(23.1)
23. MASS AND ENERGY
The best known and the most used part of the theory of relativity,
which in essence does not belong to this theory, refers to the field of physics
which deals with the questions of mass and energy of bodies, as well as
the questions of mutual relation of mass and energy. Many physicists strongly
believe that the correctness of the theory of relativity is proved in the
best and most convincing way just in this sphere.
The theory of relativity and its author became as popular as they are
thanks to the realization of some possibilities predicted by this "theory".
These unusual predictions referred to the possibility of obtaining huge
amounts of energy through transforming mass into energy, which was later
realized in nuclear explosions and nuclear reactors. With the explosion
of the first nuclear bomb the popularity of Albert Einstein and his theory
increased enormously. Many, those poorly informed, unjustifiably believe
Einstein to be a creator of atom bomb.
In classical physics mass and energy are two completely different
notions, which cannot be related. According to the theory of relativity mass
and energy are one and the same, but in different forms of existence. Mass
can be changed into energy, and likewise energy into mass. If a body gains
energy, then its mass is increased, and if it looses energy its mass decreases.
Hence, mass is greater when a body is moving than when the body is at rest,
it is greater when a body is heated than when it is cold, etc.
23.1 The classical way of determining the masses
of an electron in motion
The study of electrons in motion established, first in theory, and
later by experiment, that its mass changes depending on its speed. Long before
the theory of relativity, in his theory on electromagnetism, published
in 1892, Lorentz laid the greatest significance on the question of the
interdependence of an electron's mass and its speed. While moving, the
electron as an electrically charged particle creates an electromagnetic
field which surrounds its. The faster the electron moves, the greater the
resistance of that electromagnetic field to further increase of electron's
speed. The effect is the same as if with the increase of speed the electron's
mass increases. That is why that mass was named "electromagnetic mass".
In 1901 Kaufmann [W. Kaufmann, Gesell. Wiss. Gött. Nachr.
143, 291, 1901.; W. Kaufmann, Physik Zeitschr. 4, 55, 1902.]
experimentally confirmed that an electron's
mass increases with the increase of its speed. Using an electrical field
to accelerate the motion of an electron and an electric field as also a
magnetic field to divert the electron from its direction of motion, Kaufmann
found that the mass of the electron increases in relation to its speed
and that the electron has two masses, the so called transversal mass and
the longitudinal mass. These findings caused a great surprise among physicists
since, to that point, only one mass was known. The longitudinal mass of
the electron resists increases in velocity in the direction of its motion
as mass does in classical physics. The transversal mass of the electron,
however, resists the deviation of the electron from its direction of motion.
In classical physics there is only one mass. For example, in rotary
motion a body will tend to move at a tangent to the circle, because that
is, at every moment, its direction of movement. However, centripetal force
compels it to move in a circle. Centrifugal force and also centripetal
force are the result of the resistance of the transversal mass to move
in a circle. At first sight it seems that every body has two masses, longitudinal
and transversal. In the case of an ordinary body, however, these two masses
are of the same magnitude, so that the body will react equally to increases
in the velocity of motion and the velocity of deviation. As a result only
one concept of mass existed until Kaufmann made his measurements. Afterwards
the concepts of longitudinal and transversal mass appeared.
Abraham [M. Abraham, Ann. d. Physik, 10, 105, 1903.]
was the first to derive equations for longitudinal and
transversal mass. According to him the longitudinal mass of an electron
was given by the equation
|
(23.1) |
and the transversal mass by equation
 |
(23.2) |
where 
is the mass of the electron at rest and
the speed at which an electron moves. For very small speeds
, in relation to light speed, according to the Eqs. (23.1) and
(23.2), the masses 
and 
become equal to
, and with the increase of speed
up to the light speed that masses become infinitely large.
Abraham's theory, that is the values for the electron's mass calculated
according to the Eqs. (23.1) and (23.2) matched well with Kaufmann's experimental
results.
23.2 The relativistic way of determining the masses
of an electron in motion
Relativistic equations for the mass of a moving electron have been
derived, up to now, in different ways, and have been published in many journals
and books. All of those derivations, however, have some shortcomings and,
as a result, cannot be accepted without great reserve.
23.2.1 Lorentz equations for the masses of an electron in motion
As well as the transformation of coordinates and the hypotheses on the
contraction of a body and the dilation of time, Lorentz also proposed a
hypothesis on the deformation of the spherical shape of an electron in
motion. According to this hypothesis the dimensions of the sphere will
shorten in the direction of its motion. On this basis he derived equations
for longitudinal and transversal mass which were published [H. A. Lorentz,
Electromagnetic phenomena in a system moving with any velocity smaller than that of light,
Proc. Royal Acad. Amsterdam, 6, 809, 1904.; H. A. Lorentz, Ergebnisse und probleme
der elektronentheorie, Vortrag gehalten am 20 Dezember 1904. im Elektrotechnicshen
Vein zu Berlin] in 1904.
His equation for longitudinal mass is
 |
(23.3) |
and for transversal mass
 |
(23.4) |
Lorentz Eq. (23.4), wrongly attributed by many to Einstein, is accepted
as the general relativistic equation for the calculation of the mass of
a moving body, without any indication that it was derived for the transversal
mass of a moving electron.
Both of Lorentz equations have been confirmed by numerous experiments,
but their derivation is still controversial. Their derivation is based
on the existence of the ether, but the ether has been rejected. As a result,
many papers have been published on the derivation of the relativistic Eq.
(23.4) for the transversal mass of an electron in motion. Some scientists
have used Einstein's theorem on addition in the derivation of this equation.
But such a derivation cannot be accepted since the theorem on addition
is not correct, as was proved in chapter 19 of this book.
23.2.2 Sommerfield's derivation of the equations for the masses
of an electron in motion
Sommerfield's derivation of the relativistic equations for the masses
of the electron in motion is interesting and will be quoted in it's entirety.
Quotation: "Here we shall only investigate the changes that we
have to make in the concept of the fundamental quantity 
,
the momentum, as a result of our new relativity principle.
We have called 
a vector. This means that
the three components of transform just like the coordinates
themselves [i.e., the components of the radius vector 
] in a change
of the system of coordinates. We therefore say that
is covariant to 
.
This is valid only from the viewpoint of the Galilean transformation,
where the time is regarded as absolute. From the viewpoint of the Lorentz
transformation the radius vector is a four-component quantity, a four-vector
| (15) |  |
(23.5) |
Our relativistic momentum will similarly have to be a four-vector,
i.e., must be covariant to 
, if it is to have a meaning in
relativity theory. We arrive at this four-vector in the following manner:
a) (15) being a four-vector, the coordinate distance between two
neighboring points
| (16) |  |
(23.6) |
is also a four-vector.
b) The magnitude of this distance is certainly invariant under a
Lorentz transformation. Apart from a factor 
it is given by
| (17) |  |
(23.7) |
We follow Minkowski in calling 
the element
of proper time; in contrast to 
it is relativistically
invariant. We shall factor out in (17) and introduce
the ordinary velocity of three dimensions, to obtain
| (17a) |  |
(23.8) |
c) Division of the four-vector (16) by the invariant (17a) yields another four-vector; we call it the four-vector velocity
| (18) |  |
(23.9) |
d) Earlier we derived the momentum vector
by multiplying the velocity three-vector by a mass 
independent of the reference frame. We shall similarly deduce the momentum four-vector
from the four-vector (18) by multiplication by a mass factor
independent of the frame of reference. We shall call this mass factor the rest mass
and obtain
| (19) |  |
(23.10) |
It is proper to call the quantity in front of the parenthesis the moving
mass (since it reduces to the rest mass for 
= 0), or simply the
mass. We therefore assert that
| (20) |  |
(23.11) |
This expression was first derived by Lorentz in 1904 under very special
assumptions (deformable electron). The derivation from the principle of
relativity makes such special assumptions unnecessary. Eq. (20) has been
confirmed by many precision experiments with fast electrons. Together with
optical experiments, notably that of Michelson and Morley, it forms the
basis of the theory of relativity." [A. Sommerfeld, MECHANICS, Lecture on Theoretical
Physics, vol. I, p. 14 - 15 and 30 - 31] End of quotation.
From the above we should note the following. The derivation gives only
one Eq. (20) (following the numbering of equations on the left side in
the quoted text) for the mass, which must mean that the electron in motion
has only one mass, like an ordinary body in classical physics, and not
a longitudinal and transversal mass as Kaufmann's experiments indicated.
The equation is derived in principle and not in detail, so that it cannot
be checked its correctness.
The following quotation from the same book will clarify somewhat
more on the subject of the mass of an electron in motion.
Quotation: "Here the variation of mass as a purely internal
affair of the electron; there is no question of any momentum gained from or lost to the
surroundings. The equation of motion is therefore 
,
i.e., in view of (20)
| (6) |  |
(23.12) |
Let us first consider the rectilinear motion of an electron
acts longitudinally, that is, in the direction of
, so that 
and
.
We shall change Eq. (6) to the form
"mass · acceleration = force",
a customary procedure in the early part of the century, though unnecessarily
complicated. To this end we carry out the differentiation on the left
| (6a) |  |
(23.13) |
Now 
so that 
and hence
. Consequently Eq. (6a) becomes
| (6b) |  |
(23.14) |
The longitudinal mass multiplying the acceleration 
is therefore
| (7) |  |
(23.15) |
If, on the other hand, acts transversely, i.e.,
normal to the trajectory, only the direction, not the magnitude of the velocity
is altered. In that case 
is zero; (6) simply yields
 |
For this reason one introduced at the time a transverse mass different from the longitudinal mass and given by
| (8) |  |
(23.16) |
In view of these complications we emphasize that the above distinction
between two kinds of masses becomes unnecessary if we use only the rational
form (6) of the equation of motion." End of quotation.
