Saturday, December 8, 2007

Quantum Potential when considered as Information

In my last post I was discussing the relation between potential and information. What was discovered with this analysis was that “ordered” information could be equated with what is thought of as potential in classical mechanics. We also spoke about how entropy plays a role in disordering this information and as such the eventual elimination of the potential it describes. It was also proposed that ordering of this information was attributable to the wave as viewed in Bohmian Mechanics. Now that I’ve had further time to contemplate this, another thought has come to mind. That thought is about what is referred to as the “quantum potential” as it is found in the original formalism of Bohm’s pilot wave theory. This potential is viewed by the contemporary followers of Bohm as sort of an optional term and is only found if the theory is formulated to be what is referred to as a second order theory. This is as opposed to the way it is commonly formulated today as a first order one. What this means in approximation , is that the rate of change of positions of the particles is what is considered fundamental to the theory. In the Bohm’s second order treatment, particles are thought of as acting under the influence of forces, where the source of one of these forces is described as being resultant of what is called the quantum potential. This potential is related directly as an attribute of the wave and not that of the particle.

What we will do here, as we did with “Classical Potential”, is to consider this “Quantum Potential” as a “beable”. As you recall classical potential was realized to diminish when the effect of entropy was considered. That is the ordering of the particles was diminished by its action. Now what about this “quantum potential” is it so affected? In an attempt to find out let’s again ask the Bell question in this regard which is, “information about what”? In this case we will say it is information about quantum potential. Now as before what we must remember here is that as in classical potential what we are referring to is the ordering of information. So as before it is the ordering of information that begs explanation.

We now move on to the next Bell like question “ordering of what”? In this case, as was revealed in my last post, it is the ordering of the wave. Now ordering of a wave, how does this differ from the ordering of particles? With the ordering of particles it was their individual positions and different aspects of momentum in relation to each other that defined the ordering. In other words the information was not to be found in one single particle but rather can only be considered as the sum total of all related. Now what about the wave? With a wave we have a totally different physical entity primarily because it has no parts. That is it is a holistic entity and cannot be defined in terms of separation but rather defined in terms of its shape. How is shape of a wave defined? The way it is usually defined is in terms of its amplitude (height) and its length at points of repetition or repeated occurrences of its shape in this regard. Then there is a third way it is described and that is in terms of frequency, which is often related to its speed. However, I must warn this is a tricky thing. What it truly refers to is the rate of change in regards to its shape (the other two things) within one arbitrarily selected point in space. I could go more into this aspect of a wave but I think many of you know that in say as in the case of sound waves for instance, the medium of the wave which is air does not move in the direction of travel but rather the influence (force or energy) of the wave is what is so moving. As an (classical) example, a surfer moves forward as a result of this influence as in the case of water waves and yet he leaves the water behind.

To continue, can these waves lose this ordering as it was in the particle case? In the case of the particles it was found that this ordering can only be referenced as the sum total of all those considered as to their relative positions and velocities. Now in the case of waves we find that the information contained (the ordering) not in terms of separated entities but rather the shape and rate of change of a holistic one. In this case there is no true separation to speak of and velocity is related not to motion but rather the rate of change of the shape. In essence it has no velocity at all as it is classically described. It is then not evident how such an entity could be affected by entropy as it is currently understood.

To conclude then, unlike classical potential which does diminish with time as assigned to the effects of entropy, it appears that this quantum potential of Bohm’s cannot and thus could be considered as a “beable” (aspect of reality) as it is the true source of this ordering of information. In other words classical (temporary) potential owes itself to the quantum (permanent) potential. For me this also lends a better understanding of why particles cannot be expected to be observed in any predetermined state of position or velocity since these are not decided by something inherent of their own nature yet rather inherent of something attributable to nature of the wave. So uncertainty, as it is considered in quantum mechanics, should not be thought of as particles existing at best as only the sum total of their possible states (position and velocity) or only as figments of perception of a collapsed wave state. They are simply where they are mandated to be and at velocities determined by the region of the wave in which they are found to be influenced. As a crude analogy, would it be reasonable to say a surfer does not have (at any one instant) a velocity or position because they (or for that matter anyone) doesn’t know how exactly to determine this or that the surfer only exists if observed? I’ll let you decide.

1 comment:

Bazza said...

Hi Phil. This is Bazaa; I am going to be reviving or replacing my blog in the new year ofter a year's rest. Thanks for letting me know you had heeded my advice! This looks to be very accessiable. Good luck with the new format.