00:00:14.320 All right, I'm here with David Deutsch. David, thanks for joining me.
00:00:18.000 Thanks for having me. Sure. So we live in a world of classical
00:00:23.520 programmable computers that have been very successful in solving all sorts of problems in our
00:00:28.640 civilization, and researchers are also making strides in quantum computing.
00:00:33.200 So given our civilization success in employing concepts like information and computation,
00:00:39.760 why was a constructor theory of information necessary in the first place?
00:00:45.440 It arose out of several motivations, initially just from constructed theory itself,
00:00:51.520 because we needed to formulate rigorous concepts of things like measurement and possibility
00:01:03.120 that didn't rely on existing on particular physical theories like quantum theory. So we
00:01:10.800 needed to know what it means in principle for, say, a theory of physics to support information,
00:01:21.760 because if you think of laws of physics, any old logically possible laws of physics,
00:01:27.920 there wouldn't be information in the worlds that they describe. So what does it take
00:01:33.520 to make information? Now, if you were confined to quantum theory, you'd say, well,
00:01:42.960 an observable can store information if it has an observable with at least two
00:01:55.120 distinct states which are measurable, and something like that would do in quantum theory.
00:02:00.000 But then a quantum theory is a Hermitian operator, and it has orthogonal states,
00:02:06.800 and all those things are rooted in just quantum theory. And we want to think that it will apply
00:02:12.480 to all theories, including ones that haven't been invented yet, all reasonable theories.
00:02:17.600 In fact, this will be usable as a criterion for whether a proposed theory is reasonable.
00:02:23.920 So what is it about information that makes the prevailing conception of physics,
00:02:30.880 namely expressing laws of physics in terms of initial conditions and dynamical laws of motion,
00:02:35.920 so difficult to capture, whereas constructive theory, which is all about possible and impossible,
00:02:40.960 transformations or tasks, seems much more up to the task as it were of explaining and capturing
00:02:46.880 the regularities of information? Yes, that's exactly why. It's because
00:02:52.320 constructive theory has counterfactual properties at its heart, so possible and impossible,
00:03:04.800 are both counterfactual concepts, and information is inherently counterfactual. For example,
00:03:11.920 if I say that... Well, let's suppose somebody measures a constant of nature
00:03:24.640 like pi or something. Now, you can't use pi to send or store information,
00:03:32.160 because pi only ever has one value, whereas whether as, for example, whether a spin of an
00:03:42.080 electron is pointing up or down, it can be used to store information, and if you have more than
00:03:50.320 one spin, and they can interact in certain ways, then they can be used not only to store
00:03:55.760 information, but to process information, and so we... Using quantum theory, we can establish...
00:04:04.240 Sorry, using constructor theory, we can establish the minimum criteria for a physical system
00:04:12.080 to be able to store information and to be able to process information, which is what makes
00:04:18.160 computation classical and quantum possible. And then you can say, here's our defined class of
00:04:29.520 conceivable laws of physics, which allow information to exist, and information processing,
00:04:38.400 which means, among other things, it allows measurement and computation, and therefore
00:04:44.960 growth of knowledge. And the rest would not allow that, and we won't be looking there
00:04:53.840 for potential laws of physics, because those laws wouldn't allow physics to happen.
00:05:02.560 So following that argument, would you say that's a similar argument could be made for
00:05:09.040 why it was important to establish concepts like measurement and distinguishing between outcomes
00:05:15.120 of an experiment, which you've touched on in constructive theoretic terms, because it makes it
00:05:19.600 then easier to look for future object level laws of physics that must conform to the
00:05:25.440 constructive theoretic definitions of these concepts? Yes, of course it is possible that
00:05:31.440 constructive theory, as we conceive of it, isn't true. And somebody invents a theory of physics
00:05:40.960 which violates the principles of constructive theory. So there isn't always a thing under that
00:05:47.120 theory as, for example, information or measurement or computation, but that nevertheless,
00:05:53.040 the theory is testable in some sense that transcends our present concepts. But even then,
00:05:59.840 that would be useful, because if you had such a theory on the horizon, and it looked as though,
00:06:07.040 for example, it wasn't going to allow measurement, therefore it wasn't going to allow
00:06:10.640 science as we know it to exist, then that would be an early indication, either that the proposed
00:06:17.120 theory isn't true, or if it is true, that it requires a conceptual revolution larger than one would
00:06:25.360 at first thought think, because such a theory might arise by just changing a few innocent looking
00:06:32.400 parameters in quantum theory, and you might then get a theory that didn't support science,
00:06:39.360 and then you'd have more than just technical difficulties in physics. You'd have
00:06:46.480 profound philosophical difficulties in setting up that theory as well, and you'd construct a theory
00:06:52.160 would have been an early indication of that. But I don't think that's going to happen. I think
00:06:57.360 that future theories are going to conform to constructive theory, but that's just what I think.