In connection with this quotation we can conclude the following:
a) As distinct from the first text quoted the existence of the
longitudinal and transversal mass of an electron is confirmed.
b) bearing in mind that 
and if
= 0 then
must also be equal to 0. Therefore the derivation of Eq. (8) for transversal
mass is not correct.
c) the transversal force is equal to the product of the transversal
mass and the transversal acceleration, but not the product of the transversal
mass and the longitudinal acceleration, as stated in equation
 |
since in this equation 
. Therefore this equation would read
 |
(23.17) |
and is valid only on condition that 
. When this condition is
not satisfied we cannot determine the longitudinal or transversal mass.
For example, in case of 
we do not know which is the transversal
velocity and which is the longitudinal velocity. In that case Eqs. (23.3)
and (23.4) for the longitudinal and transversal mass, which are different,
do not make sense.
23.2.3 Einstein's derivation of the equations for the masses of an electron
in motion
In his first paper on the theory of relativity [2] from 1905, under
the title "The dynamics of a (weakly) accelerated electron" Einstein derived
relativistic equations for determining the mass of an electron depending
on its speed. He repeated this derivation in the paper [5] in 1907 under
the title "The derivation of equations of motion for a (weakly accelerated)
material point or electron". In both cases the derivations of these equations
are incorrect, both from the standpoint of physics and mathematics. A reader
can not be expected to accept these claims. Therefore it is necessary to
quote both mentioned derivations with commentary, so that the reader can
see for himself that the relativistic way of derivation of equations for
electron's mass is unacceptable, as are the relativistic equations according
to which that mass is calculated.
Quotation (from the paper [2] published in 1905):
"§10 THE DYNAMICS OF A (WEAKLY ACCELERATED) ELECTRON
Let there be a point particle with the electric charge
(in further text called "electron") moving in an electromagnetic
field; on the law of its motion we can assume the following.
If the electron is at rest in the course of a certain time interval,
then in the next time element, the motion of the electron, as long as it
is slow, will be described by the equations
 |
(23.18) |
where 
, 
and 
are the coordinates of the electron's position, the mass of
electron and 
, 
and
the vectors of the electric field.
Further, let the electron in the course of a certain time interval
have the speed . Let us find the law by which the electron moves
in the time element immediately after that time interval.
Without limiting the whole of thinking we can allow and indeed we shall
allow that in that time, when we start our observation, our electron is
found at the coordinate origin of the system 
and that it moves
along the -axis, at speed .
It is clear that in such a case, in the stated time interval (
= 0)
the electron is at rest in relation to the coordinate system 
,
which moves parallel to the -axis at a constant speed
of .
With earlier made assumptions in accordance with the principle of
relativity it follows that the equations of electron motion, observed from the system
, in the course of time, immediately after
= 0 (small values of ) have the form
 |
(23.19) |
where the marked magnitudes 
, 
,
, 
, 
,
refer to the system . If we take that
with 
must be 
these will be
the correct formulas of transformation from §3 and §6
(the transformation of coordinates and on that basis the transformation
of Maxwell's equations for vacuum. Note by M.P.) and therefore the following
equations will be valid
 |
(23.20) |
where 
, 
, 
form vector of the magnetic field and 
.
With the help of these equations we shall perform the transformation
of the given equations of motion from the system
to the system and we shall obtain
| (A) |  |
(23.21) |
Relying on the usual way of reasoning let us determine the "longitudinal" and "transversal" mass of an electron in motion. Let us write the Eqs. (A) in the following form
 |
(23.22) |
and remark firstly that 
, 
,
are the components
of the ponderomotor force, which affects the electron, wherefore these
components are analyzed in the coordinate system, which, at a given moment,
moves together with the electron and at the same speed as the electron.
(That force could be measured by spring weight, which is at rest in that
system). If we name that force simply "the force which affects the electron"
and keep the equation (for quantitative values)
 |
and if we further establish that we must measure the acceleration in
the system , which is at rest, then from the earlier shown equations
we get
 |
(23.23) |
 |
(23.24) |
Of course we shall get different values for mass in different determination
of force and acceleration, because when comparing different theories of
electron motion one should be very careful. We stress that these results
in relation to mass are also correct for neutral material points as well,
since such a material point can be, by joining with any small charge, changed
into an electron (in our sense of the word).
Let us determine the kinetic energy of the electron. If the electron,
from the coordinate system with an initial speed 0, moves all
the time along the -axis under the influence of electrostatic
force , it is clear, that the energy taken form electrostatic field
will be equal 
. Since the electron is slowly accelerated and as a
consequence of that it need not emit energy in the form of radiation, then
the energy taken from the electrostatic field must be equal to the energy
of the electron's motion. Taking into account that in the course of the
whole studied process of motion the first of the Eqs. (A) is valid, then
we get that
 |
(23.25) |
With 
the value of 
becomes, in that manner, infinitely large. As with the previous results, the same is here,
the speeds cannot be larger than the speed of light. This expression for kinetic energy
must also be valid for any mass for the earlier given proof." End of quotation.
In the paper [5] from 1907 Einstein again derives equations of electron
motion, as in the above quoted paper, but with some further, more detailed
explanations, which did not appear in the 1905 paper, which are also incorrect,
and therefore we shall quote that paper as well.
Quotation (from the paper [5] published in 1907):
"§8 THE DERIVATION OF EQUATIONS OF THE MOTION OF A (WEAKLY ACCELERATED) MATERIAL
POINT OR ELECTRON
If we take an electromagnetic field in which a particle with electric
charge (in further text called "electron") moves then we can
assume the following on the law of its motion.
If the electron in a given moment of time is at rest in (un-accelerated)
system , its future motion in the system
will then be in accordance with the equations
 |
(23.26) |
where , ,
are the coordinates of the electron in the system ,
and is a constant which we shall call
the electron's mass.
Let us introduce system
which moves relatively to
the same as in our previous analysis and let us transform our equations
of motion with the help of transformation formulas (1) and (7a) [Eq. (23.20) in this book.]
(The transformation of coordinates and on that basis the transformation
of Maxwell's equations. Note by M.P.). The first of these formulas in our
case has this form
 |
By introducing 
, etc. from these equations we get
 |
(23.27) |
 |
(23.28) |
By introducing these expressions in the earlier given equations, by
putting 
, 
= 0,
= 0 and at the same time substituting ,
, by the formulas (7a) we get
 |
(23.29) |
These equations are the equations of electron motion when at the studied
moment of time , = 0,
= 0." End of quotation.
So, the derivation of equations of electron motion is the same as in
the pervious paper with an attempt to explain how are obtained Eq. (23.22) that is Eq. (23.29)
via transformation of coordinates. However, that explanation is also incomplete
and wrong.
23.3 Objections to the Einstein's way of deriving equations for masses
of a moving electron
With a careful analysis of the quoted papers, which refer to the mass
and kinetic energy of a moving electron, every mathematician and physicist
can see that there are inconsistencies and mistakes in the derivation of
the equations. Some of these mistakes are so big that they make the derivation
of equations unacceptable. The derived equation for the transversal mass
of a moving electron is also unacceptable. In short, it is unacceptable
that a physicist, as far as physics is concerned, or a mathematician, as
far as mathematics is concerned, can make such mistakes. The impression
is that those mistakes, in the equation's derivation, are made deliberately
so that the final result of the derivation could be a desired equation.
Objections to Einstein's derivation and derived equations in the
earlier quoted papers are the following:
a) Eqs. (23.18) do not describe the motion of an electron, as it is
claimed. They are not correct, because in the equation derivation it was
wrongly asserted that the electron mass was a constant value,
while it is well known that electron mass is a variable value dependent
of the speed of its motion.
Besides, in all equation derivation, it was assumed that electron
motion is slow in relation to the speed of light, as if it was a case of deriving
classical equations, and in fact relativistic equations were derived, which
should describe the motion of electrons at high - relativistic speeds,
close to the speed of light.
b) The Eqs. (23.19) are also not correct. These are not equations of
electron motion relatively to the system , as it is claimed, because
there it is also taken that the mass of a moving electron is a constant value.
c) As has been said before, in the initial Eqs. (23.18), (23.19),
(23.21) and later in all the equations for deriving relativistic equations for
mass, it is taken that the mass of an electron in motion is constant and
of the same magnitude in both coordinate systems, which move relatively
at speed . However, according to the theory of relativity the mass
of an electron in the system ,
in which the electron is at rest is ,
whereas its mass in the system in which it is moved at
speed is 
. From this it can be seen
that the procedure for the derivation
of the equations for relativistic mass is in fact the same as the procedure
for the derivation of equations for some kind of would-be relativistic
accelerations by means of the Lorentz transformation. Later we shall demonstrate
that this is the case.
Using Eqs. (23.19) and (23.20) for longitudinal acceleration we have
 |
(23.30) |
From this it results that the relativistic longitudinal acceleration is given by equation
 |
(23.31) |
In this derivation it was taken that 
is constant,
and that 
as it is 
.
However in the derivation of the equation for transversal
acceleration, and hence for transversal mass, it is also taken that
is constant, but in distinction from the case above, in this case it is
taken that 
.
Thus in the case of transversal acceleration we have
 |
(23.32) |
which means that the relativistic transversal acceleration is given by
 |
(23.33) |
Equations derived in this way, which are related to relativistic
acceleration, are taken as equations for relativistic mass. Such a procedure is unacceptable
since, in physics mass is not simply the same as acceleration. The inconsistencies
in the derivation of the equations are no less unacceptable. In particular
the incorrect Eq. (23.24) for transversal mass is unacceptable. This equation
proves that such a method of deriving equations for the masses of an electron
in motion is not correct and cannot be accepted.
d) In the derivation of Eqs. (23.19) it is taken that the electron
is momentarily at the origin of the system and that it moves
along the -axis at a speed .
Only in that moment ( = 0) is the electron found at rest
relatively to the system , which also moves parallel to the
-axis, but at a constant speed of .
Under these assumptions, and in the course of time immediately after
= 0, the Eqs. (23.19) are allegedly the equations of electron motion
in the system . The question can be put, what are the equations of
electron motion when the time is not close to the time
= 0. Then the speed of the electron must be higher than the speed
at which the system moves, for the force
constantly works on the electron. Nevertheless,
in the final equations it is taken that the speed of the electron is equal
to the constant speed , that is the speed of the system
. Sometimes it is even taken that 
which is contrary to the main postulates of the theory of relativity,
since according to the Lorentz transformations
is the position of a spherical light wave which propagates along the
-axis at light speed, then 
.
