We have shown throughout this blog and its companion book “The Reality of the Fourth Spatial Dimension” there are numerous theoretical advantages to assuming the existence of four *spatial* dimensions instead of four-dimensional space-time.
The ability to define a mechanism which can resolve the conflict between Maxwell’s classical wave theory of light and the quantization of the electromagnetic field confirmed by the photoelectric effect is one of them.
In the article “Why is mass and energy quantized?” Oct 4, 2007 it was shown that one can understand and derive both the quantum mechanical and wave properties of energy/mass by extrapolating the laws of a classically resonating three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally it was showed why all forms of energy must be propagated in these resonant systems.
(The concept of a particle having a wave component was first formulated in 1924, when Louis de Broglie he theorized they have a wave properties. However he was unable to resolve the conflict between it and the quantum mechanical properties of a photon associated with the photoelectric effect.) Â
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 occur in one consisting of four spatial dimensions.
The existence of four *spatial* dimensions would give a matter wave 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 manifold to oscillate spatially with the frequency associated with the energy of that event.
The oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established space.
Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment.Â
Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.
Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.
Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy units of the universe.
Yet one cans also define the boundary of a quantum system in terms of the spatial properties of four spatial dimensions.
For example 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.Â
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?“
The photoelectric effect is perhaps the most direct and convincing evidence of the existence of photons and the “corpuscular” nature of light and electromagnetic radiation. That is, it provides undeniable evidence of the quantization of the electromagnetic field and the limitations of the classical field equations of Maxwell.
This conclusion is based on the observation that the emission of electrons begin as soon as electromagnetic energy of a given frequency strikes the photoelectric material. This is inconsistent with the wave theory of light because it predicts the delayed emissions of electrons.
In addition, it was observed that varying the intensity of the light does not change the velocity of the electrons ejected but only their numbers, however increasing the frequency does.
Einstein in 1905 successfully explained these observations by assuming the incident light consisted of individual quanta, called photons, that interacted with the electrons in the metal like discrete particles, rather than as continuous waves and that each one carried the energy E = hf, where h is Planck’s constant and f is the frequency. Therefore, increasing the intensity of the light corresponded to increasing the number of incident photons per unit time (flux), while the energy of each photon remained the same (as long as the frequency of the radiation was held constant).Â
These assumptions explain why varying the intensity of the light does not change the velocity of the electrons ejected but only their numbers because according Einstein’s photonic concepts that would result in increasing the number of photons with the same energy thereby causing a greater number of electrons to be ejected. However, because each photon has the same energy the electrons effect by them would carry the same average energy when ejected. Additionally it would also explain why increasing the frequency “f” of the incident radiation would increase their average energy because that would increase the average energy of the photons striking the photoelectric material thereby their increasing average energy.
However, assuming as we have done that the quantization of the electromagnetic field is a result of a resonant system formed by a matter wave on “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension allows one to resolve the conflict between those properties and Maxwell’s classical wave interpretation of light. This is because, it allows one to extrapolate the laws classical wave mechanics in a three-dimensional environment to a fourth *spatial* dimensions to explain its quantization.
Classical Wave Mechanics tells us resonant system must be quantized or have the discrete energies associated with their fundamental or a harmonic of their fundamental frequency.
Yet this means that one could interpret Planck’s constant or “h” in the equation Einstein used to calculate the energy of photon as the energy associated with the fundamental resonant frequency in four *spatial dimensions that defined a photon in the article “Why is mass and energy quantized?â€. Therefore, every photon would have a multiple “h” of that energy.
The reason why, as Einstein noted, “increasing the intensity of the incident radiation causes greater numbers of electrons to be ejected, each carrying the same average energy” is because each photon had the identical frequency and therefore, as was shown in the article “Why is mass and energy quantized?†would contain the same energy. However this means that increasing the intensity of the incident radiation must mean a proportional an increase in the number of photons striking the photo electric material. Therefore it follows that increasing the intensity of the incident radiation would cause greater numbers of electrons to be ejected, each carrying the same average energy.  However it allows his concepts to integrated into Maxwell’s wave theory of light because as was shown in that article the energy of a photon is related to the wave properties of its resonant structure.
Additionally, as Einstein also noted as one increased the frequency the average energy of the emitted electrons increases. This is consistent with the classical wave interpretation of the resonant system associated with a photon in the article “Why is mass and energy quantized?” because it defines their quantized energy in terms of the frequency of a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions. This means that according to Classical Wave Mechanics its quantized energy will be directly related to its frequency of that matter wave and therefore increasing its frequency will also increase the energy of the ejected elections.
The reason why delayed emission is not observed is because as was shown in that article energy can only be propagated in these resonant systems. Therefore if the energy associated with a quantized resonant “system” of a photon of a given frequency is sufficient it will instantly eject an individual electron off a photoelectric surface while none will be f it is not.
This shows how one can resolve the conflict between Maxwell’s wave theory of light and the quantization of the electromagnetic field confirmed by the photoelectric effect by assuming that the quantization of an electromagnetic field is caused by a resonant system formed by a matter wave moving on a “surface” of three-dimensional space manifold with respect to a fourth *spatial* dimension.
Later Jeff
Copyright Jeffrey O’Callaghan 2011