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@editor: Thank you, we quoted A. Sudbery’s paper in ours, but weren’t aware of R. Healey’s response.
@Aurelien: I agree with you and highly recommend your paper. We made similar points in our paper, though maybe too briefly. Frauchiger and Renner admit that their thought experiment is modeled on Hardy’s paradox, so we didn’t stress too much that it’s not really new.
@Mark: Indeed, I think these “extended Wigner’s friend” measurements are practically impossible, since they require a reversel of decoherence of macroscopic quantum states. Frauchinger and Renner, in their paper, have a section on how a more or less analogous experiment could be performed, but I didn’t study that carefully enough to comment.Dear Reinhard,
If a may add a word regarding the “hand-waving” objection (i.e. Travis’ point 2):
The parts of BM that you describe as “fuzzy” concern the treatment of very complex, macroscopic system. This is the stuff that physicists always get somewhat pragmatic about. At least, I’ve never seen a mathematically rigorous treatment of a realistic detector (or measurement apparatus) in ANY theory.
More importantly, the problems you want to challenge BM with, are all on the level of the wave-function and their Schrödinger evolution. These are problems that everybody has to face if he is willing to take quantum mechanics seriously and apply it to anything more than highly idealized microsocpic systems.
Of course, if “standard QM” produces results that are relevant in this context (“decoherence”, “dephasing” etc.) it’s absolutely legitimate for the Bohmian to use them. But again, rigorous, quantitative results are very difficult to come by.
If, on the other hand, you try to avoid these problems by simply denying the “universality” of quantum mechanics, by denying, for instance, that a measurement apparatus has a wave-function in the first place, then you have to face the criticism that your theory is vague and/or inconsistent because there just is no sharp divide between the microscopic and the macroscopic level.
Best,
Dustin
Dear Robert (if I may),
I would very much like to understand better the relationship between BM and the consistent history approach. I think Shelly once made the point that they are actually somewhat similar in spirit, as they aim for a consistent transition from the micro to the macro level. I will certainly take a look at your paper [1]. I’m not sure if I’ll be able to add anything meaningful, but I might try.
However, I believe the Bohmian position regarding “surrealistic trajectories” has been discussed many times. The Bohmian predictions are not wrong – they are just counter-intuitive. Of course, our classical intuition is based on locality and interactions in Bohmian mechanics are strikingly nonlocal (as they have to be). Once you’re willing to take BM seriously, “surrealistic” trajectories are not really a problem, you just have to accept them as a prediction of the theory that does conform with experiment. However, if you had an alternative theory that was just as clear and successfull as BM but which made more intuitive predictions concerning such which-way experiments, that would be a legitimate argument in favor of that theory.
Concerning your other worry about BM: In BM, the objective, physical state of a subsystem is given by (Q,psi), where Q are the positions of the particles and psi the (effective) wave-function of the system. This state determines the outcome of any measurement of a macroscopic “observable”. In this sense, the experimentalist is right that his pointer position reveals an objective fact about the measured system, although not an intrinsic property that the particles posses outside the context of measurement. Moreover, if you analyze the interactions of different particles/systems, you will find that what we call “energy” or “spin” or “momentum” etc. has pretty much the familiar functional role – although, on an ontological level, everything can be further reduced to the motion of particles.
(On a side note: the position representation is distinguished in BM, because BM is a theory about stuff in physical space. But of course, on the level of the wave-function, you are free to do all the familiar operations.)
The Bohmian usually feels that this modest anti-realism regarding quantum observables is exactly what the appearent paradoxes of SQM and the familiar no-go theorems à la Kochen-Specker suggests. However, I understand why someone would like even more realism regarding these quantitites. I the consistent histories approach can achieve this, without twisting the notion of probability too much, it would be a remarkable feat.
Best regards,
Dustin
Hi Ken,
I also wanted to give you some feedback on your paper. Unfortunately, I don’t have that much to add, because I think your discussion is very much on point. 🙂 The Schulmann model is quite interesting (I didn’t know it before) and your arguments concerning symmetry are, of course, correct.
It’s not so much a factual critique, rather a personal feeling, that you’re still giving too much credit to the Wood-Spekkens argument, though. To me, it’s just one of those meta-results that seem deep but are actually quite irrelevant. In a toy-model, where any postulation of probability distributions is ad hoc and where you might have to introduce some artificial variables, the “fine-tuning” objection seems to have some bearing. In any more serious theory, where the probability distribution is either part of – or better – derivable from the fundamental postulates/law of the theory, the Wood-Spekkens argument amounts to the claim: if the theory was different, it’d be wrong. I mean: if the Boltzmann distribution was different, pigs might be able to fly. But who cares?
