Tuesday, January 27, 2009

AWT and Bohmian mechanics

This post is a reaction to recent L. Motl's comments (1, 2, reactions) concerning the Bohm interpretation of quantum mechanics (QM), the concept of Louis de Broglie pilot wave in particular (implicate/explicate order is disputed here). Bohm's holistic approach (he was proponent of marxistic ideas) enabled him to see general consequences of this concept a way deeper, the aristocratic origin of de Broglie. It's not surprising, Bohm's interpretation has a firm place in AWT interpretations of various concepts, causual topology of implications and famous double slit experiment in particular. After all, we have a mechanical analogy of double slit experiment (DSE) presented already (videos), therefore it’s evident, QM can be interpreted by classical wave mechanics without problem..

Single-particle interference observed for macroscopic objects

AWT considers pilot wave as an analogy of Kelvin waves formed during object motion through particle environment. Original AWT explanation of double slit experiment is, every fast moving particle creates an undulations of vacuum foam around it by the same way, like fish flowing beneath water surface in analogy to de Broglie wave.

These undulations are oriented perpendicular to the particle motion direction and they can interfere with both slits, whenever particle passes through one of them. Aether foam gets more dense under shaking temporarily, thus mimicking mass/energy equivalence of relativity and probability density function of quantum mechanics at the same moment. The constructive interference makes a flabelliform paths of more dense vacuum foam, which the particle wave follows preferably, being focused by more dense environment, thus creating a interference patterns at the target.

By AWT the de Broglie wave or even quantum wave itself are real physical artifacts. The fact, they cannot be observed directly by the using of light wave follows from Bose statistics: the surface waves are penetrating mutually, so they cannot be observed mutually. But by Hardy's theorem weak (gravitational or photon coupling) measurement of object location without violating of uncertainty principle is possible. What we can observe is just a gravitational lensing effect of density gradients (as described by probability function), induced by these waves in vacuum foam by thickening effect during shaking.

Other thing is, whether pilot wave concept supplies a deeper insight or even other testable predictions, then for example time dependent Schrödinger equation does. By my opinion it doesn't, or it's even subset of information contained in classical QM formalism. This doesn't mean, in certain situations pilot wave formalism cannot supply an useful shortcut for formal solution (by the same way, like for example Bohr's atom model) - whereas in others cases it can become more difficult to apply, then other interpretations.


Arjen Dijksman said...

Thanks for the link to the Single-Particle Interference Observed For Macroscopic Objects paper.


By the way, you write therefore it’s evident, QM can be interpreted by classical wave mechanics without problem. It would be more correct to say: quantum slit experiments can be interpreted by classical wave mechanics without problem. Not all of QM may be interpreted by classical wave mechanics.

Kind regards,

Zephir said...

/*..not all of QM may be interpreted by classical wave mechanics...*/

Yep, I agree. What does word "MAY" mean here?

Well, correspondence principle requires, all aspects of one theory would be convertible into another seamlessly. But in general case such comparison can lead into unresolvable tautologies or fuzzy set of "solution landscapes", indeed. This is because every theory is multidimensional object in causal space, the dimensionality of which is defined by number of mutually independent postulates. This number defines a degree of freedom of every theory. For example, line is defined by vector, plane by 2st order tensor, etc.

When the second theory is more general and it requires lower number of mutually independent (orthogonal) postulates, no lost of information should appear during this, because first theory is observed for higher dimensional perspective, then the second one.

Currently QM is using six or so independent postulates (some of them may be dependent mutually, though), while AWT just two, being implicit theory. From AWT follows, number of postulates of any theory can be limited arbitrarily by making theory implicit and as such fractally recursive.

Arjen Dijksman said...

Meaning of word may: Fermi exclusion principle for example may not be explained by classical wave mechanics, in my view.

What are the two postulates of AWT?

Zephir said...

By AWT Universe is composed of inhomogeneous environment of infinite mass/energy density - so called an Aether (1st postulate). The appearance of reality is given by fact, we can observe only transversal waves of this environment (2nd postulate).

Fermi exclusion principle can be demonstrated by surface tension of mercury droplets, for example. While these droplets tends to merge together by weak attractive force (analogy of gravity), the strong but short distance force prohibits them in immediate merging (analogy of weak nuclear force).


By this way, large pile of tiny mercury droplets will not collapse immediately, until this collapse isn't initiated by merging of few droplets inside it - after then the avalanche-like collapse of the whole pile occurs. For example, LHC experiments can serve like initiator of terrestrial matter collapse into singularity.

Zephir said...

In 1952 David Bohm (re)formulated the EPR paradox in terms of spins, which were easier to visualize.

Zephir said...

Anthiny Valetini: Is Quantum Mechanics Tried, True, Wildly Successful, and Wrong?

Zephir said...

At the moment, when the computational power of classical computers gets already limited with quantum uncertainty, the word "quantum" cannot bring any substantial improvement. Neither quantum mechanics can beat its own theorems...;-)
Classical computers do use the quantum principles too, just from the opposite side: they're using the entangled systems of many objects (charge carriers in their transistors) and they're miniaturized up to level, which quantum uncertainty principle allows. Whereas the quantum computers are based on systems with as low number of entangled qbits as possible and their reliability is achieved with redundancy. The result in computational power is always same: the classical computers are slow but very exact and reliable, whereas the quantum computers are fast, but not quite exact or reliable. If we would consider both factors we would see, that the computational power of both types converges into the same value, determined with uncertainty principle. It means, if we would attempt to construct the quantum computer working at the same level of precision and reliability like the classical one, it would perform with the speed comparable to classical computer anyway.

Not quite surprisingly, the scientists working in quantum computer research are covering this aspect before publics carefully, because they would lose the grants and job positions. The advantage of quantum computers could get some merit only in applications, where the high precision is not required (typically data mining, optical pattern recognition, etc) and when the specialized hardware algorithms would be applied.

Zephir said...

Quantum mechanics writ large (PDF)

Zephir said...

Interpretation of quantum mechanics by the double solution theory The hidden medium of de Broglie wave mechanics is the aether. The “energetic contact” is the state of displacement of the aether. "For me, the particle, precisely located in space at every instant, forms on the v wave a small region of high energy concentration, which may be likened in a first approximation, to a moving singularity. A particle is a moving singularity which has an associated aether displacement wave." In a boat double slit experiment the boat always travels through a single slit and the bow wave passes through both.

Zephir said...

Why bouncing droplets are a pretty good model of quantum mechanics. Ross Anderson: “I think it's potentially one of the most high-impact things I've ever done,” he says, “If we're right, and reality is fluid-mechanical at the deepest level, this changes everything. It consigns string theory and multiple universes to the dustbin.

Zephir said...

Matter and Light in Flatland  see also http://yepezoj.blogspot.com