COLLOQUIUM: 'The Physics of Can and Can’t': from the universal computer to the universal constructor

I'll I'll start with a sort of grand vision and then gradually during the two back to down so don't don't get taught too much if this sounds very very ambitious let's say so I'll start with the general motivations for for this research program so take it as a as a description of a research program that is unfolding and that I'm very pleased to be able to to present here because in a way is what who was saying this is a natural continuation of the sort of revolution that happened with quantum information that was fueled by lots of discoveries that happen here at cqt as well and what I'm going to talk about is a possible way forward to use some of the tools that we have been developed in in quantum information to imagine what could be done beyond something like the universal quantum computer and so I'll start with three reasons why one might want to do that because of course we all like quantum information and it sounds like a very complete theory it sounds like it's giving us lots of good technological developments as well so one might wonder why would we ever want to do something different from that or all new or so the first point is that so quantum information theory all the hearings that we proved in this in this context assume all of quantum theories properties and and quantum theory is as we know is a very powerful general theory but it's also highly specific so in a way it's got a lot of both formal and conceptual machinery that we borrow in quantum information and we use to prove all the major results in this discipline but if you look at physics at large you will see that actually quantum theory may not be the last the last thing actually in fact there could be a better theory coming along which will UniFi quantum phenomena with with gravitation for example and so we might want to be prepared to live some of the auspices of quantum theory behind while still retaining the idea that quantum information processing is possible and so to talk about this one both needs conceptual tools and Soma tools beyond the ones that we developed so far so I think this is the one of the first motivations I want to provide for this kind of program and of course there's a second motivation which is that despite the name a universal computer is not the most universal machine you can think of so universal computer following a definition that the Deutsch gave elaborating on that the Turing proposed is a programmable computer whose repertoire contains all computations that are physically allowed so it's the is the union of all physically possible repertoire but there are some tasks that don't fall into the model of computational tasks so there are some tasks that a universal computer is not able to perform and I think this was already clear to phenomen who wrote a beautiful essay a number of beautiful essays by particular one of them I have in mind where he points very clearly out the fact that for example is a universal computer wouldn't be able to self reproduce of course imagine you're given a universal quantum computer and then you want to program it so that it will be able to create an exact replica of itself and there is no such program because the universal quantum computer is not such a machine it can operate on its workspace on its register why it's not designed to create take some raw materials and build a new copy of itself which is something on the other hand that let's say living cells do all the time so there are tasks that are not in the universal computers repertoire and the other thing of course is that universal computers must be built out of something and they can be built is actually a question that is decided by the laws of physics as a whole and not just by the principles of quantum information theory quantum information theory is a very very special application of quantum theory where we are assuming we've got unlimited resources like long qubits that we can use in order to perform computations but from cosmology we know that in reality that might not be the case and so whether or not the universal computer can be built in the first place it depends on resources available and on the particular interactions that are made available to us from fundamental physics and so out of these considerations came this idea that phenomena had to generalize the universal computer to an even more powerful machine which is a universal constructor and a universal constructor informally speaking is an object which has in its repertoire all physically possible transformations not just computations so the rule in particular be able to build a universal computer if that's allowed by the laws of physics and we'll be able to build a replica of itself - and it is quite cool and it's also cool because it kind of gets close to what we know is a special property that living systems have and I think that's why phenomena was so interested in it and not just him actually Turing to so second reason why somehow we might want to step out of quantum information theory by itself the third reason is that quantum information theory has put together in fact two ways of formulating laws of physics that we have in in fundamental physics one is dynamics of course we use a unitary transformation to compute the effect of certain gates on certain input States but the other mode of explanation in physics is the mode that uses physical principles and if you think about it is a very very different mode from from the dynamical law kind of approach okay and I put here some three examples that I find interesting of this other mode of formulating laws of physics so does the