Now Dr. Bee has posted a more detailed criticism of the theory.
One of the big disadvantages of Bohmian mechanics, that Einstein in particular disliked, is that it is even more non-local than quantum mechanics already is. That’s because the guiding field depends on all the particles you want to measure. This means, if you have a system of entangled particles, then the guiding equation says the velocity of one particle depends on the velocity of the other particles, regardless of how far away they are from each other. ...This is an important point.[Reader:] The argument against Bohmian mechanics is that it is non-local, and QFT requires locality. But didn't Bell prove that the universe is non-local (for most physicists at least; I realize you have an alternative explanation for his results)?
[Sabine Hossenfelder:] First, you cannot use a mathematical theorem to prove how the universe is. What Bell proved is that theories of a certain type obey an inequality. Experiment shows that this inequality is violated. It follows that one of the assumptions of Bell's theorem must be violated.
A violation of one of these assumptions is qua definition what people in quantum foundations call "non-locality". It is an extremely misleading use of the word and has nothing to do with that particle physicists call "non-locality" which refers to non-local interactions.
These two different types of non-locality have caused so much confusion I really think we should stop referring to quantum mechanics as "non-local". Some have suggested to instead use the term "non-separable" which makes much more sense indeed.
In any case, Bohmian mechanics violates Bell's inequality and is thus non-local in Bell's sense. This is fine and not the problem I was talking about. The problem is that the ontology of Bohmian mechanics is non-local in the QFT sense (as I explained in the video). This is not necessarily a problem, but certainly one of the reasons why it's been hard to make a QFT out of it. The other problem is Lorenz-invariance (which I refer to as the "speed of light limit).
Bell nonlocality is an abuse of terminology that only confuses people. Bohm's theory is truly nonlocal in a way that no scientific theory is. It is a fringe theory that no one has found useful for anything.
Sometimes someone claims that Bohm's theory is more intuitive, but that is nonsense. The nonlocality makes it more counter-intuitive than any other textbook theory.
When she said the "historical context is relevant", I thought that she was going to tell us that Bohm was a Commie. It is funny how he has a cult following. There is some weird ideology driving support for his theory, but even after watching the movie, I cannot figure out what it is.
Another comment:
Bohm's theory is convinient for quantum cosmology, since it avoids the problem of the system and the observer which are necessary in the Copenhagen interpretation so that the Copenhagen interpretation cannot be applied to the whole universe.The theory is nonlocal, so events in one galaxy can depend on subtleties in another galaxy. And that is supposed to be convenient for cosmology? I doubt that it has ever been of any use to cosmology.
Update: Here is a new PBS Space Time video addressing some of these issues.
Roger,
ReplyDelete1. There are many issues with the Bohmian mechanics (BM). However, IMO, when it comes to locality vs. non-locality issue, BM does not have a significantly greater problem as compared to what the mainstream QM (MSQM) itself does.
2. First, in the non-relativistic theory, the Schrodinger equation (SE) is linear, according to both the MSQM and BM. The solution method to find the $\Psi(x,t)$ evolution essentially relies, in both MSQM and BM, on the Fourier theory (FT)---which has the instantaneous action at a distance (IAD) built into it. Now, the Fourier theory is the most basic source---an in principle unremovable source---of IAD in any theory/interpretation which uses it.
The Copenhagen interpretation (CI) refuses to grant any physicality to the solution procedure or quantities used in calculations if these cannot be measured in an experiment---most salient example being, the wavefunction $\Psi(x,t)$.
Such a refusal, however, is still unable to remove IAD from the CI/MSQM. It's just that the IAD now is supposed to show up only at the time of measurement. But it's stil there, via the collapse postulate.
To some people, the phenomenon of entanglement makes the supposition of IAD more convincing. To some other people, Bell's theorem proves to be the final convincing point. So, for their theoretical discussions, they exclusively rally around the notions defined by Bell---even if it's "just" a *theorem*, a *direct* corollary of MSQM.
As to my opinion, FT is the most basic reason why Bell's inequalities are violated. (That the spin DOFs are "orthogonal" to the Schrodinger wavefunction is an extra consideration; it does not nullify the IAD introduced due to FT.)
How does the BM fare? Well, it has no collapse, and so, to some people, it seemingly does away with IAD. But not quite. They still use FT. Ergo...
3. I do not know the relativity theory, and so, consider this point (no. 3.) less than amateurish. With that said, here is how I "think" like:
In relativistic mechanics, any motion of an electron creates an additional field, the magnetic field. An acceleration of the electron makes the E and B fields go on forever propagating, in the entire universe, at a constant velocity "c". Both E and B are force fields, and hence the physics can be put in terms of potential energies associated with them. These PEs must also propagate at "c". Which puts a constraint, via the $V$ term in the Schrodinger equation, on how $\Psi(x,t)$ evolves in time.
I suppose I haven't gone too wrong thus far. (Sean Carroll has explained that there is a Schrodinger equation also in relativistic mechanics.)
