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1kEinstein was often quoted as saying “If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless.”
For example one can easily understand how a curvature in space-time can cause gravity in terms of the physical image of a marble on a curved surface of a rubber diaphragm. The marble follows a circular pattern around the deformity in the surface of the diaphragm. Similarly planets revolve around the sun because they follow a curved path in the deformed “surface” of space-time.
However the same cannot be said about black body radiation.
This is because classical physics suggests that all harmonics in a black body have an equal chance of being produced even when their number goes up in proportion to the square of the frequency. However this classical concept works reasonably well at low frequency yet it begins to diverge at higher frequencies so much so that its energy content at those frequencies should approach infinity. This discrepancy between the classical description of a black body and its reality has come to be called the Ultraviolet Catastrophe.
However Planck realized it could be explained by assuming that energy is not continuous but comes in discreet packaged define by the equation E=hv. Their observation that the energy in a black box is quantized was the basis for the development of Quantum theory.
Yet no one, up until now has been able to provide a physical image of how and why this should be so.
Up until now because in the article “The Photon: a matter wave?” Oct. 1, 2007 it was shown that one can use the observed wave properties of electromagnetic radiation and Einstein Theory of Relativity to form a physical image of how energy is disturbed in a black body.
However it is easier if one converts or transposes Einstein space-time universe to one consisting of only four *spatial* dimensions.
(The reason will become obvious later.)
Einstein gave us the ability to do this when used the constant velocity of light to define the geometric properties of space-time because it provided a method of converting the space-time displacement he associated with energy in a space-time universe to a spatial one in a universe consisting of only four *spatial* dimensions. Additionally because the velocity of light is constant he also defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.
The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming, as was done in the article “Defining energy?†Nov 27, 2007 that all forms of energy including electromagnetic can be derived in terms of a spatial displacement in a “surface†of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
As mentioned earlier the article “The Photon: a matter wave?” Oct. 1, 2007 shows how one can understand the properties of electromagnetic energy and how it is distributed in space and a black body in terms of a physical image based on the classical properties of wave motion if one assume that space is composed of four *spatial* dimensions instead of four dimensional space-time.
For example 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. A force will be developed by this displacement, which will result in the elevated and depressed portions of the water moving towards or become “attracted” to each other and the undisturbed 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, 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 become “attracted” to each other.
This would define in terms, of a physical image 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.
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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. This is because classical mechanics 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. This force is called magnetism.
This is analogous to how the vertical force pushing up of on mountain also generates a horizontal force, which pulls matter horizontally towards from the apex of that displacement.
This provides a physical image that would allow on to understand the electromagnetic wave component of black body radiation
However its quantum mechanical or particle properties can also be derived in terms of a physical image by extrapolating the laws of classical resonance to that same wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
For example as the article “Why is energy/mass quantized?” Oct. 4 2007 showed one could derive a physical image of the particle or photonic properties electromagnetic energy by extrapolating the laws of a classical wave to a fourth *spatial* dimension.
Briefly, it showed the four conditions required for resonance to occur in a classical 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 be meet by a matter wave in four *spatial* dimensions.
The existence of four *spatial* dimensions would give space (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 the shifting of an electron in an atomic orbital. This would force the “surface” of a three-dimensional space to oscillate with the frequency associated with the energy of that event.
However, these oscillations in a continuous non-quantized field of energy/mass caused by such an event would cause a resonant system or “structure” to be established in it.
Classical mechanics tells us the energy of a resonant system can only take on the discreet quantized values associated with its resonant or a harmonic of its resonant frequency.
However, one can also use the above concepts of four *spatial* dimensions to develop a physical image of the particle or photonic properties
Max Planck, as was mentioned earlier associated with black body radiation.
In classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.
Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up†or “down†with respect to a fourth *spatial* dimension.
The confinement of the “upward†and “downward†oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries associated with a particle in the article “Why is energy/mass quantized?“
These resonant systems in a continuous non-quantized field of energy/mass are responsible for the discrete or incremental energies associated with the quantum component of black body radiation.
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| The ultraviolet catastrophe is the error at short wavelengths in the Rayleigh–Jeans law (depicted as “classical theory” in the graph) for the energy emitted by an ideal black-body. The error, much more pronounced for short wavelengths, is the difference between the black curve (the wrong curve predicted by the Rayleigh–Jeans law) and the blue curve (the correct curve predicted by Planck’s law). |
However, these two articles also provide a physical image of why the energy distribution in a black body is what it is in terms of the concepts of classical physics.
A black body is an idealized object that absorbs all electromagnetic radiation that falls on it. Because no light is reflected or transmitted, the object appears black when it is cold. However, a black body emits a temperature-dependent spectrum of light. This thermal radiation from a black body is termed black body radiation.
At room temperature, black bodies emit mostly infrared wavelengths, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit visible wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature. By the time an object is white, it is emitting substantial ultraviolet radiation.
The problem is, as was mentioned earlier the laws of classical mechanics, specifically the equipartition theorem, states that black-bodies which have achieved thermodynamic equilibrium are mathematically obligated (by classical, pre-quantum, laws) to radiate energy in the form of ultraviolet light, gamma rays and x-rays at a certain level, depending on the frequency of emitted light.
However observations of black body radiation indicate that there was less and less energy given off at high end of the spectrum.
Einstein pointed out this difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck. He had hypothesized that electromagnetic energy did not follow classical laws, but could only oscillate or be emitted only in discrete packets of energy proportional to the frequency, as given by Planck’s law. In other words, the light waves of each frequency in a black body could not have any energy but are limited to a few discrete values.
However, as mentioned earlier the article “Why is energy/mass quantized?” showed energy of a photon at each frequency could be understood by extrapolating a physical image of a resonant system in three-dimensional space to a fourth *spatial* dimension similar to how Einstein was able to from a physical image of gravity.
For example as the above theoretical model shows using only the concepts of classical physics and Einstein’s theory of Relativity a photon could only have the discrete energies or frequencies that are a fundamental or harmonic of the energy of an environment which would be determined by the temperature of the one it was occupying. Therefore, according to the above theoretical model any frequency other than that would be irregular and non-repeating and would be absorbed into the fundamental or harmonic frequency of that environment.
In other words it explains in terms of a physical image based on our classical reality why black-bodies which have achieved thermodynamic equilibrium are mathematically obligated by (classical, pre-quantum, laws) to radiate energy in the form of ultraviolet light, gamma rays and x-rays at a certain discrete levels, depending on the frequency of emitted light.
It should be remember Einstein’s genius allows us to choose if we want to view the physical properties of electromagnetic energy and black body radiation in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the particle and wave properties microscopic quantum world as well as microscopic one of Einstein thereby giving us a new perspective on the physical relationship between particles and waves
Later Jeff
Copyright Jeffrey O’Callaghan 2014
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