Schrödinger’s Quantum Stagecoach!

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One of the most popular film genres of the 20th Century was the Cowboy or Western and one of the most popular themes in western movies was that of the stagecoach. The stagecoach provided movie makers with a powerful metaphor. Outside the environment was hostile, full of Indians or outlaws, hell bent on doing evil to those on the coach.  Atop the coach were the driver and his companion, riding shotgun, protecting those inside and guiding them through their torment. While inside the passengers played out their parts exploring the complexities of human relationships in the confined space within the coach.

For those of us less interested in these human dramas, the stagecoach itself provided an interesting diversion. Frequently, as the stagecoach trundled across the desert of the Hollywood back lot, we would see the wheels of the coach appearing to go backwards while the coach itself moved forwards. Occasionally the wheels would appear stationary or move slowly forwards but at a speed which did not correspond to that of the coach. Of course we instinctively know that this cannot be the case. How could it be possible for a heavy stagecoach to be born in one direction when the wheels carrying it appear to be turning at a speed which is entirely inconsistent with its motion?

Once we understand the trick, the relationship between the sampling process of the film combined with the rotary motion of the spoked wheels of the stagecoach it all becomes clear. It only becomes clear however because when we think about the situation of the coach we are applying our knowledge of the way that the world works to the interaction of film and coach to come up with an explanation. The important thing here is that our understanding stems from knowledge grounded in our everyday understanding. The situation might be completely different if we did not refer back to our understanding of the world and took an alternative view.

Suppose instead of rationalizing the apparent direction of the rotation of the wheels based on our understanding of the interaction between the discrete nature of the film process and the continuous nature of the motion of the wheel, we took the view that the laws that governed the dynamics of the stagecoach were different when viewed through the rectangular window of the cinema screen. The freedom that this new posture gives us is immense. We can now come up with explanations for the seemingly contradictory motion of the coach and its wheels which fit the facts but which conform to our new set of rules. In such circumstances the number and type of rules that we can invent are arbitrary and unlimited. We are no longer bounded by the constraints of reality, we can invent our own realities.

We could argue that in the domain of the film the wheels of the coach do indeed turn backwards or stop or move slowly forwards when the coach itself is moving forwards, that somehow the coach is floating over the desert surface independently of the motion of the wheels. When we describe the motion of the coach by saying that it is As If the wheels are turning backwards what we actually mean is that the wheels of the coach Are turning backwards in this new cinematic domain.

In the context of the western and the stagecoach we find this transformation of an observation into an axiom quite ludicrous, but this is precisely what has happened over and over again in the development of Quantum Theory throughout the 20th Century. Quantum theory is founded on the notion that the laws of physics are different on the scale of the atom to that which obtains on other larger scales. Niels Bohr was one the most vociferous advocates of this idea and once this idea took root all bets were off. For each new discovery it was now possible to modify one of these new laws or simply invent another one.

When confronted with the idea that uncertainty was somehow intrinsic to the particle Erwin Schrödinger came up with his now famous cat analogy. Originally intended as a way of poking fun at the idea, Schrödinger has his cat placed in a sealed container together with a radioactive trigger. The firing of the trigger was random and based purely on whether or not some nuclear process took place while the cat was in the box. Schrödinger suggested that the implication of Bohr’s ideas was that, during its time sealed in the box, the cat was neither alive nor dead while at the same item it was both alive and dead, that it existed in some sort of nether world awaiting the opening of the box. Once the box was opened however and we not only discovered the fate of the cat, but at the same time the entire history of the cat’s ordeal was came into being where it had not existed until that moment.

Schrödinger’s cat was meant to ridicule the idea that uncertainty was an intrinsic property of sub atomic particles. Instead the response of the physics community was to embrace the idea and suggest that this is precisely what is happening in the sub atomic world, in effect to invent a new law, a new status of being wherein the particle is in some sort of limbo state part way between its particle form and its wave form awaiting the point in time when some sort of observing process causes it to collapse to take on one or other characteristic.

If we examine this proposition in more detail then what is happening is that the status of the cat is indeterminate during the period that the box is sealed. Since we cannot determine whether the cat is alive or dead, it is as if the cat was both alive and dead during this period. What Schrödinger was poking fun at and what Bohr was asserting was that it was not just as if the cat were both alive and dead at the same time but was actually alive and dead at the same time, in effect elevating a proposition to be an axiom.

Quantum theory abounds with examples of observations where a phenomenon can be said to be as if some rule or law exists and that rule or law is then taken to be a fact.

Examples include: The wave particle duality; the notion that entities can be either waves or particles at the same time and that the form they take on depends on some sort of observing process. The notion that entities can be simultaneously in more than one place at a time, the notion that a particle in one location can communicate its status to a similar (entangled) particle over any distance instantaneously, the notion that interactions between entities take the form of an exchange of particles. And of course the granddaddy of them all, the idea outlined above; the notion that uncertainty is intrinsic to the entity, that somehow in ways that can never be fully explained, particles are somehow possessed of the property of uncertainty within their being.

