This is a dialogue between Huw Price and Travis Norsen, loosely inspired by a letter that Price received from J. S. Bell in 1988. The main topic of discussion is Bell’s views about retrocausal approaches to quantum theory and their relevance to contemporary issues. This paper is a dialogue between Huw Price and Travis Norsen, loosely inspired by a letter that Price received from John Bell in 1988. The main topic of discussion is Bell’s views about retrocausal approaches to quantum theory and their relevance to contemporary issues.As far as I can recall, I first heard about Bell’s Theorem at a workshop at Wolfson College, Oxford, in the Spring of 1977 (I was in Oxford that year as an MSc student in Mathematics). I remember little of the talk, except that the speaker noted in passing that Bell’s argument required the assumption that the properties of the particles concerned did not depend on the future measurement settings. At any rate, that is what I took him to be saying. I certainly do not recall the exact words, and we will see in a moment that there is another possibility for what he might have meant—but that was the sense of the assumption I took away.I remember even this much because I was puzzled at the time that this assumption seemed to be regarded as uncontroversial. I had read some philosophy of time by that point—enough to be convinced that past and future are equally real, and to be familiar with the idea that time-asymmetry in the physical world is a statistical matter. Yet here was a time-asymmetric assumption about what can affect what—on the face of it, not a statistical matter— playing a crucial role in Bell’s argument. Everyone seemed to agree that the argument led to a highly counterintuitive conclusion. But the option of avoiding the conclusion by rejecting the assumption did not seem to be on the table.More than 40 years later, I am still puzzled. I have returned to the issue at intervals over those years, always looking for a good reason for closing what seemed to me an open door—a door, among other things, to a potential resolution of the tension between quantum theory and special relativity. To me, nature seemed to be offering us a huge hint, a hint revealed in Bell’s work, that our intuitions about what can depend on what are unreliable in the quantum world. Yet few of my growing circle of friends and colleagues who knew about these issues—who knew a great deal more than I did, in most cases—ever seemed able to hear the hint. I often wondered what I was missing.ontological models framework )The freedom-of-choice loophole refers to the requirement, formulated by Bell, that the setting choices are “free or random”  (232). FA ... major loophole, known variously as the freedom-of-choice, measurement-independence, or setting-independence loophole ..., concerns the choice of measurement settings. In particular, the derivation of Bell’s inequality explicitly assumes that there is no statistical correlation between the choices of measurement settings and anything else that causally affects both measurement outcomes. Bell himself observed 40 years ago that, “It has been assumed that the settings of instruments are in some sense free variables—say at the whim of experimenters—or in any case not determined in the overlap of the backward light cones”.In both cases here, it is simply taken for granted that the only avenue for statistical dependence between measurement settings and ‘anything else that causally affects both measurement outcomes’ is one that involves some common cause, acting in the past .I do not want to overstate this claim of confusion. Some recent writers are admirably clear that CFH, or retrocausality, is a distinct proposal for rejecting Statistical Independence . As always, however, I am conscious that there may be objections of principle that I cannot see, and that Bell did see, perhaps. If there is any trace of such objections in Bell’s letter from 1988, I am hoping that this discussion will unearth it. I am also conscious that I have not yet touched on the idea of so-called ‘superdeterminism’, or the suggestion that something objectionably ‘conspiratorial’ is required for a proposal such as CFH. Again, if there is a valid objection to CFH of this kind, I am hoping this discussion will highlight and clarify it.Before I yield the floor to my colleague, let me mention again the (supposed) elephant in the ointment for CFH, the idea of backward causation itself. As noted above, my own early discussion of these ideas took a deliberate path via some classic philosophical work on the issue, that of Michael Dummett ,5. SinceI know of one place where Bell himself discusses backward causation explicitly. In ‘La Nouvelle Cuisine’, seeking a characterisation of the sense of locality apparently implied by special relativity, he suggests that it might be defined in terms of cause and effect  (235):… in my opinion, regarded as pure logic … it contains no contradictions; however it absolutely clashes with the character of our total experience, and in this way is proved the impossibility of the hypothesis … of a causal chain going faster than light.As far as I know, this was first argued by Einstein, in the context of special relativity theory. In 1907, he pointed out that if an effect followed its cause sooner than light could propagate from the one place to the other, then in some other inertial frames of reference the ‘effect’ would come before the ‘cause’! He wrote:Bell goes on to explain what Einstein had in mind—a case of causal loops, exploiting the fact that the effects precede their causes in some inertial frames. Perhaps this is evidence that Bell himself thought that backward causation is excluded by these causal loop arguments. If so, then the escape hatch he needed is close at hand. All such arguments depend on the assumption that backward causation could be used to signal . However as Bell himself made clear, the Bell correlations imply causality without signalling. So long as retrocausality stays on the same side of the line, it is safe from paradox .As for Einstein’s own attitude to retrocausality, this little fragment suggests an admirable and characteristically empirical attitude. The objection is that ‘it absolutely clashes with the character of our total experience’. Of course, Einstein did not know about the ‘aspect’ of our total experience that was to be revealed by Bell’s work, and by the experiments it inspired. So it would be presumptuous, to say the least, to read into Einstein’s remarks any general prohibition on retrocausal models.Thanks to Huw for inviting me to join him in what promises to be an illuminating dialogue and for perfectly setting the context with that beautiful opening statement.Since it does not involve any direct interaction with (or letters from) Bell, my own personal biography vis-a-vis Bell’s theorem is far less interesting than Huw’s. But in so far as I can reconstruct it, I can report that I first learned of Bell’s theorem from David Albert’s book ‘Quantum Mechanics and Experience’ , which IGiven what I now know of the typical attitudes toward quantum foundations in the physics community, it is rather surprising that my undergraduate professors during this period were so incredibly supportive of my interests in unorthodox viewpoints. However they must have found my passion at least a little naive, and, in hindsight, I can now see that they were not completely wrong.Huw remembers questioning a very specific and subtle assumption in Bell’s theorem the first time he encountered it. For me the story is very different. I spent years knowing that Bell’s theorem was crucially important, simply because everybody unanimously agreed that it was, but having basically no clear idea at all what to make of it, because different authors all seemed to present their own totally unique version of the theorem’s logical structure. David Albert had claimed that Bell’s theorem proved that nature was non-local, but other commentators told very different stories, usually along the lines of: Bell had refuted determinism, or the related and EPR-inspired hidden-variables program, and had therefore put the final nail in Einstein’s coffin and proved once and for all that the orthodox interpretation of Bohr and Heisenberg was the only viable one.Some semblance of clarity only emerged while I was in graduate school , when it finally occurred to me that perhaps Bell himself might have an illuminating perspective on his own theorem. Reading Bell’s collected papers  turned oStatistical Independence, which is the main focus of discussion. However to set the context and pre-empt any possible misunderstanding or miscommunication, I think it will be helpful to step back and lay out the overall structure of Bell’s theorem (at least as Bell himself understood it and helped me to understand it).Huw’s opening statement focused mostly on the notion of Statistical Independence that Huw has discussed, according to which  the measurement settings a and b are “free” or “exogenous” and therefore (at least as long as we set aside the idea of retro-causation that Huw wants us to consider) uncorrelated with the variables There are two assumptions. One is the However I wanted to make sure to acknowledge explicitly that there is also another assumption—which Bell and I and most others would consider in some sense the more central and important assumption—namely, Local Causality. Bell’s careful and important mathematical formulation of this notion is intended to capture the qualitative idea, motivated by relativity, that the causal influences on a given event are to be found exclusively in that event’s past light cone, and the causal influences of a given event (on other events) are to be found exclusively in the future light cone. The idea, in short, is that causal influences propagate (from the past toward the future) always at the speed of light or slower. Readers unfamiliar with Bell’s formulation of Local Causality are urged to read his final and clearest presentation in “La Nouvelle Cuisine”  (232) anLocal Causality is that it is totally and completely generic. The formulation is not in terms of the proprietary concepts  of some specific candidate theory, but is exclusively in terms of the un-sectarian notion that Bell invented for the purpose: “Beables”, which simply means whatever some candidate theory posits to exist. And (unlike for example the conditions known as “Parameter Independence” and “Outcome Independence”) Bell’s Local Causality does not make reference to any specific type of process or situation and in particular does not imply or require any sub-classification of beables into distinct sub-types .As a brief aside that will be relevant later, let me stress here that the core virtue of Bell’s formulation of Local Causality, that is, possesses the same virtues that Bell demanded of candidate theories when he complained that orthodox quantum theory, with its special ad hoc rules for how systems behave during measurements, was “unprofessionally vague and ambiguous” ery few physicists paid attention to Russell’s enigma. They continued to write equations in the office and talk cause-effect in the cafeteria; with astonishing success they smashed the atom, invented the transistor and the laser. The long debate about nonlocality shows that it is not just in the cafeteria that these things matter in physics, but this makes the enigma all the more urgent. What is this asymmetric relation doing in physics—or anywhere else, for that matter, in a world built on the symmetric laws of physics?Simplifying a bit, we can distinguish three contemporary accounts of CAT . This view has been defended in recent years by writers such as Kutach, Albert, and Loewer;Interventionism. The third possibility seems to originate with Frank Ramsey . Ramsey,None of these accounts of CAT seem much use to Bell, seeking to build a fundamental causal arrow into a principle for quantum foundations. The first is empty, since it makes a matter of definition that effects are later than their causes.  