But does it mean that all changes in the $\Psi(x,t)$ field must also propagate with "c"? Here, I am not sure. My imagination (rooted in simulation in the head) is this:
Start with E and B fields at t = t_0. Find the $\Psi(x,t_0)$ field at $t_0$. March the time forward by $\Delta t$. Find changes in E and B everywhere, using classical EM (e.g., the software MEEP). Use the E and B field values at $t_1$ as *fresh inputs* to calculate a new $\Psi(x,t_1)$ at time $t_1 = t_0 + \Delta t$. Lather, rinse, repeat.
Noticeably, we do not use separation of space and time parts; we do not evolve the $\Psi(x,t)$ by applying the same time-dependent part.
The step of finding $\Psi(x,t_a)$ at an arbit. time $t_a$ from $E(t_a)$ and $B(t_a)$ present at that instant, in this procedure, still would use FT.
Back to the square one! You would have an IAD lurking in there, simply because you used FT in the solution.
4. Apart from it all, I also suppose that BM uses the same $\Psi(x,t)$ as the MSQM, for relativistic SE.
If so, why spare MSQM but ascribe to BM---at least to its basic methodology---IAD?
[Continued]
[Continuing from the previous comment]
ReplyDelete5. The preceding does not mean there are no issues with BM. Yesterday I mentioned the following paper by Norsen in my tweet:
https://arxiv.org/abs/1210.7265.
I find a problem right with the most bare essential description of BM, as in the "Introduction" section of this paper.
6. I also found this comment at Dr. Hossenfelder's referred post interesting.
http://backreaction.blogspot.com/2020/10/david-bohms-pilot-wave-interpretation.html?showComment=1603029421525#c4179518118537173952
Much of it is beyond me, but I did understand these lines:
>> "But in those two examples, there exists a symbiotic relation between the particle and the field: the particle sources the field while the field guides the particle, whereas in BM there is only the latter, master-slave relation."
7. All in all, BM does lead to a lot of troubles. But I don't think the use "nonlocality" (or, using my terms, IAD) is one of them. As far as I know, *all* QM theories/interpretations have the same characteristic.
8. From what I gather (and may be, I'm wrong), it seems like Bohm was a bit misguided by the Communist propaganda, but his error seems relatively innocent. I mean, Bohm's personality seems to be much different from that of even Heisenberg, let alone of Fuchs. (I am not sure Oppenheimer's judgment was all that reliable. People do act differently during war-time tensions than they otherwise would.) Stupid? yes. Therefore dangerous? Probably yes. Sensible enough to know better if told right? Probably yes. How should they have treated him? I don't know! ... But, all said, I haven't read comprehensively about it all, nor am I interested.
But one thing is for certain. Oppenheimer telling others to refrain from discussing Bohm's papers (after he had already left USA) *also* was, IMO, a very stupid thing to do. You can't fight ideas that way---not ideas like Communism. If Oppenheimer fancied that by ostracizing Bohm's papers he was fighting Communism, he was living in a fool's paradise. It looks more like the more "ordinary" power games, turf battles, throwing others under the bus (i.e. normal office politics gone a couple of rungs or more in the downward direction) to me. I think that could be a much better explanation for Oppenheimer's actions.
But as a final point, no, I am not interested in this point. And, I don't think that BM is trouble-free. That's the bottomline.
Best,
--Ajit
Roger,
ReplyDeleteSorry, but looks like I might have (must have?) made a mistake in point no. 3. above.
If $\Psi(x,t)$ is calculated afresh at each time step, using the *updated* values of E and B fields, then, on second thoughts, it looks like to me that we are no longer applying the same time factor, and so, the IAD due to the FT might not arise. Of course, one consideration is that $\Psi(x,t)$ has to stay square-normalized at all time-steps. Might this fact be important for an IAD in $\Psi$? That is, even if we never introduce, in the *relativistic* QM, the kind of nonlinearity which I have proposed for the *non-relativistic* QM? (with fields anchored in the particles' current positions?)
... Since I haven't studied relativity theory, I can't tackle any questions of this nature right. ... Neither am I going to. Once I finish my work on non-relativistic QM, it's going to be the end of this entire QM business for me. ... Unless they pay me in terms of millions of (US) dollars and/or give me a Nobel (already for my non-relativistic QM work), that is! (In *that* case, I *might* pursue relativistic QM too, who knows. But not otherwise.)
This is a consecutive third comment. Sorry for piling on your blog. ... Even otherwise, guess it would be best if I now shut up. I am afraid how RSI is going to turn out tomorrow; it's not yet healed. ... Also, these are the election times in your country, and people get excited over any matter, even the matters not even remotely connected to the election. And, I am jobless, looking for a job in Data Science. So, it's a best policy for someone like me to keep my mouth shut up for a while. (I could always come later and discuss issues after a few weeks...)
Best,
--Ajit