Reference: A Logical Approach to Theoretical Physics
In his 1905 paper on light quanta, Einstein starts out by comparing material substance to Maxwell’s “electromagnetic state in space”. He says,
There exists an essential formal difference between the theoretical pictures physicists have drawn of gases and other ponderable bodies and Maxwell’s theory of electromagnetic processes in so-called empty space. Whereas we assume the state of a body to be completely determined by the positions and velocities of an, albeit very large, still finite number of atoms and electrons, we use for the determination of the electromagnetic state in space continuous spatial functions, so that a finite number of variables cannot be considered to be sufficient to fix completely the electromagnetic state in space. According to Maxwell’s theory, the energy must be considered to be a continuous function in space for all purely electromagnetic phenomena, thus also for light, while according to the present-day ideas of physicists the energy of a ponderable body can be written as a sum over the atoms and electrons. The energy of a ponderable body cannot be split into arbitrarily many, arbitrarily small parts, while the energy of a light ray, emitted by a point source of light is according to Maxwell’s theory (or in general according to any wave theory) of light distributed continuously over an ever increasing volume.
The following must be noted here:
(1) The statement “the energy of a ponderable body cannot be split into arbitrarily many, arbitrarily small parts” is from “particles in void” perspective. This is an unverified assumption.
(2) The idea of being ponderable, or substantial, comes from the force that is inherent to the substance. Newton referred to it as vis insita or innate force of matter. Faraday expressed it through lines of force.
(3) Radiation is generally in equilibrium with matter as in the case of black-body radiation. Therefore, we may look at matter and radiation as two substances with different substantial-ness.
(4) The radiation in space, such as light, has momentum and force. Therefore, it qualifies as a substance.
(5) Radiation is not viewed as substance in the particles in void framework. It is viewed as vibrations in a postulated substance called aether.
According to Einstein the Planck’s postulate of “energy is proportional to the frequency of radiation” is not just a mathematical device. It actually refers to the substantial-ness of radiation. He sets up the following model to demonstrate this.
Let there be in a volume completely surrounded by reflecting walls, a number of gas molecules and electrons moving freely and exerting upon one another conservative forces when they approach each other that is, colliding with one another as gas molecules according to the kinetic theory of gases. Let there further be a number of electrons which are bound to points in space, which are far from one another, by forces proportional to the distance from those points and in the direction towards those points. These electrons are also assumed to be interacting conservatively with the free molecules and electrons as soon as the latter come close to them. We call the electrons bound to points in space “resonators”; they emit and absorb electromagnetic waves with definite periods…
This relation, which we found as the condition for dynamic equilibrium does not only lack agreement with experiment, but it also shows that in our picture there can be no question of a definite distribution of energy between aether and matter…
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 thus shows that the energy of radiation is a continuous function in space at low frequencies only. As frequency increases the energy distribution becomes more discontinuous in space.
The following must be noted here:
(6) In his model, Einstein is assuming radiation to be vibrations in aether. Aether is postulated to have fixed substantial-ness.
(7) Einstein’s discovery of quanta required aether to have varying substantial-ness. Therefore, Einstein had to drop the idea of aether the way it was postulated. No evidence for aether was ever found anyway.
(8) Einstein then dealt with the requirement of varying substantial-ness by treating energy vibrations (without aether) mathematically.
(9) Radiation itself, however, may be treated as substance and assigned varying substantial-ness.
In explaining the photoelectric effect Einstein says,
According to the idea that the incident light consists of energy quanta with an energy Rßv/N, one can picture the production of cathode rays by light as follows. Energy quanta penetrate into a surface layer of the body, and their energy is at least partly transformed into electron kinetic energy…
An electron obtaining kinetic energy inside the body will have lost part of its kinetic energy when it has reached the surface….
If every energy quantum of the incident light transfers its energy to electrons independently of all other quanta, the velocity distribution of the electrons, that is, the quality of the resulting cathode radiation, will be independent of the intensity of the incident light; on the other hand, ceteris paribus, the number of electrons leaving the body should be proportional to the intensity of the incident light.
These observations are consistent with experimental results and prove that energy transferred to electrons is proportional to the frequency of incident light and not its intensity. The concept of quanta is thus real. It is not just a mathematical device as was assumed by Planck.
Einstein, therefore, concludes:
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.
The following must be noted here.
(10) Einstein is using the Newtonian “particles in void” framework to assume quanta to be a series of discrete energy particles “localized in space” that are following each other in a line.
(11) From Faraday’s “continuum of substance” perspective, however, quanta are more particle-like only because their substantial-ness has increased. They can be represented by thicker lines of force that are continuous.
(12) Therefore, quanta do not necessarily have to be viewed as discrete particles “localized in space”. Radiation may still distribute continuously over an ever increasing volume. That will affect only its intensity and not the substantial-ness.
(13) The spectrum of increasing frequency provides a spectrum of increasing substantial-ness. This results in the “continuum of substance” from space to matter. We see this occurring inside the atom along the radius from space at its surface to matter as the nucleus at the center.
(14) On the other hand the “particles in void” means only space and matter with no gradient in between. So it applies only to the macroscopic view of matter. The “particles in void” framework is simply a limiting case of the broad “continuum of substance” framework.
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Summary
The current science is based on the logic that there is either particles or void (nothing). Matter (substance) is looked upon as made up of particles. Space is looked upon as made up of nothing. Quantum mechanics is stuck with thinking that particles are made up of smaller particles to which there is a limit. But they can’t define the material, which the smallest particle is made up of.
In his 1905 paper on light quanta Einstein makes the following assumption: “the energy of a ponderable body cannot be split into arbitrarily many, arbitrarily small parts”. Per Newtonian mechanics, energy is the activity occurring in substance. If there is no substance then there cannot be energy.
The idea that energy cannot be split indefinitely means that substance cannot be split indefinitely either. This is where quantum mechanics stops theoretically.
This makes light a vibration that requires a substantial medium (aether) to propagate in. Einstein’s discovery of light quanta requires aether of variable substantiality, because the substantial-ness of quantum changes with frequency. No such aether has ever been found, and so Einstein dropped the idea of aether.
The dropping the idea of aether has left light to be a vibration in the void (pure energy without substantial basis).
Earlier Newton had handled the void with mathematics in his theory of gravity. That led to the problem of “action at a distance”, which is not yet resolved. So, Einstein handled vibrations in the void with some more mathematics, which has given us the general theory of relativity.
NOTE: The problem of “action at a distance” was resolved by Faraday but it was ignored by other scientists who continued with Newtonian mathematical approach. That is what Maxwell did. Einstein did the same.
What is coming in the way of reconciliation between quantum mechainics and general theory of relativity is the original assumption by Einstein: “the energy of a ponderable body cannot be split into arbitrarily many, arbitrarily small parts”.
The answer is that light and other radiation is not just “pure energy” but it is a vibrating substance in its own right. This substance coagulates as the frequency increases. This is the process of quantization. Therefore, the smallest particle of quantum mechanics is made up of quantized radiation.
But this logic, unfortunately, in spite of brilliant explanations of Faraday, has been unacceptable to science.
Quanta is coagulated radiation and not a train of discrete energy particles as Einstein postulated.
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