The second seems insufficiently fundamental. On the face of it, we want a theory of the quantum world that is independent of the thermodynamic environment in which a system happens to be embedded. And the third seems insufficiently fundamental for a different reason. Its dependence on the perspective of agents like us seems deeply in tension with Bell’s desire, as Travis puts it, to avoid ‘anthropocentric terms or distinctions’.For Interventionism, anthropocentricity about CAT is only one part of a broader issue. As Pearl himself makes clear, the role of intervention threatens the idea that causation itself is fundamental:If you wish to include the entire universe in the model, causality disappears because interventions disappear—the manipulator and the manipulated lose their distinction. However, scientists rarely consider the entirety of the universe as an object of investigation. In most cases the scientist carves a piece from the universe and proclaims that piece in—namely, the focus of investigation. The rest of the universe is then considered out or background and is summarised by what we call boundary conditions. This choice of ins and outs creates asymmetry in the way we look at things, and it is this asymmetry that permits us to talk about “outside intervention” and hence about causality and cause-effect directionality. In case you feel tempted to respond ‘so much the worse for Interventionism’, look again at Einstein Locality. As Einstein says, “External influence on A has no direct influence on B”. That looks very much like Interventionism. It is doubtful if we can formulate any notion of Locality, or indeed any causal notions at all, without implicitly relying on intervention. It is built into assumptions about what we treat as exogenous variables.However perhaps we can at least do without an anthropocentric temporal arrow? After all, does physics not permit a time-symmetric notion of intervention? At least in a deterministic framework, we might interpret Einstein’s ‘external influence’ in terms of an imagined change to properties in a small region of a Cauchy surface at an intermediate time. Such a change, propagated forwards and backwards in accordance with the relevant dynamical laws, will ‘produce’ changes elsewhere.  Intuitively, Einstein Locality would be the requirement that such changes propagate only by continuous processes within the lightcones. .This may be a good way to capture the sense of causality that matters to relativity, where the idea that there is some sort of fundamental temporal asymmetry seems entirely gratuitous. It might seem an attractive approach for a retrocausalist, too, but I think it throws out far too much, in two senses. First, working science is simply not like this, either in the cafeteria or the laboratory. Our ordinary notions of causality, in science as in everyday life, are those of agents embedded in time with a particular temporal orientation. Throwing all that away would leave the view hostage to the objection rightly raised against CPH that it is incompatible with the assumptions we need to do science. As I explained above, CFH is immune from that objection.Even more seriously, this symmetric option simply obscures the subtle idea at the core of the retrocausalist proposal. This idea is that even by the lights of the ordinary asymmetric perspective, it is possible that the world contains an indirect kind of retrocausality—hard-to-notice cases in which by intervening in the future, we can make a difference in the past.Summing up, I want to make three points. First, nothing we know about CAT justifies taking it as fundamental, in the sense in which Bell’s Local Causality differs from Einstein Locality. Second, it is doubtful whether Locality, or indeed any interesting notion of causality, can be captured qualitatively in wholly fundamental terms. The right response to this is not to abandon talk of causality in physics. Instead we should keep a close eye on the role of the agent’s perspective, in order to keep in mind a question like this: What sort of fundamental structure looks like this from here? .Third, coming back to something I mentioned briefly above, we are going to need a distinction between direct and indirect spacelike influence. Einstein Locality rules out the direct kind, but not apparently the indirect kind. This was clear to the pioneer of the approach, Olivier Costa de Beauregard, who pointed out a decade before Bell’s Theorem that zig zag causality, via the past lightcones, provided a potential loophole in the EPR argument . It offeFor me, [the] Costa de Beauregard zig zag in space time, which you seem to consider equivalent to retrocausation, is nothing else than nonlocality. The addition of one time-like vector to the past and one time-like vector to the future, connecting the detections, results in a space-like vector, and a causal relation between both ends, spacelike separated, amounts to a non local relation.As I said, Costa de Beauregard originally thought of his idea as a challenge to EPR. The EPR argument assumes an intuitive notion of Locality, in arguing that measurement choices at A cannot affect measurement outcomes at a remote location B. Costa de Beauregard’s point was that if we allow causal influence in both directions within the lightcones, and adapt our notion of Locality accordingly, this argument no longer works. There is now a zig zag path for local causal influence to reach from A to B. Thus in answer to your question, Travis, Costa de Beauregard’s zig zag is still the endpoint that I have in mind. As you rightly point out, it involves rejecting Bell’s version of Local Causality. But for the reasons I have sketched, the crucial thing that we need to drop—that is, CAT, the causal arrow of time—is on shaky grounds anyway, as a principle for fundamental physics. And Einstein’s formulation of Locality from 1948 looks like the alternative that we need.There is a lot going on in that response, all of it very helpful in moving us toward what I see as a possible way of making sense of Bell’s perhaps-puzzling dismissiveness about “fatalism”. It may take some time to connect the various threads, though.Statistical Independence and Bell’s Local Causality. But you would hope to preserve a different, time-symmetric notion of locality in which the causal influences on a given event cannot be at space-like separation from it, but are equally allowed to be in either the past- or the future-light-cone. You suggest calling this alternative notion “Einstein Locality” and suggest that it is well-captured by a passage from Einstein’s 1948 essay. For the record, and despite my appreciation of your praise of the book you quoted the passage from, I have serious reservations about basing the particular time-symmetric notion of locality that you have in mind on that particular  passage, and thus attributing your proposed locality concept to Einstein. But a debate about exactly how to parse Einstein’s words will be a pointless distraction here since you have made it abundantly clear what you have in mind. So, having noted my reservation, I will simply follow you in describing your proposed time-symmetric alternative to Bell’s Local Causality as “Einstein Locality”.So, Huw, your vision involves rejecting both My main concern (other than the terminology) about “Einstein Locality” is that, as you acknowledge, “we’re going to need a distinction between direct and indirect space-like influences”. From your point of view, the whole purpose of Einstein Locality is to endorse, as compatible with “the sense of causality that matters to relativity”, the zig-zag sort of multi-step, “indirect” causal influence across space-like separation that Bell’s Local Causality prohibits. Without this distinction between “direct” and “indirect”, we would be stuck saying that Einstein Locality allows the very thing that it poses as prohibiting . In that case, Einstein Locality wouldn’t actually prohibit anything, i.e., it would be rather empty and pointless.As I think we agree, it thus seems that your proposal of replacing Bell’s Local Causality with Einstein Locality swims or sinks with the project of situating this distinction between “direct” and “indirect” influences in the context of fundamental physics. And my initial gut reaction is that this project seems rather hopeless. When I look at extant theories that possess the appropriate sort of professionalism  I see causal influences taking the form of continuous propagation. There is nothing “atomic”, for example, about the sequence of steps whereby one charged particle affects the motion of another nearby charged particle via the intermediary electric and magnetic field. There are, if you like, a continuous infinity of infinitesimal intermediating steps, but in my opinion that description should be understood as a human theorist’s perspective on something that is, in reality, a seamless whole.So is one charged particle exerting force on another nearby charged particle a “direct” influence (because the process is a seamless whole) or an “indirect” influence ? I think the only good answer is to reject the question and whatever line of thinking motivated us to pose it.a to the space-like separated outcome B . It may well be true that if we restrict our use of cause-and-effect terminology to processes involving agent-intervention, it might provide a clean way to say, for example, that the zig-zag influence depicted in However to me this kind of proposal for grounding the distinction between direct and indirect causal influences also seems highly suspicious and implausible. We want, at the end of the day, an account of fundamental physics that is not afflicted by anything like a “measurement problem”, i.e., we want to avoid the use of, or need for, anthropocentric or otherwise “unprofessionally vague and ambiguous” concepts and distinctions at the fundamental level. We want, as you quote Pearl as saying, ultimately “to include the entire universe in the model”. And, when we do that, I think it is exactly right that “interventions disappear”.Of course, Pearl goes on to suggest that, in practice, “scientists rarely consider the entirety of the universe as an object of investigation”, that models always  include some parts of the world only as boundary conditions, and that “this ... permits us to talk about ‘outside intervention”’. That may well all be true, but I would nevertheless find a formulation of Einstein Locality which required explicit reference to “intervention” (to ground the distinction between direct and indirect influences) to be squarely in the “unprofessionally vague and ambiguous” category.Incidentally, it might surprise some readers to know that Bell, who of course invented and applied the concept of Local Causality, was in some sense very sympathetic to at least part of the view that Huw quoted Pearl describing as “Russell’s enigma”, i.e., the idea that, at the level of fundamental physics, causality (at least described as such) is nowhere to be found. After presenting his formulation of Local Causality in “La Nouvelle Cuisine”, for example, Bell remarks:Note, by the way, that our definition of locally causal theories, although motivated by talk of ‘cause’ and ‘effect’, does not in the end explicitly involve these rather vague notions.  (240)This, however, does not mean that  theories do not describe processes which can legitimately be characterised in causal language. Bell once wrote that, in “pursuing [his] profession of theoretical physics” he was required to “insist ... on the distinction between analysing various physical theories, on the one hand, and philosophizing about the unique real world on the other hand”  (101) CoIn this matter of causality it is a great inconvenience that the real world is given to us once only. We cannot know what would have happened if something had been different. We cannot repeat an experiment changing just one variable; the hands of the clock will have moved, and the moons of Jupiter. Physical theories are more amenable in this respect. We can calculate the consequences of changing free element in a theory, be they only initial conditions, and so can explore the causal structure of the theory.  (101)This comment occurred in the context of explaining that his concept of Local Causality  should be understood as referring to theories  rather than to the unique real world directly. Physical theories  thus not only, in Bell’s view, have “causal structures”, they are our best and necessary tool for, in the long term, discovering the causal structure of the real world.Anyway, le me summarise my concern about “Einstein Locality”. I fear that, unlike Bell’s Local Causality, this notion will never be formulatable in a meaningful and appropriately fundamental way that accomplishes, Huw, what you want it to accomplish. I fear, in particular, that it will be impossible to cleanly distinguish “direct” from “indirect” influences in an appropriately “professional” manner, and I fear that, without the terminological check provided by an appeal to explicit “interventions”, an Einstein Local theory of the sort you claim to want will be riddled through with the sort of causal influences across space-like separation that (however you might want to classify them) are just prima facie contrary to “the sense of causality that matters to relativity.” In the same discussion with Shimony, Clauser, and Horne that has been referenced several times already, Bell wrote, about the idea of saving Local Causality by rejecting Statistical Independence via the CPH:A theory may appear in which such conspiracies inevitably occur, and these conspiracies may then seem more digestible than the nonlocalities of other theories. When that theory is announced I will not refuse to listen, either on methodological or other grounds. But I will not myself try to make such a theory.  (103)Local Causality and Statistical Independence but preserving “the sense of causality that matters to relativity” with some notion of Einstein Locality. I doubt this could be done, and so am not interested in spending my own time and effort on the project, but would be delighted to listen if and when somebody puts forward a precise formulation of Einstein Locality and/or a concrete example of a candidate fundamental theory which shows, if only in principle, how this project could work.I feel this same way about the idea of rejecting both Am I correct, Huw, that neither exists at present? I have to admit that I was somewhat confused by your proposal to formulate Einstein Locality “in terms of an imagined change to properties in a small region of a Cauchy surface at an intermediate time”. That actually sounded rather promising to me, so I was puzzled that in the end you seemed to reject it as “throw[ing] out far too much”.In particular, I did not understand the worry that this was somehow “incompatible with the assumptions we need to do science”. It seems to me that this formulation is perfectly compatible with ordinary scientific practice. Indeed, do not several existing (serious candidate) theories, e.g., Maxwell’s electrodynamics, respect this condition?It seems to me that your rejection of this formulation—what I think you expressed when you said that it “obscures the subtle idea at the core of the retrocausalist proposal”—must be based on the recognition that such theories as Maxwellian electrodynamics do not appear to support the specific sort of zig-zag causality that would allow for a non-conspiratorial violation of Statistical Independence. However, it is not clear to me what would.Let me try putting all my cards on the table here. In my response so far, I have not really addressed a core aspect of your proposal, namely, the tension between the apparently time-symmetric fundamental laws, and Bell’s time-asymmetric Local Causality. You are clearly committed to the idea that time-symmetry is fundamental; as you explained from the very beginning, this is the motivation for the whole retrocausalist project. By contrast, I am more open to the possibility that some kind of Causal Arrow of Time (CAT) may remain in our fundamental physics. For one, I am not comfortable presupposing that the fundamental laws will turn out to be deterministic; maybe, as the founders of quantum mechanics seemed to believe, the world will turn out to be irreducibly stochastic. Although I never found the arguments of the founders convincing, I do not think this possibility has been ruled out, and as long as that remains true I think it is premature to insist that the fundamental laws are time-symmetric. . But even if the fundamental laws do turn out to be time-symmetric, I am not convinced this means that there can not, or should not, be something like a fundamental causal arrow of time.That said, though, such a fundamental CAT, like explicit notions of ‘cause’ and ‘effect’, may not appear as such, may be relatively invisible, in the formulation of a candidate fundamental theory—or at least a deterministic candidate fundamental theory. Indeed, in the context of such theories, my concern about the retrocausalist proposal is not so much that backward causation is impossible or unconscionable, but rather that the distinction between forward and backward causation seems to melt away. In Maxwellian electrodynamics, for example, the state of the particles and fields at one time determines the state of the particles and fields at a later time. So did the former cause the latter, or vice versa? The laws of the theory certainly do not answer that question; they just tell us that the states at the two times are necessarily connected.  So is Maxwellian electrodynamics a retrocausal theory? Maybe? I am honestly not even sure what the question means.Of course, at the non-fundamental level, where we model only some narrow part of the universe and describe its surroundings as “exogenous” variables through which we might “intervene” on the narrow part under study, the distinction between forward and backward causation seems much clearer. If the system changes due to an intervention in its past, that is forward causation, whereas if the system changes due to an intervention in its future, that is backward causation. But if we demand that the vague and anthropocentric classification of beables as “endogenous” or “exogenous”—if we demand that reference to “intervention”—should disappear at the more fundamental level, it just seems like the distinction between forward-in-time and backward-in-time influences will have to disappear too.So I tend to think that you retrocausalists fool yourself into thinking there is a meaningful program to pursue here, by taking a much too interventionist perspective on causation, i.e., by thinking too exclusively about very narrow models of specific situations in which various things are treated explicitly as “exogenous” “interventions”. And in particular I think that as soon as you try to imagine embedding one of these models, e.g., the one pictured in Could I be wrong about all of this? Absolutely. To me, the easiest and best way to find out would be to scrutinise a concrete example of a serious candidate fundamental theory that respects a time-symmetric Einstein Locality condition and which (unlike Maxwellian electrodynamics?) supports the needed kind of indirect, zig-zag causality in (but only in) the EPR-Bell type of setup where the retrocausalist needs Statistical Independence to be violated.Unfortunately, I do not think any such theory exists at present, and everything I have said here should make pretty clear why this does not surprise me. But if (or when) I am wrong, and such a theory is presented, I will not refuse to listen.In summary, these are what my cards look like. If it turns out I am (at least arguably) not wrong about all of this, there will be at least a bit more to say about how this relates to Bell’s apparent conflation of the CPH and the CFH, i.e., his perhaps-puzzling dismissal of the retrocausality program on the grounds of “fatalism”. However Huw, I think I should pause here and give you a chance to weigh in on what I have said.In my opening Section I described my view that Bell’s Theorem contains a loud hint from nature. Bell shows that if we assume Statistical Independence (SI), quantum theory implies nonlocality. The hint turns on the thought that we should read this as a reductio ad absurdum, and conclude that SI fails in the quantum realm.  This would be the obvious reading if we could already see on the shelf some plausible way in which SI might fail, but we do not. Looking further back on the shelf there are two possibilities, CPH and CFH—the former evidently much easier to see, from most vantage points. I suggested that deafness to the hint might rest on failing to distinguish them, and hence on the view that Bell’s well-founded objections to CPH would apply to any attempt to abandon SI.In response, Travis, you pointed out that Bell’s own assumption Local Causality would still fail in CFH, and asked in what sense I could therefore claim to be defending locality . I offered Einstein Locality as a substitute for Bell’s notion, and you have now said that you doubt whether the distinction between the two will be expressible in vocabulary permitted by fundamental theory.It will not matter if this turns out to be the case, in my view, because the argument can simply fall back on Lorentz Invariance. If we treat a violation of Lorentz Invariance, and the need for a preferred frame, as the absurdum avoided by giving up SI, then the hint speaks to us just as before. To put this another way, suppose we concede to my famous 2015 correspondent that Costa de Beauregard’s zig zag proposal still counts as nonlocality. No matter, so long as the zig zag offers us a path to an explanation of the Bell correlations that avoids the tension Bell himself saw between quantum theory and special relativity. It has often been noted that there are two elements to the counterintuitive character of nonlocality in contemporary physics, the first linked to relativity and the avoidance of preferred frames, and the second, obviously much older (see Newton’s remarks above), to the counterintuitiveness of action at a distance itself. A restriction to the language of fundamental physics might prevent us from expressing the latter, but presumably not the former. And this will do just fine, for the case for the hint.As I said in §2, I now feel that there are two hints, one from Lorentz Invariance and one from Time Symmetry. Concerning the latter, I want to stress again that I think that quantum theory introduces a new reason, not present in the classical regime, for thinking that time symmetry requires retrocausality. A common objection to the retrocausal proposal is a challenge I could paraphrase like this: ’What about time-symmetric classical physics? Is that retrocausal?’ This presents retrocausalists like me with a dilemma. If we say ‘Yes’, we are admitting that retrocausation is not novel or interesting, because it is common in classical physics; if we say ‘No’, we have conceded that time symmetry alone does not imply retrocausality, leaving it unclear what would do so.Travis, I take you to be expressing the latter part of this challenge in remarks such as this: ‘[S]uch theories as Maxwellian electrodynamics do not appear to support the specific sort of zig-zag causality that would allow for a non-conspiratorial violation of Statistical Independence. But then it is not clear to me what would’. In response, I want to outline what I now think of as the best case for thinking that quantum theory is different.The argument emerged from discussion in  of timelNormally, the earlier experimenter (Alice) would be able to control the inputs as well as the setting  idea in  is that Discreteness condition. Without it, the Demons have complete control over the polarisation of the photon between the two devices. Knowing Let us call the no superpositions rule the So in this artificial situation—interesting because of the way it mirrors normal circumstances at the other end of the experiment—Discreteness introduces what looks by ordinary interventionist lights to be a new element of forward causality. In effect, it gives Alice an extra degree of control over the probabilities at Bob’s end of the experiment, compared to the case in which the Demon is not restricted in this way,  HowLet me come back to the remark of yours I quoted above: ‘[T]heories as Maxwellian electrodynamics do not appear to support the specific sort of zig-zag causality that would allow for a non-conspiratorial violation of Statistical Independence. But then it is not clear to me what would’. The answer suggested by the reasoning just described is that under the constraint of time symmetry, non-conspiratorial violation of SI emerges from the same place as the Bell correlations themselves. We saw that if we consider Bell correlations in timelike settings, the EPR and Bell arguments reveal a distinctive kind of forward causality. From