The Classical Assumption

ReferenceA Logical Approach to Theoretical Physics

Since ancient times, aether has been theorized as a substance that permeates the cosmos. Aether did not play any part in Newton’s corpuscular theory of light. But when light was discovered to have wave properties, physicist started to consider light as a disturbance that traveled through aether. This meant that light was pure motion, or “pure energy”. This was contrary to Newton’s corpuscular theory that treated light as rapidly moving particles (substance in motion).

The classical assumption was that light was a wave motion (pure energy) traveling in aether.

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Faraday

Faraday saw that atomic particles touched each other through force that existed between them. The lines of force became a powerful reality to him in the electrical and magnetic phenomena. He saw force as an extension of matter. Matter was concentrated lines of force. This was consistent with Newton’s view that equated matter with an “innate force”. To Faraday, force became a much finer form of substance.

In his paper on Thoughts on Ray Vibrations (1846), Faraday says,

“The view which I am so bold to put forth considers, therefore, radiation as a kind of species of vibration in the lines of force which are known to connect particles and also masses of matter together. It endeavors to dismiss the aether, but not the vibration.”

According to Faraday light was a vibration in the lines of force that connected particles of matter. Force was the substance of light.

Thus Faraday returned to Newton’s idea of light as “substance in motion”.

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Maxwell

Maxwell focused on the mathematical description of the electromagnetic force outlined by Faraday. He saw electromagnetism as a study in states of stress and strain. In seeking consistency with Newtonian dynamics, Maxwell basically treated electrical lines of potential as having uniform density same as material particles. He used the concept of aether, which is uniform throughout space.

Maxwell did not fully implement Faraday’s conception of lines of force. These lines, through their varying thickness, represented varying density of “force substance”. He, therefore, missed the phenomenon of quantization discovered later by Einstein.

Thus, Maxwell adhered to wave theory and popularized the concept of pure energy. According to this theory, the energy density of light was proportional to the square of the amplitude. Maxwell’s equations do not describe the motion of charged particles but the effect that passes through them at the speed of light.

In Maxwell’s model, light remained a wave motion (pure energy) traveling in aether.

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Einstein

In his 1905 paper on light quanta, Einstein set up a model of blackbody radiation similar to the model in kinetic theory of gases. He then reached the following conclusion.

“We thus reach the conclusion: the higher the energy density and the longer the wavelengths of radiation, the more usable is the theoretical basis used by us; for short wavelengths and low radiation densities, however, the basis fails completely”.

Einstein showed that Maxwell’s classical assumption is valid at longer wavelengths (low frequencies). As frequency increases the energy distribution becomes more discontinuous in space like particles. Einstein thus showed that Planck’s postulate of energy quanta was more than just a mathematical device.

But Einstein also assumed radiation to be vibrations in aether. As variable frequency required a medium of variable density, aether of constant density could not serve. Einstein, therefore, dropped the idea of aether, and decided that light was “vibrations in mathematical space”.

Einstein kept the classical concept that light is “pure energy”, except he replaced Maxwell’s constant aether by a variable mathematical space.

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Quantum Mechanics

Einstein concludes in his 1905 paper:

“According to the assumption considered here, when a light ray starting from a point is propagated, the energy is not continuously distributed over an ever increasing volume, but it consists of a finite number of energy quanta, localised in space, which move without being divided and which can be absorbed or emitted only as a whole”.

This is the view of light quanta as “pure energy” in a mathematical space of variable density. Contrast this with light as a substance of variable density moving in real space. The latter is the proposal of Faraday of vibrating lines of force of variable thickness in real space.

Like Maxwell, Einstein also couldn’t see light to be made up of a “force field” that had variable density in real space (see the chapter The Quantum Particle). This created confusion between real and mathematical space, and placed quantum mechanics on a firm mathematical footing. 

Both classical and quantum mechanics view light as “pure energy” that requires either aether or mathematical “substance” for its existence.

The actual breakdown of classical mechanics occurred when the idea of quantum confirmed light to be a “substance in motion” and not a “motion in hypothetical aether”.

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