The electron moves under the effect of force 
.
The speed of the electron depends on the magnitude of that force and its duration. If the
duration of that force equals zero, the speed of the electron must also
be zero. Hence if = 0, that is if 
the speed of the electron can not be equal to the speed ,
therefore the initial conditions for derivation of the Eq. (23.19) do not make sense.
e) Eqs. (23.18) and (23.22) should describe the motion of the same
electron in the same coordinate system . Because of that their form
would have to be the same, but, for incomprehensible reasons, it is not
so. With the "passage" of Eqs. (23.18) through the system , in a
strange, magical way the following equation is realized
 |
(23.34) |
which can be only in case when 
,
that is when = 0.
However, in that case the connection with the theory of relativity is lost, since
when = 0 then there is no other coordinate system and there is
no relative motion. If, regardless of all that it is still claimed that
everything is correct, then that is where science stops and magic starts.
In fact, such a derivation of equations does look like a magician's act,
who shows an empty hat to his audience then puts a rabbit in the hat (system
) and says a few magic words, and then to the audience's
astonishment, pulls a fox out of the hat.
f) In the second quoted paper of 1907 Einstein tried indirectly to
correct his Eq. (23.24) for the transversal mass of a moving electron by
means of the system of Eqs. (23.29) which read
 |
(23.35) |
These equations are obtained by division of both left and right side
of the second and third equation from the system (23.22) by . In
this way he makes it seem that, on the left side of the of the second and
third equations "mass · acceleration", and on the right side "a force."
From this it results that 
is the transversal mass. However,
after such divisions, the right side of the second and third equations
do not represent "the force". Since the components of the transformed electric
field from the system to the system
by means of the Lorentz transformation have the following form
 |
(23.36) |
as Einstein himself wrote in the same paper of 1907 [5] by Eqs. (7a)
and by Eqs. (23.20) and (23.22) given in the paper of 1905, quoted above
[2]. Besides this, the derivation of the equations given in Eq. (23.28)
is also incorrect. For example, it cannot be 
,
but rather should be 
, etc.
g) At the present time it is well known that the change of mass of
an electrically charged particle in motion is a consequence of the creation
of an electromagnetic field around the electrically charged particle in
motion. From there some logical questions arise: "What happens with a neutral
particle in motion? Does its mass also change with its speed?" A logical
answer would be that the mass of a neutral particle does not change with
motion. Such particles in motion do not create electromagnetic fields which
would resist further increase of the particle's speed, which would manifest
as an increase of mass. Some other physical process which would affect
the particle's inertia, or the body as a whole, in motion, is not known.
Therefore, nothing else remains but to conclude that the mass of a
neutral particle, and a body in general, does not change with the change
in speed of motion. Therefore, Einstein's generalization that all bodies
change their mass with the speed in the same way as an electron is unacceptable.
h) At the end we can conclude that Einstein's derivation of relativistic
equations for the masses of a moving electron are unacceptable. The derivations
are not soundly based in physics and lack mathematical correctness. Even
in this incorrect way Einstein did not manage to derive the most important equation
in the theory of relativity 
but the incorrect equation 
.
As regards this main equation in the theory of relativity, we can say
that it is not relativistic, nor can it be derived by correct relativistic
procedure.
23.4 Concept of mass
As has been said above, the moving electron has two masses
- the longitudinal and the transversal.
In the theory of relativity, and in many other publications
it is accepted that the mass of an electron in motion, and the mass of the moving body
in general is given by Lorentz's Eq. (23.4) for the transversal mass of
an electron in motion. The longitudinal mass and the transversal mass are
almost never mentioned, only the relativistic mass 
, or simply mass
. As a result, those insufficiently versed in the subject believe
that the electron will resist an change in velocity with the transversal mass,
which is defined by Eq. (23.4).
As was said before, the longitudinal mass resists changes of velocity
in the direction of motion of the electron, or body, whereas the transversal
mass resists the deviation of the electron from a straight path. Accordingly
the longitudinal mass is more important than the transversal because it
is the measure of the inertia of the electron or body. Also the longitudinal
mass is considerably greater than the transversal at relativistic velocities.
Their relation for the electron is given by
 |
(23.37) |
The relation of the longitudinal and the transversal mass of an electron
in motion and the mass at rest, calculated according to Abraham's and Lorentz's
equations for different velocities is given in Table 23.1.
Table 23.1
 |
 |
 |
 |
 |
From Table 23.1 we can see the following:
- The longitudinal mass becomes much greater than the transversal mass
as the velocity of the electron increases.
- The values of the longitudinal and transversal masses, calculated
according to Abraham's and Lorentz's equations are in good agreement with
low, non-relativistic velocities. The differences increase, however, with
an increase in velocity. These differences become so big at relativistic
velocities, close to the speed of light that they are unacceptable. The
question, therefore arises, which equations are correct? At the same time
the conclusion offers itself, that these were only approximate equations
made on the basis of Kaufmann's test results. Bearing in mind the remarks
made above on the derivation of relativistic equations, this is quite logical.
While discussing mass, we should note that there are disagreements
about the very concept. Many well known scientists have asserted that electrons
have no mass in the classic sense, but rather, electromagnetic mass only.
The idea that inert mass is in fact an induction, appeared in a study
on the electrodynamics of electricity in motion. In the paper, "On electrical
and magnetic effects produced by motion of the electrostatic electrified
body" [Philosophical Magazine, 11, 229-249, 1881.], J Thomson considered
the possibility of reducing inertia to electromagnetism.
In accordance with Maxwell's theory, an electrical displacement
(that is a current of displacement) causes the same effects as an ordinary current.
Therefore the magnetic field originates with the displacement current.
The energy of that field, in accordance with the law of energy conservation,
must be produced to account for the motion of the electrified carrier.
But the motion of the electrified carrier appears as a source of energy,
and this is why it must tolerate resistance on moving. As a result, Thomson
concluded that, "resistance must be equivalent to the increase of the mass
of the electrified moving carrier" [Philosophical Magazine, 11, 230, 1881.].
Oliver Heaviside made considerable advances on Thomson's results in
his paper "On the electromagnetic effects which appear on the motion of
electrical charges through a dielectric" [Philosophical Magazine, 27, 324-339, 1889.].
Kaufmann came to the conclusion, after the measurement of the
longitudinal and transversal mass of an electron in motion, that "the real mass of an
electron is equal to zero, and that the mass of the electron is an electromagnetic
phenomenon" [W. Kaufman, Über die elektromagnetische Masse des Elektrons,
Göttinger Nachrichten, S. 291-296, 1902.].
On the basis of Kaufmann's experiments, Abraham concluded that, "The
inertia of an electron originates from electromagnetic field". Appearing
at a conference in Karlsbad, he triumphantly announced, "The mass of the
electron is purely electromagnetic in nature" [M. Abraham, Die Dinamik des Elektrons,
22, 24, 28; M. Abraham, Physikalische Zeitschrift, 4, 57, 1902. "Verhanlungen der 74.
Naturforscherversammlung in Karlsbad: Die Masse des Elektrons is rein
elektromagnetischer Art"].
Lorentz greeted this conclusion as "undoubtedly one of the most
significant results of contemporary physics" [G. A. Lorenc, Teorija elektronov, str.76].
Poincare declared in his book, "Science and Method", "what we name
mass is apparition only. Each inertia is electromagnetic in origin" [A. Paunkare, NAUKA I
METOD, SPb, str. 170, 1910.].
The proponents of relativity do not accept the concept of such mass of an
electron. They do not accept the fact that an electron in motion generates an electromagnetic
field, which resists increases in the electron's velocity, thus increasing
the inertia of the electron, and hence its mass.
According to the theory of relativity, the increase in the mass of
the electron in motion originates exclusively as a result of relative motion.
Physical reality and an understanding of that reality are not important
in the relativistic procedure for solving certain problems. Equations derived
for particular environments (vacuum), in some cases are used for others
(water), as in the relativistic explanation of Fizeau's test results. It
also happens that equations derived for certain particular magnitudes (acceleration)
are used for other magnitudes (mass).
Introducing the second coordinate system is an artificial procedure,
that works like the magicians wand or top hat. For example, in deriving
equations for longitudinal and transversal mass, Einstein introduces a
second coordinate system, which moves translatory to the first, by velocity
. In that second system he determines the longitudinal and
transversal mass of a moving electron by means of the coordinates of the first system.
Equations derived in that way would accord with Kaufmann's results. However
it is well known that Kaufmann and his equipment were at rest in the first
system, which was also at rest and that Kaufmann made his observations
in this system and not in some other moving system.
23.5 The kinetic energy of an electron in motion
In order to derive an equation for the kinetic energy of an electron
we can use the equation for the longitudinal mass or the equation for the
transversal mass. If we use the equation for the longitudinal mass it is
used known equation "energy = mass · acceleration · distance" in this way
 |
(23.38) |
When we use the transversal mass in the derivation of the equation for kinetic energy the procedure is almost the same, only the force being defined in another way
 |
(23.39) |
So, we obtain, in both derivations, the same correct equation for the
kinetic energy of a moving electron.
Thus the change of kinetic energy is equal to the product of the change
in the transversal mass and the second power of the speed of light. So
when the electron receives energy then it's transversal mass increases
proportionally. But, when the electron loses energy then its transversal
mass decreases proportionally to the lost energy. When the transversal
mass is changed then the longitudinal mass changes as well. The changes
in longitudinal mass are greater because the longitudinal mass is greater
than the transversal mass, especially at relativistic velocities, close
to the speed of light. These changes, however, have not been taken into
consideration.
The equations for kinetic energy (23.38) or (23.39) are very similar
and describe very clearly the transformation of energy into mass, mass
into energy, or, more precisely, transformation of energy into electromagnetic
mass, that is kinetic energy of an electrified particle into electromagnetic
energy, or an electromagnetic field.