00:07:02.560 Yeah, I guess time will tell. So let's talk about classical information in particular,
00:07:09.520 which is the world of bits, as most people are familiar with them. What is classical information
00:07:15.520 in constructor theory, and by expressing classical information in constructor theoretic language,
00:07:27.040 So the definition of classical information under constructor theory is that
00:07:37.360 system is an information medium, if it can be in at least two different states, which
00:07:47.440 can be with these states can be permuted by possible operations. That is the operations of
00:07:58.000 arbitrarily permuting those states is physically possible. So then you can, that defines an
00:08:10.480 information medium, then you can define information as being present in a system if it is in one
00:08:18.560 of those information states and could have been in the other or in one of the others. So there's
00:08:25.280 your counterfactual definition of information. And we haven't had, now apart from the fact that
00:08:36.400 this works, the only concrete results that we can display at the moment is the fact that this is
00:08:45.200 also enough to define quantum information. And quantum information, that is, it's not the same
00:08:52.960 definition, but given that framework, you can define quantum information in a very simple way that
00:09:01.680 you can say that an object can hold quantum information if it can, if it has some states that
00:09:11.360 can hold information. And if it has another state set of states that can also hold information,
00:09:18.400 and if the union of those two sets of states cannot hold information. And that, when you have a
00:09:27.840 system like that, it, it, we call it in constructive theory, we call it super information,
00:09:35.200 but the only practical theory at the moment that has super information is quantum theory.
00:09:40.880 So this, our result is that quantum information and all its important properties just follow
00:09:51.920 from this small difference in the way that information appears in the theory. In classical physics,
00:10:00.560 it appears in the way that every classical information medium has only one maximal set of states
00:10:12.640 that can hold information. We can have another one, but they won't be compatible. And then
00:10:20.800 quantum theory has two compatible sets of states where the union of the two is not a set of
00:10:30.880 information states. That is, because, by the way, because they can't be distinguished by any
00:10:38.880 physical process. They can't be reliably distinguished by any physical process. So that's our
00:10:44.800 our main result in regard to information to date. But as I think Sam told you, what we're hoping
00:10:59.840 for is that this notion of information and therefore of measurement and computation can tell us
00:11:09.600 what information can tell us a measurement theory in new proposed laws of physics such as
00:11:21.760 qubit field theory where the existing concepts are not enough. We have, we have in qubit field theory,
00:11:31.840 we have separated systems where the observables do not commute with each other and yet causality
00:11:40.640 is maintained. And that's conceptually very difficult. And so you have to build a new theory of
00:11:47.920 measurement. We're not in Kansas anymore, as we keep saying. And to build a proper theory of
00:11:55.520 measurement in quantum theory, it took like depending on how you count it 30, 40 years of
00:12:04.400 head scratching and thinking that this is this can't be right. This is this is impossible.
00:12:10.880 We think that construct a theory provides a very powerful tool for setting up a theory of measurement
00:12:19.680 within a newly proposed theory of physics, even if it's very conceptually strange.
00:12:30.960 It kind of reminds me of the fact that you can ignore fundamental principles in a given domain
00:12:38.560 so long as you're far away from the limiting case by which I mean it's easy to work in Newtonian
00:12:44.800 physics if you're not approaching the speed of light. And it strikes me that measurement kind of
00:12:50.320 feels similar where you can rely on sort of your intuitions of how measurement ought to work.
00:12:54.480 But as you said, once you start leaving Kansas as it were, you really have to
00:12:59.280 understand in physical terms what constitutes a measurement. Does that seem reasonable to you?
00:13:04.320 That's exactly right. And and what you just said about measurements applies to information.
00:13:09.600 I mean it's really the same problem, measurement and information are the same problem.
00:13:15.840 And even in relativity, Einstein had this problem of defining what measurement is essentially
00:13:25.920 and the concept of measurement had to be different because there's no such thing as
00:13:30.640 simultaneity and so on. That problem was important and he solved it, but it was minor compared
00:13:39.600 with the analogous problem that arose in quantum theory. And I think that future theories are
00:13:49.040 going to challenge our intuition more than previous ones. I mean this has been the experience
00:13:56.560 that that new fundamental theories in physics challenge our intuitions in unpredictable ways.
