05-16-2016, 08:56 AM

With the post Bohmians' self-confidence evaporates as soon as they're expected to calculate anything continues his attack against dBB theory. It contains, as usual, a lot of name-calling, now even personally against me - I'm named "crank", and a link to this forum posted in the comments was rewritten so that one cannot directly click it. Whatever, this is what has to be expected.

I agree, if one thinks that dBB makes somewhere different experimental predictions than standard quantum theory, then one has to make all the computations to find out where the predictions are indistinguishable and where one can distinguish them and find out which theory is true. But this is not the case. Where it is possible to construct a dBB theory, it is, in its experimental predictions, equivalent to standard quantum theory.

What are, in this case, the advantages of dBB theory? They are conceptual. The Copenhagen interpretation subdivides the world into a classical and a quantum part. Which is unproblematic from a pragmatic point of view, but not really nice. I prefer a theory without such an artificial subdivision. Which is dBB.

I. Schmelzer, Overlaps in pilot wave field theories, Foundations of Physics vol. 40 nr. 3, 289-300 (2010), arXiv:0904.0764 [quant-ph].

The point of mentioning some, ugly or not, extra constructions is beyond me. Of course, once there is an equivalence theorem, there is no need to repeat standard QFT computations. And for a textbook about QFT, fine, a good idea. Except that there is no need to rewrite a lot of the QFT texts themself. In such a book I would start with the basic definitions based on the dBB interpretation, so that the initial part would indeed differ. But then I would focus on the development of the standard mathematical apparatus of QT resp. QFT. There would be some shift toward lattice regularizations, away from, say, dimensional regularization, because for lattice regularizations everything is nice, we have a well-defined dBB interpretation as well as a well-defined quantum lattice theory without infinities.

Has anybody cared if one can define phonon trajectories in quantum condensed matter theory? Would this be an argument against a dBB variant for condensed matter theory based on trajectories for the atoms?

\[ \psi^{eff}(q_{sys}, t) = \psi^{full}(q_{dev}(t),q_{sys}, t).\]

As one can see from the formula, it is not the trajectory of the "real particle", which would be \(q_{sys}(t)\), which defines the collapse. But the trajectory of the macroscopic device, \(q_{dev}(t)\), which defines the result of the collapse. But don't forget that \(q_{dev}(t)\) is defined by the guidance equation, and, via the guidance equation, influenced by \(q_{sys}(t)\). And, indeed, the global wave function \(\psi^{full}(q_{dev},q_{sys}, t)\) is not influenced nor by \(q_{dev}(t)\), nor by \(q_{sys}(t)\). But the effective wave function \(\psi^{eff}(q_{sys}, t)\) already depends on \(q_{dev}(t)\), thus, is influenced by the "real particle" \(q_{sys}(t)\) too.

The effective wave function of a subsystem is, as we have seen, influenced by the trajectory, whenever the subsystem interacts with its environment.

But the effective wave function of the atom collapses. It is only the wave function of atom + EM field, and later of atom + EM field + prism + detector, and a later the wave function of the whole universe, which does not collapse.

Of course, the influence matters only as long as there is an interaction between the system and the measurement device. If there is no such interaction, and \(\psi^{full}(q_{dev},q_{sys}, t)=\psi^{dev}(q_{dev},t) \psi^{sys}(q_{sys},t)\), there will be no such influence between the two trajectories. There is also some influence if the two systems are in a superpositional state \[\psi^{full}(q_{dev},q_{sys}, t)= \psi_1^{dev}(q_{dev},t) \psi_1^{sys}(q_{sys},t)+\psi_2^{dev}(q_{dev},t) \psi_2^{sys}(q_{sys},t).\]

If, say, the wave functions \(\psi_{1/2}^{dev}\) do not overlap, and \(q_{dev}(t)\) is inside the support of \(\psi_{1}^{dev}\), then the trajectory \(q_{sys}(t)\) will be the same as if guided by \(\psi_1^{sys}\), else as if guided by \(\psi_2^{sys}\). So, there is an influence.

All this has nothing to do with any "ad hoc fixes", it is simply the application of the standard equations of dBB theory.

PS: I see that secur has been banned there too:

Last but not least, there was a time when he felt more secure about his arguments, when he has given me the participate on his blog with an Argumentation about de Broglie-Bohm pilot wave theory. He has, it seems, learned the lesson that his arguments are too weak, so that he cannot allow such counterarguments on his blog.

