A Little about “Speakable and Unspeakable in Quantum Mechanics

I have begun reading J. S. Bell’s “Speakable and Unspeakable in Quantum Mechanics.” … I began by following his advice to the lay reader that one should begin with paper nos. 18 and 20. (The book is a collection of his published papers.) I was delighted to find the following quote right on the second page of paper no. 18:

“…So I think it is not right to tell the public that a central role for conscious mind is integrated into modern atomic physics. Or that ‘information’ is the real stuff of physical theory. …”

Unusual.

I never take anyone’s comment about QM very seriously. … I might have heard/read a lot about Bell; still, I am going to read his book as if I were the first guy to do so. … Works for me. (The words to describe this attitude are: “first-handedness” or “independence”. (And yes, they are very easy…) )

I will keep you posted if I find something extraordinary… But, frankly, I don’t expect to go through some of his more technical papers at all. I guess I already know what it all would boil down to.

He further states:

“… de Broglie in 1926… answered the conundrum
wave or particle?
by
wave _and_ particle.

But by the time this was fully clarified by Bohm in 1952, few theoretical physicists wanted to hear about it …

The de Broglie-Bohm picture…, and indeed, I think any sharp formulation of quantum mechanics, has a very surprising feature: the consequences of events at one place propagate to other places faster than light. This happens in a way that we cannot use for signalling. … For me this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity…”

Well, I don’t get this passage. If this issue had been fully clarified in the de Broglie-Bohm formulation, then why does a real problem still linger on in it? Apparently, Bell, like all Brits of post-Bohm times, was too enamored by the Bohm formulation to think this way about what he was saying…

“It may be that a real synthesis of quantum and relativity theories requires not just technical developments but radical conceptual renewal.”

How true!

=======

Bell continues…

“In my opinion the following point cannot be emphasised too strongly. When we work out a problem in wave mechanics, for example that of the precise performance of the electron gun, our mathematics is entirely concerned with waves. There is no hint in the mathematics of particles or particle trajectories. With the electron gun the calculated wave extends smoothly over an extended portion of the screen. There is no hint in the mathematics that the actual phenomenon is a minute flash at some particular point in that extended region. And it only in applying the rule, relating the probable location of the flash to the intensity of the wave, that indeterminism enters the theory. The mathematics itself is smooth, deterministic, ‘classical’ mathematics… of classical waves.”

My comments:

First of all, what did Bell think stood for—the classical wave-field variable? … That’s just one example of how even good physicists unwittingly bring unexamined or traditional views to bear on a topic under discussion.

But more than that, I think the issue here is deeper.

If you take care to develop and/or understand a physical view for the mathematics (such as what I have developed), then there is no confusion as to what is it that the mathematics is concerned about.

And thus, I want to note that among the many things that must be understood clearly by physicists, one is that mathematics calculates and physics describes, and the two endeavors are and must be kept separate (even though both the things may be done by one and the same person—as often is the case in mathematical physics).

More, later. But yes, by and large, and comparatively speaking, Bell does seem to have been far more reasonable than so many researchers/commentrators of physics of his time (and those of earlier times as well!).

The Meaning of the Concept of Potential in Mechanics (and in Physics)

If someone know books/articles dealing with the meaning of the concept of potential in physics (or concerning the physical bases underlying the energy methods of mechanics) then I would very much appreciate getting to know about these.

Please note, when I say physical bases, I mean physical bases—not “simpler/prior mathematical notions/procedures, very easy to work out.” Thus, my query is for material that is primarily conceptual, not mathematical. (As an aside: Mathematical material on this topic is so easy to get that, speaking metaphorically, a stone’s throw would yield a dozen references if not 1200. … But I was talking about treatment that is not exclusively mathematical. Essentially, a counterbalance to La Grange is what I was looking for.)

Also note, by potential, I do not mean the limited context of electromagnetism (EM) alone. Indeed, if you ask me, energy methods are far more valuable in mechanics than in EM primarily because the (statically) indeterminate case is so easy to run into, in mechanics. The momentum approach isn’t, therefore, most convenient.

I have already browsed through Lanczos (The Variational Principles of Mechanics) and find it helpful. Just the right sort of book, even though if I were to have the material to write this book, I wouldn’t present it in the order that he does. … Anyway, apart from this book, is there any other source? That’s the question I have here.

I might as well mention here that for my purpose here, Goldstein (Classical Mechanics) has been a big let down (both in terms of the contents as well as their ordering) and so has been Weinstok (Calculus of Variations). I remember having browsed very rapidly through Morse and Feschback a few years back, but without finding anything directly useful in this context.

So, there. Any indicators/links other than Lanczos would be very much appreciated. If there aren’t any, I guess I might myself write up a research article on this topic.

Thanks in advance for any links/references.