Still, the Schulmann model is nice as an “intermediate step”, because it demonstrates how the “correct” (i.e. non-signalling) distributions can be justified by deeper principles (e.g. symmetry).
Best, Dustin
Hi Rod,
thanks for your answer. I understand that eq. (1) is supposed to be a projection. I’m pretty sure that, if psi(x,x’) is really a multitime wave-function, the expression, as it stands, is not correct. But I’m mostly concerned about the fact that “after an interaction has occured” or “two wave-functions have ceased interacting” is ambiguous in a relativistic setting. That’s why I think it’s important to be precise about these things, to make sure that the relevant expressions are actually well-defined and Lorentz-invariant.I don’t want to get caught up in equation (1), though. There are several points in the model where I’m not sure if I just don’t understand the mathematical formulation, or if the notation is actually deceptive in that it sweeps serious problems under the rug.
Anyway, I’m happy to discuss this in more detail. You can email me at: [email protected] . Or, I just get in touch with you.
Best, Dustin
Dear Miroljub,
I believe the attitude I described has nothing to do with BM, in particular. Every mathematical physicist has to be very selective with the kind of problems he or she choses to work on. (Of course, this applies to every scientist, but to mathematical physics in particular, because the average time you have to invest in one publication is quite long).
You could spend a lifetime on mathematically rigorous treatments of more and more realistic detector models in Bohmian mechanics. Ok, I must admit: the problem is actually somewhat interesting. Maybe someone will pick it up, eventually. There are just more interesting problems out there. (Not to speak of the sociological fact that it sounds like a real career killer for young scientists.)
Anyway, I honestly doubt that Reinhard (or anyone else) would have seriously changed his attitude towards BM if Shelly or Detlef had invested a considerable amount of time to provide a satisfiying answer to his problem. Nevertheless, to the degree that Reinhard’s issues with BM are mathematical, we should be self-critical enough to say: ok, point taken, maybe we could do more and better work in this respect. I just don’t believe that, at its core, the controversy is really about mathematics or the alleged lack thereof.
On a related note: Detlef and Shelly and Travis and others have spent many many years adressing all sorts of questions and objections about Bohmian mechanics. When another paper comes out, claiming to prove that BM is wrong, more often than not someone from the Bohmian community will make the effort to reply and completely eviscerate that argument.
Unfortunately, it’s an empirical fact that no one who is fundamentally opposed to the theory (for whatever reasons) ever changes his mind when you resolve any concrete issue that he claims to have with Bohmian mechanics. This doesn’t mean that one should stop debating or answering serious questions, of course. It just means that there’s no point in jumping on every challenge that someone throws at you.
Best, Dustin
Dear Reinhard,
I really appreciate you sharing your point of view and I have thought (and will continue to think) about some of your arguments. If you don’t mind me saying: I believe that the discussion could have been even more productive, though, if you hadn’t been so polemic, at times. E.g. Bohmians don’t write papers or theses, they write “pamphlets”. I think that’s really unnecessary and disrespectful.
My comment regarding the philosophical prejudices was just to challenge your claim that BM has to rely on naive philosophical ideas, while your (operationalist?) view doesn’t.
In any case, what I take away as a criticism of BM is that it relies on a lot of “in principle” statements. Like: “In principle it’s possible to describe the measurement aparatus in a Bohmian way an receive the correct results.” I admit that the arguments we have to offer in support of these claims are a bit hand-waving. They rely on approximations and idealization.
The Bohmian believes that he’s hand-waving about the “right” part of the theory. QM tells us that the measurement aparatus has to play a crucial role in “bringing about” the measurement outcomes and a measurement aparatus just is an extremly complex system from a microscopic point of view. Moreover, we believe that deriving the entire quantum formalism under reasonable approximations and idealizations is good enough to validate/corroborate the microscopic theory. The situation is, again, similar to classical statistical mechanics where kinetic gas theory is corroborated/valiadted by the fact that you can derive the laws of thermodynamics under reasonable approximations and idealizations.
However, I understand and respect your position when you don’t see much value in such “in principle” statements and the “handy-waving” arguments we have to offer in support.