All of this comes about because physicists in the 1930’s and in particular Niels Bohr became convinced that the laws of physics were different on the scale of the atom to that on any other, larger scale . Unfettered by the conventional laws of physics and mechanics, physicists were free to invent their own laws.

Of course, once we can start drafting our own physical laws, the universe is our oyster. When something is observed which does not quite fit with our current model there is no problem. All we need to do is to draft a new law or redraft an existing law, get it passed by the parliament of peer review and everything is hunky dory.

And that is what has happened, over and over again. When physicists could not explain what forces could overcome the repulsion between protons within the atomic nucleus all they had to do was to invent a new particle, call it the Gluon and endow it with whatever properties were necessary to allow it to fulfill its new role. Never mind that no one has ever seen a Gluon and that the only evidence for its existence is circumstantial and takes on the form of a self-fulfilling prophecy. The Gluon must exist because the forces of interaction between nuclear protons behave as if the Gluon exists.

When the mathematics of special relativity cause an upset in the model for the base energy states of hydrogenic atoms: no problem, it is as if the conventional laws of physics do not apply on the scale of the atom and so they don’t and we can discount the effects of special relativity. We can invent a new type of angular momentum, call it Quantum angular momentum which is not quite the same as regular angular momentum and in so doing dispel the nasty Gamma term that would upset our calculations.

Physicists are no longer in the business of discovering the laws of nature, but of inventing the laws of nature.

Like the stagecoach, it is only when we apply our knowledge of the way the world works from within our existing framework that it all begins to make sense. It is when we try to invent solutions, in effect to create new physical laws that things go astray. Even if the laws of nature are different on the scale of the atom, and I remain deeply skeptical about this, it is essential if these new laws are to be credible, that they should relate back to a common frame of reference. That frame of reference has to be the laws as we understood them before we embarked upon the theorizing about how things behave on the quantum level. In other words it is essential to relate quantum phenomena back to the classical laws of physics if they are to bear any serious scrutiny.

The idea that the universe was quantized in some way dates back to the end of the 19th Century when Max Planck first discovered that energy emitted by a black body had to do so in discrete amounts or quanta. Later Einstein showed that this came about because electromagnetic radiation was formed from a stream of particles, later called photons.

The point at which quantum mechanics deviates from classical mechanics can however be dated quite precisely. It coincides with the Bohr model for the hydrogen atom. This model represents the point at which it first becomes necessary to either reject the model or to modify our understanding of the laws of mechanics. Bohr’s model was known to be deficient because it required particles to be capable of moving between two points without occupying anywhere in between. Such a discontinuity of position is not possible using Newtonian mechanics.  It was at this point that physicists decided that it was necessary to invent a new set of physical laws, rather than to modify the existing ones.

If the Bohr model is flawed, the postulate which underlies the Bohr model; that angular momentum is quantized must itself be suspect. De Broglie sought to get around this by suggesting that particles were in fact waves and calculated a value for their wavelength. A closer examination of this suggestion however reveals that it is simply a restatement of Bohr assumption. Nevertheless and despite this, de Broglie’s wave explanation is taken as fundamental and forms the basis for all models which have come along since.

The fundamental problem therefore which underlies all of the difficulties faced by Quantum theory dates back to its very beginnings, to this assumption. The entire edifice of Quantum theory rests like an inverted pyramid on this one assumption. The assumption can be justified only in terms of Quantum mechanics, which itself rests on this same assumption. It forms a circular or ontological argument in which quantization of angular momentum can only be justified based on calculations that themselves rely on the implicit assumption that angular momentum is quantized.

If quantization of angular momentum is to form the basis of quantum theory it is necessary to justify this quantization, not in the domain of quantum mechanics, but in the domain of classical mechanics. In other words it is necessary to find the mechanism which underlies such quantization.  I am of the opinion that this is not possible and that we must look elsewhere, other than angular momentum, to find the roots of quantization within the atom.

Clearly there is a deficiency in our understanding of classical mechanics. Bohr applied the rules of classical mechanics and came up with a model that required there should be such a thing as discontinuity of position. Bohr’s model took no account of the effects of special relativity, which at the time (1916) was a novel idea. It would appear therefore that this is the one area where we might look to modify our understanding of classical mechanics in order to come up with a viable model for the atom.

Since the effects of relativity are only felt at speeds close to that of light, it requires that we consider an atom in which the orbiting electron has a velocity close to that of light. If this is all we do then the model is not viable, the forces acting on the electron are too large for it to be stable. If however we postulate that the orbital velocity of the electron is itself affected by relativity (See Relativity and Angular Momentum), then we not only obtain a model for the atom which is stable (See Sampling the Hydrogen Atom), but we also find that we have described a mechanism that leads to quantization. In this model it is not angular momentum that is quantized, but is instead the relativistic Gamma term (See Quantization of Angular Momentum?) .

The model fully explains the dynamics of the atom and the mechanism which underlies the quantization of energy levels within the atom, but it does much more. It provides a simple mechanical explanation for the mysterious Fine Structure Constant. It results in a model for the atom in which the orbital radius is constant for all energy levels. It provides an explanation for the wave nature of the electron in terms of its circular motion around its orbit, effectively doing away with the need for an ether or its latter day equivalent.

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