MATTER, MASS AND ELECTROMAGNETIC MASS

There are many theories and definitions concerning the concepts of matter and mass. One artificial and ad hoc theory, electromagnetic mass, has been incorporated into many current theories, including Special Relativity. However, it turns out that electromagnetic mass is not really a mass of matter, but rather only a theoretical resistance of the medium through which matter and some electromagnetic phenomena pass.

**A. What is Matter and
what is Mass?**

The Greek word ‘maza’ originally
meant an inferior quality of bread.[1] Archimedes used the related word ‘masse’ to
mean a lump or block. The Latin word of
the early Christian Church, ‘*Id*.,
p. 19) Then, in the 13^{th}
century, a disciple of Thomas Aquinas, Aegidius Romanus, conceived the idea of *quantitas
materiae* (‘quantity of matter’) “as a measure of mass or matter,
independent of determinations of volume or weight.”[2] (*Id*., p. 45) Throughout most of recorded history, matter
and mass were thought of as synonymous terms. For example, Galileo considered ‘mass’ as
“another name for matter itself.”
(Jammer, 1961, pp. 51 – 52)

Kepler, Galileo, Descartes, and *Id*., pp. 55, 56) *corporis vel massae*) with the quantity of matter* *(*quantitas
materiae*), however his three laws of motion made no explicit mention of
mass. The concept of mass is only
implied by the acceleration of a body in his second law.[3] (*Id*., p. 65) Thus, it was left for Euler in 1736 to
explicitly state a formula for ‘inertial mass:’
“Force equals mass times acceleration.”
(Jammer, 1961, p. 89)
Reciprocally, m = F/a. Inertial
mass is sometimes also referred to as ‘mechanical mass.’ (see Feynman, 1964, p. 28-3)

During the early part of the 18^{th}
century, German scientist Gottfried Leibniz (1646 – 1716) invented complicated
and confusing theories of mass and matter.
In the mid 18^{th} century, Immanuel Kant criticized ^{th} century, French physicist Bané de
Saint-Venont, Maxwell, Ernst Mach and Hertz all attempted to invent new
definitions of mass. Mach and
Saint-Venont each rejected *quantitas materiae*, but failed to come up
with an improved alternative, although Mach did arrive at an acceptable
theoretical construct.[5] (*Id*., p. 100) Maxwell’s theory assigned a priority of force
over mass, and Hertz’s definition essentially redefined mass by weight. (*Id*, pp. 103, 105)

During the early 20^{th}
century, the Italian school attempted numerous contrived definitions of mass
but without much success. Their attempts
resulted in several definitions of ‘gravitational mass,’ which we shall briefly
discuss in Chapter 40. (*Id*., p.
110) Later, scientists Hans Herm (in
1938), Pendse (in 1939), Herbert Simon (in 1947), and Alfred Tarshi attempted
to define the concept of mass as a ‘primitive’ concept, without using other
concepts to make it meaningful. (Jammer,
1961, pp. 112 – 119) Two of such
attempts merely resulted in mass ratios that can be obtained by Euler’s
formula, and the others attempted to define mass by statistical inference. All involved the motion of bodies by reason
of force. Jammer concluded that in
general: “no attempts to formalize
Newtonian mechanics by a precise explicit definition of mass have been very
successful,” and he gave as an example of such circular definitions:

“We obtain our knowledge of
forces by having some theory about masses, and our knowledge about masses by
having some theory about forces.” (*Id*.,
p. 120)

Thus, it
may be impossible to devise a meaningful qualitative definition of mass without
resort to an empirical, mechanically covariant and quantitative interaction
between the variables of Euler’s formula:
m = F/a.

Definitions of ‘matter’ have been
equally frustrating. Is it atomic in
nature, composed of quarks and gluons or strings (quantum mechanics
definitions)? Is it electromagnetic in
nature? Is it merely stored energy? Is it the effect of an interaction between
particles and some phenomenon called the Higgs field? (Close, pp. 192 – 193) Does matter even exist? There are many very confusing theories
concerning both matter and mass. As one
sage writer concluded: “Mass is a mess.”

**B. What is Electromagnetic Mass?**

‘Electromagnetic mass’ is a highly theoretical concept
that was concocted by physicists and mathematicians around the turn of the 20^{th}
century. The reason why we need to
discuss and understand this concept a century later, is two-fold: 1) Einstein based his concepts of
‘relativistic mass’ and ‘relativistic dynamics’ on electromagnetic mass,
and 2) vestiges of electromagnetic mass
remain with us in the form of other dubious theories.

Remember that in Newtonian mechanics, the concept of
inertial mass (m) was defined and empirically quantified by Euler’s
formula: m = F/a.[6] However, during the mid 19^{th}
century it was realized that this formula was only an idealization, because it
ignored the __resistances__ present in the body’s environment, such as air,
radiation and friction. A body’s (or a
particle’s) environment of resistances were later referred to by the terms
‘medium’ or ‘field.’ Because of such
inertial resistances, the acceleration of a terrestrial body is less than the
idyllic acceleration that theoretically exists in empty space. Therefore, the terrestrial mathematical
inertial mass that is empirically defined by the factor F/a is greater than the
idyllic mass in empty space. (see
Jammer, 2000, p. 32) This ‘greater
mathematical mass,’ its magnitudes and its theoretical variations are the
subjects of our discussion in this chapter.