that point, modulo the assumption mentioned about an ontological basis for this causality, insisting on time-symmetry gets us to the violation of SI. Travis, I appreciate that you are less convinced than I am about both time symmetry and CAT. As you say, you want to hold open the possibility that one or both fail, perhaps independently. For me, both these options fall in the ‘I would not refuse to listen’ box. However what matters for present purposes is not our differing credences about these things. We seem to agree that—contrary to what many seem to think—a time-asymmetric CAT does not have the status of a well-established piece of physical or metaphysical lore, something that can simply be invoked without argument, in order to dismiss the hint. On the contrary, work outside physics makes a significant case that the causal asymmetry is not fundamental—which means that we have at least some reason to be suspicious of proposals within physics that assume otherwise, implicitly or explicitly. Similarly, work inside physics gives us enough reason to take time symmetry seriously to imply that we certainly can not take its failure for granted. So again, there is no sign here of something sufficiently well-grounded to dismiss the hint.The issue you raise of what goes into fundamental theory is very interesting, and in my view quite difficult. It is hard to make sure that we have eradicated the conceptual traces of our human perspective, especially our asymmetric temporal perspective. We are predictive creatures, always acting for the future on the basis of limited knowledge of the past. It is no surprise at all if we describe the world in terms appropriate for such a viewpoint. However we need to keep an open mind to the possibility that the fundamental level need not be described in these terms. These lessons are as important for retrocausal approaches as for anyone else. For one thing, there is a risk that in pursuit of time symmetry, retrocausal approaches find themselves doubling-up ontology that would be better discarded. At the fundamental level we should try to prune away elements that reflect our time-asymmetric viewpoint, not balance them by adding elements reflecting a time-reversed viewpoint. In my view the so-called Two State Vector approach may be guilty of this mistake .With these ‘meta’ issues about fundamental theory still open, and the path to CFH invisible to most in foundations of physics, let alone in physics more broadly, I think it is no surprise that we retrocausalists do not yet have anything that could claim to be a ‘serious candidate fundamental theory’, as you put it. I recommend ,18 for rIn the spirit of putting cards on the table, I will take this opportunity to record a couple of preferences. First, I think that the de Broglie–Bohm theory (dBB) provides an attractive and under-explored framework for this approach. It has the advantage of an ontology both clear and sparse—I am thinking especially of the sense in which position is the only fundamental property, other properties being contextual and relational. This sparsity reduces the risk that we unwittingly build our own epistemic viewpoint into what is intended to be fundamental ontology. Another virtue is that in dBB, probabilities emerge much as in classical statistical mechanics, from a distribution over initial conditions. We do not need fundamental time-asymmetric chances, or anything of that kind.  Finally, the dBB ontology offers an obvious place to hide some subtle retrocausality—in fact, two places, namely the particle positions and the pilot wave itself, if we give the latter an appropriate ontic status. There has already been some work exploring retrocausal versions of dBB: see, e.g., ,36). SeeSecondly, and independently, I like proposals that seek to show how non-conspiratorial SI-violating correlations might emerge from global constraints—e.g., recent work by Wharton , Palmer Let me close by coming back to the idea that if we stick to the language of fundamental physics, it will be impossible to draw my distinction between CPH and CFH. If I understand you correctly, Travis, you think this may explain Bell’s apparent wish to lump the two together. I am thinking of remarks such as this:Indeed, in the context of such [fundamental] theories, my concern about the retrocausalist proposal is not so much that backward causation is impossible or unconscionable, but rather that the distinction between forward and backward causation seems to melt away. In Maxwellian electrodynamics, for example, the state of the particles and fields at one time determines the state of the particles and fields at a later time. So did the former cause the latter, or vice versa? The laws of the theory certainly don’t answer that question; they just tell us that the states at the two times are necessarily connected.  So is Maxwellian electrodynamics a retrocausal theory? Maybe? I am honestly not even sure what the question means.In response, I want to distinguish two questions. First, does causal language appear in the fundamental theory? I think we agree in saying ‘No’ to this, at least if we set aside your lingering attachment to a fundamental CAT.Second, does fundamental theory make distinctions which, when viewed from the ordinary perspective of agents like us, map onto the distinctions we make in causal language ? Here I say ‘Yes’. Why? Well, consider the corresponding questions about colour. Are red and green categories in fundamental theory? Obviously not. Do we expect fundamental theory to mark the difference between red things and green things? In some sense, obviously, yes—that is what it is to take colour to supervene on fundamental physics.If there is a difference between the colour case and the causation case, it is that causal concepts are much more deeply embedded in scientific practice. Some philosophers would see in this an argument for thinking that causation itself needs to be fundamental, but set that aside. Here we are considering the possibility that causation is not fundamental, or at any rate not part of fundamental physics. My point is that this gives us no reason to reject the supervenience of causation on physics. We should expect causal distinctions to depend on lower-level differences, just as we expect for colour .This means that I see no reason to think that fundamental physics will not continue to provide the distinctions we need to make causal judgements, including those needed to distinguish between CPH and CFH. However even if I turned out to be wrong, I think it would leave the case for retaining SI no better off. If we throw out the vocabulary we need to distinguish CPH and CFH, we also throw out the terminology we need to raise Bell’s objections to rejecting SI. Even if we set aside such explicitly anthropocentric terms such as ‘free will’ and ‘fatalism’, the remaining objection turns on the idea that science treats measurement settings as exogenous variables. You are imagining that even this notion ‘should disappear at the more fundamental level’. However if we do not have that notion in our vocabulary, we can not make Bell’s objection, and if we do have it, then we can distinguish CPH from CFH. Even worse, we saw that the case for CFH  runs very close to the EPR and Bell arguments themselves. If it really were true that fundamental theory prevented us from making the former, I think it would follow that we could not discern the latter. So there is a danger that by blocking the hint we would deprive ourselves of the vocabulary to describe the problem itself.In response to my skepticism about  Einstein Locality, you suggest that we “can simply fall back on Lorentz Invariance”. However Lorentz Invariance is nearly as ambiguous and problematic as the various notions of locality we have been discussing. For example, theories with something like a “preferred frame”  can be Lorentz Invariant and indeed can be argued to be fundamentally relativistic in a serious sense ,43. I alHowever even leaving that issue aside, I remain confused by the same big-picture point I raised initially. We know that it is possible to violate Bell’s Local Causality in a Lorentz Invariant theory, in several distinct ways ,42,44. TOn that issue of coherence, I must admit that I remain somewhat unsure about how to answer the question—“What about time-symmetric classical physics? Is that retrocausal?”—that you explained poses a dilemma for the retrocausalist. I think your answer must be no, because otherwise I would not understand why you would bother with the somewhat complicated setup and associated argument purporting to establish “that quantum theory is different”—different, I gather you mean, from straightforwardly time-symmetric theories  in supposedly possessing the somewhat subtle and previously-unrecognised sort of causal  influences that you discuss.Unfortunately, though, I find this argument totally unconvincing. It is based completely on the orthodox/textbook version of quantum mechanics including, in particular, the collapse postulate whose presence is the very core of the measurement problem. The crucial assumption you call Discreteness is just a kind of time-symmetrised collapse postulate, and, as you acknowledge in the more detailed discussion of , the argYes, as you point out there, this does not mean that such theories necessarily exclude retro-causality. Indeed, as I indicated before, the fundamentally time-symmetric character of the dynamical laws in those theories makes me perfectly open to admitting that they have retro-causality to exactly the same degree or extent, whatever that is exactly, that they have regular forward-causality. But I gather, from the fact that, if I am understanding correctly, you suggest somehow changing or supplementing dBB—“to hide some subtle retrocausality”—that you do not see any retro-causality, of the sort you want and need, in that theory’s standard extant formaultion. However I do not understand that proposal at all. In  you suggTo me, that is, it appears that the idea that dBB is somehow a promising candidate for retro-causality of the sort you want and need, arises only from a failure to appreciate that dBB can and should be thought of as a candidate fundamental theory, which does not need  special ad hoc exceptions to the basic dynamical postulates, associated with measurement or anything else. To me it instead seems clear that the only sort of retro-causality one could plausibly attribute to the de Broglie–Bohm theory is just exactly the sort that one could, with equal plausibility, attribute to the Everettian quantum theory, Maxwellian electrodynamics, or classical particle mechanics. However, again, and as far as I can tell, this is a sort of retro-causation that you acknowledge is not what you need, so you do not even call it retro-causality.To summarise that point, it seems to me that in order to find the sort of thing you are looking for, you retrocausalists need to set aside the best extant candidate fundamental time-symmetric quantum theories (dBB and Everett) and instead work with a time-symmetrised version of a theory that suffers from “measurement problem” issues  from the morning windstorm—would be reconciled in such a theory. Maybe the theory would say that a and b are, alone, sufficient to determine The new point I want to make here is that I do not see, exactly, how violating Statistical Independence instead with the CFH leads to a less conspiratorial picture. Suppose I keep an open mind and allow for the possibility that some hypothetical future theory might include, in some meaningful and compelling way, retro-causal influences from the settings This is precisely the sort of correlation, between seemingly-random details of the states of seemingly-unrelated phenomena in the past, which we regard as unacceptably conspiratorial in the context of the CPH. Why should such correlations be considered any less conspiratorial in the context of the CFH? For this reason, to me, the distinction between violating Statistical Independence with the CPH, and violating it with the CFH, becomes blurry at best when we zoom out, include more of the world in our system, and refrain from treating various elements in a special way, as “exogenous interventions”.You claimed, at the end of your most recent contribution that to whatever extent we lose the ability to