I can. I have no problem with lumo coming here for "debunking" all this "crackpot nonsense" here. He would have to restrict himself to arguments about the content, personal attacks would not be allowed, this is all. I would guess, if he has some arguments about the content, he would make them here too. But if there are no such counterarguments about the content, it would be unreasonable for him to appear here. We will see

Quote:He obviously meant that it was done in proper quantum field theory governed by the standard, "Copenhagen" postulates of quantum mechanics (at most reformulated with a different "accent" but not a different "content"). And because he must believe that Bohmian mechanics has "conquered" the standard quantum mechanics and may claim credit for all of the successes of quantum mechanics (while taking no responsibility for the alleged drawbacks), he just doesn't need to write anything, he believes.Not that I believe that one does not need to write anything - what I believe is that one has to prove an equivalence theorem. Only if such an equivalence theorem is proven, one can use the computations made in one theory in the other theory too.

I agree, if one thinks that dBB makes somewhere different experimental predictions than standard quantum theory, then one has to make all the computations to find out where the predictions are indistinguishable and where one can distinguish them and find out which theory is true. But this is not the case. Where it is possible to construct a dBB theory, it is, in its experimental predictions, equivalent to standard quantum theory.

What are, in this case, the advantages of dBB theory? They are conceptual. The Copenhagen interpretation subdivides the world into a classical and a quantum part. Which is unproblematic from a pragmatic point of view, but not really nice. I prefer a theory without such an artificial subdivision. Which is dBB.

Quote:These Bohmian people often make claims such as "all the physics of QFT works just fine in Bohmian theory". References to incoherent preprints that make similar claims are the "evidence" you may get. All these preprints contain some "extra" (and very ugly) mathematical constructions that are absolutely different from the standard QM/QFT and it's obvious that they can't be producing the same predictions in general. But if someone claims that the Bohmian theory makes sense, shouldn't he be able to write the "proper modern [Bohmian]" textbook replacing the existing textbooks of quantum field theory? At least a few chapters, up to a calculation of some annihilation processes of QED.The last time I have seen a really serious objection - serious enough to question the equivalence of dBB field theory and its viability - I have made some computations and published them, here is the reference:

I. Schmelzer, Overlaps in pilot wave field theories, Foundations of Physics vol. 40 nr. 3, 289-300 (2010), arXiv:0904.0764 [quant-ph].

The point of mentioning some, ugly or not, extra constructions is beyond me. Of course, once there is an equivalence theorem, there is no need to repeat standard QFT computations. And for a textbook about QFT, fine, a good idea. Except that there is no need to rewrite a lot of the QFT texts themself. In such a book I would start with the basic definitions based on the dBB interpretation, so that the initial part would indeed differ. But then I would focus on the development of the standard mathematical apparatus of QT resp. QFT. There would be some shift toward lattice regularizations, away from, say, dimensional regularization, because for lattice regularizations everything is nice, we have a well-defined dBB interpretation as well as a well-defined quantum lattice theory without infinities.

Quote:By its definition, the Bohmian mechanics must have a result for the measurement of the "photon position" that is ready before the measurement. Except that there can't be any equations – at least not local or otherwise natural equations – that could govern the motion of such "real Bohmian photons".The point being? The dBB picture I prefer is not using photon positions as beables, but, instead, the EM field. There are problems introducing photon trajectories into a dBB picture? Fine, so don't do it.

Has anybody cared if one can define phonon trajectories in quantum condensed matter theory? Would this be an argument against a dBB variant for condensed matter theory based on trajectories for the atoms?

Quote:Well, it's simple. In quantum mechanics, the energy conservation follows from the collapse of the wave function and by the very definition of the Bohmian mechanics, Bohmian mechanics avoids the collapse at the moment of the measurement. In any Bohmian picture, the measured values must be already prepared a femtosecond before the measurement. ...No, dBB theory does not avoid the collapse, it describes the collapse, giving the evolution equation for the effective wave function of the subsystem in terms of the global wave function (which contains the macroscopic measurement device too) and the (macroscopically observable) trajectory of the measurement device, by the formula:

The Bohmian theory never collapses the atom's wave function to an energy eigenstate. In fact, in the Bohmian theories, the "real particle" doesn't influence the pilot wave at all!

\[ \psi^{eff}(q_{sys}, t) = \psi^{full}(q_{dev}(t),q_{sys}, t).\]

