Modern scientific enquiry aims to be as objective as possible. The mechanism that has evolved to meet this requirement is called the Scientific Method. The Scientific Method is predicated on the idea that new theories are developed based on a set of assumptions or postulates. To be useful the theory must be capable of making predictions which can then be tested by experiment. If a well conducted experiment fails to match the predictions then the theory is disproved and the assumptions that underlie it are called into question. If the experiment matches the prediction it does not necessarily mean that the theory is correct, later experiments may go on to disprove it. Hence it is only ever possible to disprove a theory, we can never prove it to be absolutely true; all we can ever hope to do is to reinforce our confidence that the theory is correct.

Einstein understood this very well and wrote his papers with these ideas in mind. He was a past master at developing ideas in his papers which made predictions even though the phenomena he predicted may have already been observed. In his 1905 paper on the motion of atoms in a liquid he develops the argument based on the idea that atoms in a liquid are in a constant state of motion and uses this to predict that larger particles in suspension would also move in a similar way. He was predicting the existence of Brownian motion, even though Brownian motion had been described some 80 years before.[1]

This type of retrospective prediction is not so much a foretelling as it is an explanation of some phenomenon which has already been observed . Such ideas can be valuable in testing a scientific hypothesis by examining whether or not it explains phenomena that are already known. Here I want to examine some of these explanations as they relate to the structure of the hydrogen atom described in Sampling the Hydrogen Atom and see how they compare with the widely held so called Standard Model of Quantum Theory.

In Sampling the Hydrogen Atom, it was shown that, by introducing a simple postulate; that orbital velocity is affected by relativity, we can obtain a model for the atom in which the component parts are objectively real particles. That is the electron and proton which make up the atom are both point particles in the classical sense, having deterministic position and velocity.

By combining this with a second postulate; that gravitational mass is bipolar in nature and therefore that antimatter has negative mass, we obtain a model for the photon in which it is seen as a composite binary system made up of an electron and a positron locked in mutual orbit and that these two are objectively real particles. The model is explained more fully in Shedding Some Light on the Nature of the Photon.

Both of these theories challenge the currently held Standard Model, in which particles are not considered to be objectively real and in which the photon is poorly described as a packet of energy travelling through space, without any explanation as to just what this is or might be..

The structure of the atom in the Standard Model can trace its history to Bohr’s model for the hydrogen atom which he developed in 1916. In particular it is based on the same assumption that Bohr used in developing his model, namely that angular momentum is quantized and yet this assumption is highly suspect. It requires that three independent variables can somehow collude with one another in such a way that a fourth dependent variable can only take on values which are discrete. In Quantization of Angular Momentum I examine this assumption in more detail and question whether it could be valid.

Compare this to the model proposed here, in which orbital velocity is affected by relativity. When we make this assumption we find that it is not angular momentum that is quantized but the Lorentz factor Gamma which takes on a series of values which are integer multiples of a base value. That base value turns out to be related to the hitherto mysterious Fine Structure Constant providing a simple mechanical explanation for its existence and value. In this context the Lorentz factor is a function of a single variable, so there is no need for any complex interplay between independent variables. Furthermore the model provides a simple mechanism which explains precisely why the Lorentz factor can only take on this series of discrete values, something which Bohr’s model completely fails to do – the quantization of angular momentum remains an arbitrary and expedient assumption, unproven and unprovable.

There is a great deal of mathematics which purports to show that angular momentum is quantized, but none of this forms what can reasonably be described as a proof. All such arguments are ultimately ontological in nature because they all begin with the tacit assumption that angular momentum is quantized and go on to show that therefore it must be quantized. In order to be valid, any such proof of the idea that angular momentum is quantized must begin from the perspective of classical mechanics and proceed from there.

And so to the quantum leap itself. In Bohr’s model the radius of the orbiting electron increases as the square of the energy level, while the orbital velocity varies as the reciprocal of the energy level. In other words as energy level increases the electron orbits at an ever larger radius and at an ever slower speed. It is this change in orbital radius with energy level that leads to the idea of the quantum leap and its later manifestations. When there is a change of energy level the electron is required to leap from one orbital radius to another without ever occupying any position in between the two orbits.

In the relativistic velocity model it is seen that the effect of relativity on the mass term of angular momentum exactly cancels with the inverse term affecting the velocity and this leads to the idea that an electron orbiting at near light speed is constrained to do so at a constant radius. If the orbital radius is constant then there is no quantum leap. Energy changes are not accompanied by a change in position but are achieved entirely by a change in orbital velocity; something which is perfectly consistent with an electron which is a particle in the classical sense. There is no need to introduce the idea of a quantum leap, it is simply not necessary. Incidentally it follows that a constant orbital radius is a necessary condition for objective reality, since anything else inevitably requires the quantum leap or its equivalent.

It is all very well showing that a model based on relativistic velocity is a better model than the Bohr model. The quantum theorists answer is to point out that Bohr’s model is no longer accepted and has been superseded by other more sophisticated models.