make the CPH/CFH distinction, we will also lose, to that same extent, the ability to argue for the reasonableness of Statistical Independence (or even to rehearse the EPR argument and Bell’s theorem) in the first place. I do not understand this. As discussed in the exchange with Shimony, Clauser, and Horne that Bell referenced in his letter to you, the main case for Statistical Independence is a practical and empirical one. In particular, Statistical Independence is assumed in virtually every scientific experiment. Think, for example, of a randomised controlled drug trial whose standard interpretation requires assuming that the (say) coin flips, determining which patients got the drug and which the placebo, were uncorrelated with the previous health of the patients: If all of the patients who got the real drug survive and all the patients who got the placebo die, we would ordinarily infer that the drug works well to prevent death. However, of course, it is possible that the drug has no positive effect at all; instead, the coin came up tails for, and hence the placebo was given to, all and only those patients who had some other health condition, totally unrelated to that targeted by the drug, and were destined to die of that. As Shimony, Horne, and Clauser put it, in a passage you quoted earlier but which bears repeating here, denying Statistical Independence:...will essentially dismiss all results of scientific experimentation. Unless we proceed under the assumption that hidden conspiracies of this sort do not occur, we have abandoned in advance the whole enterprise of discovering the laws of nature by experimentation. Science, that is, relies on the Statistical Independence assumption, and science unquestionably works.a and b  should not be conspiratorially correlated with the specific facts which influence the sequence of particle pair states This practical case for Statistical Independence does not appear to me to rely on any interventionist perspective on the applicability of causal terminology to fundamental theories. Indeed, it is easy enough to understand what Statistical Independence means in the context of such theories. For the randomised drug trial, it means that the specific facts, in the distant past, which determine the precise sequence of coin flips (used to assign placebo or drug to each patient) should not be conspiratorially correlated with the specific facts which determine whether those individual patients will or will not die of some unrelated malady. Similarly, in the EPR-Bell case, Statistical Independence means that the specific facts which determine the sequence of measurement settings a and b and (on the other hand) Of course, Huw, you will want to say I am begging the question here by inserting the word “conspiratorially”. Your whole point is that, if the settings retro-causally influence the pair states, the needed correlations between (on the one hand) By way of concluding, let me try to summarise the several reasons I have explored, throughout this dialogue, for being sceptical of this project.First, I am sceptical that, at the level of a fundamental candidate theory  the idea of retro-causation, of the rather special sort you want and need, even makes sense. .Second, I am sceptical of the claim that, if you did somehow produce a candidate fundamental theory that somehow made your desired sort of violation of SI compelling, the theory would respect some meaningful “Einstein Locality” or Lorentz Invariance condition. .a and b retro-causally influencing the pair states a and b, will presumably still have to have some influence on The new, third, grounds for scepticism that I have been trying to raise here has to do with the fact that, even in a (deterministic) candidate fundamental theory in which it somehow made sense to speak of the settings A concrete candidate theory could, in principle, cleanly refute any or all of the grounds for scepticism I have expressed here. However, so far I have never seen a candidate retro-causal theory with the appropriate “pretension to physical precision”. I have instead only seen various sorts of toy models that focus on some narrow system, postulate “interventions” by treating certain variables as “exogenous”, and (hence) suffer from a kind of “measurement problem”. I have not, that is, seen anything that refutes my scepticism, so I remain unconvinced that the retro-causal program generally, and the distinction between the CPH and CFH in particular, can survive the translation to a more serious, candidate fundamental theory.Was it similar reasoning that led Bell, in the letter reproduced in That, at any rate, is where I, having been profoundly influenced by Bell, end up. At least for the time being.Travis, it is a little frustrating to close at this point, when your latest comments raise several points for further discussion. However, wrap up we must, so I will confine these closing comments to just one issue, that of ‘conspiracy’. Before that, I want to say a very warm thanks to you for taking this on. As you know, the idea for this dialogue originated in an exchange of Facebook comments, after I shared my letter from Bell there. Some fascinating discussion takes place on Facebook these days, but it has been a pleasure, as well as an education, to do this the old, slow way ).Now to conspiracies. Helpfully, you suggest an answer to your own objection:a and b and (on the other hand) [Y]ou will want to say I am begging the question here by inserting the word “conspiratorially”. Your whole point is that, if the settings retro-causally influence the pair states, the needed correlations between (on the one hand) That would do, but I want to say a bit more. For one thing, I want to make sure it is clear why I take CFH to be much less vulnerable to the conspiracies charge in the first place.I introduced the term ‘conspiracy’ into our discussion in §2. It occurs there in the quote from Shimony, Clauser, and Horne  that youIn your account of the conspiracies objection, you note that physicists (notoriously playful folk) can easily put measurement settings under the control of such things as the number of blueberries in a pancake. And you point out—rightly, if you are talking about CPH—that this means that any theory trying to break Statistical Independence is going to have to concern itself with blueberries. Just look at the two (fortuitously) blue arrows in a with properties a is an exogenous variable, on which interventions are possible.) Once we have these guts, the story about the blueberries follows for free. Blueberries are simply one among the endless ways that ingenious experimenters can devise to control the value of an exogenous variable  random experimental interventions, in a project to test the hypothesis that settings of the handset have a causal influence on the television. In that project it would be absurd, of course, to assume statistical independence between the handset settings and the state of the television—what we would be looking for would be, precisely, violations of such independence. This trivial example shows that science does not assume such Statistical Independence everywhere, and that it is indeed begging the question against CFH to assume it in the form of the principle we have been calling Statistical Independence.So CFH is far less vulnerable to the charge of conspiracy than CPH. If there is something seemingly conspiratorial in CFH, it is the fact that the particles ‘already know’ the measurement settings, in some sense, before they arrive at the measurement devices. This certainly looks strange to ordinary intuitions, and words such as ‘conspiratorial’, or ‘teleological’, do something to capture this strangeness.If someone objects to CFH on this basis I am inclined to accuse them of a temporal double standard—in other words, as I used the term in , applyinI am not suggesting that CFH involves a time-reversed version of the familiar thermodynamic asymmetry. However, if anyone objects to this remaining sense in which CFH looks conspiratorial, I will ask them whether they would still object to the time-reversed version of the same theory, in which a particle and a measuring device are correlated in virtue of a lawlike constraint on an interaction in their common past. If not, I will accuse them of a temporal double standard. That is close to the charge of begging the question, but a bit more specific in a useful way (I discuss these issues at length in  [Ch. 5])Obviously there is more to say here. For one thing, I have not said anything about your concern that CFH requires I share the sense that we are only now getting warmed up. However I think, rather than be frustrated to wrap up just when it feels like we are finally getting to the heart of the issues, we should appreciate the progress that getting to this point represents. And of course the end of this particular dialogue is not the end of dialogue as such. Our illuminating and highly enjoyable discussion here can hopefully generate and influence further constructive discussions in the future .By way of wrapping up, I will just touch briefly on two points, making a special effort not to unfairly lob any new rhetorical grenades. In particular, I want to flag, for the purposes of future discussion, a point where I think we may have a substantive and unresolved disagreement. And then I will attempt to clarify my  use of the word “conspiracy” in my previous contribution.So, first, the flag. You said that my argument “that any theory trying to break Statistical Independence is going to have to concern itself with blueberries” would apply “if you are talking about CPH”. I think you meant to imply that this argument does not apply in the context of CFH. But the whole point of my admittedly silly parable involving blueberries and windstorms, is precisely that it should still apply, either way.You wrote that, for you, “the crucial difference [between CPH and CFH] was simply that unlike CPH, CFH treats measurement settings in the normal way, as exogenous variables”. But perhaps the fundamental theme running through everything I have written here is that everything we might want to say about the EPR-Bell scenario needs be compatible with the perspective of a candidate fundamental theory which is free of “measurement problem” issues and in which, in particular, there are no exogenous variables.Therefore, if the reason you think that the CFH is not “going to have to concern itself with blueberries” is that the CFH by definition treats measurement settings as exogenous , then I would regard that as a fatal flaw in the CFH program.As always, though, I suspect there may be some mutual misunderstanding that makes our differences appear greater than they really are. In particular, your reference back to the  blue arrows in a and b are all on the same future-directed causal chain. But there would be nothing remotely conspiratorial about the failure of Statistical Independence in this kind of case. We would just blame the failure on an exceedingly stupid experimental design by the experimenters.But I believe the way you are thinking of Statistical Indepedence being violated here, in the context of the CPH, is not what I had in mind. It is of course true that Statistical Independence could easily be violated if, instead of the particle pair source spitting out pairs in a pre-defined order determined by the precise moment and location of the windstorm, the pair source instead spits out a sequence of particles in states that are, say, determined by the output of the very same random number generator (seeded by the blueberry count) that is also determining the settings. This sort of arrangement would seem to be the sort of thing you had in mind  blueberries affecting the other. To me, the interesting question is whether Statistical Independence might still be violated in this kind of case. And of course it might be. But its being violated  would require certain subtle details in the kitchen of the diner to be correlated, just so, with certain subtle details of the weather pattern across town. The usual attitude, though, is that there is no reason those details should be correlated. So positing that they are—that is, rejecting Statistical Independence—amounts to asserting something that has a highly implausible, “conspiratorial” feel to it.What I had in mind—what I