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On the nature of photon

Alexander I. Korolev,

alex-korolev.jimdo.com

St. Petersburg, Russia

The article considers physical properties of photon as a quantum of electromagnetic

wave in luminiferous medium. An experimental evaluation method for its energy and

mass based on radiation pressure effect was presented. The of “photon amplitude”

concept was introduced, through which energy is represented similarly to quantum

(phonon) energy of elastic mechanical wave. A model of photon as a wave packet in

the medium was considered, which based its volume evaluation. The resulting

equation for energy corresponds to commonly known, regarding the first degree

frequency proportionality, while it is more informative.

St. Petersburg, Russia

03.0217

1. Introduction

A photon was introduced as a quantum (piece) of electromagnetic wave [1]. EM wave as a whole

is described by intensities oscillations. The photons are radiated and absorbed by atoms during

elementary particles interactions, as well as by stand-alone elementary particles moving

accelerated relative to propagation medium (“physical field”).

An analogue of physical field for mechanical waves is atomic and molecular medium. As it is

known, the field in mathematics and other branches is considered as a static structure where

operations may be carried out and movements may occur. There is an old concept in physics for

such conventionally static media of electromagnetic waves propagation, which is the “luminiferous

aether”. It corresponds to “field” concept in a general sense. Electric and magnetic fields in the

“aether” are those only in relation to slow processes. When the sources of the “fields” or finite

propagation velocity are considered, it is more accurate to talk not about the fields, but rather

about flows. Actually, movement and rest are peculiar for all physical phenomena, and it is

important to use these concepts properly. When it refers to underinvestigated substance of space,

it is better to confine to “medium” term. A photon is considered as a quantum of EM disturbance of

luminiferous medium in the article.

2. Energy and mass evaluation method

Basic concept at consideration of any physical phenomenon is energy. Energy is defined as a

measure of bodies motion and interaction and, according to that, divided in two main types:

kinetic and potential. Existing types of electromagnetic waves and flows show luminiferous

medium is endowed with both longitudinal and transversal elasticity. In mechanics, energy density

of elastic oscillations at some frequency can be expressed [2] in terms of oscillating speed v

a

(kinetic part) and pressure amplitude p

a

(potential part) (1).

(1) ε = 2

ρ·v2

a+2

β·p2

a

Here, p

is medium density, β is coefficient of compressibility. The value being measured in practice

is

square pressure. Density of EM wave energy flow is determined by the Pointing vector and,

in case of polarized monochromatic wave is proportional to electric intensity (2).

(2)S=E[ × B] ~ E2

At that, luminiferous medium movement is not considered, thus, kinetic part of energy retires

from sight.

In the other way, the time average value of electromagnetic wave density ε

em

can be evaluated

using the Langevin equation [2] for reflection of plane sound wave from a mirror (3).

(3)εem =P

1+R2

Here, P

is pressure of EM wave against mirror, and R is reflective index. P

and R

are

determined experimentally. To obtain single photon energy E

p

from ε

em

is possible by division

into photons concentration n

within incident collimated beam propagated to the mirror (4).

(4),nEp=n

εem = Nt

ct·s

Here, N

t

is an average number of events of atoms radiation from a source for the time t

directed

to the mirror, experimentally measured. s

is mirror surface. If essentially divergent beam is used,

divergence angle should be taken into consideration in concentration formula.

Photon effective mass m

p

can be obtained by means of measurement of radiation pressure force

against the mirror F.

If the reflective index of mirror is close to 1, then (5):

(5)mp=F t

2cNt

Due to the fact that photon structure is not certain to date, the described method can be

used at first approximation.