00:14:07.040 And we've constructed theory, we hope to have a tool that helps us to formulate our intuitions
00:14:16.240 properly given the new theory whatever it is. So is it fair to say that with your and
00:14:23.840 Kiara's work on constructive theory of information, you've effectively unified classical and quantum
00:14:29.440 information and it's only that they differ in one property? Yes, I think that that is what this
00:14:38.880 work has done and I would hold that out as I just said that as as being our one concrete results
00:14:48.720 of the constructive theory of information so far. Maybe Kiara's results in constructive theory
00:15:00.000 of thermodynamics also count as because she uses the constructive theory of information there as
00:15:07.600 well. So maybe maybe her results in thermodynamics count as well. But the real fun is going to
00:15:15.920 begin when we apply constructive theory to physical theories that go beyond quantum theory,
00:15:30.560 that are incompatible with quantum theory. And that's what we mean by not being in Kansas anymore.
00:15:36.720 And I think that is when constructive theory will come into its own. My guess is
00:15:42.880 that it will not be just won't be practically possible to make progress without an overarching
00:15:52.240 framework like constructive theory. Now as I said constructive theory could be wrong but in that case
00:15:59.360 trying to develop it will show us what is needed instead. I don't think we can make progress
00:16:06.640 without such a framework. Right, right. And you know, even if constructive theory is wrong,
00:16:14.240 as you say, every error will kind of show us maybe why it's wrong and we can progress in other
00:16:18.400 ways. Either way it seems like it's kind of a revolutionary conceptual revolution as I think you
00:16:23.280 mentioned earlier. I think so. Yes, I think that's very much the case. So much of constructive
00:16:29.360 theory is about and is expressed in principles which are laws that constrain other laws. And you've
00:16:35.920 conjectured in your paper with Kiara several principles that explain or capture the regularities
00:16:43.040 of information. So let's just go through a couple examples. So first of all there's the interoperability
00:16:49.120 principle. So what regularity of information does that capture? So we take for granted that if we have
00:16:58.080 information in one physical medium let's say a book. Even if it's an ancient book that was
00:17:08.560 produced by a culture that we don't know about, we don't yet know what the symbols mean or what
00:17:15.840 their language was and so on. We take for granted nowadays that the information content of this
00:17:25.920 book and therefore the knowledge content as well can be faithfully copied into a different medium
00:17:37.520 for example magnetic domains in a in a in a microchip or into sound waves when when somebody reads
00:17:50.080 it to somebody else or indeed into into our retinas and brains as well and so on. So all these
00:17:57.120 are examples of information transcending the substrate in which it's instantiated. So information is
00:18:07.040 this weird hybrid of a thing that information can only exist in physical form and yet it is
00:18:16.080 independent of the of the specific physical form in which it is ever instantiated. So but this
00:18:24.720 what I've just described now although it's extremely familiar and taken for granted is not logically
00:18:30.400 necessary at all. It is conceivable that physics could be different and not satisfy this principle
00:18:38.240 so that you could have some physical objects that that have information and have science possible
00:18:46.560 and you know observables and measurements and and even the civilization and so on and that it
00:18:56.880 simply wasn't translatable into another physical system which could also have science and
00:19:05.440 and and so though the whole the whole edifice of knowledge and yet they weren't into translatable
00:19:13.360 so in theory so aliens from another planet could could be based on different physics
00:19:21.520 not just different physical object but different aspects of physical laws could come and visit us
00:19:28.960 and could be fundamentally unable to communicate with us. This is logically possible
00:19:38.160 but the principle of constructive theory says that it is not so and all known physical theories
00:19:48.320 have the property that wherever they instantiate information it is indeed interoperable
00:19:53.520 with with other information. So it can be it can be information in electron spins
00:20:01.440 can be translated into information in microwave cavities which can be written down and published
00:20:08.400 as income paper and you know the whole works and it all with arbitrarily reliable copying.