thought we agreed would count as unacceptably conspiratorial—is instead the possibility that Statistical Independence could be violated  with a more sensible experimental design, in which the causal chain leading up to the pair states So much for the flag. Now to the clarification.a and b retro-causally influence the pair states The point I was making previously is that, by considering the CFH  that both CPH and CFH are, I think, committed to, when discussing those correlations from the point of view of the CFH. The correlations are the same, whether we adopt the CPH or the CFH, but their conspiratorial-ness is not the same.However my intention was not to beg the question. Partly I developed the parable and pushed this point just because I think it is important to acknowledge that violating Statistical Independence implies these sorts of correlations, regardless of how exactly one does it. (Treating measurement settings as exogenous variables tends to obscure this fact).In addition, just because these sorts of correlations (in so far as they arise via the CFH) should not be described (and subsequently dismissed) as “conspiratorial”, does not mean they are beyond reproach. For example, as I think you hinted at, their existence raises questions about how to reconcile the posited retro-causation with the statistical/thermodynamic arrow of time. And I have to admit that I feel a vague additional sense of unease about such correlations, stretching, as they would clearly have to, all the way back to the big bang. I have a hard time putting my finger on the reason for this queasiness. Of course, one possibility is that, try as I might, I can not quite get myself to take retro-causation fully seriously, so, in my gut, I respond just as I would to the conspiratorial character that those same correlations would have in a theory without retro-causation.I do think there is more to it than that, however, and what I meant to gesture toward before was the thought that maybe this could explain what Bell wrote in his letter to you. If “fatalism” is the uncomfortable idea that our apparent freedom (or even just apparent randomness) is illusory—that what we choose to (or just happen to) do has, in fact, been pre-written in a script going all the way back to the big bang—then is there not a kind of time-reversed fatalism inherent in your CFH? For me at least, and perhaps for Bell, the idea that my apparently free choices  end up causing incomprehensibly subtle correlations in the early universe, is no less uncomfortable than the idea that incomprehensibly subtle correlations in the early universe are the true causes of my apparently free choices.However, is there more to this discomfort than a lingering bias against retro-causation? Answering that will, I think, require further reflection, discussion, and debate. I look forward to that, and I thank you again for inviting me to participate in this.


In view of the urgent need for intelligent rehabilitation equipment for some disabled people, an intelligent, upper limb rehabilitation training robot is designed by applying the theories of artificial intelligence, information, control, human-machine engineering, and more. A new robot structure is proposed that combines the use of a flexible rope with an exoskeleton. By introducing environmentally intelligent ergonomics, combined with virtual reality, multi-channel information fusion interaction technology and big-data analysis, a collaborative, efficient, and intelligent remote rehabilitation system based on a human’s natural response and other related big-data information is constructed. For the multi-degree of the freedom robot system, optimal adaptive robust control design is introduced based on Udwdia-Kalaba theory and fuzzy set theory. The new equipment will help doctors and medical institutions to optimize both rehabilitation programs and their management, so that patients are more comfortable, safer, and more active in their rehabilitation training in order to obtain better rehabilitation results. With the increasing populations of the disabled and the elderly, scientific and technological innovation to maintain and improve the health of members of these populations has become a strategic need in many countries ,2. The rA rehabilitation robot is a kind of automatically operated machine that is designed to improve movement in persons with impaired physical functioning . The rehIn terms of the control method and dynamic modeling, Hogan  first prIn fact, robotic devices are already used in clinical practice as well as in clinical evaluation. Some of them have succeeded to target the subject group such as Kiguchi’s , Cheng’sIn traditional rehabilitation robots, a driving motor is placed at every joint of the exoskeleton, which leads to a large number of connections with the human body, and seriously affects the motion characteristics of the rehabilitation robot. Combining the rope-driven robot with the exoskeleton robot, the advantages of both can be used, in terms of the characteristics of force application and motion output of the human body in ergonomics, especially the force of arm control and the design criteria of relevant motion mechanisms . A rope In the design of the exoskeleton of the manipulator and wrist, starting from the human body structure, the rotation axis of each joint should be in the same line with the rotation axis of the human body joint. The shoulder joint may be approximated as a ball joint, but it is impossible to achieve the intersection of three degrees of rotational freedom of the shoulder joint in the interior of the shoulder joint at present. In this paper, the exoskeleton is driven by the flexible rope to assist the shoulder joint of the human upper limb in using three degrees of freedom of movement in order to achieve the desired flexibility. The elbow and the wrist each have two degrees of freedom. The exoskeleton is used to achieve the four degrees of freedom of joint movement in order to ensure the full freedom of movement during rehabilitation of the upper limbs. The targeted motions for the rehabilitation device are determined according to different injury causes, different patients, and different needs of different rehabilitation training periods.The rope-driven system is generally composed of casing and rope with relative motion, which has the advantages of a simple structure, flexibility, and the long-distance transmission of power. There are two common methods of rope transmission, single-lasso transmission, and double-lasso transmission. The single-lasso drive is generally used to achieve linear reciprocating motion of the mechanism. The drive end can only provide one direction of rotation, and rotation in the other direction is generally provided by a spring and other elastic elements. The double-lasso drive is used to achieve rotary movement of the mechanism, and the drive end can provide two directions of rotation. The joint of a shoulder joint rehabilitation device is a rotary joint. Therefore, the double-lasso transmission mode is adopted. The lasso transmission mode is shown in A goal of the research is to enable doctors and patients to better interact with robots and make the rehabilitation process better, safer, and easier to accept, based on the basic principles of human-machine interaction , using We first built the external sensor system of the robot, which can perceive the patients, doctors, and rehabilitation environment, and obtain relevant information. The sensors involved include a stereo vision sensor, auditory sensor, force sensor, proximity sensor, and electromyographic (EMG) sensor. The stereo vision sensor collects and recognizes the patient’s actions and expressions. The auditory sensor collects and recognizes the patient’s and doctor’s language. The force sensor detects the force of pulling on the rope. The proximity sensor detects obstacles in the rehabilitation process and the EMG sensor collects the EMG signal of the patient during the rehabilitation process. The construction of a multi-sensor system can reduce the shortcomings of using a single sensor, such as having limited or incomplete information and uncertainty, and can describe the human-machine environment of the robot comprehensively.Each piece of information is different in space, time, expression, and purpose. Therefore, a multi-information processing method is needed for information processing and management to coordinate the work of each sensor with each other sensor and deal with all kinds of information of the multi-sensor system more effectively. This paper constructs the following processing method. First, the information collected by the external sensors of the robot is classified with the classification corresponding to the form of the information, which can be divided into redundant information and complementary information. Redundant information can improve system fault tolerance and reduce system uncertainty. Complementary information can improve the integrity and correctness of the system description environment. Second, the coordinated management of multi-sensor information is achieved by sensor selection, coordinate transformation, data transformation, and using a sensor model database. Lastly, a method of fusing the information based on parameter estimation is adopted by the information fusion processor to coordinate the management and fusion of the multi-sensor information.A human-machine natural interaction method based on the multi-sensor system and coordinated information is designed based on actual needs of patients and existing technologies, as shown in It is important to construct a human-machine cooperative rehabilitation system for the rehabilitation robot, patient, doctor, and environment. Therefore, the theory and principles of machine learning and deep learning are applied to the rehabilitation training platform, which is human-friendly, machine-friendly, and environmentally-friendly ,47. A muIn view of the shortcomings of existing upper limb rehabilitation robots, such as the lack of autonomy, adaptability, and intelligence, the limitations of the human-machine interaction, and the single data connection, which all result in a lack of collaborative control among multiple platforms when ergonomics are introduced to the robot. The natural interaction, accessibility, cognitive needs, cultural factors, and aesthetics are comprehensively considered for four factors: the rehabilitation robot, patient, doctor, and environment. At the same time, the multi-channel integration of visual interaction, speech recognition, gesture input, tactile feedback, and other interactive information technologies are combined with virtual reality technology to build a Kinect-based upper limb rehabilitation training interaction system, and form a rehabilitation training platform with friendly collaboration among humans, machines, and environmental elements, as shown in The Kinect-based upper limb rehabilitation auxiliary equipment is a multi-coupling system that integrates action capture, information interaction, and virtual reality, and can design corresponding rehabilitation training control strategies, according to the clinical characteristics of patients in different rehabilitation stages. In addition, the interactive software system based on virtual reality technology integrates a variety of interesting games, which supports relevant rehabilitation training courses, and even simulates real-life activities such as cooking, cleaning, and playing chess to improve patients’ initiative to participate in rehabilitation training and achieve better rehabilitation training results.On the basis of the upper limb rehabilitation equipment equipped with multi-intelligent sensors, a hierarchical progressive rehabilitation training mode  is designed according to the different rehabilitation stages and different rehabilitation needs of patients.In the early stage of rehabilitation, the fuzzy sliding-mode variable-structure control algorithm is used. Based on the preset path, the upper limb rehabilitation training robot pulls the affected limb for passive-mode training. The system diagram is shown in The admittance control algorithm based on the minimum interference principle is adopted for patients in the middle stage of rehabilitation. According to the deviation in movement of the