conservation of energy which rules out a perpetual motion machine it's very funny when you browse the internet for this perpetual motion machines incidentally you find also some very inventive proposals that unfortunately don't work but this one was by guy called Boyle who was trying to use some principles of the way in which water flows in small capillaries to try to to create perpetual motion and of course it doesn't work because actually water can creep up like this only if this is lower than the level of this water fluid here but so if you you have a kind of moment to go on the internet and browse for these things do because it's really fun so conservation of energy rules this out but to know that this is this is impossible you don't have to compute specific consequences of dynamical laws the principle is just formulated like that a professional motion machine of the first kind is impossible there are no dynamical laws no initial conditions you could then prove that certain dynamical laws is compatible with this principle but the principle is more general it somehow transcends dynamics so you know in a sense is more powerful and quantum information is full of these principles is is full of these kind of statements such as things about channel capacity and statements about what one can do with entangle states and let's say local operations on subsystems of an entangled pair and so on the second principle of course is the second law of thermodynamics which rules out a different kind of perpetual motion machine which converts completely heating to work and unfortunate we also know that's not possible again on the internet you go and you see this very nice image where there's a boat which is sort of propelled forward from kind of drawing up heat from the from the water and converting the whole of that into mechanical work with no waste and unfortunately it doesn't work again and then we have a maybe more positive principle here which we there's a question mark there because we don't know whether that's true it's the principle that says that the universal computer is possible and there's a kind of question mark there because we actually it doesn't stand in the same classes the other two principles because let's say it's more like a conjecture and what is there is an interesting cartoon which represents a the one of the first computers mechanical computers were proposed by this guy called Babbage and by Ada Lovelace who together try to realize this machine which was called the analytical engine and if you look into their into the nice notes you will see that actually this is one of the first ideas for a programmable Universal machine and this came well before curing is just that unfortunately they couldn't realize it so they ran out of funds you know I feel kind of good because you know it was just a struggling with funding but you know this was already a problem in Victorian here and I think actually ADA went into gambling where she was going to horse races to try to raise funds for this thing it didn't work and I'm just saying I mean I'm gonna so yeah I know there's always some kind of last resource I can resort to if I'm really desperate as far as funding is concerned but never mind so this is just a curiosity why it's a fun fact so these three are examples of principles and so we can maybe imagine a generalized lesson from from these three principles the question is is it possible to use this principle based way of explaining things and providing laws etc to to have predictions to make predictions about physical systems just as well as we do given dynamical laws such as Newton laws the laws of gravitation and the laws of quantum theory but with with with the gain which is that we don't have to commit to a specific dynamics but we can make this more general statements and try to apply these principles even in cases like when you're considering a gravitational system which interacts with a quantum system where we don't have a necessarily a dynamical or ready and known and so I will try to convince you that it is possible and also we try to say that solving this problem somehow is also helpful to address the other important problems that we mentioned in the first two slides so all these things go hand in hand in hands and construct the theory is supposed to provide a way of using this logic yes a specific proposal or dynamics what could you hope yes that's a great question by the way if you want to interrupt for questions I welcome them so please do the so one way is to use approximation schemes so of course we've been doing this for long while in physics so things like open system dynamics is one example in quantum theory where you might decide to neglect part of your environment because you might not be able to model it fully or but then you can make some assumptions about a general behavior of this environment such as energy emerging weak coupling you can imagine various approximations that you can make in order to solve a certain dynamical problem for a smaller system let's say so that's one way you can go about so making approximations but somehow it seems to me that if you choose that road you will still have to make a certain number of very stringent assumptions about the dynamics and maybe you will lose the generality that you have here so the the hope in a way is to combine these other ways of going about when you don't know exactly what the dynamics is with this more general approach to make progress okay okay so here is an example this is not constructed theory but it's an example of what logic should be when you decide to leave dynamics behind so Bondy is a physicist who's interested was a physicist interested in in filter