The Dimension of “Mass”

ReferenceA Logical Approach to Theoretical Physics

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. Light quanta had actual substantiality like a gas molecule.

A quantum of light has substantiality. That indicates mass of certain concentration.

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Classical to the Quantum View

Newton’s corpuscular theory viewed light as having substance. The wave theory changed this view to light being energy of a wave traveling through a stationary aether. In wave theory the particles of medium oscillate about a stationary location and do not move with the wave. The energy of the wave is proportional to the square of the amplitude of the wave.

But this view encountered a major setback with Einstein’s theory of Light Quanta. Einstein showed that light approximated particle behavior, therefore, the medium of stationary aether was not required. The light energy was more like the kinetic energy of a particle—a function of mass and velocity. In the case of light, however, that “mass” was determined by a variable “frequency”.

The frequency of light represents a “mass concentration” that becomes denser as frequency increases.

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Quanta as “Mass Particle”

A variable mass concentration based on frequency was a revolutionary concept, because matter has a constant mass concentration in terms of atoms. Einstein had difficulty in accepting the variability of mass concentration. He proposed a mass-energy equivalence as E = mc2 and declared quantum to be an “energy particle”. For Einstein, light did not have mass, because it did not have the same “mass concentration” as that in a material particle.

Einstein concludes in his 1905 paper on light quanta:

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, localized in space, which move without being divided and which can be absorbed or emitted only as a whole.

But a particle can be treated as discrete in space only when it can be viewed as a point particle. A material particle can be viewed as a point particle because its mass can be treated as being concentrated at a center. That is called the center of mass. The uncertainty principle essentially says that a quantum particle does not have a center of mass because its location cannot be pinned down. In other words, as particles are continued to be divided, they lose their center of mass beyond a certain limit, and they merge into each other forming a fluid-like continuum.

Einstein’s conclusion about discreteness of quanta was based on the assumption of “constant concentration of mass” Einstein did not become aware of the inconsistency of his assumption because he conflated energy with mass. It is true that quantum can have discrete energy interactions, and that the concentration of mass could be so low that its significance can be appreciated in energy units only. But it is also true that there can be no concept of energy without an underlying concept of substance.

Unlike matter, quanta has variable “mass concentration”. It is a fluid-like continuum with rapid intrinsic motion.

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Variable Mass Concentration

In matter, mass has a concentration that we find in a neutron or a proton. These particles have a certain volume, but they may be treated as point particles because of their center of mass property. This property arises because of their rigid structure.

Mass is 1840 times less concentrated in an electron that makes the size of the electron about 1840 times larger than the size of the proton. An electron is no longer rigid, it does not have the center of mass property and it flows like a fluid. An electron cannot be treated like a point particle.

Mass is still less concentrated in a photon, and its size may be considered much larger than an electron. It flows more like a fluid without center of mass. Richard Feynman, in his book QED: The Strange Theory of Light and Matter, shows calculations that treats light as such a fluid. Feynman, however, thinks of those calculated values as “probabilities” because he thought of photon as a “point particle”.

Matter, as it loses its rigidity of high concentration, becomes a field of much lesser mass concentration. The field does not have a center of mass. It is fluid with rapid motion. Field is not just a mathematical reality as considered by Maxwell and Einstein. This is an actual reality as visualized by Faraday with his lines of force. There is no limit to which the concentration of mass can be diluted as a field. The ultimate limit may be the gravitational field as “space”.

Current physics does not acknowledge the dimension of “mass” that exists at every location in space due to varying concentrations.

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