3. Photon properties

Let us consider semiclassical theory of electronic orbitals in atom [3]. In the Bohr model, electrons

are considered as spherules orbiting the nucleus. Energy of electron on the n

-th orbit is inversely

proportional to the orbit radius R

n

(6):

(6)En= − kqe

2Rn

Here, k

is the proportionality factor of Coulomb’s law, q is the nuclear charge, e

is the electron

charge. Being considered as a wave, the electron on the orbital is appears to be the de Broglie

wave of certain frequency and wavelength λ

dB

. At that, stable orbitals include a whole number

of λ

dB

, which is described by formula (7):

(7)πRλ2 n= μ dB

Relation of wavelength to frequency is given by the known correlation, which, in

particular, for electron wave on n

-th orbital is as follows:

(8)πωn= 2 un

λdB

Here, u

n

is electron velocity on the orbital. Considering the electron moving along the circular orbit

as a particle, u

n

appears as follows:

(9) un=√kqe

m R

e

n

where m

e

is mass of the electron. Substitution of the wavelength from (7) and velocity from

(9) into (8) results in:

(10)R, ξ ωn= ξ n

−2

3 = μ√me

kqe

Energy of the photon absorbed or radiated by n

-th electron orbital, in the popular theory, equals to

the product of frequency by Planck constant. Thus, according to (10), it will be proportional to

radius raised to power -3/2

. But this does not agree with inverse proportionality in (6), which

indicates a problem in the theory. In quantum mechanics, the problem has no solution, but

becomes “uncertain”.

In mechanics, the time average electromagnetic density of elastic waves can be expressed in

terms of frequency [4] as per formula (11):

(11)ρaωε = 2

1 2 2

Here, a

is medium particles oscillation amplitude, and ω

is cyclic frequency. Elastic mechanical

wave quantization has physical sense if a single quantum (phonon) corresponds to elastic

vibration of atom, molecule or some agglomeration of them. At that, energy of the phonon can be

obtained by division of ε by the phonons concentration in a wave. Therewith, proportionality to

squares of amplitude and frequency will be maintained.

Dependence on amplitude

It is known from mechanics that, for resonance pulse excitation at the certain frequency (tone),

not only pulse period, but its amplitude (of displacement or acceleration) have meaning as well.

With increase of the amplitude, besides primary tone, other frequencies of object free oscillations

begin to become excited too. The same should take place for electromagnetic waves. Atomic

orbitals are some kind of resonators which absorb and emit photons at proper frequencies. The

value of electron jump from the one resonator to another shall depend not only on frequency of

absorbed or emitted particle of EM wave, but also on its amplitude.

Dependence on frequency

Mechanical resonance characteristics, as well as frequency distributions of sound attenuation

factor, are similar by shape to black body radiation spectrum. This points to the fact that the

electrons in atoms absorb and emit quanta of EM radiation within a certain frequency range

similarly to the way of whole atoms absorb and emit phonons. Even if one considers elastic waves

in free electron gas, i.e., electric current, there may be found analogous resonance characteristics

and frequency distributions for scalar impedance.

This indicates totality of physical properties of different nature waves. Resonance absorption

does not occur for waves of too low or high frequency. The medium absorbs them due to other

causes. For electromagnetic waves at low frequencies, the degree of absorption is determined by

electrical conductance of shield (electron mobility in its medium), and by nuclei massiveness and

their concentration at high ones. At medium frequencies, absorption and radiation are

characterized by structure of the electronic orbitals. In the last case, the photons may be referred

to as “atomic”.

The described similarity of experimental data for different waves allows obtaining of the following

formula for photon energy E

p

(12):

(12)m a ωEp=2

1

eth

2

p2

Here, m

eth

= ρ

eth

V

p

is the mass of luminiferous medium with density ρ

eth

within photon volume V

p

, and a

p

is photon amplitude. When considering the processes of radiation or absorption,

related to interorbital transfers, ω = ω

n

.

For the acoustic wave, correlation of square oscillations amplitude with average density of

energy is given by [3] as in (13):

(13)εa2=2v2

ργ ω

2 2

Here, v

is phase velocity, γ

is the ratio of heat capacity at constant pressure to heat capacity

at constant volume. Correlation of ε with excessive pressure amplitude (14):

(14)ε = 2ρ

(Δp)

m

2

Using similarity of (2) and (14), one can find that density of polarized, in-phase and

monochromatic flux of electromagnetic energy shall be as follows (15):

(15)ωS~ap2 2

Generally, the luminous flux consists of unbonded wave pieces- quanta, it is similar to sound flow

from the source with shape variable in time and space. At that, the Pointing vector makes sense

only for individual quanta fields.