00:20:18.880 So it seems to be a feature of our universe it is as far as most people can conceive
00:20:28.800 as far as I can conceive it is a necessary feature for knowledge and for science as we know it
00:20:35.920 to exist at all and although it is a feature of all known physical theories there's no known physical
00:20:47.040 law or the had been before constructive theory there is no known physical law that implies it
00:20:54.400 it happens to be a feature that laws as far as we know obey but unlike say the law of conservation
00:21:04.240 of energy that there's no no one has expressed this regularity as a law until constructive theory
00:21:13.120 came along and so that's the principle of interoperability of information. And you had mentioned
00:21:20.560 the scientific method in your answer so I just want to talk about one more principle and first of all
00:21:27.200 it does seem like from your work in the constructive theory of information that you're actually
00:21:32.480 integrating parts of the scientific method itself into fundamental physics I mean tell me if I'm wrong
00:21:37.040 but that's certainly what it seems like so yes I would rather say that we're expressing parts
00:21:44.240 of the scientific methodology and constructive theory it specific principles like interoperability
00:21:56.080 could be modified without without making the rest of constructive theory fall it just that it
00:22:10.320 could only be modified in a way that was compatible with the rest of the theory and if the theory
00:22:14.480 has to be modified too much then it's a matter of degree whether you call it the same theory you
00:22:21.120 know it might be some conceptually different framework from constructive theory so the
00:22:34.480 interoperability of information is related to the comprehensibility of the universe in this way
00:22:42.640 if the universe isn't wholly comprehensible which by the way on philosophically I think that's
00:22:49.680 ridiculous but as a physicist I have to allow it as a possible property that the theory might have
00:22:57.520 then in some ways constructive theory could be altered to reflect that but as I said earlier
00:23:10.240 at least it would give us an early warning that something profound is happening when we
00:23:17.040 postulate that something which has profound implications for physics for the laws of physics as
00:23:23.280 we know them some some the laws of physics have to be formulated not just differently but
00:23:31.520 with different modes of explanation not not just with different explanations
00:23:36.640 which have yet to be discovered constructively would give us an early warning of that and
00:23:43.520 you know if these new theories had that property and made sense then they might be
00:23:52.720 accommodatable in a modified version of constructive theory but we're being very speculative now
00:23:59.840 I don't think any of that is going to happen I think constructive theory will be a reliable guide
00:24:05.920 to what not to what the next theory is but to what the next theory can't be or what the next
00:24:14.880 theory can't be without a revolution bigger than it looks at first sight right right so part of
00:24:24.320 the one of the features of constructive theory is that because it's kind of in a way a theory about
00:24:30.400 theories if forbids certain kinds of theories from being possible whereas in the prevailing
00:24:38.400 conception the theories forbid just what physical phenomena are possible so it's kind of a level
00:24:44.480 it's a higher level theory in that sense yeah well the prevailing conception theories forbid
00:24:50.640 what is possible under that particular theory so that theories don't speak about each other so
00:24:57.680 they don't say they don't say laws of dynamics don't say that a perpetual motion machine is
00:25:06.720 impossible they say a perpetual motion machine is impossible under Lagrange and dynamics let's
00:25:14.240 say but but somebody can but there physicists have conjectured for for over a hundred years that
00:25:27.200 that there is a principle of physics the principle of conservation of energy that is a principle
00:25:33.120 about other theories including ones we don't know yet and so we use the principle of conservation
00:25:40.240 of energy as a guide to conjecturing new theories because we know that if a new theory
00:25:47.920 violates the principle of conservation of energy then something the either it's false or something
00:25:54.320 we have to reconceptualize the world under that theory it's not just the change of the type
00:26:02.080 of changing the parameter or adding a new term in equation right right and it speaks to the fact
00:26:09.680 that merely falsifying theories is not quite as straightforward as sometimes it's made out to be
00:26:17.280 there's always background knowledge and so forth that's right yes and with conservation
00:26:23.520 of energy this has in fact happened that for a start with neutrinos that's our favorite example
00:26:32.400 neutrinos we discovered because people noticed that energy apparently wasn't being conserved
00:26:39.280 and therefore some new process must be involved and this turned out to be weak interactions
00:26:45.520 weak nuclear interactions but another example is relativity itself where the notion of the principle
00:26:55.760 of the conservation of energy well principle of conservation of energy can be expressed in a number
00:27:02.560 of different forms which in pre relativistic physics were all equivalent to each other
00:27:11.600 but with relativity it turned out that some of those some of those formulations were
00:27:22.320 incompatible with relativity and fortunately there are conceptions of the law of conservation
00:27:29.920 of energy which are compatible with general theory of relativity now it could be that some
00:27:38.000 modification of relativity like if there was a good theory of dark energy for example which
00:27:46.240 violated the principle of conservation and energy some people have proposed then the principle of
00:27:52.640 conservation of energy would have been refuted but this very fact guides our theorizing about
00:28:04.880 dark energy because having a theory of dark energy that makes it incompatible with any kind
00:28:12.320 of principle of conservation of energy would be a big revolution much bigger than it looks
00:28:19.200 if you just look at the an additional term in Einstein's equations.
00:28:25.120 So let's talk about one more principle so that listeners can get a taste of what the
00:28:31.600 construct what principles look like in construct a theory really but more specifically in
00:28:36.880 construct a theory of information the principle of consistency of measurement you expressed in
00:28:43.440 your paper with Kiara I wonder if you could elaborate on that principle and talk about what
00:28:47.920 regularities you're capturing there that we all sort of take for granted already.
