this is just a tiny bit of a problem and there are all these other kinds of disunities that need to be taken into account as well and we need to consider our grounds for rejecting these theories. And then it becomes clear that this is much more relevant to scientific practice, to real problems in physics, where, you know, the standard model suffers from a certain degree of disunity in some of the respect that that indicates and is regarded as unsatisfactory for that reason, but it's a serious problem in physics. The account of unity just given can be extended to theories that are not theories in two ways. First of all, one could treat T, I mean, T is now not a theory, but Newton's eternal theory or something. it is a theorem, that's a thing. Or in assessing the relative unifying power of T1 and T2, consider the unity K plus T1 and K plus T2, where K is the rest of accepted fundamentalistic theory or laws in the absence of theory. And if this has greater than this, then T2 is greater than T1. And then there's just a comment here about functions as mathematicians use the word function this second function here I've distinguished between functions that I call invariant and functions that are not invariant, is just as good a function as this function as just as good a function as this function but of course in terms of what I'm talking about

1:25:00 one has to assume that the functions that arise in our laws are of this kind and not of this kind and I Mathematicians don't employ the situation, and mathematicians' friends told me there's no way of making it precise. But at least one can say that if our functions in physics are analytic, then they satisfy the requirement. We have finished. so I think there is a major implication for adopting this view of what unity means if we accept that we're persistently accepting unifying theories in preference to potentially more successful disunifying theories that would have been caught but never actually considering scientific practice then it means that the whole enterprise of physics is making a persistent assumption about the world that there is to some extent to some degree and science would be more rigorous physics would be more rigorous if this implicit assumption a metaphysical assumption were made explicit so that it would be scrutinised criticised and consider alternatives it. In other words, we need at least to see physics in this way, as making this metaphysical assumption, and theories get accepted insofar as they satisfy empirical requirements and also as far as possible comply with this assumption. I think if you accept that's clearly unsatisfactory what is this assumption and what are our grounds for accepting it and I think that if you follow this up then it leads to a new conception of science and some of this I try to spell out in some of these books and papers which I urge you have a look at

1:27:30 Thank you. sense of disunity one that you had are you saying the same thing about different spatio-temporal regions if you do a gruelite transformation on it, it could then at least appear to be saying different things, you know, emeralts are grueling in this region but emeralts are green on this other region of space and time and a simple thing would happen for your invariant functions if you do a sort of invariant coordinate transformation, won't you be transforming a functional relationship that's invariant in your sense into one I think I'm going to give you a copy of my paper because the last section is all about that. But I think that the discussion in the literature that I declare seems to me to be horribly confused and constantly makes it is ambivalent about how we're talking about and also are we talking about adopting different conventions about what we mean by the same or not? what I mean by when I say there ought to be the same laws in two regions of space and all possible systems I mean what we all really mean by the same of course I accept that there may be aliens somewhere and have funny ideas about what the same and I mean what we relative to that that always arises and that's more to be said about this I agree I would also like to question this idea about unity being clarified by focusing on content instead of form because of course this thing about what the theories say about the world is of course that's very controversial what a theory says about the world that's why we have all the interpretational problems of quantum mechanics say and also interpretational problems about other theories general relativity, quantum electron dynamics, and even internal physics, maybe.

1:30:00 apart from this thing about it's very hard to say what exactly is the theory actually saying about the world, you are also then into the other problem, a serious problem in the philosophy of science, namely, what is actually the relation between that theory and the world? Is it a one-to-one correspondence? Is there some kind of other? How we are to conceive of that relationship? whole lot by just saying that it's, you just have to look at what the theory says about the world. Because that is in itself very important. That's exactly the perception of Gordon Fennig. Of course, there are all sorts of questions about, you know, in a new theory about what is it, or for example, if you think the quantum theory, matrix mechanics and turning away mechanics and are they really equivalent are they saying the same things about the world and theories of course can be given different interpretations and then there can be all sorts of quarrels about which interpretation is best and are they really different or are they really the same I accept them I mean in a sense what this means is that we have the page, and then there are debates about what we should interpret, how we should interpret this and what it is asserting, or what the propositions are, if you like, that relate to these sentences. But I don't think, I mean, the fact that this can be controversial about this, especially when you have other theories that have problems with the black content theory, and so there is this kind of built-in ambiguity, and the possibility of taking a distance from it. I don't think that this is a proposed solution to the problem at all. I mean, the fact that we have problems about, we have disagreements about the problem. It's your fundamental criterion. Well, that's okay. We can use, you know, a set of equations to say different things about nature.

1:32:30 And it may well be that it might even be that some of the different interpretations will lead to different answers as to what the underlying unity is. That's possible. But it doesn't seem to me to damage what that's for my first solution. I mean, you know, that corresponding to a formalism, there may be a touch of theories What is being asserted about the phenomena? And that it may be that they haven't been able to do it. There are several questions in the audience, but would you say, well, that's the question. If I understood correctly, you said that success in the empirical theories, empirical success is not enough. Then, the unity ends. Is this correct? That empirical success is not enough. Yeah. And you suggested that maybe there are a lot of theories that are even more empirical successful than the one that becomes established. Yeah. Could you please put me one example on some game theory more successful than general relativity or more successful than quantum mechanics even though they do not do you have yeah I can but let me give you a simple an earlier example which by the 1970s we discovered it seemed to be reputed by the American law of Mercury at the start in about 1880 put forward a modified version of Deuteronian theory, which was a sort of field theory. Actually, it was made up of two fields of rather arbitrary stuff together. And he was able to show that this not only recovered all the predicted success of Deuteronian theory, where it was successful, but it was also successful for the orbit of Mercury. And it had excess empirical content because it would have applied to similar systems elsewhere in the universe. And even the author never took this seriously, even though it had greater inferior success and wasn't refuted when Newton is refuted, because of its arbitrariness.

1:35:00 And all theories, I mean, Lakota actually went so far as to say at one point all theories are born refuted and remain refuted. All theories have difficulties. Most work, a lot of work in physics out clashes between experimental results and accepted theories. So one can always substitute the given theory with a much more horribly complicated theory, which just, when it comes to the phenomena that refute the theory, you just specify, instead of the theory you cancel the law, the predictions for those phenomena, and just specify the experimentally established laws. And you can do this and add on extra independently testable and we can always do this and such things are never done not really it's such a gross violation of unity thank you