in general activity and astrophysics he was he proposed it's very interesting argument to argue for this phenomenon that is called redshift which is actually a consequence of general relativity but without actually using the laws of general activity at all that's kind of cool and I want to kind of walk with you through the steps of this argument to see how it works so the assumptions are energy conservation which is a principle and then you have the equivalence of mass and energy which allows you to say somewhat that if you have an atom which is on the sort of ground state like that you can assign some mass to it and if it's in this excited state you can assign a different mass which is larger than this little m here and now you can try to imagine what would happen if you didn't have redshift of photons in a gravitational field whereby the frequency of a photon which is clumping up climbing up these fields should change imagine you don't have that and you still hold tight to these two principles you will end up with a contradiction so you particularly will violate the conservation of energy therefore there must be something like redshift that's the kind of logic that we are following here so you're imagining a seesaw which is made I mean this is very challenging of course it can't be done experimentally but it's an imprint people it's a thought experiment so the pivot here this is a seesaw light thing there's a gravitational field out there and you start in this configuration when the excited out on which is heavier is here and the D excited autumn is there and then you trigger with producing some work you can use some laser or something to you trigger some emission from this excited atom which therefore goes into the excite into the non excited state and here you have the photon and two mirrors that are perfectly reflective now this photon will hit the mirror here and imagining a very very efficient process the photo will climb up gravitational field is here and at this point will be reflected by these other perfectly reflecting mirror and absorbed so this guy will have now a higher energy therefore a higher mass and at this point you can see that because of the gravitational field here this isso will be such that this part this M here goes down and this one goes up so you end up in this configuration and you can extract mechanical work at this step you can put some spring here from flywheel which will get mg d worth of mechanical work and now you can apply a very neurotic swap so you just go back to this original configuration by rotating the two masses for the two apples however you want to consider them and you're back so you got a cycle and interestingly you spend w0 which is a constant fixed amount and you have gained mg d and by making D as large as you like you will be able to extract as much work as you like from this and clearly this is a contradiction of the conservation of energy so it can't be therefore something must have gone wrong in these steps and what went wrong is that I didn't consider that the photon climbing in the gravitational field changes its frequency and therefore it won't be absorbed with the same efficiency one which I assume there so this scheme won't work deterministically because there is redshift okay so this is just a digression to say in what way this kind of logic is useful yes and so it's not surprising that using this logic you come to the same well the principle of dynamic of least action is a specific principle that you assume within a certain dynamical framework whereas conservation of energy in this form is much more general in the sense that you can define it within any theory that allows the concept of energy the one that I can use to derive well not just souls - there's also the equivalent spirit dolls there are a number of other assumptions right and also of course the laws of GR are much more precise because they allow allow you to say exactly by how much the photon frequency has to change which this of course doesn't tell you that but suppose you didn't know about the laws and you run this argument this would be a guideline for let's say conjecture in the laws so on the one hand you can say that the principles if you prefer to think of them like that they are like a general guideline for approaching the problem of conjecturing new laws okay okay so now I'll outline briefly what the general ideas of constructor theory are as they were originally conceived they're now going to three applications of this logic which are something I've been working on so the product we constructed here is two instead of using dynamics as your primitive element to formulate laws as scale independent principles about what tasks are possible what tasks are impossible and why and so the dynamics is not assumed but it should be a consequence of these principles and some of these principles will be new principles different from those that we already know so that's important to bear in mind and so this is like the program as David Deutsch conceived of it while ago and the the question is of course you know you might be by the by now be very skeptical about all of this because you will say okay you know drop dynamical laws where do I start well if you drop dynamical laws you still have a concept of state and you still have a concept of transformation so you can at least say what a task is so I said the laws have to be formulated as statements about possible and impossible tasks or physical transformations so tasks are formalized in this way and lots of people working here on resource theory and and maybe also category Theory will see a number of nice form of connections with with this stuff and the the core