00:28:52.880 Yes so this is this is one of the principles that that we use to make sense of information
00:28:58.720 in the context of measurement which is the main context we originally wanted it in.
00:29:06.320 Now we assume that that this consistency of measurement has to do with information in the sense
00:29:13.840 that when you measure something of say a physical quantity like like the speed of your car
00:29:22.480 what you're doing is you're causing an information variable to go into a state that represents
00:29:31.840 that the physical property of in this case the car so that your speedometer for example
00:29:38.560 that showing that the needle is at a certain place that's an information observable with a certain
00:29:46.480 sorry an information medium in a certain state and that according to the theory by which it
00:29:56.240 was designed that represents a physical property of the car. Now thing is you can also measure the
00:30:04.880 that that physical property of the car by a physically very different process for example the
00:30:13.040 policeman might be measuring your speed with a radar gun and the principle of consistency of
00:30:21.040 measurement says that the speed on your speedometer and the speed indicator on the radar gun
00:30:28.640 if both of those are working properly will be the same and that's really if that weren't true
00:30:39.920 then they wouldn't really be such a thing as measurement in the way we normally conceptualize it
00:30:46.080 and again conversely if it wasn't true the situation might be rescuerable by a new conception
00:30:54.800 of measurement but that would be a big thing it would be a change in our philosophical framework
00:31:03.680 of what science is and so on that is much bigger than just than could be expressed by just saying
00:31:11.040 that that needles on speedometers and indicators on the display of a radar speed measuring device
00:31:22.160 aren't necessarily equal that sounds like a very tame thing to say and it is a tame thing to say
00:31:29.840 in terms of the object level theories involved but in terms of the principle involved it's a huge
00:31:39.120 would be a huge change and again we think that that's not going to happen we think that the world
00:31:44.640 in fact obeys the principle of consistency of measurement so with these principles that you've
00:31:53.360 conjectured again with Kiara and the the results that you have from your initial
00:31:58.640 constructor theory of information paper do you expect constructor theory to solve
00:32:04.480 further problems down the road within information theory itself whether classical or quantum
00:32:10.160 and I say that to contrast with what we've been talking about which is that you expect construct
00:32:15.440 the theory of information to help physicists or scientists discover future theories
00:32:23.040 yes the again Kiara has been working on this the construct theory of information does help
00:32:34.400 with existing theories in in situations where although there is no new physics involved we don't
00:32:44.480 know what physics is involved so for example in in a situation where systems are interacting two
00:32:52.720 systems are interacting via another system that is not understood or which is too complicated
00:33:00.160 to analyze explicitly then construct it because of the principles of constructed theory applying
00:33:07.520 we can say something about that interaction we can make predictions about that interaction
00:33:12.560 that are independent of the intervening process provided that the intervening process obeys
00:33:20.720 constructor theory yeah you can do the same thing with with energy you know you can you can say
00:33:27.840 that regardless of the fuel that the rocket uses if you have this amount of fuel you cannot reach
00:33:39.120 if you have this amount of energy in the fuel you cannot reach more than a certain height
00:33:45.200 so you can say that not knowing what form of energy is being used by the rocket and similarly
00:33:53.600 when you have information being exchanged between systems like gravitational field and
00:34:02.960 electromagnetic field and the states of an electron and so on under quantum theory and the whole
00:34:10.640 thing is is only parts of the system are understood exactly and the rest on the medium that
00:34:21.520 is transferring the the force or whatever it is from one well understood system to another
00:34:31.840 well understood system isn't well understood you can still make predictions using constructor theory
00:34:37.360 that the kyara and black co have several ideas where they have elaborated this into a useful form
00:34:49.680 that may even be usable in real experiments at some point
00:34:57.920 so since the constructor theory of information principles are expected to be universal
00:35:03.520 you had mentioned i think dark matter earlier or maybe dark energy but shouldn't those whatever they
00:35:10.320 are would we expect them to also conform to the constructive theoretic principles of information
00:35:15.680 and the rest of constructor theories principles yes i mean in my opinion it's not on the cards
00:35:22.480 that they want to be it of course i could be wrong and as i said if i am wrong that they
00:35:27.360 would still be useful things to be found from constructor theory but yes i think there is no sign
00:35:38.080 in any of the problems arising from either dark matter or dark energy there is no sign that
00:35:44.720 constructed theoretic principles are being violated
00:35:51.680 all right david well this has been very interesting and very informative and i really appreciate your
00:35:55.520 time well thank you very much it it was enjoyable answering these questions and i always
00:36:03.840 learned something yeah well you and me both have a good rest of your day thank you
