The Wave interpretation of the Compton Effect
The Compton effect is one of two pillars on which quantum mechanics has laid its foundations historically. The other is the photoelectric effect, which we will reinterpret below following an examination of the structure of the atom based solely on waves. It constitutes the basis for the particle interpretation of the interaction between radiation and elementary matter in the most basic interaction in microphysics between a single photon and a single free electron.
Quantum mechanics used the corpuscular interpretation of the Compton effect to demonstrate that classical wave models could not be applied to a world dominated by individual exchanges of quantum energy.
In the Compton experiment, which has by now become a classic, a single photon strikes one of the superficial electrons of a graphite crystal and transfers a portion of its energy to it. This sets the electron in motion in a particular direction and at a consequent velocity.
The photon in turn is knocked in another direction as it has been deviated to a particular degree and possesses less energy than before as it has transferred a specific proportion of its energy to the electron in the collision.
From a conceptual perspective, the original corpuscular interpretation of this phenomenon assumed the behavior typical of a billiard ball.
One body (the photon) strikes another body (the electron) and transfers a discrete and well-defined proportion of its quantum energy to it as kinetic energy.
No other interpretation seemed both simpler and possible and least of all an interpretation based on waves, which classically involved the continuous transfer of the wave’s energy.
Picture 22. Arthur Compton and the Compton effect in its classical interpretation.
Quantum mechanics demonstrated that it was impossible for classical Wave Theory to describe the Compton effect in terms of radiation and explain the quantized results the experiment produced.
This lent credence to its fundamental assertion that “only a description based on particles remained plausible”.
In the phenomenon, the transfer of discrete quantities of energy took place according to probabilistic functions. And as these were the entities represented by quantum mechanics, this remained the only theory capable of explaining the Compton effect.
We will present step by step here an alternative new description of the phenomenon using only waves. This will allow us to refute the particle interpretation adopted up to now and provide a better “causal” explanation of the Compton effect.
- To do this, we will use the Principle of Relative Symmetry in the new explanation of the pressure of radiation to explain the transfer of energy from the photon to the electron.
- And the wave modification to General Relativity to determine the deviation by “diffraction” of the photon understood to be a “pure” wave train.
If our attempt is successful, we will have demonstrated that General Relativity can be applied to quantum interactions between radiation and elementary particles.
And we will have used the wave description of the field correctly in the context of Relativity to provide a wave interpretation of basic phenomena to quantum mechanics.
Will this finally fulfill Einstein’s dream of a relativistic theory that can describe quantum phenomena in strictly causal terms?
To assess whether this is in fact the case, picture a virtual experiment that is closely linked to the experimental reality already demonstrated in Compton’s experiments.
Picture 23. According to its interpretation in terms of waves, the Compton effect introduces the same assessment of the geometry surrounding the mass for this strictly quantum phenomenon that was made by General Relativity for the deviation of light by the mass of the Sun.
Observe the Compton interaction in a virtual experiment in five succeeding steps involving a photon with wavelength λi = 10-10 meters deviated 90 degrees by a free electron in a space with no significant fields.
- During the first step, the photon approaches the source of the field of the electron and its energy is added to the energy of the waves of the field of the electron in the zone close to the center of the sources of the wave-electron.
- During the second step, the Principle of Relative Symmetry spurs the electron into motion in the same direction as the photon colliding with it.
Before this second step, however, a phenomenon occurs in which the obstructing electron purely and simply diffracts the wave train photon in which the energy of the diffracted photon remains unvaried.
Picture 24. Diagrams showing the experimental evidence of the two wave lengths captured in the Compton effect.
This phenomenon has been observed experimentally as an observation of light following the normal angle of deviation, but without revealing any other decay. (Article in Physical Review (1923) A. Compton).
There was an attempt to explain this as an effect of vibrations caused by the photon in the electron on the basis of the classical model of interaction in Electromagnetic Wave Theory.
Quantum mechanics was unable to interpret this phenomenon directly and was forced to invoke the assistance of classical electromagnetic theory with considerable embarrassment and as the final word.
This was the same theory that it was designed to replace completely with regard to phenomena involving actions with quantized amounts of radioactive energy.
The Wave Theory of the Field can now explain this same phenomenon rationally and in a completely consistent and causal fashion.
The observation that a component of the deviated radiation possessing the same energy as the incoming radiation exists should be attributed to the fact that the electron impacted by the incoming photon is at that time a simple irremovable obstacle.
It has not yet had time to accelerate under the influence of the Principle of Relative Symmetry and is overrun by the first wave surfaces from the incoming photon that travel at the speed of light.
Picture 25. The wave fronts of the photon can be compared to a line of people chasing a bus: each of them pushes the bus slightly to make it achieve a velocity v1. Each of them then gets on and holds on to a pole to move onto the bus in a direction orthogonal to their velocity. The distance between the people in the line will increase as a function of the speed of the bus.