Nevertheless, concerning also your exchange with Detlef and Shelly, I believe that the reason why we don’t have more rigorous results to offer are mostly pragmatic. The Bohmian community is small, our time is limited and many-body problems are very very hard. Most of us just don’t see much value in spending too much time and effort to proof a result that we understand / accept anyway and that – to be honest – still wouldn’t convince you or any other critic.
Best, Dustin
Hi Travis,
thank you very much for your very detailed feedback! That’s a lot to think about and I certainly won’t be able to give a satisfying answer to all of your questions/objections right away. For now, I can just add a few remarks.
You’re right that the discussion in the final section would have been different with Bell’s 1990 picture in mind. That’s a good point! I guess I just used the definition of locality/conspiracy most suitable to the point I was trying to make. Anyway, in the end, the relevant question is not whether “no-conspiracy” is formally violated, but whether the physical account is morally conspiratorial in a way that undermines its explanatory power or even the whole idea of empirical tests. I believe that as far as my toy-model is concerned, this is rather not the case or at least it’s up for debate.
My goal is not to save or restore locality, at least I wouldn’t put it that way. Let’s agree that nonlocality is a fact of nature. Period. Advanced interactions are merely one possible way to implement/understand/explain nonlocality. And it may be a way to implement nonlocality that is more compatible with relativity than other approaches. That’s one good reason to keep an open mind about it.
Your second point is a very good one, too. You’re right, as a metatheoretical concept, nonlocality à la Bell is a much more fruitful than the “absence of direct space-like interactions”. I didn’t mean to dispute that, though. People who are sympathetic to retro-causation rather like to point out that when you assume time-symmetry as an a priori, some form of nonlocality were to be expected. They/we then usually see that as one (very important) explanatory success of the hypothesis. But then again, not everyone is impressed.
I agree that, in the end, “measurements” should be part of the theory. For a time-symmetric/retro-causal theory, it would thus be ok to require final boundary conditions for the entire universe. It would not be ok to assign a special status to individual measurement results. On this issue, I might stand closer to you than to Rod and Ken (as far as we understand their position correctly).
I believe, however, that in the end, when you have a complete theory, the process of measurement and preparation will turn out to be somewhat special in that they’re irreversible in a thermodynamic sense. And I believe (although my ideas on this are still very vague) that they will turn out to have a special role in defining “macro-causality”, because they have to do with our sense of agency. Under this premise and under this premise alone I think it’s legitimate to treat “measurement” and “observation” on a somewhat different footing when discussing simplified models (such as mine).
In other words, to the degree that “measurements” have a special status in retrocausal models, this should not prevent the models from being – at least in principle – embedded into a complete qtwo. Rather, a complete qtwo should be able to explain (away) the specialness.
In any case, I would never claim that, as of today, any retrocausal model is superior to or less mysterous than nonlocality in Bohmian mechanics (let’s say.) I would only maintain that such an approach is not a priori absurd or doomed to fail. And unless we have a complete relativistic qtwo, we should stay open minded towards different possibilites. There is no cheap way of reconciling quantum non-locality and relativity, that’s for sure.
Best, Dustin
Dear Rod,
thanks for your patience. If you can help be better understand your model or if maybe even I could help you with some of the formalities, I’d be happy to stay in touch even after the workshop.I’m also happy to answer questions about the DGZ-paper. It took me a while to fully appreciate the result, but it’s worth it. I think it’s fair to say that it’s accepted by the majority of the Bohmian community as a proof/derivation of Born’s rule, although there is no consensus. But then again, there isn’t even consensus about the foundations of classical statistical mechanics.
Best, Dustin
Dear Rod,
I was trying to study your paper. I think your motivations are exactly right and the paper contains a lot of exciting ideas. I must admit that I have great difficulties understanding the model, though. In part, it may just be an issue of (bad) notations, but many things don’t even make sense to me on the formal level.
For instance, at the very beginning, you introduce x and x’ as space-time coordinates. Hence, Psi(x,x’) is a multi-time wave-function of two particles. I don’t even know then what you mean when you talk about the wave-functions “before” and “after” measurement, since all the wave-functions seem to be defined on the entire space-time (or multiple copies thereof).
In the following, I already don’t understand equation (1). The right-hand-side of the equation seems to depend on the time-coordinate of particle 2, whereas the LHS doesn’t. And even if you fixed a particle time t’, the expression would be strikingly not Lorentz invariant, since you integrate over one particular spacelike hypersurface in one particular frame.