difference from the idea of a dynamical trajectory comes here because we say that the task physical transformation is impossible if there is a law of physics that forbids it's being performed to arbitrarily high accuracy and it's possible otherwise so think of the difference between possible task as defined here and allow transformation in a dynamical law in a dynamical law any trajectory which is a solution of the dynamical equations is an allowed trajectory here a possible task is not just that it's a transformation which can be performed to arbitrary high accuracy on a system when it's coupled to any kind of environment so if you think of let's say what happens when you imagine a not gate being performed in in a computational network the fact that we think that the not gate is possible means that we know that the laws of physics allow for an ever improving sequence of gates that approximately perform not but the reason what we think is possible is that we don't have any law that says that it's that there is a finite value of accuracy beyond which we can't go so when you say that something is impossible conversely you are stating that there is this limit that there is this fundamental limitation so for example in the case of the conservation of energy that implies that there is a fundamental limitation beyond which you can't go as far as professional motion machines are concerned they will always be very faulty no cloning is another example if you try to create the cloning machine that clones to non orthogonal states you will see that there is a fundamental limit in accuracy beyond which you can't go and in that case we say that the task is impossible otherwise the task is possible and if the task is possible you can model what that means imagining a dynamical law so to have a model in terms of dynamics of what possible means you can think of it as meaning that for a possible task there exists a system which is a constructor which has the property that when coupled to the system in question can perform the transformation and stays unchanged in the ability of course in the transformation again so it can act like a psycho so again those who work on resource theories this will be very reminiscent of the concept of catalyst ok but in this case is supposed to be more general and so that's that's all as far as general constructed here is concerned now I will give you three examples of where this logic is useful so this is a general program and there are three cases where this approach was useful to show something of interest so the first application is the one that I was mentioning so imagine you have a system which is which I called a hybrid system again the word has been used in the past for to mean other things but I'll give you your definition under which I'm working so a hybrid system is one where there is some mystery system that's what does an am there a system about which we know very little may not obey quantum theory which is coupled to a quantum system so this could be for all practical purposes a qubit and you're trying to make some predictions about the composite system you can assume that these two can couple at least in some basis let's say but you're not sure whether em really obeys quantum fear or not and you therefore are not sure whether you can for instance apply some approach like master equations or open system dynamics kind of logic so we want to do something more general here why is this interesting well this is interesting because there is an um there are a number of cases where we are actually looking at a system like this in current contemporary physics one is the case where m is the gravitational field and Q is some mass which is behaving like a qubit and this superpose across two different locations and this is a problem that bothers Fineman already I think Lachlan and others have already talked about this topic a number of times here in security the the problem here is we have this system where a quantum object interacts with gravity and we would like to make some statements about whether gravity obeys quantum theory too and behaves in such a way that for example it gets entangled with this qubit just like the photon field would or it's it's a completely classical field or in fact it behaves in more exotic ways which we don't yet know I think this is general problem that that quantum gravity people are worried about so that's one example another example that comes to mind is when you're thinking of a quantum system interacting with some object that may well obey overall quantum theory but may be undergoing some coherence let's say and so I am could be a living system biological system for instance that you want to show as some coherent behavior together with Q so there's a kind of different scenario where we know the laws that the system obeys but yet we can't assume that they hold over all four qnn together okay so in this case in constructed here you can formulate a general year of information which allows you to make some assumptions about em that eventually lead to making predictions about the composition QM together and this is nice implications for for gravity and so I'll go through some of the definitions that one proposes in this constructive information so the the important key thing is the concept of an information media so an information medium is a generalization of a familiar classical bit so it's a system with the set of attributes which can be all permuted so if you think of a bit there are two states 0 and 1 and can be over muted so 0 can go to 0 and 1 and likewise for 1 1 can be sent to itself and 2 + 2 0 and another task is also possible and this set of attributes of the information medium it's