Bohmian Hidden-Variables & Feyman Sum-over-Hstories ?

[Widdekind]

Physicists Jim Al-Khalili (Quantum, pp. ~150) discusses David Bohm's "Pilot Guide Wave" (my words) HV interpretation of QM, as well as Richard Feynman's Sum-over-Histories approach. He produces colorful pictures for both, highlighting the the "spider-man-web-from-wrists spread" of various paths that the point particles actually "consider" taking (as it were). I will try to scan these images as soon as I can.

 

The similarity of the pictures prompts me to ask, if the Bohmian HV approach might be particularly well-suited, to Feynman's SOH approach ??

 

Also, if Feynman's SOH approach considers "every possible path", between two points (spacetime events) A to B, "weighting" them by their path-integrated actions, could some of those "possible paths" trespass outside of the future lightcone of A ? To wit, could some paths possibly "warp", at "Mach 1000", from A, out to the Coma Cluster 100 Mpc away, and then "warp back" to Earth, at B ?? How could you calculate the action, for such superluminal paths ??

[Widdekind]

According to Jim Baggott's Beyond Measure, in Bohm's HV approach, the "pilot wave", which is computed from the real part of the standard Wave Function, imposes upon the particle that "generates" (my word) the field, the momentum condition, that the particle's momentum is the gradient, of the phase, of the wave function.

 

Now, what happens, in bound-state orbitals, like the Hydrogen wave functions? There, the L=0 Schrodinger-solution wave functions, have spatially uniform phase. Wouldn't that make the particle's momentum equal to zero? And, then, why wouldn't all S-state electrons plummet into their nuclei?

 

Moreover, if, as in Bohm's HV approach, electrons are still regarded as actual point particles, then why, when they're "zipping" around in atoms, cutting across trillions of trillions of times per second, don't they rapidly radiate away energy, from all their accelerations?

[Bob_for_short]

...if Feynman's SOH approach considers "every possible path", between two points (spacetime events) A to B, "weighting" them by their path-integrated actions, could some of those "possible paths" trespass outside of the future lightcone of A ? To wit, could some paths possibly "warp", at "Mach 1000", from A, out to the Coma Cluster 100 Mpc away, and then "warp back" to Earth, at B ?? How could you calculate the action, for such superluminal paths ??

 

In a non-relativistic approach every path is possible. Factually such an integral is a good zero anyway.

[Widdekind]

Would Bohmian point-particles, having positive mass, but zero radius, be Black Holes ?

[Bob_for_short]

Would Bohmian point-particles, having positive mass, but zero radius, be Black Holes ?

 

To be a black hole, it is not necessary to be a Bohmian particle but a compact mass with the gravitational radius smaller than the body size, it seems to me.

 

Next, a point-like "particle" is an inclusive (average) picture when you replace the real body with only three coordinates of its center of mass (or its geometrical center). All bodies are of finite size, actually.

Edited August 25, 2010 by Bob_for_short

[Widdekind]

I understand, that QED is built upon the assumption of true, zero-size, point-particles, in order to keep compliant, with (Einsteinian, aetherless, absolute-rest-frame-less) Relativity [Davies & Brown. Ghost in the Atom, pp. 48-9]. If all particles have finite size, as intuitively seems much more realistic, then all elementary quantum objects must possess instantaneous "internal" communications capacity:

 

There are serious logical problems with the quantum theory, when it applied to the electron, or other point-like particles. One of the important terms, in the mathematics of QED, is the "self-energy" of a charged particle, such as an electron, which has an electrical potential energy assumed to be given by V = e²/r. The self energy of a charged particle depends on the radius r according to 1/r. Thus, if the particle size is shrunk down to a point r --> 0, the self energy goes to infinity. Besides being impossible, the equation becomes useless. This is a problem.

