Throughout "The Imagineer’s Chronicles" we have shown observations of our environment suggest space is composed a continuous non-quantized form of mass and four *spatial* dimensions instead of four-dimensional space-time.

However, if this were true one would think that black body radiation should be continuous over its entire range of values.

In the article "The Photon: a matter wave?" Oct. 1, 2007 it was shown that the electromagnetic energy is propagated by a wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth spatial dimension.

Later the article "Why is energy quantized?" Oct. 4 2007 showed that one could derive the particle properties electromagnetic energy in terms of a classical resonating system made up of a continuous non-quantized form of mass and four spatial dimensions.

There are four conditions required for resonance to occur in a classical Newtonian 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.

The existence of four *spatial* dimensions would give a continuous non-quantized mass component of space 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 with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, these oscillations in a continuous non-quantized form of mass caused by such an event could generate a resonant system or "structure" to be established in a continuous non-quantized form of mass.  These resonant systems are responsible for the discrete or incremental energies associated with black body radiation.

A black body is an idealized object that absorbs all electromagnetic radiation that falls on it.  No electromagnetic radiation passes through it or is reflected from 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 that 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.

Unfortunately, for classical laws, when a black body gets hot enough, the amount of radiation, according to the equipartition theorem should begin to approach infinity.

However, observations of black body radiation indicate that there was less and less energy given off at high end of the spectrum.

The conflict between the predictions of classical laws and observations came to be known as the Ultraviolet Catastrophe.

Einstein pointed out this difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck.  Planck postulated 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 was shown in the article "Why is energy quantized?" the energy of light at each frequency is determined by a resonant system which is, in turn determined by  the environment it is occupying. This is because it will only support the discrete energies or frequencies of light that are a fundamental or harmonic of that environment.  Therefore, according to classical mechanics, any frequency other than that would be irregular and non-repeating and  would be absorbed into the fundamental or harmonic frequency of that environment.

This means the energy contain in a black body should be limited to a discrete values based on classical mechanics if one assumes the causality of energy quantization is a resonant system formed by a matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This shows one can derive a mechanism that can explain and predict the observe properties of black body radiation in terms of classical laws if one assumes space is composed of a continuous non-quantized form of mass and four *spatial* dimensions as we have done in "The Imagineer’s Chronicles".

This is not possible if one defines space in terms of four-dimensional space-time because time is only observed to move in one direction forward and therefore could not support the bidirectional movement or spatial oscillations required to define a classically resonating system.

Later Jeff

The "Shadows" of four spatial dimensions

Copyright 2009 Jeffrey O’Callaghan

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