Wednesday, December 26, 2007

Christmas Bohmian Style

In the spirit of the season I have recently come across a “conventional quantum” explanation of Santa’s delivery of presents to children on Christmas morning and how this in a quantum sense could all be done in the space of one night. Below find this explanation written by Sean Smeltzer, Croydon, Surrey; published in the journal New Scientist, January 16, 1999:


I have recently received a number of distinctly unfestive emails pointing out the impossibility of Santa Claus delivering presents to all the children in the world in just one night.

We are all aware of the flaws in the conventional Santa Claus theory, but seem to accept it quite readily. Children are not quite so gullible and require a more rigorous proof of his existence. The answer to this problem lies in quantum theory.

Consider this: On Christmas night, Santa is in a superposition of quantum states, smeared out all the way around the planet, and each quantum state delivers presents to a single child. This explains why is is so important that children are asleep, because if just one child sees Santa, he immediately collapses into a single state, in accordance with Heisenberg. This would mean that no other children would receive presents that Christmas. This theory elegantly avoids all the flaws in the conventional theory. The only problem is that you will have to explain quantum theory to your children before you tell them about Santa.

After reading the above, I thought to myself; how could this all be looked at from a Bohmian’s perspective? I therfore offer the following:

A Bohmian’s Quantum Christmas

Santa delivering presents is a “quantum potential”, not merely just a possibility. A quantum potential is not realized, yet rather actualized without the need for observation. Many children accept this aspect of potential and thus it is actualized for them. I also would wager that children and others could more readily understand how all this works, as opposed to the quantum algorithm (lest I say fairytale)

As one can see this is by far a more straight forward and consistent explanation as opposed to the first and as I maintained could be actually understood. It also has the advantage that observation plays no role in the actualization of the event at all and better explains why, no single, or any child’s observation of Santa has ever spoiled Christmas:-)

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.

Sunday, December 2, 2007

Potential when considered as Information

I have recently had some exchanges with a physicist about the misunderstandings of Bell’s ideas within the physics community in general. In thinking about this my mind wandered back to a proposal he made about a year ago. That proposition was the elevation of “potential” as a “beable” ("The beables of the theory are those elements which might correspond to elements of reality, to things which exist. Their existence does not depend on 'observation'). That is, would it be of any use to give it status above that of being merely considered as a linking element within physical description? Then I thought how one could conceptualize potential, as say potential energy like in electric or gravitational potential as being an actual aspect of reality.

One way to do this is to consider potential as being effected by change, at the fundamental level. Now as we know, entropy in terms of its action is one of the most rudimentary concepts in all physical theory when considering change. Imagine a crossbow being cocked with an arrow set in it (elastic potential). In this model the flight of the arrow is thought of as the realization of this potential. Next, if we simply allow time to pass, what then transpires? If left for instance in our earthly environment, the bow’s latch may simply corrode and have its potential realized. Now what if we moved this setup to deep space? According to our current understanding the tension and thereby this potential of the bow will relax (diminish) over a period of time, to the point where it is gone entirely. This of course is related to the role entropy has in this regard.

To continue, entropy has recently been connected with "information”, such as in Hawking’s view. It could therefore be stated, that entropy has acted to eliminate (dissipate) this potential. In this way, potential could be simply considered as the sum total of information as it is ordered. So, following this down, potential can be considered as a consequence of the presence and ordering of information. We now ask J.S. Bell’s question when confronted with this “all is information” concept as to what is the physical world. This question is “information about what”? The answer then suggested would be it is information about potential. Of course the thing that can’t be neglected here is the “order” of information. That is, without the ordering, there is no real information and thereby no potential to be realized. The point here of course, is that information, on its own, is not a fundamental entity, rather ordered information is. Then we continue with how I would suppose Bell would by asking, “ordering of what”? This is where the concept gets stuck since there is nothing considered real outside what is called information which as demonstrated is actually ordered information. It must be reminded here that in this example we are not dealing with what would be generally considered as physical at all in that what is so described is potential.

Now the question, from whence came the order? Bohm’s reply would be that it is a fundamental aspect and thereby consequence of the wave. Looked at this way then “actualization” of information or its potential is the “particle” (i.e. ones and zeros) aspect of reality, while the ordering is the “wave” (i.e. program) aspect. This suggests, as Bohm and his proponents have insisted, that there must be a dual ontology to nature. Now what should be considered as a reasonable explanation of reality? “Information” ordered by “what”, or “particles” guided by “waves”.

Sunday, November 25, 2007

Wave or Particle, Old or New?