My difficulties with the presentation continue from there. For instance, I’m not sure what <x|i> means if |i> is a two-particle wave-function.
I’m not even sure what you mean by the expression <f|i>. Is this a scalar product on 4-dimensional space-time or on a 3-dimensional hypersurface? In the first case, I’m not sure if it defines a transition amplitude. In the second case, the expression (and hence the modified 4-density) is not Lorentz-invariant, since initial and final states are prescribed on certain hypersurfaces.
Maybe it’s just me, as a mathematician, being unfamiliar with the notation or being to picky und unflexible about formalities. But if all of this makes sense, I think your presentation would benefit a lot form being more precise and explicit about these things since they matter in this context.
On a more conceptual level, I don’t understand what your equations of motions are supposed to describe. As far as I can see, your Lagrangian involves only field degrees of freedom. What you call the particle 4-velocity u is actually a velocity field. In so far as your theory is supposed to be inspired by (or similar to) Bohmian mechanics, you seem to confuse the guiding field with the actual velocity of Bohmian particles and/or the variable in the wave-function with the actual position of Bohmian particles.
I’m sorry if I criticize your paper out of mere ignorance, but so far, I wasn’t able to understand what you’re doing and I’d really like to, since if your theory achieved what you claim it does, it would be nothing short of brilliant.
Best, Dustin
Hi Travis, thank’s for clarifying! I’m not sure that Reinhard was thinking about planets and the “classical limit” of BM, though. I thought he was referring to the (indeed undisputed) fact that, on the microscopic level, particles interact via the wave-function, so that the interactions are strikingly nonlocal and need not depend on the actual positions in the way classical intuition would dictate.
For instance, if you take a beam splitter and you wiggle the mirror on the left and you see that the point on the screen is wiggling as well, you cannot conclude that any Bohmian trajectory was actually passing by the left mirror.
At least, that’s the kind of argument that I always hear from Lev Vaidman or Nicolas Gisin. And it’s not a bad argument, I think. It’s were for me, the debate usually hits a dead end. Because either you’re willing to take BM seriously and except these things as (correct) predictions of the theory and maybe unavoidable consequences of nonlocality. Or you insist that you can’t take the (microscopic) trajectories seriously, unless they are somehow operationally accessible. And indeed, that’s not quite what the Bohmian has to offer.
I’m sorry to interfere in your exchange. Of course, Reinhard doesn’t need me to come to his defense. 🙂 I’m just eager to see how you (Travis) will respond to this particular argument.
Dear Reinhard,
thank you very much for your very nicely written responses. I’m still not sure that your hostility towards BM isn’t fueled by some factual misunderstandings (the things that Travis keeps pointing out), but I think I’ve got a better sense for where your objections come from.
Please allow me to add a few remarks. I don’t try to change your mind, I just try locate the core of the disagreement a bit better.
1) BM does not presuppose realism (whatever you mean by that, exactly). Accepting BM, you can take any philosophical attitutude you look like towards the particles and their trajectory. You can, for instance, take the anti-realist stance that they’re mere theoretical entities but still endorse BM as the most conceptually clear way of doing QM.
Of course, you CAN take BM seriously as a “realist” description of the physical world. At least it makes sense to ask: what would the world look like if BM were true (and how well does this agree with our actual physical world). It doesn’t make sense to ask: what would the world look like if textbook QM were true, because textbook QM does not provide a clear, coherent picture of the microscopic regime.
2) Micro-to macro transition is indeed a very subtle business. It’s probably not a coincidence that so many Bohmian have their background in this particular field of mathematical physics. I understand, on some level, why you would like to avoid this business, that you describe as “fuzzy”.
I just don’t think that it’s a good idea to embrace instead a set of “rules” that are fuzzy and vague to begin with and that don’t even try to achieve constiency between the microscopic and the macroscopic level. And I refuse to believe that your problems go so far that you literally don’t understand atomism, i.e. how a prediction about the distribution of particles in 3-dimensional space amounts to a prediction about the actual, observable world.
3) I don’t think anyone could convince you that BM solves any problems, because you’re obviously an expert in quantum phyiscs and you probably feel that, on the level on which you care, there are no problems with the theory. So let’s assume for the sake of argument that BM doesn’t solve any practical problems.
Still, as a quantum theory, it comes with a lot of virtues: mathematical precision (everything is defined by equations), observer-independence, consistency between the micro- and the macro level, just to name a few.