Such a transformation of mass into energy is called the defect of mass,
and it is connected with nuclear reactions, such as fission and fusion.
In the course of such reactions the mass of the material concerned decreases
and this partial decrease is accompanied by the release of an enormous
amount of energy in the form of radiation and the kinetic energy of the
particles.
The equation which describes the kinetic energy of an electron in motion
is not relativistic, nor should it be treated as such since the equation
for the mass of an electron in motion is not a relativistic equation at
all.
23.6 The energy of a body
The equation for the amount of energy contained in a body,
, where
is the mass of the body, is the most famous equation in physics. Its simplicity
is dumbfounding, particularly when we bear in mind that it defines one
of the most complex processes known to physical science, the total transformation
of matter into energy and energy into matter. This equation has contributed most
to Einstein's fame and to the fame of the theory of relativity, although it is not
a relativistic equation nor was it derived by Einstein. There is also doubt that
it is accurate. Besides that Poincare first derived that equation in implicit form in 1900.
23.6.1 The accuracy of the equation
Determining the energy of the electromagnetic field generated by an
electron in motion, Heaviside found that the energy of an electron at rest
is 
where is the mass of the electron
at rest. In order to calculate the energy of the field caused by the motion of an electron,
and compare it to the energy of an electron at rest, Heaviside used Maxwell's
theory by which the energy of the electromagnetic field generated by a
moving electron is [Philosophical Magazine, 27, 324-339, 1889.]
 |
(23.40) |
where 
is the vector of the magnetic field,
is an element of the volume,
is the distance from the electron,
is the radius of the sphere of the electron,
is the speed of motion of the electron,
is the speed of light
and 
= 4.803204197·10-10 stat C
is the electric charge of the electron.
Magnitudes , ,
, and 
in Eqs.
(23.40), (23.41) and (23.42) are in the units of the CGS system.
Bearing in mind that the energy of the field is equal to the kinetic
energy of the electron, and that at low speed of the electron 
he found that the mass of the electron at rest could be determined using
the equation
 |
(23.41) |
Using this finding, and taking that the total electromagnetic energy
out of the stationary sphere with a radius
and with the electric charge
on its surface, is equal to 
, which can be shown
by simple integrating. He found that
 |
(23.42) |
and from there
 |
(23.43) |
or generalising
 |
(23.44) |
The discussion on whether the energy of an electron at rest or a body
in general is best expressed by or 
is not yet finished.
Here is what Einstein [A. Einstein, The most
urgent Problem, Sci. Illustr., I, 16-17, 1946.] himself said about the accuracy of the
equation : "It is taken that the equivalence of mass and energy is
expressed (although it is not completely accurate) by formula ."
However, generalizations given by equation (23.44) and by equation
are not sure, and the discussions about accuracy of those two
equations do not make sense.
In the first case it is allegedly the energy of the electrical field
of an electron at rest only. The energy of motion inside of the electron does not take
into consideration. Besides, the energy in equations (23.42)
and (23.43) are related to the energy of the electrical field of the electrified sphere,
whose charge is and radius .
At that we should take into consideration that the charge of the sphere is formed by
a great numbers of electrons. However, in case of electrical field of an electron,
that charge is unit charge, that is, the charge of one electron only.
The energy , in the second case, is the
result of motion of the electron as an electrically charged particle, that is, the energy
of electromagnetic field generated by motion of the electron.
In the both cases, those energies are not energies originated
by transformation of some real mass.
23.6.2 Poincare's derivation of the equation
In his paper of 1900, entitled "Lorentz's theory and the principle of
counteraction" [H. Poincaré, La théorie de Lorentz et le principe de
réaction, Archives Néerlandaises des sciences exactes et naturelles, 2, 232,
1900.] Poincare characterises electromagnetic energy as
"a flux that possesses energy." He was the first to indicate that electromagnetic
radiation has a total momentum equal to Poynting's vector divided by the
speed of light squared
 |
(23.45) |
Taking that 
, where
is the electromagnetic energy absorbed by the body whose mass is ,
he applied the law on the conservation
of momentum in order to calculate the speed of the retreat of the absorbing
body using the following equation
 |
(23.46) |
On analysis of this equation it becomes apparent that the mass, or
inertia of electromagnetic radiation is equal to 
.
In his paper "Determining the relation between mass and energy"
[Journal of the Optical Society of America, 42, 540-543, 1952.] of 1952 Ives
reconstructed Poincare's article in detail and in the light
of "Poincare's principle of relativity" and demonstrated that Poincare's
arguments, if we hold to the final conclusion only, necessarily lead to
the following relation of electromagnetic energy and mass
 |
(23.47) |
where is the change of inert mass and
is treated energy (absorbed or emitted).
Consequently, Heaviside in 1889 derived the equation
. Poincare in 1900 derived an implicit form of
. Later it will be shown that
Einstein did not create the equation . His derivation of 1905 and
later was incorrect and thus unacceptable. But in spite of this the equation
is still considered to be Einstein's.
23.6.3 Einstein's derivation of the equation
Einstein gave the first derivation of the equation
in his
paper [3] in 1905 under the title "Does a body's inertia depend on the
energy contained in it?", and he gave the second derivation in the paper
[4] from 1946 under the title "Elementary derivation of equivalency between
mass and energy". In both cases the derivation of equations was not correctly
done so the final result can not be accepted, nor can it be
accepted that it is a relativistic equation. To show that it is best to
quote the mentioned papers on whole and then to point out the incorrectness
in the equation derivation, which will be done below.
Quotation (from the paper [3] from 1905):
"DOES A BODY'S INERTIA DEPEND ON THE ENERGY CONTAINED IN IT?
The research results, published [Ann. Phys., 17, 891, 1905.] earlier,
lead us to a very interesting
result from which I drew a conclusion that I will give in this paper.
In previous research I started not only from the Maxwell - Hertz
equations for vacuum and Maxwell's formula for electromagnetic energy of space but
also from the following principle.
The laws, according to which the states of physical systems change,
do not depend from that on which of the two coordinate systems, moving
with uniform translation relatively to each other, these changes of state
refer to (the principle of relativity). Starting from that I have personally
come to the following result.
Let a system of plane waves of light, relatively to the coordinate
system 
, have the energy
and let the direction of the
ray (normal to the front of the wave) form an angle 
with the -axis.
If we introduce a new coordinate system 
moving uniformly
and rectilinearly relatively to the system and if the origin
of the first system moves at the speed along the
-axis then the mentioned light energy,
measured in the system will be
 |
(23.48) |
where is the speed of light. In the further text we shall
use this result. [This Eq. (23.48) originates form Einstein's relativistic
Eq. (21.13) for the Doppler shift in which a wave frequency is substituted
by wave energy, for the energy is proportional to the frequency according
to Planck's equation 
where 
is Planck's constant, and 
is a frequency of a photon or a wave. Plank's equation 
does not
valid in the case of electromagnetic waves generated by motion of free carriers of
electricity as they are radio waves. Their amplitudes and energies are not quantified
because they can be changed continuously at the same frequency by the change of applied
voltage on an antenna. Note by M.P.]
Let there be an unmoving body in the system ,
and the body's energy relative to the system equals
. Let the energy
of that same body relative to the system which is moving, as
we said, at the speed , be equal to 
.
Let that body send a plane light wave with the energy
[measured in relation to the system ]
in the direction which forms an angle
with the -axis, and at the same time let it send the same
amount of light in the opposite direction. Thereby the body will remain
at rest relatively to the system . For that process the law on the
conservation of energy must be satisfied and that being (according to the
principle of relativity) relatively to both the coordinate systems. If
we mark with 
the energy of the body measured in the system
after the emission of light and the adequate energy with
relatively to the system ,
and using the above given relation we get
 |
(23.49) |
 |
(23.50) |
By subtracting the first equation from the second we get
 |
(23.51) |
In this relation both differences of the form 
have a simple physical meaning. The magnitudes and
represent the values of energies of one and the same body in two
coordinate systems which move relatively to each other while the body is at rest in one system
[in the system ].
In that way it is clear that the difference
can deviate form the kinetic energy 
of the body,
taken in the relation
to the other system [system ], only for an additive constant
, which depends on the choice of arbitrary additive constants
in the expressions for the energy and .
Therefore we can put that
 |
(23.52) |
since the constant does not change with the emission of
light.
In that way we get that
 |
(23.53) |
The kinetic energy of the body relatively to the system
decreases with the emission of light by the quantity which
does not depend on the nature of the body. Moreover, the difference 
depends on speed in the same way as the kinetic energy of an electron [see chapter
10 of the earlier quoted paper, that is the quotation in chapter 23.2.3
of this book and the Eq. (23.25) in the above given quotation. Note by
M.P.].
Neglecting the small magnitudes of the fourth and higher orders we
can get
 |
(23.54) |
From that equation it immediately follows that if a body emits energy
in the form of radiation then its mass decreases by the value
. Thereby,
it is, obviously, not important that the energy, taken from the body, directly
passes into the energy of emitted radiation, consequently we can reach
a more general conclusion.
The mass of a body is the measure of the energy contained in it; if
the energy changes by the value , then the mass changes by the value
. The energy is here measured in ergs,
and mass in grams." End of quotation.
Let us now study Einstein's second derivation of the equivalence of
mass and energy [4] published in 1946. In this case we shall also quote
the paper so that the reader can have the full picture.
Quotation: "ELEMENTARY DERIVATION OF THE EQUIVALENCE
OF MASS AND ENERGY
The law of equivalence, here given, which has not been published before,
has two advantages. Regardless of the fact that special principle of relativity
had to be used, this derivation does not demand the application of a formal
apparatus of theory, but it relies on the three laws known from before.
 |
(1) The law on the conservation of momentum.
(2) The expression for the pressure of radiation, that is for the
momentum of a wave packet which moves in a set direction.
(3) The known expression for the aberration of light (the affect of
the motion of earth on the position in which unmoving stars are seen - Bradley's law).