the task of copying the states in in in the inset acts so an information medium is one is a system that has at least one such set and of course you can think of a quantum system with one of the orthogonal basis will qualify as an information medium we know we can use it for classical information processing note the the fact that we stayed this by using the concept of possible and not using canonical laws now you can then formulate a principle about this media which is called the interoperability principle and this is a bit like it imposes some kind of nice group theoretic property on the on these sets in the sense that it says that if you take any two information media and you put them together the combined object is still an information medium so think of an example if you if you consider a qubit which is instant is kind of embodiment photon and imagine it interacting with a solid state system qubit we never bothered to think with it but it is possible to consider the combined entity of the two qubits as being a system which can as a whole encode at least four bits of information we just assume that to be the case but it's a very remarkable property of physical systems and this principle just exposes what it is about the physical systems that we are assuming in that case which will be very important to make predictions in the case that I mentioned earlier where you have a quantum system and another system that you don't know exactly how it works so under this framework you can show that quantum systems are in fact a special case of information media and you can define a class of objects called super information media the generalized quantum systems in the sense that they have all the qualitative properties of a quantum system but they don't necessarily obey quantum theory they only obey these general constraints about possible impossible transformations so armed with this setting you can then go back to the problem that we were considering earlier and try to prove something about the situation where you have this quantum system interacting is something that you don't know exactly what was you move so to do that we need to with this framework we need to define what non classical means and no classical in the following will mean that a system has at least two information variables X and said that are not copyable simultaneously to the same actor so of course here you see a lot of properties that are implicit in quantum theory but we try not to assume that and then we can assume to more general principles locality which is well-known principle and this interoperability information that I mentioned earlier and then we can go back to this problem that I was considering earlier to a slight variant of it where we have a system made of this mystery system M of which we are trying to establish at least if it's classical non classical and then we have two quantum systems that probe it and so we can prove this nice theorem that says that if these two quantum systems start in a state which is not entangled and then they end up being entangled through interaction with N and n is assumed to be at least an information medium so it's assumed to have at least one classical basis where you can encode information then actually M must be no classical so this is an example where by using these general principles you can end up making an interesting prediction throughout and by saying that if it can entangle to other quantum systems then it has to be at least non classical in the sense as I said earlier it may not be fully quantum we don't know but it's a nice prediction because you can then go back to this problem of gravity and say well what if I thought by we were able to entangle to quantum masses just through gravitational interactions something that su got oboz in London and blood can I and and cigar to steam have been thinking about quite a lot over the past years the question is what if you could entangled actually two masses each one of which is a qubit through this mediator m and M being gravity using this general theorem you can conclude that the mediator gravity has at least to have these non classical features that we mentioned so it may not be a full quantum system but it cannot be completely classical in the way that the science theory of general activity or quantum field theory in curved space and would suggest so this is an interesting application ok and of course this is just illustrating that some people in Oxford produce with with cubits where they were trying to illustrate the principle behind this entanglement formation where the mediator here the mystery system is simulated by these two qubits and these other external qubits are the two quantum systems that you're trying to entangled and of course when these are qubit is obvious why the intermediate system as well coherence in order for these two qubits to get entangled but the point of the simulation is to show that you can make this conclusion even when you don't assume that these two intermediate qubits are actually qubits in fact in the case of gravity if it can be used to entangle two other quantum systems it must be itself let's say very close to a qubit so it has to be no classical okay so there was the first application and of course here there are some more applications of his logic that I just mentioned earlier that you can you can try to use the same logic to show that lets say a bacterium or say photo what doesn't I mean bacterium that is sensitive to light and couples to the to the light field has to have some non classical feature in it when it's capable of entangling let's say two photons or two subsistence of the of the field of light so that's one application