 

To avoid the infinity dilemma, one is tempted to abandon the idea of a point particle. But relativity will not allow this, as seen from the following argument. If a particle is elementary, it must react as a unit. However, if it has a finite size, and an electro-magnetic signal should arrive at one side, the other side must simultaneously know of the arrival of the signal, in order to react as a unit. But this implies that the signal travels with infinite speed, which is prohibited by relativity. The only way out, is to have a point particle. (Or, no particle at all, if you could find a way to represent mass & charge w/o it).

 

M.Wolff. Exploring the Physics of the Unknown Universe, pg. 132..

[Bob_for_short]

....If all particles have finite size, as intuitively seems much more realistic, then all elementary quantum objects must possess instantaneous "internal" communications capacity...

 

And if a particle of a finite size is not rigid but soft? Who said that it should be rigid? Who said that it should be elementary if it is in interaction?

 

How to "detach" a charge from its electromagnetic field which is the main characteristic of the charge? Nohow. They are permanently coupled. They possess an infinite number of degrees of freedom. Some of these degrees describe the center of inertia of the system (3 coordinates suffice), the others describe "internal" or "relative" motion in the system (photons).

 

I have a pet theory about this, if you like.

 

I understand, that QED is built upon the assumption of true, zero-size, point-particles, in order to keep compliant, with (Einsteinian, aetherless, absolute-rest-frame-less) Relativity [Davies & Brown. Ghost in the Atom, pp. 48-9].

 

Yes and no. Yes, because the point-like and decoupled electron is used as the initial approximation, and no because after renormalizations and the infrared problem resolving QED deals with the dressed electrons, i.e., with real electrons permanently coupled to the EMF degrees of freedom. My pet theory deals with the dressed electrons from the very beginning. According to my model, the real QED electron is "large" and "soft". You cannot push it without making radiation = perturbation of the initial relative motion state = radiation of photons. Cool?

Edited August 25, 2010 by Bob_for_short

[Widdekind]

If spatially extended, De-Localized, fundamental 'particles' are possible, you could, in theory, treat the Wave Function as a real, tangible, (two-component) entity, whose amplitude squared represented (essentially) the mass & charge density of the 'particle'. Perhaps, if fundamental 'particles' need not react, to external stimuli, as elementary units, then a real tangible Wave Packet for a 'particle' could be compatible with what you've said.

 

What about 'Delayed Choice' experiments? How could even a super-luminal Bohmian HV 'pilot wave' retroactively choose "which way", after it had already passed the initial beam splitter ?

[Bob_for_short]

If spatially extended, De-Localized, fundamental 'particles' are possible, you could, in theory, treat the Wave Function as a real, tangible, (two-component) entity, whose amplitude squared represented (essentially) the mass & charge density of the 'particle'. Perhaps, if fundamental 'particles' need not react, to external stimuli, as elementary units, then a real tangible Wave Packet for a 'particle' could be compatible with what you've said.

 

Our problem is in classical perception of psi-squared and trajectories. No, it is not a particle density. It is the probability density and to get it we need many experiments. For example, to draw the experimental atomic form-factor squared |F(q)|² we have carry out many experiments.

 

A narrow wave packet is still a wave function rather than a a localized particle. Why can't we look at the psi squared as at a photo of a complicated source instead of one electron/photon?

Edited August 26, 2010 by Bob_for_short

[Bob_for_short]

I have a theory where an electron is a part of photon oscillators. Such is their intrinsic coupling in my construction. What is interesting - the electron oscillates in such a construction and the state of particular oscillators determines the total picture. It may look as "hidden variable" influence although in my construction the nature of variables is apparent and physical.

[Widdekind]

I have a theory where an electron is a part of photon oscillators. Such is their intrinsic coupling in my construction.

 

Gluons can "quantum split" into quark-antiquark pairs.

 

Photons can "quantum split" into electron-positron pairs.

 

Could there be some kind of connection* ??

 

*

Were one to view

photons

, as localized 'packets', of oscillating

electrically

positive & negative aether particles (

+/-

)... then could one view

gluons

, as localized 'packets', of (triply)

color

positive & negative aether particles (

blue/orange, red/green, yellow/purple

) ??