We shall now study the following system. Let a body
be free and let it be at rest relatively to the system
. Two wave packets 
and
, each with the energy 
move in the positive and negative direction of the -axis
respectively and they are absorbed by the body .
As a result of that absorption the energy of the body
increases by . Under those circumstances the body
remains at rest relatively to the system
because of the symmetry.
Now we shall study that process relatively to the reading system
, which moves at a constant speed
relatively to the system
and in a negative direction of the -axis. Relatively to the
system that process is described in the following way. The
body moves in the positive direction of the
-axis at the speed .
The direction of the two wave packets form the angle
with the -axis of the system .
In accordance with the aberration law, in the first approximation
where is the speed of light.
From the study of the process in the system we know that the
speed of the body remains the same after the absorption of the
wave packets and .
 |
Let us now apply the law on the conservation of a momentum of our system
relatively to the -axis in the
reading system .
I Let be the mass of the body
until absorption; then 
represents
the expression for the momentum of the body
(in accordance with classical mechanics). Each wave packet has the energy
and because of that, in accordance with Maxwell's well known
theory, has the momentum of 
. Strictly speaking, that momentum of
the wave packet is relatively to the reading system
. However, when the speed is small
relatively to , then the momentum remains the same relatively
to the system with the accuracy up to small value of the second
order (
in comparison with 1). A component of that momentum along
the -axis equals 
, or with the sufficient
accuracy (if we neglect small magnitudes of higher orders) 
or 
. Therefore the components of the momentums of the wave packets
and
along the -axis,
taken together, equal 
. In that way
the total momentum of the system until absorption equals
 |
(23.55) |
II Let 
be the mass of the body after the
absorption. Earlier we have taken into account the possibility of mass increase with
absorption of the energy (that is essential so that the final
result of our study should not be contradictory). Then the momentum of the system
after the absorption will equal
 |
Finally let us apply the law on the conservation of momentum in the
direction of the -axis. That gives the mutual relation
 |
(23.56) |
or
 |
(23.57) |
That mutual relation expresses the law of equivalence of mass and energy,
The increase of the energy is connected with the mass increase
by . In so far that energy is usually determined with the accuracy
up to additive constant, we can choose the last so that
 |
(23.58) |
End of quotation.
23.7 Objections to Einstein's derivation of the equation
In reference to the last two quoted papers a number of objections can
be made in relation to the derivation and the derived equations on the
basis of which Einstein gave the general conclusion that a body's mass
is the measure of energy, that is that . However we shall concentrate
on two important objections which will suffice to show that the relativistic
way of derivation given in those papers was incorrect. The objections are
as follows.
a) It is generally accepted among scientists that Einstein first gave
a complete theory on the inertia of energy [Maks Born, Atomnaja fizika, str. 72, 1965.].
Reference is often made to his article "Does the inertia of the body depend on the energy
contained in it?" which was published in 1905. As we saw above Einstein asserts that
"if the body emits an energy in the form of radiation then
its mass decreases by ". Generalising from this Einstein concludes:
"The mass of a body is the measure of the energy contained within it".
However, he failed to prove the assertion in the article mentioned.
It is historically interesting that Einstein's conclusion that
as it was published in "Annalen Physik" was logically wrong.
The conclusion is based on an argument that just would prove [20]. In this article, where
Einstein attempts to prove that the mass of a body decreases when the body
emits radiation, this loss of mass is not taken into account in the procedure
by which the equation is derived.
Ives proved that Einstein derived the equation incorrectly
[Journal of the Optical Society of America, 42, 540-543, 1952.]. We shall
now summarise that proof. Ives's numbers of the equations are given on
the left.
Ives found that Einstein derived Eq. (23.50) correctly, that is the
next to come (23.59)
| (1) |  |
(23.59) |
and after that he says the following
Quotation: "However, if we mark with
and 
the mass of the
body before and after radiation respectively, then the kinetic energies
of the body 
and 
relative to the system will be
| (2) |  |
(23.60) |
and
| (3) |  |
(23.61) |
At this point Einstein mistakenly states that 
and 
and in this way, by means of subtraction,
and on the basis of Eq. (1) gets
| (4) |  |
(23.62) |
and as an approximation
| (5) |  |
(23.63) |
Taking into account Eqs. (2) and (3) he must get
| (6) |  |
(23.64) |
which combined with Eq. (1) must give
| (7) |  |
(23.65) |
or the two next relations would be treated as different
 |
(23.66) |
and
 |
(23.67) |
Comparing these equations
with Einstein's equations
and we see that Einstein inadvertently asserts that
| (8) |  |
(23.68) |
which, strictly speaking, should be proved [20]". End of quotation.
At the end of the above mentioned article Ives gives
the following conclusion: "It emerges from Einstein's manipulation of
observations by two observers because it has been slipped in by the
assumption which Planck questioned. The relation
was not derived by Einstein."
From the above it becomes quite clear that Einstein did not present
the theorem on the inertia of matter, or prove that in his
paper of 1905, although some known physicists continue to refer to that
paper. Relativists refuse to accept that Einstein made a mistake even when
the mistake is evident.
The quoted Ives's article is sufficient for an estimate of the
correctness of the Einstein's relativistic derivation of equations. However, Einstein's
article and the relativistic way of the derivation of equation have also
the others shortcomings.
b) In the chapter 21 of this book it was shown that the relativistic
formulas for the Doppler effect are unacceptable and that they are more
like a mathematical game than physics. This is particularly true for the
case of relativistic speeds. In his paper [5] Einstein gave relativistic
formula (21.13) for the Doppler effect for the frequency of reception when
the receiver of radiation is in motion, and the source of radiation is
at rest, as well as the formula (21.14) for the case when the source of
radiation moves, and the receiver of radiation is at rest.
In Einstein's first paper, here quoted, he stated that the radiating
body is at rest in the system which is at rest. In that case
the energy of light waves in the system which moves with uniform
translation relatively to the system is given by Eq. (23.48).
On the basis of that equation the final Eq. (23.53) was derived.
In case of two or more systems, which move relatively to each other,
there is no possibility of determining which system is at rest and which
of them moves. It can only be established that the systems move relative
to one another, that is that one moves relatively to the other and that
for each of them can be equally claimed to be at rest and to be moving.
According to the theory of relativity which rejected the ether as an
absolute system, all inertial systems are equal. Therefore, in case
of two inertial systems we can analyze some physical phenomena in two ways,
that is by observing that phenomenon from one or the other system. Obviously,
the event should be in one system, and the observer in the other. According
to the theory of relativity the result of the analysis must not depend
on which system the event is observed from, because all inertial systems
are equal. By the way, in connection with this Einstein, in the first quoted
paper, himself wrote: "The laws, according to which the states of physical
systems change, do not depend from that on which of the two coordinate
systems, moving with uniform translation relatively to each other, this
changes of state refer to." In the spirit of this let us put a source of
radiation of plane waves, from the first quoted paper, in the system
so that it is at rest in that system, which moves.
In that case, according to the Eq. (21.14), the energy of light waves measured
in the system is
 |
(23.69) |
By using the Eq. (23.69) in the same way as it was used in the first quoted paper Eq. (23.48) and in the same procedure of deriving equations we get the next equation for kinetic energy
 |
(23.70) |
which is significantly different from the responding Eq. (23.53) in
the quoted paper, which also proves that the procedure of relativistic
derivation of the equation for kinetic energy is not correct. The final
result depends on whether the radiation is in the system at rest or in
the system which moves. Since we cannot say which system is at rest, and
which one moves, then we cannot claim which of the two different equations
is correct. If the theory was good the equations would have the same form
in both cases.
c) On the basis of the equation for kinetic energy (23.53) Einstein
draws a general conclusion, which cannot be accepted without some reserve.
So, by using the equation
 |
he takes the first two elements of the order and he neglects the others,
which must not be done in the case of higher speeds. For example, with
the value of neglected elements of the order is greater
than the taken element 
. With that kind of selection he reaches
a corrected equation for kinetic energy and compares it with the classical equation
 |
(23.71) |
From this comparison he concludes that 
,
that is 
, and from there that .
So, he took a small speed, used in classical equations
and very small energies, which refer to small mass defects, that is the
mass, which an electrically charged particle gains or loses with the change
of the speed of motion. On that basis, which is definitely uncertain, he
draws a general conclusion.
This applies particularly when we take the following into consideration.
According to Heaviside the energy contained in the mass of an electron
at rest is given by Eq. (23.43) which runs 
. However, for the proton
as the first composite stable and positively charged particle, that formula
does not apply because, according to Eq. (23.41) from which Heaviside's
Eq. (23.43) is derived, the proton would have to have a radius 1836.16
times smaller than the radius of the electron. It is believed, however,
that these particles have roughly the same radius. In addition, the equation
does not refer to the mass of an electron at rest or a body in
general, but rather electromagnetic mass which is attributed to the energy of the
electromagnetic field created by the movement of a charged particle.
d) The other quoted paper does not belong to the theory of relativity
because "it does not demand the application of a formal apparatus of theory,
but relies only the three laws known from before," as Einstein says himself.
Nevertheless, let us consider the way Einstein derives the equations
and conclusions.
This derivation is not in accordance with classical physics nor with
the theory of relativity.
It is necessary to be reminded of some facts, connected to the classical
and relativistic explanation of aberration, before an analysis of the Einstein's way of
consideration of the process and derivation of equations.
According to the classical explanation of aberration, light rays
from a star are approaching to the moving observer from the direction of the real position
of the observed star. Because of that, there is no aberration of the light rays at their
approach to the some body or telescope. Aberration seemingly originates while the light
rays are passing through the telescope. However, the light rays do not change the direction
of motion while passing through the moving telescope, too (See chapter 22.1).
The determination of the angle of aberration and explanation
of the phenomenon of aberration in relativistic procedure is based on two coordinate
systems which relative move. At that, it is taken that the first system is at rest and
the second is moving, so that the source of the light is at rest in the first system,
and the observer is at rest in the moving system. Aberration is originating in the moving
system and the light rays approach to the observer, body or telescope from the direction
of the seeming position of the observed star.
