tag:blogger.com,1999:blog-8148573551417578681.post3109044632600341951..comments2022-08-14T18:21:15.167-07:00Comments on Dark Buzz: Dr. Bee on Bohmian pilot wave theoryRogerhttp://www.blogger.com/profile/03474078324293158376noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-8148573551417578681.post-84343000807632707822020-10-22T02:37:47.368-07:002020-10-22T02:37:47.368-07:00Roger,
Sorry, but looks like I might have (must h...Roger,<br /><br />Sorry, but looks like I might have (must have?) made a mistake in point no. 3. above.<br /><br />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?) <br /><br />... 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.)<br /><br />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...)<br /><br />Best,<br />--Ajit<br /><br />Ajit R. Jadhavhttps://ajitjadhav.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-50341414674555497402020-10-22T01:36:00.028-07:002020-10-22T01:36:00.028-07:00[Continuing from the previous comment]
5. The pre...[Continuing from the previous comment]<br /><br />5. The preceding does not mean there are no issues with BM. Yesterday I mentioned the following paper by Norsen in my tweet: <br /><br />https://arxiv.org/abs/1210.7265. <br /><br />I find a problem right with the most bare essential description of BM, as in the "Introduction" section of this paper. <br /><br />6. I also found this comment at Dr. Hossenfelder's referred post interesting.<br /><br />http://backreaction.blogspot.com/2020/10/david-bohms-pilot-wave-interpretation.html?showComment=1603029421525#c4179518118537173952<br /><br />Much of it is beyond me, but I did understand these lines:<br /><br />>> "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."<br /><br />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. <br /><br />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. <br /><br />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.<br /><br />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.<br /><br />Best,<br />--Ajit<br />Ajit R. Jadhavhttps://ajitjadhav.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-83222138063645250322020-10-22T01:25:08.101-07:002020-10-22T01:25:08.101-07:00Roger,
1. There are many issues with the Bohmian ...Roger,<br /><br />1. 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.<br /><br />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.<br /><br />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 $\Psi(x,t)$. <br /><br />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. <br /><br />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. <br /><br />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.)<br /><br />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...<br /><br />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:<br /><br />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. <br /><br />I suppose I haven't gone too wrong thus far. (Sean Carroll has explained that there is a Schrodinger equation also in relativistic mechanics.)<br /><br />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:<br /><br />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. <br /><br />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.<br /><br />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.<br /><br />Back to the square one! You would have an IAD lurking in there, simply because you used FT in the solution. <br /><br />4. Apart from it all, I also suppose that BM uses the same $\Psi(x,t)$ as the MSQM, for relativistic SE.<br /><br />If so, why spare MSQM but ascribe to BM---at least to its basic methodology---IAD?<br /><br />[Continued]Ajit R. Jadhavhttps://ajitjadhav.wordpress.comnoreply@blogger.com