Edited August 27, 2010 by Widdekind

[Bob_for_short]

Gluons can "quantum split" into quark-antiquark pairs.

 

Photons can "quantum split" into electron-positron pairs.

 

Could there be some kind of connection* ??

 

*

Were one to view

photons

, as localized 'packets', of oscillating

electrically

positive & negative aether particles (

+/-

)... then could one view

gluons

, as localized 'packets', of (triply)

color

positive & negative aether particles (

blue/orange, red/green, yellow/purple

) ??

Yes, there is a connection called interaction. When two charges scatter (= interaction of charges), they produce photons and final charge states. In a particular case of charge annihilation the photon energy is just higher. It is just like atom-atomic scattering without and with nucleus fusion: the relative motion of atomic electrons in final atoms changes (gets excited).

[Widdekind]

In a non-relativistic approach every path is possible. Factually such an integral is a good zero anyway.

 

Electro-dynamic potentials ([math]\vec{p} \rightarrow \vec{p} - e \vec{A}[/math]) affect particle momentum, and hence (path integrated) phase, yes?

 

With suitably sophisticated micro-manipulation, of electromagnetic fields, then, one could -- conceivably, if but barely so -- "micro-manage" the phases, of all those paths passing through one's "territory". Since, as you said, most far-out paths are "good zeros anyway", then such "coherent phase manipulation" could conceivably create a "united voting block", which could exert unexpectedly profound influence, on remote events, non-locally, yes (like a small symphony being "heard" over a cacophonous babbling din) ??

[Bob_for_short]

Electro-dynamic potentials ([math]\vec{p} \rightarrow \vec{p} - e \vec{A}[/math]) affect particle momentum, and hence (path integrated) phase, yes?

 

With suitably sophisticated micro-manipulation, of electromagnetic fields, then, one could -- conceivably, if but barely so -- "micro-manage" the phases, of all those paths passing through one's "territory". Since, as you said, most far-out paths are "good zeros anyway", then such "coherent phase manipulation" could conceivably create a "united voting block", which could exert unexpectedly profound influence, on remote events, non-locally, yes (like a small symphony being "heard" over a cacophonous babbling din) ??

 

The paths in the integral do not depend on A. The phase factors do. You cannot manipulate with paths because they are given. You cannot change the integral value because it is unique, like 1 + 2 = 1 +1 + 1. You always hear the sum = 3.

[Widdekind]

The paths in the integral do not depend on A. The phase factors do. You cannot manipulate with paths because they are given.

I meant to say, manipulate the phase factors, of various paths, by manipulating [math]\vec{A}[/math] along those paths. You yourself said that "the phase factors do [depend on [math]\vec{A}[/math]]". So, by suitably manipulating [math]\vec{A}[/math], you could manipulate the phase, and hence action, associated with those paths. Wouldn't that, then, affect the particle's dynamics, via the principle of least action (action minimization) ?

[Bob_for_short]

I meant to say, manipulate the phase factors, of various paths, by manipulating [math]\vec{A}[/math] along those paths. You yourself said that "the phase factors do [depend on [math]\vec{A}[/math]]". So, by suitably manipulating [math]\vec{A}[/math], you could manipulate the phase, and hence action, associated with those paths. Wouldn't that, then, affect the particle's dynamics, via the principle of least action (action minimization) ?

Of course, it would. Accelerators are designed in a way to get the desired beam path. It is exactly A who is "manipulated".

[Widdekind]

So, in theory, Bohmian HV would allow, for an "[math]\vec{A}[/math] manipulating apparatus" (of suitable size & sophistication), far away from an electron diffraction experiment, to affect the electrons in said experiment, in a non-local way. It would do so, by suitably adjusting [math]\vec{A}[/math] along each electron path, so that all the paths running through the apparatus wound up with constructively interfering phases (instead of being "good zeros" which is what would happen typically). (?)