Einstein starts to consider the process using two coordinate systems
and which relative move. In consideration
of such start the procedure should be relativistic.
However, Einstein puts the body and the
sources of the wave packets and in
the same system which is at rest (See Fig. 23.2). Because of that,
the consideration of the process is neither classical nor relativistic.
At such arrangement, the body absorbs the wave
packets and stays in the balance because of symmetry of the effect of the wave packets. After
that, he takes that the body moves by velocity
relative to the system . The system does not
exist in the farther consideration (See Fig. 23.3). Then, he takes that the aberration
allegedly originates relative to the system , because the body
moves in this system. So, the wave packets allegedly reach the body
at an angle 
, where
is allegedly the angle of aberration. However, as it is said before, according to the classical
explanation of aberration, this angle does not change at motion of the
body and must be 90 degrees. Apart from that he is taking that absorbing
body and the sources of the wave packets are in the same coordinate
system, and aberration originates in the system at rest. It is two big mistakes at the same time.
Because of that, farther consideration of this process and derivation of equations do not make sense.
But, the problem is not only in the misconception of aberration and
application of aberration. There are also the other incorrectnesses in this article. For example,
he did some neglecting in the derivation of equations and in this way he got incorrect,
but wished result.
In deriving the Eq. (23.72) he uses components of energies of wave
packets in the direction of the body motion, which are the result
of allegedly aberration. At that, he does not take into consideration the decrease of absorbed
energies because of a retreat of the body from the sources of the wave
packets. In this way he finds total impulse of energy in system in the
direction of the -axis.
 |
(23.72) |
where is an angle of allegedly aberration in the system
given by classical equation.
After that he applies the law of conservation of the impulse in the
direction of the -axis and yields
 |
(23.73) |
and from there
 |
(23.74) |
where is the mass of the body before
absorption of energy of the wave packets and is the mass
of the body after absorption of that energy. On the base
of it Einstein gave general conclusion
 |
(23.75) |
In deriving the Eq. (23.72) Einstein did not take into consideration
the decrease of absorbed energy of the wave packets caused by the retreat of the body
from the sources of the wave packets in conformity with
Eq. (21.3). If he had done this he would have got that Eq. (23.75) reads
 |
(23.76) |
Eq. (23.76) shows that even thought incorrect mixture of classical
and relativistic procedure do not yield wished results. Besides, from Eq. (23.76)
results that the mass of the body decreases when its velocity increases. Such finding
is wrong and unacceptable.
Finally, let us suppose that everything is correct in connection
with the comprehension of aberration and its application in this article, and let us
apply relativistic procedure with the use of classical equation of aberration. Then,
the absorbed energy of the wave packets in the direction of the body
motion, in conformity with Eq. (21.13), will be
 |
(23.77) |
and the momentum of that energy
 |
(23.78) |
In transforming the mass from system to system
he have to decide which mass to take into consideration,
the longitudinal mass or the transversal. Naturally this is valid only on condition that
any body has the two mentioned masses in the same way as an electron in
motion.
We have noted before that the electron has a longitudinal mass which
resists changes in speed in the direction of motion and a transversal mass
that resists deviations from the direction of motion. Relativists assert
that the equation valid for the electron, as a charged particle,
is also valid for neutral particles and for bodies in general. Sticking
to this, and bearing in mind that the action on the momentum of the energies
is in the direction of motion of the body , we are was obliged to
take the longitudinal mass into account. In that case we will conclude
that the mass of the body in system ,
given by Lorentz's Eq. (23.3) is
 |
(23.79) |
Using Eqs. (23.78) and (23.79) and the law on the conservation of momentum
in the direction of the -axis in the system
we obtain
 |
(23.80) |
and from there
 |
(23.81) |
The conclusion given by Eq. (23.81) is completely unacceptable, since
in this case the increase in mass 
of the body
in system ,
caused by the absorption of energy by the body
in system , depends on speed
of any system relative to the system
. Besides, from Eq. (23.81) results that the mass of the body
decreases when its velocity increases.
The transversal mass can be taken into consideration in the quoted
derivation of the desired equation, since the relativists use it in the case of the
longitudinal motion as well. Then the
mass of the body in system would be
attained using Lorentz's equation
 |
(23.82) |
Using Eq. (23.82) to accomplish the same procedure for the derivation of the desired equation we get
 |
(23.83) |
and from there
 |
(23.84) |
The equation derived, (23.84) cannot be accepted either for the reasons
given above in connection with Eq. (23.81).
At the end the following can be said. Einstein did not derive
the equation for a body's total energy on the basis of the theory
of relativity, hence that equation cannot be considered as a product of that theory. It
was developed by generalization on the basis of the equation for an electron's
kinetic energy 
, which is also not a product of the theory of
relativity. Besides it was concluded that the energy of a particle is not only proportional
to the change in the moving particle's mass but that it is also proportional
to the particle's total mass, and also that the energy of a body is proportional
to the body's mass on the whole. In that way a daring conclusion was made
that the energy of a body is the measure of its mass and vice versa. That
this is really so was allegedly confirmed by the annihilation of matter
and antimatter.
It is believed that the best example for the total transformation of
matter into energy and energy into matter is the annihilation of electrons
and positrons at the moment of their collision and the appearance of electron
- positron pairs at irradiation a matter with gamma rays, whose energy
is greater than 1.022 MeV. However, in chapter 26 of this book it will
be shown that the annihilation of electrons and positrons does not exist,
the same as the transformation of their total mass into energy of the gamma
radiation does not exist. Therefore one should be very careful and accept
with reserve the proposition that the total energy of a body equals the
product of its total mass and the speed of light squared. It seems that
it is still unknown how much energy is concentrated in the mass of a particle
at rest, nor in the mass of a body as a whole.
23.8 The derivation of the equation
by the classical procedure
Equation which defines the relationship
between mass and energy, is not a relativistic equation but purely classical. I have derived
that equation according to the correct classical procedure, using well-known
physical laws that have been confirmed many times in practice.
Maxwell put forward the theory that the energy flux of electromagnetic
radiation behaves as if it contains a momentum that exerts pressure on
obstacles to the propagation of that radiation which can be defined by
the equation
 |
(23.85) |
where is the energy of the radiation which falls on a unit
of the surface of a body, in a unit of time, is the speed of
light and 
is the coefficient of reflection of the body's surface.
Maxwell also theoretically explained the phenomena of the pressure
exerted by electromagnetic radiation and determined its magnitude. Later,
the pressure exerted by radiation was confirmed experimentally. We can
see the pressure exerted by radiation in nature when a comet develops a
tail. The head of a comet, which consists of one or more large solid parts,
always points towards the sun. The tail, which consists of gasses and ice
particles streams away from the sun. This is the result of the pressure
exerted by solar radiation on the gasses and particles of the tail.
The equation can be derived by correct
classical procedures, using the phenomena of the pressure exerted by
electromagnetic radiation.
The equation has indeed been derived on the basis of the pressure
exerted at the total absorption of light. The derivation of the equation
on the base of the total absorption is less convenient.
The reason for this is the impossibility of determining the quantity of
the absorbed energy spent in the mechanical work under the force of the
pressure of radiation. We know that the energy absorbed from the radiation
is expended in heating the body and on mechanical work, but we do not know
in what proportion.
I derived the equation using the phenomena
of the pressure of light at total reflection [The concept of the total
reflection of radiation is understood as the reflection of light at which the
energy of the incoming light is equal
to the sum of the reflected energy and the energy spent in mechanical work.], the Doppler
effect and Plank's law, as follows.
 |
Let us assume that light with energy 
and frequency , falls at an angle of 90° onto a thin,
moveable, totally reflective plate of area . The plate moves from
point 
to point 
over a distance
, under the pressure of the light radiation, as shown
schematically in Fig. 23.4. The greater part of the incoming energy which
we denote 
is reflected back. A very small part
is spent on the mechanical work needed to move the plate
from to .
If 
is the pressure exerted by the light,
then 
is the force of the pressure on the area
, and the mechanical work realised
 |
(23.86) |
If the flow of light is constant over the time ,
then the force of the pressure is constant too. In these circumstances, the plate will
accelerate with the mean velocity 
. In this case we have
 |
(23.87) |
from which we get (23.88)
 |
(23.88) |
where 
is the momentum transferred to the reflective
plate through the pressure exerted upon it by the light rays over time
.
The reflective plate will retreat under the pressure of the radiation.
Therefore, the frequency of the light radiation that falls on the plate,
which as receiver of radiation retreacts, is
 |
(23.89) |
According to Huygens' law the irradiated plate becomes the source of radiation. In compliance with this and bearing in mind that the reflective plate, as the source of radiation is retreating, we can write that the frequency of the reflected radiation is
 |
(23.90) |
According to Planck's law, the energy of a light wave is proportional to its frequency. As a result of this and in the light of Eq. (23.90) the energy of the reflected radiation is
 |
(23.91) |
Using Eq. (23.91) and taking into account that
we get
 |
(23.92) |
From Eqs. (23.88) and (23.92) we have
 |
(23.93) |
and from there
 |
(23.94) |
If we ascribe a certain mass ,
to the energy of light, and bearing in mind that on the reflection of light elastic
collision occurs, then we can conclude that the momentum transferred to the small reflected
plate, is equal to double the momentum of the mass ascribed to the light energy.
So we can write
 |
(23.95) |
From Eqs. (23.94) and (23.95) we have
 |
(23.96) |
and from there, finally
 |
(23.97) |
By the way, according to Maxwell's well known theory, as we said before,
the energy flux of electromagnetic radiation possesses an momentum
. On the base of that Poincare concluded that
and from that , where
is the mass ascribed to the energy .
And thus it is clear that the equation which describes the relationship
between mass and energy, , is a classical equation. It is not a
relativistic equation because it has not been, nor can it be derived according to correct
relativistic procedure.
