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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
1. Sivukhin D. V.
Obschiy kurs fiziki [General guidelines in physics]. — Moscow. — Vol. IV. Optika
[Electricity and magnetism. Waves. Optics].
2. Entsiklopediya fiziki i tekhniki [Physiscs and Technics Encyclopaedia] www.femto.com.ua.
3. Savel’ev I. V. Kurs obschey fiziki [Course in General Physics] Study guide. In 3 vols., Vol. 3.
Kvantovaya optika.
Atomnaya fizika. Fizika tverdogo tela. Fizika atomnogo yadra i elementarnykh chastits
[Quantum optics. Atomic physics. Solid-state physics. Nucleus and elementary particles
physics]. — Moscow.; Nauka, Main editorial office for physical and mathematical literature,
1987.
4. Savel’ev I. V. Kurs obschey fiziki [Course in General Physics] Study guide. In 3 vols., Vol. 2.
Elektrichestvo i magnetizm. Volny. Optika [Electricity and magnetism. Waves. Optics]. —
Moscow.: Nauka. Main editorial office for physical and mathematical literature, 1988.
5. Shidlovsky A. I. Atom vodoroda - samii prostoi iz atomov. Part 1. — Minsk: VEVER. 1997.
6. Optical vortex, https://en.wikipedia.org/w/index.php?title=Optical_vortex&oldid=754569931 (last
visited Feb. 26, 2017).
7. Korolev A. I., Magnetodynamic waves in the air, JMMM, 327 (2013) p. 172–176.