affected limb, the control area is divided, and the auxiliary force provided by the robot is adjusted to help the patient complete the semi-passive-mode and semi-active-mode training. The system diagram is shown in An active rehabilitation training strategy based on admittance control and virtual reality games is adopted for patients in the later stage of rehabilitation to enhance interaction with and interest in the training process. The patients resist the force imposed during active training treatment, as shown in When patients participate in rehabilitation training and immerse themselves in rehabilitation games, multi-modal information such as EMG signals, kinematics signals, and dynamics signals are collected continuously. Since the EMG signal has a high correlation with the force produced by muscle contraction, and affects the patient’s final movement, the force or moment sensor signal can accurately and reliably reflect the movement information of the upper limb. Therefore, by extracting features from the collected signals, the patient’s intended motion can be recognized.Through intelligent sensors and Kinect, a large amount of multi-modal information such as EMG signals, kinematics signals, and dynamic signals related to the natural responses of the human body, such as responses related to vision, hearing, and touch, are collected. Based on the characteristics of the movement task, methods such as neural network methods, big-data analysis, and deep learning are used to achieve the accurate modeling and prediction of the individual movement mode of the patient, and to continuously improve recognition of the human’s intended motion. Thus, the interactive training system based on the natural responses of the human body and other related big-data information can be continuously improved.Through the effective collection and arrangement of the multi-platform and multi-system rehabilitation data of different patients, doctors, and rehabilitation robots, a multi-dimensional rehabilitation training and evaluation database can be established. A three-layer intelligent rehabilitation platform based on data collection, data analysis, and data service can be built by using the theory of big-data analysis and deep learning. Thus, a multi-level linkage rehabilitation system is formed to maximize the use of rehabilitation information resources.First, according to the scientific quantitative evaluation method, which truly reflects the sports function, a quantitative evaluation table is made and a personalized training scene is designed. Then, according to different training scenarios, a scientific, quantitative evaluation method is developed based on big data, and a comprehensive evaluation model of rehabilitation is established based on AHP . Lastly, a multi-dimensional intelligent rehabilitation system guided by data analysis results is formed to assist doctors in decision-making. The multi-dimensional intelligent rehabilitation system is shown in The dynamic model of the rehabilitation robot is very important for the design of the system controller, which is related to the control accuracy and other important performance indexes of the system. For this kind of complex, multi-body mechanical system, especially a multi-body system with a closed-loop structure, the existing mechanical system dynamic modeling methods, such as the Newton-Euler method and Lagrange method, are difficult to use for modeling and for obtaining the analytical dynamic equations. That is because the Lagrange multiplier method relies on problem-specific approaches to determine the multipliers and it is often very difficult to find the multipliers to obtain the explicit equations of motion for systems that have large numbers of degrees of freedom and a mass of non-integrable constraints. The Udwadia-Kalaba dynamic theory ,52,53,54There are three steps to establish the dynamic model of the rope-traction and exoskeleton-multiplexing upper limb rehabilitation training robot using the dynamics theory of Udwadia-Kalaba. First, for the rope traction and exoskeleton, the unconstrained motion equations of each subsystem are obtained by the Newton-Euler or Lagrange method, and then the unconstrained motion equations in matrix form are obtained. It should be noted, however, while Newton-Euler or Lagrange method is not easily applied to a multi-body system, it is available for each subsystem of the whole system. Second, all the motion constraints of the system are written in second-order form, and the second-order structural passive constraint equation in matrix form is obtained. Lastly, the constraint force is obtained based on the Udwadia-Kalaba equation and added to the unconstrained motion equation. These steps result in the dynamic equations of the robot.With the dynamic model, the control system can be designed. Because of the high nonlinearity of the robot and the uncertainty of some control parameters, controller design is generally difficult. Therefore, an optimal, adaptive robust control theory based on fuzzy set theory is proposed, as shown in In the system, the rope traction part of the system is a redundant driving system, which increases the difficulty of robot compliance control. Therefore, an impedance control strategy based on the inner force loop and the outer position loop is adopted, and the position of the shoulder joint node is controlled by the driving forces and positions of rope 1, rope 2, and rope 3. The control structure diagram is shown in Now, according to the design principles and requirements of the system, the exoskeleton control system of the upper limb rehabilitation robot can be completed, as shown in Now we design the adaptive robust control based on the Udwadia-Kalaba theory proposed in The desired trajectory of each joint is given by the formulas below.The simulation results are shown in (1)A new structure for an upper limb rehabilitation robot is proposed. It combines a flexible rope with an exoskeleton in order to ensure that the moving parts connected with the patient’s upper limbs are light, accurate, and flexible.(2)Applying the theories and technologies of ergonomics, virtual reality, information fusion, big-data analysis, and deep learning, a collaborative, efficient, and intelligent remote rehabilitation system based on a human’s natural response is constructed.(3)For this multi-degree-of-freedom robot system, the Udwadia-Kalaba approach is applied to establish the dynamic equation of the system. Based on this explicit dynamic equation, optimal adaptive robust control design with fuzzy set theory is presented for the motion control of the system.(4)The new design will help improve the interest of patients in participating in the training and improve the effects of the rehabilitation, help doctors design a good rehabilitation training program, and help hospitals manage patients in real time and summarize the experiences.To better heal upper-limb injuries and improve the ability of doctors to optimize both medical solutions and the management of medical institutions, this paper studied upper limb rehabilitation instruments, based on the research and development of existing instruments and their problems. The main focus was to design a natural interaction and collaboration-intelligent upper limb rehabilitation training robot. The designed robot’s innovations and effect are as follows.Our future work will mainly focus on the experimental verification. A large number of case trainings will be done to verify the flexibility, comfort, and safety of the system.


Comprehensive analyses of lncRNAs in aging have been lacking because previous studies have mainly focused on the protein-coding genes during aging. Here, we describe a protocol for the organism-wide analysis of murine lncRNAs during aging. We provide step-by-step instructions to identify lncRNAs that contribute to aging and to determine their underlying functions in each tissue. We further describe methods to compare the lncRNA expression patterns and dynamic changes among multiple tissues.For complete details on the use and execution of this protocol, please refer to   •Differential gene expression and aging-regulated lncRNA identification•Functional annotation specific for lncRNAs•Tissue-specific analysis for aging-regulated lncRNA Comprehensive analyses of lncRNAs in aging have been lacking because previous studies have mainly focused on the protein-coding genes during aging. Here, we describe a protocol for the organism-wide analysis of murine lncRNAs during aging. We provide step-by-step instructions to identify lncRNAs that contribute to aging and to determine their underlying functions in each tissue. We further describe methods to compare the lncRNA expression patterns and dynamic changes among multiple tissues. This project aims to study the dynamic regulation of lncRNAs and their functional implications across multiple rodent tissues during aging. This study includes data collection, preprocessing A and datFor differential gene analysis, we make use of negative binomial model in DESeq package to identify AR(aging-regulated) mRNAs/lncRNAs in multiple tissues.For functional annotation, we first use Pearson correlation to identify co-expressed mRNAs of each AR-mRNAs. Then we perform BP enrichment analysis to discover the role of those co-expressed mRNAs during aging, so as to infer the potential functions of each AR-lncRNA.For tissue specificity analysis, we define and calculate the tissue specificity score of each lncRNA, which is used to compare the tissue specificity between AR-lncRNAs and ANR-lncRNAs/AR-mRNAs.For dynamic network analysis, we first use Pearson correlation to calculate the relationship between each AR-mRNA and each AR-lncRNA at each age point and then make use of the Walktrap community finding algorithm in igraph package to identify modules where AR-mRNAs and AR-lncRNAs are connected.Note: For example, we chose mouse as our focused species and considered 11 tissues in our published study. From 8, 26, 60, 78, 104 weeks, 5 replicates of each tissue were collected. That is, we had 5(replicates) × 5(different time points) × 11(different tissues)=275 samples in total. The number of lncRNAs was 21,981 and the number of mRNAs was 12,533, which were consistent in all samples.Note: The background among replicates should be matched as closely as possible.In this protocol, we make use of RNA sequencing expression data to identify those lncRNAs functioning in aging among different tissues. Since correlation between lncRNAs and mRNAs is used to predict the regulatory roles of interested lncRNAs, the samples of interest should include RNA sequencing reads of both mRNAs and lncRNAs from a series of tissues in a specific species. In order to study the transcriptome alternations across the lifespan of a selected species, the samples should come from different age points for each tissue.Timing: 3-4 daysNote: Use conda create command in conda to create an environment specific for RNA-seq preprocessing.Note: We begin with FASTQ files. If the raw files are in the form of SRA, fasterq-dump in sratoolkit can be used to transform data formats.1.a.Access the quality of data with fastqc (v0.11.9), which will generate two result files for each sample in the form of zip and html .b.i.The report consists a series of items, showing data quality in multiple aspects. Mainly focus on Basic Statistics, Per Base Sequence Quality and Adapter Content.ii.If some of the samples failed to pass the above mentioned quality control items, using trim galore (v0.6.5) to apply adapter and quality trimming to raw fastq files .Merge the results from fastqc with multiqc (v1.9), which will result in a single quality control report across all samples in the form of html .i.The rec.Make sure all samples are of good quality by fastqc again.Quality controlNote: Step-c requires repeating step-a and step-b(i). Only samples passing the mentioned items after adapter and quality trimming are considered as “of good quality” and used for following analysis.2.a.https://www.gencodegenes.org)  with parameter of sjdbOverhang149 in our published study.Use STAR (v2.7) to map sequence reads to a known genome according to the interested species . The refnes.org) .Note: Fob.i.Transform SAM files, the output files of STAR, to BAM files by view command.ii.Note: BAM files are binary