23.9 The derivation of the equation
by the classical procedure
The equation , which was derived in the previous
chapter, is used to derive the equation . This is done because it is
well known that electromagnetic radiation acts on electrons by exerting pressure. In this
way the electron receives energy which is transformed into mechanical work,
i.e. the motion of the electron, which changes the mass of the electron
in relation to its velocity of motion. Such interaction between an electromagnetic
field and an electron are well known as the photoelectric effect, or Compton's
effect.
According to Newton's second law
 |
(23.98) |
from which follows
 |
(23.99) |
or
 |
(23.100) |
If the mass changes with the velocity, as it does with an electron or some other electrified particle, then
 |
(23.101) |
The work of the force 
on the path
is equal to the spent energy so that
 |
(23.102) |
By multiplying Eq. (23.101) with we get
 |
(23.103) |
From Eqs. (23.102) and (23.103) we have
 |
(23.104) |
[Eq. (23.104) can also be derived in this way: 
.]
If is the energy of the electromagnetic
radiation, then, according to Eq. (23.97)
 |
(23.105) |
because the speed of light is constant.
From Eqs. (23.104) and (23.105) we get
 |
(23.106) |
After separation of the variables we have
 |
(23.107) |
Since, at the speed = 0, the mass of an
electron is equal to its mass at rest ,
and at speed
its mass is equal to the mass , we can write
 |
(23.108) |
and from there
 |
Substituting the limits we get
 |
that is
 |
and finally
 |
or
 |
(23.109) |
So another very important, allegedly relativistic equation, which cannot
be derived by correct relativistic procedure using two inertial coordinate
systems moving relative to one another, can be derived according to purely
classical procedure. Like , this is not a relativistic but a purely
classical equation.
In connection with these two equations it is necessary to discuss some
seeming contradictions.
According to Eq. (23.109) every mass which moves at the speed of light
is infinitely large. Therefore the Eq. (23.109) conflicts with Eq. (23.97)
even though this Eq. (23.109) was derived from Eq. (23.97). From this it
necessarily results that the photons and also the energy of electromagnetic
radiation have no mass at all. It also means that electromagnetic radiation
is not corpuscular in nature but only wave like. Because of this we said
above that the mass was ascribed to the energy of light
, but not that the energy of light
possessed mass .
The pressure exerted by light, or by electromagnetic radiation in
general, is not the result of some real mass, contained in the radiation
which moves at the speed of light. The pressure exerted by light is the
result of the electromagnetic wave action on the reflecting conductible
layer in the following way.
The electric field of the electromagnetic wave acts by force on the
free electrified particles in the conductible layer and causes them to
move. Well known Lorentz force acts on electrified particles because of their motion
in the magnetic field of the electromagnetic wave. This force is transmitted
to the conductible layer and manifests itself as the pressure exerted by
electromagnetic radiation. The electric and magnetic field of the electromagnetic
wave also acts on the ions and electrified particles bound to the atom.
Under the influence of the electric field of an electromagnetic wave displacement
of bound electrified particles occurs in insulators, creating a displacement
current.
In fact, the mass that we ascribe to the energy of radiation is
electromagnetic mass and is, in fact, the energy of the electromagnetic field generated
by electrified particles in motion. Only such a "mass", electromagnetic
mass or the energy of an electromagnetic field, can move at the speed of
light only and not increase to infinity at this speed.
Consequently, if by mass it is understood electromagnetic mass or the
energy of an electromagnetic field, then Eqs. (23.109) and (23.97) do not
conflict. Therefore, the derivation of Eq. (23.97) using the phenomenon
of the Doppler effect, and the total reflection of light radiation, and
also the derivation of Eq. (23.109) on the basis of Eq. (23.97), are logical
and correct. The two equations are closely connected and express the connection
between electromagnetic mass and electromagnetic fields, so that the energy
of the electromagnetic field is equal to the electromagnetic mass and the
second power of the speed of light. Therefore Eq. (23.97) should read
 |
(23.110) |
where 
is the electromagnetic mass.
According to Eq. (23.110) we should take the mass of the electron (or
some other electrified particle) at velocity = 0 to be equal to
the mass , and at velocity its mass is
equal to the mass 
. In which case Eq. (23.108) would read
 |
(23.111) |
Solving Eq. (23.111) we get
 |
(23.112) |
Electromagnetic mass is the apparent increase in the mass of an electron
with velocity. As a result we can say that the total mass of an electron
contains the electromagnetic mass and mass at rest
, and that the electromagnetic mass leaves the electron in the
form of electromagnetic radiation as its speed of motion falls (by braking, on transition
from orbit to orbit, or in some other way).
The velocity , in Eqs. (23.98) to (23.112),
is the velocity of motion of an electron relative to an ether in which the electron moves.
As it is well known that the charge of an electron is negative and
the charge of a proton is positive. However, absolute values of the magnitudes of these
two charges are equal. From this results that an electron and a proton will generate the
magnetic fields equal magnitude at the same velocity of motion. Consequently, the increase
of an inertia of the proton in motion must be equal to the increase of the inertia of the electron in motion.
Therefore, the equation (23.112), which relates to the electromagnetic mass of an electron
in motion, for the proton in motion would read
 |
(23.113) |
For the same reason, equation (23.109), which relates to the total mass of an electron in motion, for the proton in motion would read
 |
(23.114) |
The correctness of equations (23.113) and (23.114) can be experimentally
proved by measurement of the wavelenght of the braking radiation which originates
at the brake of motion of a proton got by ionization of hydrogen. The proof of the
correctness of these two equations would be great contribution to physics in comprehension
of the conception of allegedly change of mass of the body in motion, and also great
contribution in comprehension of mutual relation of mass and the energy.
23.10 The pressure of electromagnetic radiation, the red shift
and the cosmic rays
The stars emit a continuous spectrum and also line spectrums. From
the position of the lines in the spectrum of the radiation from a star
we can determine the chemical composition of the star, since every element
has a distinctive pattern of lines in its spectrum. The line nature of
these spectra make possible to calculate the velocity of the approach
or retreat of the star using equation for the Doppler effect
 |
(23.115) |
where 
is the wavelength of radiation when the source of
radiation is at rest, relative to the observer, 
is the wavelength
of radiation when the source of radiation is moving relative to the observer
and is the speed of light.
If the body emitting the radiation is retreating from the receiver
- observer , then the observer will notice that the lines shift towards
the red end of the spectrum by 
. This shift of the lines in the
spectrum of starlight is termed red shift. The red shift increases with the radial
speed of the star as a source of radiation, that is with the velocity of
its retreat. If the star is moving towards the observer a blue shift will
occur.
When Hubbell studied the spectra of the radiation from distant galaxies
in 1929, he discovered that the characteristic lines in the spectrum of
this radiation shifted, en-mass, to the infrared without changing their
relationship. Hubbell also observed that the greater the distance of the
observed galaxy, the greater the red shift. On the basis of this observation
it was concluded that the farther away the galaxy, the faster it is retreating,
which means that the universe is expanding. The next conclusion drawn was
that this expansion must have had its beginning. Thus came about the big
bang theory in which the cosmos was "born". Some astronomers assert that,
at that moment, space, matter and time came into existence. It is also
asserted that, before the big bang, all the matter in today's cosmos was
concentrated in "primordial atom", whose density was about
1096 kg/m3
[16] and which was considerably smaller that the size of an electron.
In this way we have come to the conclusion that today's universe is
spatially limited, that is, it contains a limited amount of matter and
has a limited age. Einstein asserted the same. Accepting Friedman's [A. Friedmann,
Zeitschr. f. Phys., 10, 377, 1922.] method, he calculated that the hypothetical density
of the matter in the universe was 
3.5·10-23
g/cm3 and that the universe is 1.5·109 years old.
He claimed that the cosmos is spatially limited in the form of a hypersphere,
the volume of which is 
and the radius
 |
(23.116) |
Today, Einstein's calculations, as given above, are not considered
acceptable. The universe is now considered to be much older and larger.
This succeeded thanks to the discoveries that have made possible the use of much
better observation instruments and methods which have enabled the discoveries of more
distant galaxies and thus changed outwards limits of the universe in time, space and
quantity of matter.
So, it turns out that the cosmos is so big as far as we are
able to see it. Many allegedly great scientists accept this strange assertion
that the cosmos is limited and that its dimensions enlarge.
All the above mentioned conclusions are based on the accepted
explanation of the red shift. According to this explanation the red shift is the result
of the expansion of the universe, or better put the dispersion of the universe.
No other explanation of red shift has been discovered.
However, astronomers discovered, on the base of red shift,
that the velocities of removing of the most distant quasars are about 5.8 times
higher that the speed of light. This finding disputes Hubble's hypothesis about
the cause of the red shift, since the speed of light is a maximum possible speed.
In order to accept the assertion that the cosmos was born in the big
bang we must address the question of what existed before. Regretfully,
no such explanation has been forthcoming, and there is no logic in the
assertion that the whole substance of the universe was concentrated in
the "first atom" for an infinitely long time.
At the same time, in order to accept the idea that the universe is
expanding and is spatially limited, we must consider the question of what
is beyond its present limits. Some may say that there is nothing, but that
in turn begs the question, of whether anything can or does exist in that
nothing. For example, does the electromagnetic radiation from the most
distant, or other galaxies in some way penetrate this void?
If electromagnetic radiation spreads beyond these bounds, which it
is quite logical to accept, since the speed of light is higher than the
radial velocities of the galaxies and starlight propagates in all directions,
then electromagnetic radiation at least, has to exist outside the so called
limits of the universe.
If the galaxies originated in a big bang, then it would be logical
to expect their velocities to decrease with distance from the place of
origin as a result of the constant effect of gravitational forces originating
from the remained mass of the radially dispersing matter. However, allegedly opposite occurs.
Physicists and astronomers have not an acceptable explanation
for this paradox. In connection with the spreading of the cosmos and dispersion of galaxies
Einstein gave very strange hypothesis. According to that hypothesis the antigravitation
exists as well as gravitation.
