A Heuristic Model of the Creation and Transformation of Light

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The Development of Our Views on the Composition and Essence of Radiation
by Albert Einstein , translated by Wikisource
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Maxwell's theory of electromagnetic processes in so-called "empty" space differs in a profound, essential way from the current theoretical models of gases and other matter. On the one hand, we consider the state of a material body to be determined completely by the positions and velocities of a finite number of atoms and electrons, albeit a very large number. By contrast, the electromagnetic state of a region of space is described by continuous functions and, hence, cannot be determined exactly by any finite number of variables. Thus, according to Maxwell's theory, the energy of purely electromagnetic phenomena (such as light) should be represented by a continuous function of space. By contrast, the energy of a material body should be represented by a discrete sum over the atoms and electrons; hence, the energy of a material body cannot be divided into arbitrarily many, arbitrarily small components. However, according to Maxwell's theory (or, indeed, any wave theory), the energy of a light wave emitted from a point source is distributed continuously over an ever larger volume.

The wave theory of light with its continuous spatial functions has proven to be an excellent model of purely optical phenomena and presumably will never be supplanted by another theory. Nevertheless, we should consider that optical experiments observe only time-averaged values, rather than instantaneous values. Hence, despite the perfect agreement of Maxwell's theory with experiment, the use of continuous spatial functions to describe light may lead to contradictions with experiments, especially when applied to the generation and transformation of light.

In particular, blackbody radiation, photoluminescence, generation of cathode rays from ultraviolet light and other phenomena associated with the generation and transformation of light seem better modeled by assuming that the energy of light is distributed discontinuously in space. According to this picture, the energy of a light wave emitted from a point source is not spread continuously over ever larger volumes, but consists of a finite number of spatially localized energy quanta that move without dividing and are absorbed or created only as a whole.

Subsequently, I wish to explain the reasoning and supporting evidence that led me to this picture of light, in the hope that some researchers may find it useful for their experiments.

Contents

[edit] Ultraviolet Catastrophe in the Theory of Blackbody Radiation

We begin by applying Maxwell's theory of light and electrons to the following situation. Let there be a cavity with perfectly reflecting walls, filled with a number of freely moving electrons and gas molecules that interact via conservative forces whenever they come close, i.e., that collide with each other just as gas molecules in the kinetic theory of gases. In addition, let there be a number of electrons bound to spatially well-separated points by restoring forces that increase linearly with separation (Hooke's law). These electrons also interact with the free molecules and electrons by conservative potentials when they approach very closely. We denote these bound electrons as "resonators", since they absorb and emit electromagnetic radiation of a particular frequency.

According to the present theory of the generation of light, the radiation in the cavity must be identical to blackbody radiation (which may be found by assuming Maxwell's theory and dynamic equilibrium), at least if one assumes that resonators exist for every frequency under consideration.

Initially, let us neglect the radiation absorbed and emitted by the resonators and focus instead on the requirement of thermal equilibrium and its implications for the interaction (collisions) between molecules and electrons. According to the kinetic theory of gases, dynamic equilibrium requires that the average kinetic energy of a resonator equal the average kinetic energy of a freely moving gas molecule. Decomposing the motion of a resonator electron into three mutually perpendicular oscillations, we find that the average energy \bar{E} of such a linear oscillation is

\bar{E} = \frac{R}{N} T

whereR is the absolute gas constant, N is the number of "real molecules" in a gram equivalent and T is the absolute temperature. Because of the time averages of the kinetic and potential energy, the energy \bar{E} is 2/3 as large as the kinetic energy of a single free gas molecule. Even if something (such as radiative processes) causes the time-averaged energy of a resonator to deviate from the value \bar{E}, collisions with the free electrons and gas molecules will return its average energy to \bar{E} by absorbing or releasing energy. Hence, in this situation, dynamic equilibrium can only exist when every resonator has an average energy \bar{E}.

Similar considerations may be extended to the interaction between the resonators and the ambient radiation within the cavity. For this case, Planck has derived the condition for dynamic equilibrium; treating the radiation as an completely random process, he found

\bar{E}_{\nu} = \frac{c^{3}}{8 \pi \nu^{2}} \rho_{\nu}

Here, \bar{E}_{\nu} is the average energy of a resonator of eigenfrequency ν (per oscillatory component), c is the speed of light, ν is the frequency, and ρνdν is the energy density of the cavity radiation of frequency between ν and ν + dν.

If the net radiative energy of frequency ν is not to continually increase or decrease, the following equality must hold

\frac{R}{N} T = \bar{E} = \bar{E}_{\nu} = \frac{c^{3}}{8 \pi \nu^{2}} \rho_{\nu}

or, equivalently,

\rho_{\nu} = \frac{R}{N} \frac{8 \pi \nu^{2}}{c^{3}} T

This condition for dynamic equilibrium does not agree with experiment. Moreover, eliminates any possibility for equilibrium between matter and aether, since the radiative energy of the cavity increases with an increasing range of frequencies without bound

\int_{0}^{\infty} \rho_{\nu} \, d\nu = \frac{R}{N} \frac{8 \pi}{c^{3}} T \int_{0}^{\infty} \nu^{2} \, d\nu = \infty

[edit] Planck's Derivation of the Fundamental Quantum

[edit] The Entropy of Radiation

[edit] Molecular Theory of the Volume Dependence of the Entropy of Gases and Dilute Solutions

[edit] Interpretation of the Volume Dependence of the Entropy of Monochromatic Radiation using the Boltzmann Principle

[edit] Stokes' Rule

[edit] Generation of Cathode Rays from the Illumination of Solid Bodies

[edit] The Ionization of Gases by Ultraviolet Light

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