How Can the Photons Tolerate Each Other?

Tesla TOE Member Quest Prime Numbers

Light is among the most complicated of all the mysterious phenomena in nature, so complicated that the deciphering of light will certainly be an “open sesame!” to a more progressive science and technology.

This writing is an expedience for the purpose of violating the wave-energy theory of light by pure mathematics, taking into consideration the opinions I have set forth in an article titled "Interrelation of Standards and Industrial Development". The afore-mentioned article has been published online at the ToeQuest Research Library, http://www.toequest.com/library.

Diffraction phenomenon is perhaps the most convincing evidence that light has a wave nature, because it has been explained to some extent by the wave theory of light. The diffraction pattern is formed when light from a distant point source vertically falls on a razor blade or on a circular aperture punched on an opaque plate. The writer believes the diffraction phenomenon (or the separation of light from darkness) could be justified by the photon-particle theory of light. In other words, I want to show that sometimes the cutting edge of reality is stranger than fiction.

The photons or the quantum of energy, as a natural phenomenon with too large population, must have a natural behavior. Therefore, the quanta of energy, like many random variables that occur in nature, behave as though their distribution is normal or approximately normal. Because of this, here we use the Normal, or Gaussian, Distribution Law in the probability theory as our mathematical model in which the random variable is the energy of photon.

The normal distribution is of theoretical importance because it can be used to approximate the distribution of many random phenomena.

The sharp edge of a razor blade, or something like that, is a simulation of large quantity, but finite, of geometrical point sources forming a straight line. Along this line there isn't any distance between the adjoining sources. Consequently, the diffraction phenomenon appears only in the direction perpendicular to the blade's edge, on a screen parallel to the surface of blade.

Let us suppose that the subject of our investigation is the photons of a monochromatic light in the range of E=Ē ± 3σ diffracted from the edge of a blade, as a linear source, and fall on the screen. We are going to study this random variable (quantum of energy) between Emin and Emax which includes 99.73% of the photons.

Emax - Emin = E+3σ - E-3σ = 6σ = TE = Tolerance of random variable
(Emax + Emin)/2 = Ē = Mean value (Mathematical Expectation)
σ = Standard Deviation

To prevent any misunderstanding arising from the use of synonyms in different regions of language, it is worthy of mention that here the phrase "Tolerance of random variable" is the same as "Uncertainty of random variable". To put it more clearly, TE is that very uncertainty in quanta of energy with the mean value equal to Ē, ∆E=6σ.

Here another hypothesis could be raised for explaining the diffraction phenomenon.

Those photons having an energy more or less about Ē are compatible with each other and form their own collection around Ē. In fact, these photons with the largest population belong together and the average of their energy is equal to the most normal level. These kinds of photons can be categorized as the group "Cipher".

Emin = E-3σ E-2σ E-1σ Ē E+1σ E+2σ E+3σ = Emax

Quantum of Energy

Some photons deviate from the normal level so that the average of their energy is one Standard Deviation more than the normal level (mean value). These photons form their own collection around E+1σ and have a population less than the group Cipher. They belong to the group "P1".

E+1σ = Ē + 1σ

But, there exist some other photons the average of their energy is one Standard Deviation less than the normal level. They belong to the group "M1" and gather around Ē-1σ. The population of this group is theoretically the same as that of the group P1.

E-1σ = Ē - 1σ

This principle is also valid for the formation of the groups P2, M2, P3 and M3. The average deviation of these groups from the Mathematical Expectation is +2σ, -2σ, +3σ and -3σ, accordingly. The distribution of all seven groups singly and jointly is normal.

Beyond the range of tolerance (TE), the population of photons is so small which can be discussed later.

The pattern of diffraction phenomenon could be more evident when two parallel linear sources with an optimum distance to be used. It can be simulated by a slit of about 0.15 mm width in an opaque plate. In this case, the diffraction patterns of both linear sources inversely coincide to and normalize the effect of each other.

When the diffraction phenomenon appears by a circular aperture, the pattern is radial. In this case, the cutting edge of aperture plays the role of a ring-shaped source of light.

This analysis shows us what has been known (measured) as the speed-of-light limit (c = 300,000km/s) is the speed of those photons having an energy very close to the mean value. Because, Ē is a Mathematical Expectation only and it never happens. Furthermore, in astronomical dimensions the probability of even these photons to travel in straight line is zero.

The God not only does play dice, but has also created it.