The proponents of the big bang say that in the cosmos there are about
10 billions galaxies and in each of them about 10 billions stars, whose
average mass is aproximately equal to the mass of the sun. If the total
mass of the cosmic gases and dust and the other cosmic bodies is greater
even four times than the mass of all stars in the cosmos is, then the total
mass in the cosmos would be about 1051 kg. If the density of the mass
in the primordial atom was 1096 kg/m3, as the proponents of the
big bang say as well, then the volume of the primordial atom was 27 times
smaller that the volume of an electron, or 6·1014 times smaller than
the volume of the smallest atom.
It is more logical to postulate that after the big bang comes a big
collapse, and after the big collapse again a big bang and so on ad infinitum.
This would constitute some form of natural process of birth and death for
galaxies, or groups of galaxies, but not for the whole universe.
The history of science is full of incorrect assertions and hypothesise.
The science of astronomy is no exception. For example, astronomers started
with a geocentric system and moved on, via the heliocentric system to the
big bang.
At the same time, many experiments have been performed that failed
to produce the desired results. The Michelson - Morely experiment is a
case in point, it has been repeated many times without a positive result.
Sometimes experiments produce quite unexpected results, as was the case
with the Fizeau's test. Indeed, far more experiments produce negative results
than positive.
Assertions about the limits of the universe and its age, or its origin
in a big bang are difficult to accept without serious reserve. In connection
with this I do not believe that the galaxies are dispersing radially, but
that their courses of motion are governed by the gravitational forces
originating from other galaxies. As a result, the red shift in the spectrum
of their radiation cannot be the result of the Doppler effect, caused by
radial dispersion, and must be due to some other cause. Accordingly, I
have dared to put forward a new hypothesis on the cause of the
red shift and a test that might confirm the hypothesis. True, the chances
of success for such an experiment are small, but nonetheless I think it
would be worth performing.
The interaction of photons and cosmic rays could be the cause of the
red shift. It is known that the photoelectric effect or Compton's effect
and the phenomena of the pressure exerted by light are based on the interaction
of photons and electrified particles, where the photons deliver part or
all of their energy to the electrified particles.
Primary cosmic rays consist of protons, alpha particles, electrons
and other electrified particles. Appearance of those electrified particles
in the cosmos is the result of the ionization of cosmic gases (hydrogen,
helium and the others) upon the influence of electromagnetic rays
(
-rays, X-rays, UV-rays), which originate at the nuclear
and other processes in the stars. Besides, high energy cosmic rays, produced
in this way, perform the ionization of the cosmic gases too, and thus produce
new cosmic rays.
When photons interact with these rays, part of their energy is
transferred to the electrified particles. At this point the photon loses energy, and
thus, its wavelength is increased. The greater the distance, that the photon
travels through the universe, the greater the chances that it will
interact with electrified particles. The more interactions of this type
the greater the energy loss for the photons and consequently, the greater
the red shift. Thus, the fact that photons from the most remote galaxies
have the greatest red shifts is not a result of the Doppler effect caused
by the dispersion of those galaxies. The universe is not expanding, and
if that is the case, we have to accept that there was no beginning of that
expansion; in other words, the big bang did not occur. All the theories
about the birth of the universe with the big bang and the temporal and
spatial limitations of the universe may in fact be groundless.
The blue shift observed in the spectra of some galaxies may only occur
in the case of relatively close galaxies that are moving towards the earth.
In these circumstances the blue shift may indeed be caused by the Doppler
effect which would cancel out the red shift caused by the interaction of
electromagnetic radiation from these galaxies with cosmic rays.
The energies of the cosmic rays can be up to 1020 eV.
Up to now there was no acceptable explanation of the origin so enormous energies
of the cosmic rays. However, in order to explain this phenomenon, we must know that
at every collision of a photon and electrified particle (cosmic ray) in the cosmos,
the photon gives over a part of its energy to electrified particle, and shifts to red.
Therefore, if we have this in mind then we can assert that the origin of the enormous
energies of the cosmic rays can be also explained by the numerous interaction of the
cosmic rays and photons (-rays, X-rays, UV-rays, and so on).
Electromagnetic radiation also exerts pressure on particles of matter,
molecules and the atoms of gasses. As we mentioned before, this phenomena
is well known and can be seen in the tails that comets develop at perihelion.
In this case a portion of the energy of the solar radiation is spent on mechanical
work in the pressure exerted by the radiation on the tail of the comet.
Due to the energy loss at this point the wavelength of the radiation is increased,
resulting in a red shift in the spectra of reflected radiation.
When radiation and particles of matter or gasses interact the
scattering of the radiation only occurs when the particles of matter or the molecules
of the gas are large enough in relation to the wavelength of the radiation,
otherwise, the interaction takes place without the occurrence of scattering.
For example, a particle 20 nanometers in diameter will scatter
as much light as 1012 separate atoms. Raleigh found that the scattering
of light radiation by the molecules of atmospheric gases is proportionate
to the fourth power of the wavelength of the radiation.
This factor 
shows that the scattering blue radiation (
400 nm) is six
times greater than the scattering of red colour ( 640 nm).
As a result, the molecules of the
upper atmosphere for the most part, scatter radiation blue in colour, which gives
the sky its blue shade.
The scattering of electromagnetic radiation in the earth's atmosphere
is a consequence of the interaction between the electrical and magnetic
field of electromagnetic radiation and charged particles, free, or bonded
to atoms, molecules and particles of matter.
In the process of scattering of radiation in the molecules
of a gas or the particles of dust or smoke the molecules and particles are forced
to retreat by the pressure of the radiation. As a result the Doppler effect
is observed in the scattered radiation, that is, a red shift is observed
in the spectrum of the scattered radiation. The magnitude of the red shift
is proportional to the speed of the retreat and the velocity of the retreat
is proportional to the energy of the radiation spent in the mechanical
work performed under the influence of the pressure force of the radiation.
However, when discussing
the scattering of light by the molecules of gasses we should bear in mind
that the scattering occurs in the direction of the movement of the radiation
as well. It is clear that during the interaction of electromagnetic radiation
with the charged particles in the molecules of a gas, the energy of the
radiation is expended in mechanical work. This work is performed during
the exertion of pressure by the radiation upon the molecules of the gas.
In conformity with Planck's law an increase in the wavelength of the radiation
occurs.
Consequently we arrive at the conclusion that the red shift may
also be the result of interaction between electromagnetic radiation and the
charged particles in the atoms and molecules of gases in the universe.
Similarly we can conclude that the red shift may also appear in the spectrum
of solar radiation after the passage of that radiation through the earth's
atmosphere.
The radiation from the sun is more and more red as the sun nears
the horizon. This is the result of the greater attenuation of radiation at
shorter wavelengths due to dispersion and absorption by particles
of dust and smoke and gas molecules in the atmosphere. Also the rays of
the sun are passing through the lower layers of the atmosphere close to
the ground where the dust and smoke particles and gasses are most concentrated.
It is possible that a red shift occurs at this stage, due to the interaction
of solar radiation with the electrified particles and gas molecules in
the atmosphere. It should also be remembered that the gasses of the atmosphere
are partially ionised, and that the atmosphere contains free charged particles.
It is obvious that the distance travelled by the rays of the sun
through the ground layer of the earth's atmosphere
is negligible in comparison with the distance travelled by light
from some star. The density of the atmospheric gasses near the earth's
surface is, however much greater than in intergalactic space. As a
result we still cannot exclude the possibility of a slight red shift in
the spectrum of solar radiation at sunrise and sunset. In order to detect
such a red shift it would be necessary to have readings for the spectrum
of solar radiation from above the earth's atmosphere, and to obtain a mean
value for the position of the lines in the sun's spectrum at sunrise and
sunset. The spectrum of solar radiation would be taken on the same plane,
at sunrise and sunset to ensure that the distance travelled by the solar
radiation through the earth's atmosphere is the same. It would be necessary
to ensure that the spectrum was taken at the maximum possible lenght of the way of the
sun's rays through the atmosphere and this would demand that the experiment
were made under conditions of excellent visibility, certainly outside urban
areas where the density of aerosols is lower.
The Doppler effect caused by the motion of the spectroscope,
in relation to the sun is annulled by the use of mean values for sunrise and sunset.
We should also note that if the earth's ether exists it will complicate
the measurement because we do not know its thickness above the earth and therefore
cannot determine the Doppler shift. For all these reasons
the use of mean values for the lines in the spectrum of solar radiation
is recommended.
Instead of the solar spectrum taken above the
atmosphere, one could also use the solar spectrum made at great elevation, when the
sun is at its zenith and atmospheric conditions are exceptionally good. In such
circumstances the influence of the atmosphere on the spectrum of the solar
radiation would be at its minimum.
The line spectrums of hydrogen and helium, taken in the
laboratory on the earth, can also be used for the comparison with the line spectrums
of hydrogen and helium in the spectrum of the sun's light coming through
the ground layer of the atmosphere.
Finally, the appearance of the redshift in the spectrum of the
light passed through earth's atmosphere, can be proved by means of a laser. For that
experiment are need a suitable high power stabilized laser whose radiation is well
collimated, and spectrometer for the measurement of the wavelenght of the laser's
radiation. The lenght of the way of the laser beam, from the laser to the spectrometer,
should be as long as possible in order to be realized enough large and measurable
redshift. The length of the way of the laser beam limit the earth's curve and
atmospheric attenuation of the laser's radiation. That length of the way, from the
laser to the spectrometer, can be more than hundred kilometers at exceptionally
atmospheric transparency. However, if one use a special prismatic retroreflector then
the lenght of the way of the laser beam from the laser to the retroreflector and back
to the spectrometer can be more than two hundred kilometers. The power of the laser
beam can be very high. Besides that the laser's radiation is coherent and its emission
line is very narrow. Consequently this method is simple, easily practicable and the
most reliable for the proving or disproving the hypothesis about the appearance of the
redshift in the spectrum of the light passed through the earth's atmosphere.
If a red shift were discovered in the spectrum of light radiation
passing through the atmosphere, in the manner described above, it would be of great
significance to astrophysics and astronomy in the whole.
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