Until not so long ago, these features were considered as highly desirable by almost all scientists. I think they are still considered as highly desirable by most. However, at the advent of QM, many physicists gave them up, because they – mistakingly! – thought they had to.
Still, you are free to believe that these features are not only not desirable but actually very bad. That’s fine, I guess, it’s ok to have different preferences about what a physical theory should do. Just don’t pretend then that Bohmians have some naive philosophical prejudices, while you don’t. At the very least, we are all just as prejudiced, only in opposite directions.
Best, Dustin
Thanks, Travis. If you find the time to revisit my paper, I’d be honored to receive your feedback. The model is essentially the same as in the arxiv version, but the discussion has been corrected and refined in certain important aspects. That reminds me that I should probably update the arxiv version…
Dear Rod,
I am very interested in your model. I hope I’ll be able to study it in more detail and ask more qualified questions before the workshop is over. Until then, I’d like to address your previous post and point out that in standard Bohmian mechanics, the Born rule CAN be derived from first principles in a rigorous way.
This was done in a seminal paper by Dürr, Goldstein and Zanghí titled “Quantum Equilibrium and the Origin of Absolute Uncertainty”. You can find the online version here: http://arxiv.org/abs/quant-ph/0308039v1
The argument is very similar to Boltzmann’s analysis for classical statistical mechanics. It is shown that Born’s rule is true in typical Bohmian universes, i.e. in quantum equilibrium. More precisely, it is shown that for typical initial configurations (of all the particles in the universe), the particle positions in an ensemble of subsystems with effective wave-function psi are distributed according to |psi|^2.
I would expect that the quantum equilibrium analysis doesn not – without further ado – carry over to the time-symmetric version of the theory, where you have two boundary conditions. However, a colleague of mine is currently working on a “timeless” extension – using a “history measure”, so to speak – that might.
Best wishes,
DustinDear All, If I may, I would like to add some general remarks. They might not do justice to all of your previous points and concerns, but maybe it doesn’t hurt to “dump things down” a bit (to borrow Travis’ phrase).
1) I believe that “realism” is a very unhelpful notion and that every scientific or meta-scientific discussion benefits from avoiding it altogether. That said, to the degree that “scientific realism” has a clear meaning, it is not presupposed by Bohmian mechanics. Both “realistic” and “anti-realistic” attitudes can be taken towards Bohmian mechanics, by either regarding the particles as ontological or as merely theoretical objects. However, BM can be taken seriously as a description of physical reality, in contrast to standard QM which can’t be taken seriously in this way, even if we wanted to.
2) What Mister Healey describes as “Einstein’s realist program” is not an invention of Einstein’s, but was the scientific tradition starting from the pre-socratics to Galilei to Newton to Maxwell to Boltzmann and so on. In the early days of quantum mechanics, people thought they had good reasons – even in form of mathematical proof – to abandon this “program”. These reasons – without exception! – turned out to be wrong.
3) If anything, Bohmian mechanics shows that if we abandon the idea of a precise, unambiguous, objective description of the physical realm, it’s not out of necessity, not as a consequence of the quantum phenomena, but by deliberate choice. Admittedly, when it comes to relativistic quantum theory i.e. quantum field theory, the Bohmian, or, let’s say, the “ontological” alternative is not completely worked out, yet. However, from what I know and understand so far, there’s no doubt in my mind that it can be done.
Hence, whatever reasons one may have to abandon Einstein’s program – which was simply the scientific program until not so long ago – they also lie “outside of physics”!
Hi Travis,
thanks for shedding some light on this background story. I know your scholarpedia article on Bell’s theorem – which is a great article btw – but I didn’t know about the discussion you had with Nathan, of course. I guess Nathan could cite many other sources who neglect the possibility of retrocausal explanations, but I wouldn’t be surprised if he had you in mind, as well. 🙂
Anyway, concerning your other points, I like to emphasize once again that the violation of the Bell inequality in my toy-model does not simply come down to a violation of “no-conspiracy”, i.e. correlation between “lambda” and the “settings”. The issue turns out to be somewhat more subtle (and I think somewhat more interesting).
The relevant lambdas in the (causal) past of the measurement events are not sufficient to “screen off” the correlations – and they are not correlated with the parameter choices. Hence, if you consider only lambdas in the past, the no-conspiracy assumption is formally satisfied, but the locality assumption is violated. It is only when you admit “future common causes” that you can screen off the correlations while (formally) violating no-conspiracy.