and there are more number of other designs of experiments and simulations that you can imagine along the lines of trying to simulate these systems that obey this general constructive healthy principles but not quantum theory as a whole so let's go for the second application so the the second application is on a different along a different line and it is to do with the problem of irreversibility so it's well known that so early when I mentioned the principles I talked about the second law of thermodynamics it's actually a principle that is quite different from the others that I mentioned so it's different from the conservation of energy because unlike the conservation of energy the second law of thermodynamics is scale dependent principle so it's home.you lated usually at a certain level of coarse graining it relies on a number of statistical approximations or procedures so it's only valid in a certain domain of applicability which isn't say called the macroscopic domain so the idea is that irreversibility and the time reverse metric laws it's usually emergent once you make a certain number of assumptions and these assumptions are those that statistical mechanics is concerned with now using the idea of a constructor maybe there is an additional source of irreversibility we can see in a system even on the time reverses metric laws and this is what I would like to mention here so there is a different way of formulating the second law which was known to the founding fathers of thermodynamics so Kelvin clauses and Planck's specifically which is stated in a very constructive ethnic way if you like because it says it's possible to construct a device which can lower which solution can increase the temperature of a fluid by mechanical means only so you can imagine here this is a stirrer there's a wait and the temperature increases once the weight goes down imagining this container to be sealed that you're vertically isolated but if you try to create a similar machine that only by mechanical means cools the water down that is impossible what you need is a heat thing you need another kind of side effect in addition to the mechanical means like side effect so it's very interesting that this is not just about the impossibility or the possibility of a certain trajectory but it's about the possibility or impossibility of a machine that does a certain transformation according to so only having a certain mechanical side effect now we can try to imagine a toy model that expresses this kind of irreversibility and this is based on a general idea of your acidity which says that a certain task X goes to Y let's say is possible but its transpose is not so read here a constructor is allowed for this task but it's not allowed for the Transpo starts when univer being put on the output and this is a different kind of irreversibility from the standard one is considered in thermodynamics and in statistical mechanics in general so it's more similar to this phenomenological thermodynamics which currently has been slightly neglected I would say in favor of the of the statistical mechanics approach and it's interesting now the the tomah that I want to consider uses a very interesting [Music] quantum information tool which was was devised by some people here and their collaborators which is called the homogenization machine this is very simple tool to describe what happens when a system equilibrate with a larger bath or system which is at a certain temperature but it does so in a very nice unitary and quantum theory compliant way so just follow me as I'm explaining this so the homogenization machine scheme which is a model that I used to prove the point about reversibility is made of is a system made of n qubits so you see them here you imagine this as being an array that goes round here with periodic boundary conditions in a way so 1 2 3 and then n minus 1 N and they're all prepared in the same state and you can couple it with an external qubit through it unitary transformation which is partial swap operation which leaves the qubit alone with a certain probability cause ether squad and it swaps it with the qubit in the reservoir with 1 minus that probability and what is proven in these nice works is that this is a universal machine to perform a task of sending a qubit from any state road to any States I this is just another way of saying that if you have a very large system and you put another system close to it in different state it will rapidly equilibrate and assume the same status approximately as the systems inside the reservoir with an accuracy which increases as the number of systems in the reservoir increases now therefore it looks like that this is an equally good machine for any such task so if you take any two states Rogo Suk's i for instance a pure state goes to a maximal unique state this scheme will just work as well when you're trying to do pure to mix compared to the case where you have mixed to pure which is the reverse task now what happens though is that if you try to consider how well this machine performs as a constructor in other words how resilient it is how many times you can reuse it after use it once so if you want to now bring a second qubit and use the same machine to perform the same task so that what you're looking at whether this is a good constructor for the tasking question there is an interesting universe v that pops up and so if you consider the special case of a task which has a pure state going to a maximal mixed state it turns out that this quantum homogenizer does very well in you consider just one usage of the machine but when you consider repeated usages the case where you're trying to send a pure state to a maximum mixed age