A quantum was, at first, proposed as a mathematical concept by Max Planck that explained the distribution of the Black body radiation. It was a groundbreaking concept in the sense that it expressed energy as a function of frequency instead of amplitude of the waveform.
Einstein, in his groundbreaking paper on Light quanta, was able to show that the entropy of monochromatic radiation follows the same rules as the entropy of a perfect gas. Einstein thus showed that Planck’s postulate of energy quanta was more than a mathematical device. It was real in a physical sense.
In the classical view, wave represents a motion traveling through a medium. In this view the particles of medium simply oscillate about a stationary location and do not move with the wave. But this is not so with light. Einstein showed that there was no stationary aether in which light moved as a disturbance. Instead light approximated the motion of the particles of gas in which the particles themselves move. This meant that light was its own substance that moved like a wave.The frequency of light represents its density as a substance. The substance of light becomes denser as its frequency increases.
Energy of light is a function of its frequency because light is a substance that is in motion. Light is not a classical wave that represents pure motion in a medium.
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The Model for a Quantum Particle
A material particle is like a “point particle” with all its mass concentrated at one point. A material object is made up of discrete point particles rigidly structured relative to each other. Because of this rigid structure, a large material body, like the earth also has a center of mass.
The uncertainty principle essentially says that the location of a quantum particle cannot be pinned. In other words, a quantum particle has dimensions. At the same time a quantum particle is not structured because it does not have a center of mass. But it has a density. We shall refer to this density as “mass density” instead of energy density to emphasize that light has substance that is in motion.
If we assume a point particle to have the mass and dimensions of the nucleus of the hydrogen atom, then an electron of the same mass shall be about 1900 times the size of the nucleus (about the size of the hydrogen atom), and a photon of the same mass shall be 270 million times the size of the hydrogen nucleus. So, it is incorrect to think of a quantum particle as a point, or rigid particle like that of matter.
As explained in the chapter Mass Density and Motion, the electronic region is in rapid motion around the nucleus because of its low density. An electron roughly the size of an atom shall serve as a model for a quantum particle. But a photon as a quantum particle shall be millions of time larger in size compared to an electron with corresponding reduction in its density and increase in velocity.
The quantum particles do not have individual centers of mass. Therefore, they are not discrete like material particles; instead they form a fluid like continuum of substance. This substance moves very rapidly with wave-like characteristics.
The lower is the density of the quantum particle, the larger is its size and the greater is its velocity. The quantum particles combine to form a fluid like continuum with wave-like characteristics.
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Limitation of Quantum Mechanics
In the absence of a realistic model of a quantum particle, quantum mechanics has become unreal and mathematically abstract.
In his 1905 paper on light quanta, Einstein makes the assumption: “the energy of a ponderable body cannot be split into arbitrarily many, arbitrarily small parts”. In other words, Einstein assumes that the solidity of a particle is fixed in terms of its density. It cannot be cut into smaller particles indefinitely, while its density remains fixed.
The truth is that the solidity of a particle can become less solid without limit.
In the essay, Relativity & Problem of Space, Einstein interpreted Newton as follows,
But in this [Newton’s] theory, acceleration can only denote “acceleration with respect to space”. Newton’s space must thus be thought of as “at rest”, or at least as “unaccelerated”, in order that one can consider the acceleration, which appears in the law of motion, as being a magnitude with any meaning.
But acceleration is a change in velocity of an object, which relates to its density. Space cannot be at rest as it has no substance. If the density of space is zero then its velocity is infinite.
This confusion of basic concepts essentially derailed quantum mechanics theoretically.
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