Compton scattering: A Classical approach | Unifying Quantum and Relativistic Theories

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Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, called the Compton Effect. Part of the energy of the X/gamma ray is transferred to a scattering electron, which recoils and is ejected from its atom (which becomes ionized), and the rest of the energy is taken by the scattered, “degraded” photon.

Inverse Compton scattering also exists, where the photon gains energy (decreasing in wavelength) upon interaction with matter. Since the wavelength of the scattered light is different from the incident radiation, it is an example of inelastic scattering, The amount the wavelength changes is called the Compton shift.

The effect is important because it demonstrates that light cannot be explained purely as a wave phenomenon. Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain low intensity shifts in wavelength. (Classically, it is assumed that light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light, but the effect would become arbitrarily small at sufficiently low light intensities regardless of wavelength.) In other words the results of Compton’s experiment convinced physicists that light behaves as a stream of particle-like objects (quanta) whose energy is proportional to the frequency.

However one can integrate the quantum or photonic properties of light such as Compton scattering with its wave properties by extrapolating the laws of a Classical three-dimensional environment to fourth *spatial* dimension.
For example In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown one can derive the quantum mechanical properties of energy/mass and a photon in terms of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension by extrapolating the classical laws of resonance in a three-dimensional environment to one of four.

Briefly it showed the four conditions required for resonance to occur in a classical Newtonian three dimensional environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would occur in one of consisting of only four *spatial* dimensions.

The existence of four *spatial* dimensions would give a “surface” of a three-dimension space manifold (the substance) the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or a photon interacting with an electron. This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

Therefore, these oscillations in space, would meet the requirements mentioned above for the formation of a resonant system or “structure” in it.

The energy associated with resonant system in three-dimensional space can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

These resonant systems in four *spatial* dimensions are responsible for the incremental or discreet energies associated with photon and all other quantum mechanical systems.

While one can derive the electromagnetic wave properties of a photon as was done in the article “Electromagnetism in four *spatial* dimensions” Sept. 27, 2007 by extrapolating the laws of classical wave mechanics to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Briefly a wave on the two-dimensional surface of water causes a point on that surface to be become displaced or rise above or below the equilibrium point that existed before the wave was present. Classical wave mechanics tells us a force will be developed by the differential displacement of the surfaces, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the surface of the water.

Similarly a matter wave on the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension would cause a point on that “surface” to become displaced or rise above and below the equilibrium point that existed before the wave was present.

However, as just mentioned classical wave mechanics, if extrapolated to four *spatial* dimensions tells us the force developed by the differential displacements caused by a matter wave moving on a “surface” of three-dimensional space with respect to a fourth *spatial* dimension will result in its elevated and depressed portions moving towards or becoming “attracted” to each other.

This defines the causality of the attractive forces of unlike charges associated with the electromagnetic wave component of a photon in terms of a force developed by a differential displacement of a point on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, it also provides a classical mechanism for understanding why similar charges repel each other because observations of water show that there is a direct relationship between the magnitudes of a displacement in its surface to the magnitude of the force resisting that displacement.

Similarly the magnitude of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by two similar charges will be greater than that caused by a single one. Therefore, similar charges will repel each other because the magnitude of the force resisting the displacement will be greater for two similar charges than it would be for a single charge.

One can define the causality of electrical component of electromagnetic radiation in terms of the energy associated with its “peaks” and “troughs” that is directed perpendicular to its velocity vector while its magnetic component would be associated with the horizontal force developed by that perpendicular displacement.

However, Classical Mechanics also tells us a horizontal force will be developed by that perpendicular or vertical displacement which will always be 90 degrees out of phase with it. The attractive force associate with this horizontal displacement is called magnetism.

This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls or attracts matter horizontally towards from the apex of that displacement.

Yet as shown in the article “Why is energy/mass quantized?” the matter wave responsible for the propagation of electromagnetic energy must travel through space in quantized resonant structures that is responsible for the quantum mechanical properties of a photon.

Therefore the articles “Why is energy/mass quantized?” and “Electromagnetism in four *spatial* dimensions” explain both the electromagnetic and wave properties of a photon and electron because it defines one in terms of the other.

Yet it also allows one to explain how the low intensity shifts in wavelength of X and gamma rays occur when they interact with charged particles in terms of Classical wave mechanics because if the causality of their electromagnetic and particle properties are as suggested above related to the resonant properties of a matter wave then it tells us that interference will occur no matter how small the intensity of their interaction is.

This is because the velocity of all forms of electromagnetic energy including gamma and X rays is constant and therefore it cannot change after an interaction occurs with particles such as an electron while an electron’s can be altered by a change in its velocity. Therefore, the only way to alter the energy, direction or momentum of a gamma or x-ray is by “degrading” or changing their wavelength. Yet, if the electromagnetic and particle properties of both a photon and electron are a result of a matter wave is as suggested above then classical wave mechanics could define their interaction in terms of the interference of their electromagnetic wave properties. However this also tells us their scattering at very low light intensities could take on any arbitrarily small value regardless of wavelength.

In other words if one assumes the electromagnetic and particle characteristics of both a photon and electron is a property of a physical displacement created by a matter wave on in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension as is done here then one can Classically explain why it is not necessary to accelerate a charged particle to a relativistic speed to cause the low intensity shifts in wavelength associated with the Compton effect.

This shows how one can explain the inelastic scattering of photons in matter which results in the decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, called the Compton Effect by extrapolating the laws of classical wave mechanics to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Later Jeff

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