version of SAM files, which can increase the execution speed in gene abundance quantification.Sort BAM files by sort command.Use SAMtools (v1.11) to deal with file format .i.TransfAlignment of sequencing reads3.a.i.Specific parameter -p counts fragments instead of reads. It is only applicable for pair-end reads since single-end reads will always be counted as reads.ii.Parameter -a should be followed by the name of the annotation file. (GTF file obtained in step2-a)iii.Parameter -o should be followed by the name of output file including read counts (txt format). Another file including summary statistics of counting results will also be generated.Assign reads to genes and determine the abundance by featureCounts (v2.0.1) .i.Specifb.Use cut command to extract gene names and gene counts, from the output file (txt format) of featureCounts.Quantification of gene abundanceNote: The 2nd to 6th columns include information of genes. Only gene names (the 1st column) and gene counts of each sample (the 7th to (7 +(N– 1 ))th column, where N represents the total number of samples) is necessary.Note: This section will generate a G × N raw count matrix including samples from all of the tissues, containing the expression of mRNAs and lncRNAs, where G is the total number of mRNAs and lncRNAs and N is the total number of samples. To be specific, if there are M tissues and CRITICAL: All of the following analysis will be executed in R statistical environment (v3.6.1).Note: In the following parts, we give variable names to some R objects , shown in the form of italics, to make our protocol more understandable. The names of R objects can be adjusted according to the projects.Note: In the following parts, R functions are in the form of ‘<functionname> command’.4.a.raw.Import raw read counts matrix as a dataframe b.i.dds_norm. The only necessary input is the dataframe raw.Use DESeqDataSetFromMatrix function to create a DESeqDataSet object ii.dds_norm to perform normalization. Then use counts function with a parameter of normalized=TRUE to obtain a normalized matrix norm.Use estimateSizeFactors function with Perform normalization of raw read counts by the method of Median of Ratio in DESeq2 package.i.Use DEc.norm by the log1p function and only keep genes with expression > 0 in at least 20% samples for each tissue.Carry out log transformation of matrix d.Take the mean expression value for all the replicates at a specific time point for each tissue separately.Normalization and filtering 2Note: This section will generate a series of M is the total number of tissues, gi is the number of filtered genes and ni is the number of samples in this tissue. ni is the number of different age points after taking the mean value of all the replicates.Note: It is recommended to use the list structure to store raw and processed counts  for each tissue. Intermediate results in subsequent parts can also be saved in this way.Timing: 2hNote: Differential expression analysis is performed in each tissue.Note: Raw counts are used in this part.1.a.dds. The input arguments include CountData, ColData and Design.i.CountData is a matrix containing the raw read counts of selected groups. Filter the read counts to keep the same genes as the processed counts after data preprocessing. Each row represents a gene. Each column represents a sample in the interested young and aged groups.ii.ColData is a matrix containing sample information. Each row represents a sample, in the order of columns of countData. Each column represents a type of group information, including age and other covariates such as sex.iii.Design is a formula representing how the gene counts rely on the variables in colData. Include the interested variables or their interactions in this formula.Note: For example, to examine which genes are differentially expressed during aging, only need to use ∼age as the design  of each gene.Note: DESeq function contains three steps for the analysis of differential gene expression . As a substitute, you can also execute the three functions step-by-step.Using DESeq function with c.2FC| ≥ 0.75 and FDR ≤ 0.05.For each of the aged group, the differentially expressed genes are identified with the criteria of |logPerform pairwise differential gene expression of the youngest group with each aged group using DESeq2 (v1.28.1) package . FigureAa.Use DE2.Differentially expressed genes in the interested aged groups are identified as aging-regulated (AR) genes.Note: Up/Down-regulated AR-genes can be identified according to the positive/negative log2FC values.Note: ln most organs, the number of differentially expressed lncRNAs increases during aging (AR-mRNAs)/Aging-regulated lncRNAs (AR-lncRNAs) (ng aging C. The dilncRNAs) B.Timing: 4hNote: Functional annotation is performed in each tissue.Note: The mean value of processed counts of different replicates are used in this part.Note: The clusterProfiler (v3.16.1) package requires the gene ID to be EntrezID for the functional annotation. If the type of gene ID is already EntrezID, please skip step 3.3.a.http://bioconductor.org/packages/release/BiocViews.html#___OrgDb.Note: A series of org.Xx.eg.db packages including annotation for common species are required when performing the transformation of gene ID type. For example, we chose org.Mm.eg.db as our published study was conducted on mice.Find genome-wide annotation package for the species of your experimental model from b.i.Input your gene id for ‘geneID’.ii.Use keytypes function to see the supported ID types for ‘fromType’ and ‘toType’.iii.Note: The following GO analysis is performed for each set of co-expressed mRNAs of each AR-lncRNA.Note: It is recommended to execute the following steps of functional annotation based on the loop structure, since it is a great deal of work to conduct functional annotation for co-expressed mRNAs of each AR-lncRNA separately and integrate the results.The name of selected org.Xx.eg.db package is used for ‘OrgDb’.Use bitr function to perform ID transformation. The parameters, including geneID, fromType, toType and OrgDb, are used for the essential inputs.Transform gene ID to EntrezID for mRNAs using the bitr function in the clusterProfiler package .a.Find g4.a.Perform Pearson correlation between AR-lncRNAs and mRNAs and calculate p-value using rcorr function in Hmisc (v4.4) package.  Take thb.For each AR-lncRNA, its co-expressed mRNAs were selected with a cutoff at absolute Pearson correlation coefficient ≥ 0.8 and FDR ≤ 0.05 in each tissue.Identify the co-expressed mRNAs of each AR-lncRNA  Figure A.a.Perfo5.a.go.Note: The parameter ‘ont’ can be selected as ‘MF’ for molecular function, ‘BP’ for biological process and ‘CC’ for cell component, or can be selected as ‘All’ to contain all of three. BP enrichment is most widely used.Use enrichGO function to perform BP enrichment in GO analysis. Set ‘ont’ as ‘BP’ and ‘qvalueCutoff’ as 0.05. This step will return enrichment GO categories, b.go into the form of data frame, go1. Filter go1 to remain columns including ‘ID’, ‘Description’, ‘p.adjust’, ‘geneID’ and ‘Count’.Use data.frame function to turn Perform GO analysis by clusterProfiler package .a.Use enNote: The go1 data frame for each AR-IncRNA can be combined during each loop by rbind function, which faciliates the following steps.6.a.Calculate the total number of associated AR-lncRNAs for each of the significantly enriched BP terms.b.Rank the BP terms according to the decreasing order of associated AR-lncRNA numbers.Analysis of the number of lncRNAs associated with each BP terms. Ba.CalculTiming: 2hNote: Tissue specificity analysis is performed at each time point.Note: The mean values of processed counts of replicates are used in this part.7.Definition of tissue specificity score n represents the total number of tissues, Tij represents the average expression of a given gene i in a given tissue j.  and may not provide accurate outcomes. If you have ≥ 10 samples for each age points, you can skip this step.Combine the samples from the neighbor age points into 4 stages .c.cor1, cor2, cor3, cor4. Use p.adjust function in stat package to adjust p-value by the method ‘fdr’.For expression matrix in each stage, evaluate Pearson correlation for each AR-lncRNA and AR-mRNA using rcorr function in Hmisc package . Take td.When a pair of AR-lncRNA and AR-mRNA has the absolute correlation coefficient ≥ 0.9 and adjusted p-value ≤ 0.05 in either or both of stage1 or stage4, keep the AR-lncRNA and AR-mRNA pair in the subsequent dynamic network construction.e.i.exp to store higher correlation coefficient in stage1 and stage4 between each pair of filtered AR-lncRNA and AR-mRNA, where each line of the first and second column represents pairs of AR-lncRNA and AR-mRNA, the third column represents their correlation coefficient.  package .i.ConstrIdentification of modules in dynamic interaction networksNote: The step highly depends on computing resources.Note: The cluster_walktrap function only keeps modules with gene number ≥ 30.10.a.mod.Note: The order of AR-lncRNAs and AR-mRNAs become exactly the same in four different stages.Rearrange the rows and columns of correlation coefficient matrix in each stage, which adjusts the order of AR-lncRNAs and AR-mRNAs, in the order of module information (from module 1 to module n) of each AR-lncRNAs and AR-mRNAs in dataframe b.cor1, cor2, cor3, cor4. Set cluster_rows = F,cluster_cols = F.Use pheatmap function in pheatmap package (v1.0.12) to plot heatmap of Construction of the AR-lncRNA∼AR-mRNA networkThe differential gene expression analysis will lead to a list of differential expressed mRNAs/lncRNAs at different age points in each tissue C. The diThe functional annotation identifies the BP terms that are associated with AR-lncRNAs. You can also make comparisons of top BPs connected with AR-lncRNAs between different tissues C.The tissue specificity analysis calculates the tissue specificity scores for each lncRNA at different age points. These score can be used to investigate the tissue specificity of AR-lncRNAs B and 4C.The dynamic interaction network construction can reveal the modules of highly correlated AR-lncRNAs and AR-mRNAs for different tissues at different age stages. The growth of modules generally indicates the enhanced functional and regulatory relationshipB. FunctiThe quality of raw data have a strong influence on the analysis, e.g., level of abundance, batch effect, duplicate rate. A principal component analysis (PCA) can be performed by plotPCA function in DESeq2 package on normalized counts. If the data are of good quality, transcriptomes are likely to be grouped according to organ identity instead of age points.Removing batch effect.Batch effect results from a subset of experiments running on different days, by different technicians or using different reagents, chips or instruments. Measurements with batch effect will have qualitatively different behaviours among conditions, which are uncorrelated with experimental variables in a particular study.If the sample are not from the same batches, the removeBatchEffect function in limma package can help to solve this problem. Input the raw data and batch information and execute this function to remove batch effect, which can ensure the robustness of following analysis.Selection of normalization methods.Comparison of common normalization methods are listed below , and 3.To make the gene expression data more comparable within or between samples, normalization is often a prerequisite. The main factors that normalization methods accounted for include sequencing depth, gene length and RNA composition.In practice of TMM method, which scaling to library size, the gene length is absorbed into the parameter of the number of transcripts. As a result, TMM method will not use gene length as an input . HoweverIn this protocol, we make a slight change here by using Median of ratios method in DESeq2 package for normalization. It was reported that among all common normalization methods, only Median of ratios and TMM performed well in both differential expressed genes detection and false positive rate control . So thissun.lei@duke-nus.edu.sg).Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Dr.Lei Sun (This study did not generate new unique reagents.https://github.com/Xinyue-Lu.An example RNA-seq raw data is NGDC: PRJCA002140. An example code for this protocol is on