The electron thus limits itself, as we saw in the case of solar deviation and optical diffraction, to simply diffracting the first part of the wave train of the photon, which maintains its energy levels unchanged.
In the meantime, the Principle of Relative Symmetry sets the electron in motion by means of the asymmetrical variation that takes place in the electron wave field and sets it an initial velocity v1.
3) A decrease is observed in the photon’s energy level, which increases its wavelength relative to the electron that is moving in the same direction as the photon, which “sees” it as a wave prolongated by the Doppler effect.
One may wonder how what the electron “observes” can have any influence on our own observations.
The fact is that the electron’s dynamic behavior conditions the decay in the photon’s energy level as a function of the velocity it itself gains. The wave mechanism can be described in the physical situation illustrated in figure ( 26 ) below.
Under the influence of the Principle of Relative Symmetry, the electron ceases to accelerate and moves at the acquired velocity v1 . The photon, which moves at the speed of light, is certainly faster than the electron, which moves at velocity v1 (which is about 1/100 the speed of light). The photon therefore overtakes the electron, passing it on one side, and is then diffracted by the electron’s spherical wave field at an angle of α = 90°.
The degree of diffraction is governed by a new term added to the General Relativity formula:
λo ² / r λ i .
In keeping with the modification in the General Relativity theory, the value of the ratio of the wavelength of the photon li and the radius r of the mass causing the diffration is prevalent over the value of the first term when the relativistic formula describes an interaction with a large mass.
Both the dividend and the devisor in the ratio now share values that are very similar, which makes the angle of diffraction 90°, equal to:
π/2 = 1.57079 for radiants, very close to the unit.
The radius ” r ” is the minimum distance from the center of the source of spherical waves-particles the incoming photon can reach before being diffracted.
This radius will assume a determining role in the following. It will introduce the new descriptive tools the Wave Theory of the Field makes possible for quantum physics using the new interpretation of General Relativity in terms of waves.
New causal effects emerge from phenomena considered unobservable by definition in quantum mechanics’ description. The phenomenon in fact occurs in a closed box inside which the photon and the electron interact and from which the only observable objects — the electron in motion and the decayed photon — emerge randomly.
We are now opening the box and it is revealing all its internal mechanisms to us which will allow us to follow the causal chain that characterizes the Compton effect step by step.
If we know the wavelength of the incoming photon and of the mass of the particle causing the diffraction, we can predict the photon’s maximum angle of deviation.
This has experimental relevance as it allows us to foresee a new experiment in which will predict and then verify or refute the value of the greatest possible angle of diffraction for photons of a particular initial energy level that interact with the electron.
It will also allow us to predict the minimum radius of the curve described by the photon with the greatest diffraction around the center of the wave field of the particle causing the diffraction, which will have important explanatory significance when we construct our model of the electron below.
Now move on to the fourth step to consider the new interactions between the photon that has been deviated at a right angle and the electron that is in motion in a direction perpendicular to the photon’s trajectory as it moves away from it. We again observe an asymmetrical imbalance in the energy surrounding the electron’s wave source.
The photon that has suffered the decay and is now traveling away from the electron with wavelength l i1 intervenes unilaterally to achieve a new effect creating a new asymmetrical imbalance in the energy within the electron.
The photon now decayed triggers a new push in accordance with the dictates of the Principle of Relative Symmetry and as a result induces a new quantity of motion in the electron in a direction perpendicular to its previous trajectory.
The situation is now slightly different, as the electron’s wave field has already been deformed by the relativistic Doppler effect to which it has been subjected by the velocity it has already acquired.
The wavelength of the waves of the mass of the electron, that propagate perpendicular to the direction of the velocity, is now smaller than it was before this happened.
Picture 26. An electron diffracting a photon, which moves away in a direction orthogonal to the velocity v1 after its energy has decayed for the first time. The mass of the photon moving away from the electron is now equivalent to its transverse relativistic mass.
As a result of its reaction to the violation of the laws of energy symmetry and the fact that it is now in motion at a consistent speed, the electron’s mass is now greater than it was before.
This new mass is exactly equal to the “transverse mass” predicted mathematically by Special Relativity but has never before been explained in any physical model.
The fact that particles thrown out at velocities close to the speed of light possess increased mass is, as we saw above, perfectly comprehensible in the context of waves as a product of the Doppler effect on the wave source, which progressively decreases the wavelength of waves emitted in the direction of motion as the body’s velocity increases.
This is the result of the velocity imposed on the mass and the effect is the Doppler effect, which shortens the wavelength of the source of waves-mass in front of itself in the direction of motion.
In the same way, the “transverse mass” can be explained using the same model as a decrease due to the Doppler effect in the wavelength of the waves emitted by the electron, which propagate at an angle of 90° from the direction of motion.
Thus, for the photon that moves away from the electron following diffraction, the mass of the electron is equal to the transverse mass in Relativity.