The quantum leap provided Bohr with an impenetrable barrier, there appeared to be no way around it until in 1921 the French physicist Louis de Broglie dared to suggest that perhaps the electron was not a particle but was instead a wave. Louis de Broglie proposed that the wavelength of the electron was equal to Planck’s constant divided by the particle’s linear momentum. He went on to suggest that the orbit at each energy level then contained a whole number of wavelengths of the electron as a wave and that the energy levels therefore formed a sort of harmonic sequence. De Broglie’s idea of what has since come to be called the wave particle is the cornerstone of the standard model. The idea that what we traditional regarded as a simple classical particle could somehow be considered to be either a wave or a particle depending on the circumstances lies at the heart of quantum theory and the Standard Model.

There are a number of fundamental shortcomings with de Broglie’s idea. Principle among these is de Broglie’s identification of the wavelength as being derived from Planck’s constant divided by the linear momentum. When we look at any orbiting object from the viewpoint of an external observer, and a good example would be a moon orbiting a distant planet, then we see a sinusoidal wave. We identify the amplitude of such a wave with the orbital diameter, similarly the wavelength is identified with the orbital circumference and the orbital velocity with the wave velocity. This is true whether the object is a star orbiting around a galaxy, a planet orbiting a star, a moon orbiting a planet or a child whirling an object around on the end of a string. The orbital radius, and by implication the wavelength, of such a system is easily calculated by dividing the angular momentum of the object by its linear momentum. Not so for Louis de Broglie, he chose instead to identify the wavelength of his wave particle with Planck’s constant divided by the linear momentum, while knowing full well that Bohr had assumed angular momentum to be quantized as an integer multiple of Planck’s constant. There is little wonder therefore that the energy levels of the electron appear as a harmonic sequence of these artificially conjured up waves. It is a foregone conclusion born out of Bohr’s original assumption simply expressed in terms of waves.

With relativistic velocity the orbiting electrons still have wavelike properties; wavelength, amplitude and the like, but unlike the artificial constructs of de Broglie, these derive from the same associations we make for any orbiting object on any other scale. The electron is a classical particle orbiting at a fixed radius with a wavelength related directly to the orbital circumference. The wave can be considered an attribute of the particle, a sort of property related directly to its motion.

This is not the case with de Broglie’s waves. The electron still has an orbit, it is just that it is occupied by a whole number of de Broglie’s waves. And this brings us on to the second fundamental problem with de Broglie’s idea.

Waves can only exist by virtue of the motion of a substance, the idea of a wave itself is somehow abstract. So for example a wave on the ocean is caused by the collective motion of billions of water molecules. Even with the wave of the hand, it is the motion of the hand which describes the wave and for there to be a wave the presence of the hand is therefore essential. For a wave to exist something which is external to the wave has to be moving. As soon as we divorce ourselves from the notion of the particle as an objectively real entity such a thing no longer exists. There has to be something waving, but the particle as such does not exist, so it cannot be the particle, it must be something else. But what can it be?

For a long time it was suggested that there was something, some sort of substance, not made of atoms but made of something else, which had just the right properties to sustain the waves of such wavelike particles. It was variously called the Plenum or the Ether or more recently it has been dubbed the ”fabric of space-time”. The trouble with this idea is that existence of the ether was disproved in the late 1900’s, long before de Broglie came up with his ideas about wave particles. Quantum Theory is therefore caught in an intellectual cleft stick. Wave particles need something in which to exist as waves, but the only possible medium has been shown not to exist.

There is no such difficulty with the model based on relativistic velocity, since it is the objectively real electron in orbit around the atomic nucleus which describes the wave, which is then seen as an attribute of the particle not a substitute for it. This makes even more sense when we think about how we understand waves and the collective movement of real particles. What we have here is the limiting condition where there is only one such particle and that is the source of the wave.

The next on the scene was Erwin Schrödinger. He basically took de Broglie’s idea of the wave and developed a set of equations which describe them. Relativistic velocity leads to the idea that the orbital radius remains constant for all energy levels and if we substitute this into Schrödinger’s wave equations they degenerate into the simple form necessary to describe the wave motion of the objectively real electron about the orbital nucleus.

As de Broglie’s ideas of the wave/particle took hold it became necessary to provide some sort of explanation as to just how the wave particle could make the mysterious transition between its various manifestations. This more or less coincided with the development of ideas by Schrödinger and Werner Heisenberg concerning the degree to which the properties of a particle could accurately be measured.

The eponymously named Heisenberg uncertainty principle describes the limit to which certain properties of sub atomic particles can be measured, for example it is not possible to measure both position and velocity of a particle to arbitrary accuracy. It seems there is always a tradeoff, if we measure the position we are bound to lose track of the velocity and vice versa. While Heisenberg based his analysis on matrix mathematics, Schrödinger did so based on his wave equations, but eventually the ideas coalesced and were shown to be equivalent.