I have been in some way, quite amused, as to how many consider this particle or wave debate in quantum physics as something new as in that quantum realities such as non-locality as that being a recent concern. That is, if you count recent as being within the last hundred years or so. Truly this debate has persisted for millenniums, more so then just in the last century. It actually all began with the concept of Atomic Theory first proposed in India in the 6th Century B.C.E. and then again about a hundred years later in ancient Greece with the first notions of the concept. Most notably within what is considered the era of modern science, the debate has continued as to what constitutes action and physicality in nature.

This is most poignantly demonstrated in terms of the nature of light. As we know, Newton considered light to be a particle phenomena and published a theory in support of it. Then enters Thomas Young who in the early 1800’s, with his famous two slit experiment demonstrates the wave nature of light. During the same period Augustin Fresnel, who as I have often found to ironically have being born in Broglie France, came up with a complete wave theory of light. This theory was challenged by Simeon Poisson in a proposed experiment suggested by results he calculated from the formalism of Fresnel’s theory. What the theory indicated, by Poisson’s calculation, is that if a narrow beam of light was cast onto a small round object, the effects of wave interference produced would have light bend around the disk to form a bright spot within the middle of the shadow cast. This Poisson (a Newton supporter) claimed to be absurd and set up a experiment to show Fresnel the error of his ways. Unfortunately for Poisson, but fortunate for Fresnel, the bright spot in the centre of the shadow appeared exactly as the theory had predicated. Thus Poisson was embarrassed and Fresnel won a prize in relation to this along with being elected to the French academy of science and then after made a fellow of the Royal Society. Ironically this phenomena ever since has been referred to as Poisson’s spot as apposed to Fresnel’s.

Then in 1905, Albert Einstein was to reverse this all again, with his paper on the photoelectric effect, where only a particle explanation would satisfy the results of then recent experiments. This resolved what was called the ultra-violet catastrophe, yet in turn only served to broadened the mystery, for now it appears as nature acts sometimes as a particle and in other situations as a wave. Then in the early 1920's this was to be all reversed once more, with the birth of Quantum Mechanics, first with what came to be known as the Copenhagen Interpretation. This was the result of the combined contributions of Neils Bohr, Werner Heisenberg, Wolfgang Pauli and Erwin Schrodinger. In this theory all again was attributed to a wave or more appropriately the function or action of a wave, where particle phenomena is said to be the collapse of such only upon observation. This as to say that particles are not so much, more or less, figments of our imaginations, yet rather figments of our perception.

Now as to the non-local aspect of the issue. This also is often taken as something relatively new, beginning with Einstein’s objection and culminating with the experimentally demonstrated results of John Bell's theory. However, where I would say the whole thing began was with Pierre de Fermat when in the mid 1600’s he proposed “the actual path between two points taken by a beam of light is the one which is traversed in the least time”. This became known as Fermat’s Least Action Principle and was criticized not for its inability to predict outcome, yet rather for its inference as to how nature behaves. In truth, this action as it relates to the economy of nature, is still used and considered in physics and forms the base of Lagrangian mechanics, developed by Joseph Louis Lagrange. However, at the time it was largely scoffed at for what it appeared to infer. In fact it was first immediately rebuffed by Claude Closely (a optics expert at the time) as he said, “Fermat's principle can not be the cause, for otherwise we would be attributing knowledge to nature: and here, by nature, we understand only that order and lawfulness in the world, such as it is, which acts without foreknowledge, without choice, but by a necessary determination.”

In the the contemporary context what we are referring to with this aspect of the debate is if nature behaves at some level as non-local? Thst as in instantaneous or faster then light, at the quantum level?. At this juncture, I recall reading that when Richard Feynman was first presented with this contention of Fermat’s, by his high school teacher, he thought it equally absurd. Later he would go on to develop his “Sum Over Histories approach to quantum mechanics. I have often wondered how this served as a resolution to Fermat’s conjecture? That is I never was able to fathom where all these histories were to happen and then be free to cancel themselves to the allowed paths. That is unless one subscribes to Many Worlds or John Crammer’s ideas.

Alas in the end, one should not dispair, as there has been, despite the perceived paradox existed a fully consistent explanation of this for all to see for quite some time. And that is Bohmian Mechanics, better described as the deBroglie-Bohm pilot wave theory. It’s only that many have chosen not to look. With this I am reminded as in Plato’s Allegory of the Cave that still many refuse to look at the light to see what it may truly be. That is except for Bohm and even now his mostly ridiculed disciples, who have come to find, as Bohm discovered and Bell reminded, that it is not “particle or wave”, but rather “particle and wave”. This all has taken a little less then three thousand years. Let us hope the rest will not take as long.