which in a way is an easier task because maximum each states are as we know more robust than pure states in that case the homogenizer is very robust and they're pre-qualified as a constructor if you like but if you consider the reverse task it's no longer the case and so there is a sense in which the there is an irreversibility induced by the requirement of the system being a constructor in one case the system is a constructor if you consider the transpose task where you go from a maximum each state back to a pure state the system is no longer a constructor so this is a new illustration of why this idea of possible and impossible might be an interesting useful idea to solve some of these problems to do with incorporating behaviors that we think are not compatible with time reverse symmetric laws within the dynamical picture in a way that's exact and it could be a an alternative route to the statistical mechanics route and so there's a big question mark as to how the two relates to one another it's kind of that's object of some future work that I'm doing [Music] [Music] yes but this is true just if you consider the task sorry this will be true even just considering the task being performed once if you discard the reservoir or if you consider if you forget about the correlations between the qubit and the reservoir you could do the unitary transformation backwards of course so in so there is actually in these two papers this is the thing that's being pointed out which is part of the reason why we expect organization to work is because we are forgetting about correlations but there is an additional reversibility in the sense that has to do with the capacity of the constructor to be reused in one way in one case or in the other so the let's put it this way the performance of this machine for the forward task is somehow the same if you just consider one single shot event but if you then consider how resilient the machine is by keeping the same scheme and you consider the two tasks on the forward task in the reverse task you will see that the machine performs differently in one way or another as a constructor so as a cycle so in one case you can actually approximate to be able to recycle well in the case where you go from a pure to a maximum mixed state whereas you can't the other way around yes so it's a bit like saying that there is an additional reason why you would expect irreversibility yes that's correct yes but then it would be a different machine so let's say you don't need it in the forward direction in the backward direction you do need it so so that's actually a nice way of putting it yes this is correct there's a subtlety that will would come out if I could show maybe I can discuss it later with with on the whiteboard but so the subtly the subtlety is this the asymmetry shows up only if you consider reusing the same machine with the second or third or n cubed which so therefore the efficiency for a single usage is the same in both directions but it's a bit like you know you have a fridge you put a can of coke inside and you want it to be refrigerated then you want to use it again for a different kind of and so on and the point is that in this case for the forward direction the fridge seems to keep up with the task fairly well for a number of usages whereas for the reverse task there is a rapid deterioration which no doubt is due to of course the kind of task I chose because it's a pure to a mixed state maximum in each state so there is a special case in a way but it's not immediately explained through our neglected correlations so it does it it's an additional let's say source of irreversibility and kind of we can debate how it relates to the other and whether it's the consequences of the other or not but it's just to draw attention to this notion of a constructor which adds to let's say the understanding of what's going on in this particular situation so third application and I'm reaching yen it's going to be very quick it's a captive audience right so there is this statement like the audience is locked in and can't go so you're not captive so I'll try to reach the conclusion fairly quickly so this question has been considered a number of times I think in ways the tried question and some people in the audience will have thought about it carefully because they're interested in foundations and from many many different angles some other people may be a bit more dismissive of foundations as well so they would have thought about the question from that angle to now the point I want to make here is that so you've got this point here quantum theory and this is an imaginary space as I was drawing this slide I thought it wouldn't make any sense actually because I noticed later that you might be a bit confusing but never mind still makes the point I hope so one way in which you could try to vary a theory is to vary its formalism its formal aspects so you can let's say you know Plus you can add a term in the dynamical equations you can modify the parameters of here in the modified equation the equation in question and you can do a number of other things so this that you can bear it's formalism but you can also vary let's say the principles it's supposed to obey so for instance you know you to base to base the conservation of energy let's try to see what happens if you suddenly no longer does to the degree that we suppose the theory I mean do you really that we expect the theory to to obey the principle of course conservation energy is not a good idea but there are the principles a quantum theory obeys which could be varied in which we could see what what exactly in quantum theory would then have to be disposed or left behind so of course