Photon volume depends on the shape and internal structure. Let us consider the model of photon

as a wave packet of EM disturbance in luminiferous medium. Spatial distribution of electric and

magnetic intensities in the photon determine its structure and internal medium movements. In this

regard, photon amplitude makes sense of average by volume peak value of subphoton medium

particles displacement in perpendicular direction. Square amplitude determines effective cross

section area of the photon. For “atomic” photon near its source this should be . Hereafter, ifRap~ 2 n

collimation conditions are absent, the photon shall diffuse, reducing its amplitude. Longitudinal size

of photon

is determined by the number of wavelength radiated per emission act. At this time the sourceλκ

can shift, spin, and be influenced by neighboring atoms. Shape of the photon, therefore, may be

significantly distorted. So, photon volume can be evaluated as follows (16):

(16)Vλa p~ κ 2

p

Expressing wavelength by terms of frequency and velocity of speed c

, we obtain (17) for photon

energy:

(17)ρca ωEp~ κ eth

4

p

This expression agrees with popular formula regarding the first degree frequency proportionality.

But at the same time, there remains some inconsistency described at the beginning of the

paragraph. It is explained by the fact that the formula is applicable only at sufficient distance from

an atom when photon has already developed. During electron transfer to other orbital, only a part

of energy is used for photon constituting. The other part can be used by the nucleus, transmitted

to adjacent orbitals, as well as to luminiferous medium as so called “zero-point oscillations”.

Amplitude of oscillation speed for the particles of luminiferous medium in photon can be found as

follows (18):

(18)aueth = ω p

4. Conclusion

Providing the photon energy defined as per method from para. 2 for quasi-plane, polarized,

monochromatic light wave, its amplitude can be obtained by the formula (17). Coefficient κ

may be obtained as the ratio of photon emission duration to its period. The duration for

“atomic” photon corresponds to the time of interorbital transfer of emitting electron. The

density of luminiferous medium can be taken from astrophysical calculations of dark matter

density. If the experiment succeed in creation of in-phase photon beam and direct

measurements of electric intensity amplitude therein, it will be possible to verify correlation

(15) for density of EM energy flux and to find the proportionality factor.

Knowing the volume of photon, it is possible to evaluate mass of luminiferous medium m

eth

therein which should be distinguished from effective mass m

p

.

It is worth to describe the features of photons movement. At the moment of occurrence, they

escape in the direction of compelling reason activity. For example, in case of forced

emission, originated photons are codirectional with the absorbed ones. If the emission is

“spontaneous” (caused by disturbances in luminiferous medium) or thermal, critical impact on

excited electron orbital can appear from any direction. Therewith, particle yield from atom will

be equally probable in all directions. Then, during propagation, the photon can change its

initial direction due to interaction with obstacles (diffraction), or along with luminiferous

medium, affected by gravitational field. At that, it still can be rotating, which is manifested by

experimental data on polarization. In the cause of optical vortex [6] photons move helically

around the propagation direction.

The photons vary both by frequency and size. Fusion of photons of the same frequency can

result in either damping, or increase of the amplitude (interference). Photon extension ability

during propagation accompanied by amplitude decrease indicates the ability of its division into

parts being new photons. Multitude of photons in vicinity form large electromagnetic wave.

Besides the electromagnetic photons, electrodynamic and magnetodynamic [7] ones, as parts

of corresponding varying fields (flows), can be distinguished. It is difficult to create more

accurate theory of photon until its structure is not known vaguely, and its basic physical

parameters, such as mass, amplitude, size and, of course, energy, are not measured. This

article throws a “particle of light” upon the physical properties of photon.

References

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visited Feb. 26, 2017).

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