Particle, Quantum and Density

ReferenceA Logical Approach to Theoretical Physics

We all are familiar with the idea of a particle of matter. At chemical level the smallest particle is considered to be an atom. An atom is a particle of matter. It has mass.

The idea of quantum was born out of the study of black body radiation in an effort to explain the radiation spectra.


Black Body Radiation

The above graph shows the relationship of Spectral radiance to wave-length of the radiation. Spectral radiance is the radiance of a surface per unit wavelength. It is also called “specific intensity”. It provides the specific rate of energy transfer.

The Classical theory assumes that vibrational modes can increase infinitely. It predicts an energy output that diverges towards infinity as wavelength approaches zero. Measurements of the spectral emission of actual black bodies reveals that the emission agrees with the classical theory at large wavelengths but diverges at low wavelengths; reaching a maximum and then falling, so the total energy emitted is finite.

Max Planck found a mathematical expression fitting the experimental data satisfactorily. But he had to assume that the energy of the oscillators in the cavity could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. In other words, energy could be released only in packets (quanta) that were proportional to the frequency. Such quanta become fewer at high frequencies (low wavelengths), and, as a result, spectral radiance decreases.


Maxwell’s omission

Fifty years prior to Planck, Faraday had expressed in his lecture on Ray Vibrations that radiation could be expressed as vibrating lines of force. Such lines of force could increase in numbers (intensity), but also in density. The energy output was determined by both intensity and density. Maxwell modeled Faraday’s lines of force (or field) mathematically to come up with his theory of Electromagnetism. Maxwell, however, accounted for the intensity only. He omitted the density because he did not associate any substance with the lines of force.


The Quantum

These lines of force are not just mathematical entities as treated by Maxwell. They not only have substance, but also have densities. Per Classical theory the energy output per vibrational degree of freedom is the same. If the energy output depends on both the number as well as the density of the lines of force, it is easy to see that intensity shall decrease as density increases. The density is proportional to the frequency. We may relate Planck’s quantum to the density of radiation.

Radiation is a substance that has density. Planck’s quantum can be explained in terms of density of radiation.

As density, the quantum is a continuum, similar to frequency. It does not occur in jumps.


The Photoelectric effect

In explaining the photoelectric effect Einstein says,

“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 ever increasing volume affects the intensity of but not the density, which depends on the frequency of light. This density, like mass, contributes to the momentum, which expels the electron. This density (quanta) is the characteristic of light, which is uniformly spread out in space. It is not “localised in space” as assumed by Einstein.

Light is thinned out in space (less intensity), but it maintains the same density (quanta) throughout the space.

Quantum does not occur in discrete “jumps” in space either. Quantum provides the dimension of density for the substance of radiation.


The Quantum Particle

As outlined in Einstein’s 1905 paper on light quanta, a light quantum has particle-like property. But this characteristic of particle comes from density and not from any discrete appearance.  Just like a matter of different densities can have discrete appearance of any size, similarly, radiation of different densities can have discrete appearance. This discrete appearance may be called particle, but it does not have a fixed size.

Compared to matter, radiation has extremely small density. If you take a “point particle” of matter and spread its mass over several square miles, it would appear as a field of certain minimal density. This is a quantum. Thus a quantum is unique only in terms of its density, and not in terms of its discrete size.


Wave-Particle Dilemma

The key difference between a matter particle and a quantum particle is that a matter particle has a structure, and, therefore, it has a center of mass.  A quantum particle, on the other hand has no structure. It is kind of sloshing around, and the disturbance within it is traveling at the speed of light. So it has no center of mass.

Therefore, a quantum particle behaves like a mass particle around obstacles that ar much larger than it. But it acts like a wave around obstacles that are smaller than it. This representation puts to rest the wave-particle dilemma.



Light is a substance. As a substance it has density. It does not require an external medium (aether) to travel because light is its own medium. The light quantum refers to the density of light, which is proportional to its frequency.  

The interesting fact is that mathematics can be accurate, while it may have inaccurate interpretation. An accurate interpretation of mathematics shall be consistent with reality. If certain mathematics cannot be interpreted then the understanding of the underlying phenomenon is missing.


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