the two things are not independent because you change the formalism you might end up having a theory that no longer be is for instance certain principles that quantum theory obeys and likewise if you modify some prints to the quantum she obeys you might end up also changing its formalism but the point I want to make is that I would like to now go into this direction trying to modify some of the principles that the theory obeys and this goes into that direction so before you read these slides just listen to what I'm saying the so the quantum theory has a number of actions and we all encounter them and as we go through various courses on the topic and among these actions there is this one called the born rule which is interesting because it adds on top of an otherwise deterministic theory a an aspect which is probabilistic so it says that the expected value of a certain observable is a certain function of the observable and the quantum state or if you like it can be formulated in other ways too but it adds the probabilistic element to a theory that otherwise is not probabilistic because the training equation or the Heisenberg equation of motion is just a domestic law and so in a way it's it's an interesting actions and there's been lots of attempts to try and derive it from other actions or principles this way is using some of these information theoretic principles that I mentioned earlier to derive this spoon rule like behavior and possibly the reason why this is interesting is that the principles that one can use in order to derive the ball or light pattern that we expect by just using some principles and quantum theory without the volu is that these principles are information theoretic in nature so you will go back to this reason why it's interesting to discuss it here because the principles I'm talking about are I want discuss them here I can discuss them later in the questions they have these information theoretic bases and so it would be interesting to see what happens if we vary those principles slightly what would happen to the ball rule itself so once you can show that you derive the born rule from those principles then you can modify them and then see what type of rule emerges out of these modifications and I think it's a nice open question that I would like to to consider in in the future and so future directions there is an interest from number of people including PhD sinner I'm working with to endow this theory with a deeper mathematical structure so drawn from category theory which is like a nice tool to describe these kind of structures with tasks and hopefully it will clarify also the idea of possibility as routining this notion of a constructor of course then quantifying the various degrees of of non classic ality within the framework that that I described earlier without having to use all the tools that content theory gives us and this might involve throwing a connection with current other approaches such as GP keys and you may have applications to understanding a bit better the the information theoretic structures of current proposals for quantum gravity such as loop quantum gravity and then there is this interesting challenge which came out of this toy model that I presented which is to understand how the second and the third law that I didn't mention of thermodynamics could be phrased with this emphasis on possible impossible rather than on allowed trajectories which is the focus of statistical mechanics and then going into crazier and crazier directions which is what sounds like a good ending point of course ultimately if this program works it would be very nice to have a I mean it would be necessary to have a way of deriving the current dynamical laws from the principles and then there is this problem therefore driving dynamics out of these timeless principles and not that this is a problem that has been to some degree addressed in quantum theory there are some proposals there's this nice page and with this proposal that was made at some point in the eighties and number of developments on that in in in various fields including quantum gravity but let's say constructed here will have to deal with this problem so that's one of the things that will be will have to be solved and of course there is this issue that I mentioned the start of understanding under what conditions the generalization of a universal computer which is this Universal constructor might be possible and just the last point I want to mention is this fact that we have this interesting branch that was somewhat very important for the early days of quantum information which is complexity theory complexity theory is somewhat concerned with computational tasks of course it would be nice to have a complexity theory of any kind of task and so this complexity theory should be somewhat generalized to incorporate the idea of a universal constructor so if the idea of a universal constructor works then you would have to also to expand the field of complexity theory to cover a machine that can perform any physical transformation is physically allowed and so with these broad ideas I'll conclude and this is my quote for the day since science one is always concerned with putting the best face on one's ignorance the scientists knowledge is always very limited and one is to make the best with what one Scott and I hope I did that today thank you for listening you

Channel: Centre for Quantum Technologies

Views: 12,638

Rating: 4.9352751 out of 5

Keywords: physics, quantum mechanics, quantum technologies, CQT, Centre for Quantum Technologies, National University of Singapore, Singapore

Id: 0xkTqlzCfEg

Length: 57min 24sec (3444 seconds)

Published: Sun Mar 01 2020