Moreover, as primitive as my toy-model may be, it is actually “ontological”. And while the parameter choices are somewhat “outside the system”, I don’t believe that the consistency of the account depends on it.
So it would be very helpful (at least for me) if you could elaborate on your objection to retrocausal accounts of nonlocality. Then I’ll know if I can say anything to help you overcome your hostility. 🙂
By the way: I’d like to emphasize that I’m not an advocate of retrocausation per se. I have some sympathy for it because it is suggested by time-symmetry. Mostly, though, I understand that there is certainly some price to pay if we want to reconcile nonlocality and relativity. And I think that, in the end, retrocausation may not be that much worse than the alternatives. That’s why we should stay open-minded.
Dear Nathan,
thank you very much for your feedback and for pointing out your paper that I’ve read with great interest. I relize that I should have referenced your paper – I just didn’t know about it before!
Anyway, I think we’re definitely on the same page. Maybe your argument is more general, while my model can help to illustrate your point.
However, I’m not sure to what extent it’s correct that the “causal arrow” is never spelled out as an assumption of Bell’s theorem. At least formally, it appears ecplivitely in what you called “causality” and I called “no conspiracy” assumption. I think many (though not all) people realize that this assumption can be logically denied by assuming a retrocausal influence of the control parameters a and b on the lambda. However, most of them will immediately dismiss any such account as conspiratorial or even absurd.
If my contribution succeeded in adding anything to yours (which it better should, otherwise it would be quite superfluous) it’s to spell out and statistically analyze a specific retrocausal toy-model rather than ‘postulating’ a particular statistical dependence between lambda and a and/or b. I think that this can be quite helpful as an intuition pump.
Moreover, it then turns out that, in fact, \lambda IS statistically independent of the control parameters (unless one also admits lambda’s in the future light-cones of the measurement events). That’s why I hope to convince people that such a retrocausal account need not be conspiratorial (as they usuall assume) in the sense that the retrocausal effects do not need to infringe on the freedom of the experimentalist to prepare a system as she likes.
To be honest, though, I’m not sure if I convinced anyone. Usually, people who are open to retrocausality are somewhat sympathetic to my paper, while people who are hostile usually remain just as hostile even after reading it…
Best, Dustin
Dear Ken,
thank you very much for your comments. It’s nice to get feedback from someone who is so skilled in this area.
Let me try to briefly respond to your points:
1) You are right, the model – as it stands with the 1st order dynamics – is actually not time-symmetric! That’s why I also had to change the title btw. 😉
I don’t think the (appearent) asymmetry in the measurement process is the problem, though, since I believe that, when properly analyzed, (quantum-)measurements turn out to be irreversible in a thermodynamic sense.
Concerning the dynamics, the “solution” that I have in mind – rather than going 2nd order – is that, in the end, you will still need something like a wave-function or quantum state to manifest the structure of entanglement. And this object, whatever it is, may itself have a nontrivial transformation under time-reversal. E.g. in Bohmian mechanics, the guiding equation is first order but the wave-function get’s complex conjugated under time-reversal, compensating for the sign.
Anyway, in order to make the points I was trying to make, it was more convenient to work with a toy model that involves advanced and retarded actions in an asymmetric way. But of Course I believe that if one considers a more serious retrocausal theory, it should be motivated by time-symmetry.
2) You’re right, if you have free fields, the distinction between the advanced and retarded part is somewhat arbitrary. However, I don’t believe in free fields. 😉
3) Yes, absolutely! As I said, the toy-model doesn’t actually explain or account for “entanglement”, i.e. why a pair of particles should be able to interact over arbitrary distances without being disturbed by others. The problem is not the light-cone structure, though. The light-cone structure is a good thing, as it makes the interactions intrinsically relativistic. However, I believe that any more serious theory will need additional ingredients, to account for a structure of entanglement.
4) A colleague of mine is working on such “history space” measures in a somewhat different context. I agree that this is probably the way to go for a statistical analysis of time-symmetric theories, but it’s not that easy. If you have more references on that I’d be very interested.
5) I wasn’t familiar with Gerchberg-Saxton, I’ll look it up! References are very welcome.
6) I agree. The ontological level matters most when assessing whether a theory is “conspiratorial”. In my brief discussion, I was trying to make the connection between the ontological level and the formal “no conspiracy assumption” which enters the derivation of Bell’s inequality. I’m not sure how well I succeeded, though.