This model is simple and so comprehensible that it is not possible to raise any argument against it that makes any sense. But its simplicity should not mislead us to underestimate its explanatory power, which can only develop as a result of our new approach based on wave theory.
Picture 27. The relativistic mass of a body varies as a function of the observer’s perspective. If the object in motion is observed from a 90° angle, its mass will be equal to Einstein’s transverse relativistic mass. The wave length that can be attributed to this mass is equivalent to the one that can be attributed to a wave source subject to the relativistic Doppler effect observed from the side.
To continue with our description of the interaction, we see the electron reacting to the presence of the photon with the wavelength li1, and, in accordance with the dictates of the Principle of Relative Symmetry, it acquires a new velocity v2 at right angles to velocity v1.
The portion of the photon that continues to revolve around the wave source in diffraction decays further by the Doppler effect. It behaves as if it had been emitted by the electron and moves definitively away from thlie wavesource-electron, which is in motion at velocity v2 after modifying its wavelength further to
λ i2.
The diffracted photon has suffered overall a decay that can be calculated using the necessary mathematical procedure as a variation in its wavelength, which has become longer by a particular amount, Δ λ i:
Δ = λi2 – λi = 2.44 . 10 –12 meters.
The electron in turn has acquired its final velocity
ve = v1 + v2.
As a result of the effect of the relativistic transverse mass, the sum of these two velocities is not a simple vectorial sum.
Lievelyn Thomas has demonstrated (in a very difficult mathematical treatise with a purpose different from our own that was a direct result of Special Relativity, but which surprised Einstein so much that he admitted candidly that he had never thought of it) that a Lorentz transformation of velocity v1 followed by a second transformation of velocity v2 in a different direction does not result in the same inertial reference as a single Lorentz transformation of velocity v1 + v2.
In comprehensible words, all this means simply that calculations normally made to assess the relativistic velocity of a body that has received two pushes “simultaneously” in different directions lead to different results when they are calculated for the same body,
“if the push in one direction follows the other, which was imposed at an earlier moment on the same body in a different direction.”
The wave model makes the reason for this behavior clear. The causal sequence appears clear once the origin of the transverse mass is understood in terms of waves
- In the first case, A, a body, with a given mass at rest receives the two pushes simultaneously and its mass is the same for each push.
- In the second case, B, the body receives the first push when it still has its mass at rest, whereas the second push comes at a later time when its mass has already increased as transverse mass as a result of the velocity acquired through the first push, so that the second push has less effect than in case A.
Picture 28. Two representations, A and B, of a vector with a relativistic variation of the transverse mass.
The resulting velocities for the masses are different in the two cases and different explanations can be made of these behaviors consistent with the wave explanation of the field of the mass.
At the various stages in the causal chain in the wave model of the Compton effect illustrated above, physical conditions are present that provide opportunities for further experimental tests.
The experiment we have followed in its exclusively causal development confirms the variation in General Relativity, which introduced it with the correct result obtained.
The experiment also provides confirmation of the Principle of Relativity Symmetry as the causal instrument in determining the interaction of radiation and matter. This demonstrates its validity both in observing phenomena made known by the Compton effect and in discovering hitherto unknown and inexplicable interactions involved in this same effect.
The validity of the wave model should not be assessed solely in terms of possible experiments that verify its predictions, however, but also in terms of its effectiveness in organizing the causal elements of the phenomenon and its consistency.
Einstein, who had a special love of consistency and perhaps a somewhat excessive love of modesty, wrote in 1930:
I consider the most important aspect of the General Relativity not to lie not in its ability to predict some extremely small observable effect but in the simplicity of its foundations and in its logical consistency.
As some of you will have noticed, modesty is not the most obvious of my defects, whereas I do like to taste the sweet pleasure of another vengeance. Einstein’s cheerful spirit, if it existed now, would leap for joy and stick out its tongue at the people who criticized him at the time for involving General Relativity in the quantum physics of the Compton effect.
The closed box to which quantum mechanics relegated the phenomenon of the interaction between the photon and the electron is now open. It will be interesting to continue testing the wave model against the other key phenomena in physics and to use our new skeleton key in the most important locks in our system of physical knowledge.
We will do that below. For now, we must proceed to discover the explanation in terms of waves of a fourth physical phenomenon that continues the series of three that led us to the Compton effect.
We will now analyze what is perhaps the most important phenomenon in the entire new physics based on waves. It derives from a possible development due to the interaction between photons and electrons in the Compton effect, which up to now has remained completely unsuspected.
Our analysis of the chain of cause and effect in this evolution of the Compton effect makes it possible for us to create a wave model of the electron that proves our initial assumption that the source of the mass field could be a source of spherical subquantum (elementary) waves.
In other words, we will now discover how it is possible to conceive of the rational existence of a mechanism consisting solely of waves, that can produce the elementary spherical waves characteristic of the electron in a consistent causal continuity.