Heisenberg originally developed a theory to underpin his mathematical findings based on the practical considerations of measuring the properties of an object when the measuring tools were of the same order of magnitude as the object being measured. This heuristic explanation is called the Observer Effect. Bohr saw in the uncertainty principle the get out clause which could explain how a particle could be both a wave and a particle at the same time. He argued that uncertainty is somehow intrinsic to the wave particle which is neither one nor the other until it is observed in some way. He argued that it has neither position nor velocity until it is observed in some way. When subjected to what Bohr described as an Observing Process it reveals itself to have a particular property, say a particular velocity, but in doing so it loses the conjugate property, in this case its position. He argued that its existence as either a wave or a particle is a similar pair of conjugate properties.

This idea of intrinsic uncertainty is fraught with difficulties but nevertheless forms an integral part of Quantum Theory and the Standard Model. It can be seen alongside the wave particle duality as a sort of magic fairy dust but the bottom line is that is poses as many questions as it answers. If, for example, a wave particle does not have a deterministic velocity how can it have deterministic energy, since the two are related? How then is energy carried within the wave particle? It cannot be as kinetic energy because its velocity is indeterminate. It cannot be as wave energy because there is nothing that can wave and in any event the energy of a wave is related to the kinetic energy of its constituent particles.

There are no such difficulties with the model based on relativistic velocity. Here the energy of the electron is simply kinetic energy. Its position and velocity are both deterministic, but in determining its position we are bound to destroy any possibility of measuring its velocity due to the observer effect and vice versa, in determining its velocity we are bound to destroy its position.

In Bohr’s model, the size of the atom increases as the square of the energy level, hence in the second energy state the orbital radius is four times that of the base state, in the third energy state it is nine times and so on. If this model is to be believed then the size of the atom increases dramatically with energy state, to the point where in the 100^{th} energy state for example it should be clearly visible under an optical microscope. If instead it is argued that the size of the atom relates to the de Broglie wavelength then things are a little better. Here the wavelength of the harmonic wave increases in proportion to the energy state. So in the second energy level it is double that of the base state and so on. Nevertheless the idea that the size of the atom changes with energy state presents a number of severe problems which Quantum Theory simply overlooks.

The physical and especially the chemical properties of an atom are intimately associated with its morphology. Chemical bonding takes place because electrons orbiting the atomic nucleus are shared between atoms forming covalent bonds. It is unlikely therefore that a hydrogen atom in the second energy state would have the same chemical properties, the same propensity to form covalent bonds, if it was twice the size of the same element in the base energy state, never mind if it were four times the size. A situation which gets worse as the energy level of the atom increases.

With a model based on relativistic velocity there is no such problem. The atom remains the same size for all energy states. In the case of hydrogen the only real different between an atom in the base energy state and that in the maximum possible energy state is that the orbital velocity differs by 0.002669%. To all intents and purposes the morphology of the atom remains the same for all energy levels.

An electrically charged object following a circular trajectory can be expected to emit so called synchrotron radiation. Bohr chose to ignore this in his model for the atom. Subsequent theories side step the issue by arguing that this is particle like behaviour but when it comes to synchrotron radiation the orbiting electron can be regarded as a wave.

Once again there is no such difficulty if orbital velocity is taken to be affected by relativity. In this case the electron is constrained by the effects of relativity and the value of Planck’s constant to always orbit at a fixed radius. It is as if the electron were orbiting on a hard surface from which it cannot deviate and which it cannot penetrate. This is akin to the situation with massive bodies under general relativity, to them space itself is warped to the point where they believe they are following a straight path in what turns out to be a curved space. The same is true for the electron in orbit around the atomic nucleus. As far as it is concerned it is following a straight line path in a space which is warped by the combined effects of relativity and Planck’s constant.

At every twist and turn the model based on relativistic orbital velocity matches what has been observed and does so in ways that are far more rational and simple than does the Standard Model of Quantum Theory.

Why identify the wavelength with Planck’s constant divided by linear momentum? – when at every other scale the wavelength of an orbiting object is identified with the total angular momentum divided by the linear momentum.

Why invent wave particle duality? – when we can explain the particle like behaviour of the electron perfectly well as having the deterministic properties of an objectively real particle and we can explain its wavelike behaviour simply as a consequence of the orbital motion of such an objectively real particle.

Why insist that uncertainty is intrinsic in ways that are totally indescribable? – when the observer effect provides a far more rational and simpler explanation when the particle is viewed as being objectively real.

Why assume that angular momentum is quantized? – when not mechanism exists sot support the idea and when it requires the complex interactions of three independent variables in ways that have never been described or discovered and when there is a simple mathematical and mechanical explanation to explain just how and why the quantization of energy levels within the atom comes about.

Why support a theory that is incapable of explaining just how energy can be stored in the atom? – when a simple alternative theory can explain it as being kinetic in nature.

Next time I will explain how these ideas can extend to cover the photon and go on to show how the ideas of relativistic velocity and bipolar gravitational mass might be used to make novel predictions which would go a long way towards proving that these ideas are correct.

[1] Einstein, Albert; R. Fürth, transl. by A. D. Cowper (1926, reprinted in 1956). “*On the Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat”. Investigations on the theory of the Brownian motion.* Dover Publications. ISBN 0-486-60304-0.