As one can see from the formula, it is not the trajectory of the "real particle", which would be \(q_{sys}(t)\), which defines the collapse. But the trajectory of the macroscopic device, \(q_{dev}(t)\), which defines the result of the collapse. But don't forget that \(q_{dev}(t)\) is defined by the guidance equation, and, via the guidance equation, influenced by \(q_{sys}(t)\). And, indeed, the global wave function \(\psi^{full}(q_{dev},q_{sys}, t)\) is not influenced nor by \(q_{dev}(t)\), nor by \(q_{sys}(t)\). But the effective wave function \(\psi^{eff}(q_{sys}, t)\) already depends on \(q_{dev}(t)\), thus, is influenced by the "real particle" \(q_{sys}(t)\) too.

Quote:This is a rather brutal feature of the Bohmian theory: the theory is very loud about the influence of the pilot wave on the particle but it basically assumes that the particle doesn't affect the pilot wave at all. You should always be suspicious about theories with similar "asymmetric" influences. They sound like a theory about God who can influence everyone else but can't be influenced. In proper physics at the fundamental level, all interactions go in both ways.This is, indeed, a strange feature of dBB theory. One which is worth to be considered and discussed. But it is, in fact, only relevant for a hypothetical, theoretical entity: the wave function of the whole universe.

The effective wave function of a subsystem is, as we have seen, influenced by the trajectory, whenever the subsystem interacts with its environment.

Quote:The absence of the collapse in Bohmian mechanics means that the atom can simply never collapse to an energy eigenstate, even though the photon that has known about the atom's energy has gone through the prism and was detected. The wave functions of the Bohmian mechanics never really collapse.

But the effective wave function of the atom collapses. It is only the wave function of atom + EM field, and later of atom + EM field + prism + detector, and a later the wave function of the whole universe, which does not collapse.

Quote:And the positions of the electron and proton aren't affected by the detection of the photon – even though they should really be correlated with the photon's energy.That's wrong. Once there is a nontrivial interaction between the atom and the EM field, the trajectory of the configuration of the EM field is influenced by the trajectory of the atom. How? By the guiding equation. Because to define the velocity \(\dot{q}_{atom}(t)\) by the guiding equation, we need the full wave function \(\psi^{full}(q_{EM},q_{atom}, t)\) as well as the actual configurations \(q_{EM}(t),q_{atom}(t)\) of all relevant parts at that moment of time.

Of course, the influence matters only as long as there is an interaction between the system and the measurement device. If there is no such interaction, and \(\psi^{full}(q_{dev},q_{sys}, t)=\psi^{dev}(q_{dev},t) \psi^{sys}(q_{sys},t)\), there will be no such influence between the two trajectories. There is also some influence if the two systems are in a superpositional state \[\psi^{full}(q_{dev},q_{sys}, t)= \psi_1^{dev}(q_{dev},t) \psi_1^{sys}(q_{sys},t)+\psi_2^{dev}(q_{dev},t) \psi_2^{sys}(q_{sys},t).\]

If, say, the wave functions \(\psi_{1/2}^{dev}\) do not overlap, and \(q_{dev}(t)\) is inside the support of \(\psi_{1}^{dev}\), then the trajectory \(q_{sys}(t)\) will be the same as if guided by \(\psi_1^{sys}\), else as if guided by \(\psi_2^{sys}\). So, there is an influence.

All this has nothing to do with any "ad hoc fixes", it is simply the application of the standard equations of dBB theory.

PS: I see that secur has been banned there too:

Quote:BTW I saw your explanations on Schmelzer's crackpot website how you play with your nicknames and why you came to my server. This is in clear violation of the basic integrity rules required on this server so you were banned.Looks quite natural: If one has only bad arguments, one has to ban those who may easily refute them.

Last but not least, there was a time when he felt more secure about his arguments, when he has given me the participate on his blog with an Argumentation about de Broglie-Bohm pilot wave theory. He has, it seems, learned the lesson that his arguments are too weak, so that he cannot allow such counterarguments on his blog.

I can. I have no problem with lumo coming here for "debunking" all this "crackpot nonsense" here. He would have to restrict himself to arguments about the content, personal attacks would not be allowed, this is all. I would guess, if he has some arguments about the content, he would make them here too. But if there are no such counterarguments about the content, it would be unreasonable for him to appear here. We will see