Thanks again for your comments!
Dear Reinhard (if I may call you Reinhard),
there seems to be a misunderstanding. Of Course, according to Bohmian mechanics, macroscopic objects are composed of microscopic (Bohmian) particles. And indeed, as Travis explains, the empirical content of the theory is in the position/configuration of macroscopic objects, including measurement devices, records and so on.
Now you seem to suggest that the fact that you cannot observe the trajectory of a Bohmian particles implies that you couldn’t observe the trajectory of a macroscopic object composed of Bohmian particles. But this is not correct.
“Absolute uncertainty” – which is a Theorem in BM – implies that you cannot know more about a system than its psi^2-distribution, psi being its effective wave-function. Applied to a single particle, this means that you cannot know/measure/observe its precise trajectory. Applied to a macroscopic object, composed of a great number of particles, this means that you cannot know its exact microscopic configuration, i.e. the position of every single constituent particle. However, a huge number of different microstates coarse grain to one and the same macrostate.
In other words: you don’t have to know/measure/observe the exact position of 10^24 microscopic particles composing a table to know/see the position of the table in your office.
Of course, if you were to spell out the Bohmian account in more Detail, it would involve decoherence and the fact that macroscopic wave-function can be sufficiently well localized on sufficiently large time-scales and it would involve the fact that typically, the microscopic configuration is roughly where the bump in the wave-function is. But these are all theorems in BM, i.e. they can be proven.
To summerize: that, according to BM, you cannot observe the trajectory of microscopic particles is true, but not really a problem. That, according to BM, you cannot observe the macro-trajectory of macroscopic objects would be a problem, but it’s not true.
@Miroljub No, I don’t agree that Bohmian explanations require a huge leap of faith and yield only modest benefit. I’m not sure why I should.
That the Bohmian trajectories are (in principle) unobservable is, of course, a very common objection against Bohmian mechanics. This objection is usually based on two things: 1. a positivist dogma and 2. a misunderstanding of the logical relationship between Bohmian mechanics and Quantum mechanics.
You also seem to misunderstand the spirit and content of Bohmian mechanics when you think that it is based on or motivated by a “naive realism about the position operator”, but I guess that’s not the main point.
In any case, your argument is based on the assumption that BM is essentially standard quantum mechanics plus an (adhoc) addition of particle trajectories. If that was the case, one could make an occam’s razor argument to the effect that the trajectories add no predictive power or empirical content and thus should be despensed with. In fact, even this statement wouldn’t be correct since (the constituents of) macroscopic objects also move on Bohmian trajectories. Indeed, the whole empirical content of the theory is in the particle positions, i.e. the distribution of matter in space. But let’s grant that the trajectories of subatomic particles per se have no empirical content.
However, Bohmian mechanics is NOT Quantum mechanics plus trajectories. In fact, the Bohmian has quite a bit of work to do in order to derive the usual quantum formalism from the two dynamic equations defining Bohmian mechanics.
Indeed, Bohmian mechanics is the microscopic theory and QM is the measurement formalism derived by statistical analysis. BM is not an extension of QM, but a REDUCTION of QM. The quantum formalism is derived from and explained by BM.
BM is logically prior to and conceptually simpler than textbook QM. Everything follows from two precise mathematical equations rather than a set of fuzzy axioms involving “measurement” or “observers” or “operators” or whatever. For both reasons, the occam’s razor argument doesn’t actually hit BM.
If you forget about the microscopic theory, i.e. about particles and their trajectories, you don’t necessarily lose empirical content. After all, the Bohmian agrees that the standard quantum formalism is – for all practical purposes – correct. However, you lose the physical content of the theory, i.e. the way in which the qauntum formalism actually relates or refers to stuff in the physical world. You literally don’t know what you’re talking about when you do your operator business or solve Schrödinger’s equation or compute transition amplitudes.
Now, you may say that for you, the physical content of a theory is only in observable (macroscopic) quantities. You may say, for instance, that the trace in a cloud chamber is physical – because that’s what you can see – but a microscopic particle that a theory posits as the “cause” of this trace is unphysical, because that you cannot see.
I guess this position is defendable, to some degree. It certainly agrees well with the old Copenhagen school of thouht. But then you are the one who’s being dogmatic, adhering to a very particular positivist philosophy, and who displays a lack of imagination. There’s nothing sophisticated about not believing in atoms.