When the influence of environmental resistances upon a
body’s acceleration was realized in the mid 19^{th} century, this
phenomenon at first resulted in a concept known as ‘hydrodynamical mass.’ Every body that moves through a fluid medium
quite naturally experiences a resistance to its motion. Therefore, the force exerted on the body by
the medium results in less than an idyllic mathematical acceleration (a = F/m),
the magnitude of which depends upon “the shape of the body and the nature of
the medium.” (Jammer, 2000, p. 33) When algebraically expressed in mathematical
terms of m = F/a, the reduction in acceleration ‘a’ algebraically resulted in
an increase in mass ‘m,’ and such increase has sometimes been called a ‘virtual
mass.’ This mathematical convention of
arbitrarily referring to the effect of an environmental resistance as an
increase in the mass (or inertia) of the body moving through such environment
(or medium) is the root cause of much of the confusion about mass that has
followed. If Euler’s equation had simply
been changed to m = F/(a – R), where R is the environmental resistance or the
resistance of the medium, then much of such confusion (and many dubious
theories and interpretations) could have been avoided.

What happens if the medium is not a fluid but rather an
electromagnetic field, and the body is a charged particle such as an
electron? In 1881, by analogy to the
hydrodynamical mass scenario, British physicist J. J. Thompson (1856 – 1940)
theorized that the electromagnetic field (induced by the relative motion of the
charged particle itself) caused a retardation or resistance to its acceleration
that was “__equivalent to an increase in mass__ of the charged moving
sphere.”[7] (Jammer, 1961, pp. 136 – 137) This type of electromagnetic resistance was
later described as ‘self-induced.’ (see
Feynman, 1964, pp. 28-4 through 28-8)

In 1889, a paper published by British physicist Oliver
Heavyside (1850 – 1925) dramatically expanded Thompson’s analogy to
hydrodynamical mass by referring to the theoretical increase in mass __as if__
it was a physically significant phenomenon.
For Heavyside, the electromagnetic resistance was “not only analogous to
mechanical inertia but an inertial effect *sui generis*. In fact, Heavyside speaks explicitly of an
‘electric force of inertia.’” (Jammer,
1961, p. 141)

Whereas, before Heavyside’s paper there were mechanical
theories of electromagnetism (such as Maxwell’s), after the publication of
Heavyside’s paper there were numerous __electromagnetic theories of mechanics__
which asserted that inertial mass was basically an inductive effect of
electrodynamics. (*Id*., pp. 136,
141 – 142, 144) Imaginative concepts of
‘electromagnetic mass’ and ‘electromagnetic momentum’ were soon introduced by
Poynting, Abraham, Lorentz, Wein, Kaufmann, Poincaré, Bucherer, Einstein, and
others. (*Id*., pp. 142 – 145; see Figure 17.1) However, they were only myths, because
‘electromagnetic mass’ is only a myth.
In reality, it is merely an electromagnetic __resistance__ in the
environment of a charged particle (i.e. an electron). It might even be more correct to describe the
effect as ‘electromagnetic inertia.’[8] (see Feynman, 1964, p. 28-10)

**C. The Electromagnetic World Picture**

The concept of electromagnetic mass
ultimately resulted in the theoretical attempt to “explain __all__ processes
in nature in terms of convection [electric] currents and their electromagnetic
radiation.” It was dubbed the
‘electromagnetic world-picture’ by its most ardent advocate, German
mathematical physicist Max Abraham (1875 – 1922).[9] (Jammer, 2000, p. 35) It was necessary for the proponents of this
view to describe and deal with mass totally as an electromagnetic
phenomenon. (Goldberg, p. 133) This was nothing less than an attempt to
strip matter of its substance, and to negate the existence of material
mass. As German physicist Walter
Kaufmann (1871 – 1947) conjectured: “the
total mass of the electron is merely an electromagnetic phenomenon;” and his
colleague Max Abraham proclaimed: “the
inertia of the electron originates in the magnetic field.” (Jammer, 2000, pp. 35, 36) These conjectures may be regarded “as the
first field-theoretic treatment of elementary particles.” (*Id*., p. 35; see Chapter 34)

In 1901, Kaufmann began experiments
to measure the inertia and the mass of electrons that were theoretically moving
at speeds near to that of light.[10] Kaufmann was attempting to measure the ratio
of the fixed charge of the electron to its mass, as a function of the
electron’s velocity. He concluded that
such ratio decreased as the electron’s velocity increased, which he interpreted
as an increase of the electron’s mass.[11] (see Figure 17.1B) The problem then was to invent a theory that
might account for this effect.
(Goldberg, p. 134)

In 1902, Abraham postulated that the
electron was a rigid sphere. [12] After much conjectured theorizing, he
calculated the magnitude of the electromagnetic mass of the electron depending
upon its speed and __direction of motion__.
The mass of the electron in its direction of motion relative to the __ether__
he called the ‘longitudinal mass.’ Since
no experiment has ever been devised to measure longitudinal mass, its *ad hoc* theoretical magnitudes remain
completely speculative. The electron’s
mass in the direction __perpendicular__ to its motion Abraham called the
‘transverse mass.’ After many
complicated mathematical calculations he concluded that his *ad hoc*
magnitudes for the transverse mass of the electron substantially agreed with
Kaufmann’s experimental deflection results, even though such results were not
certain. (Goldberg, p. 135)

In April 1904, Lorentz published a
paper that contained his radical transformation equations and his attempts to
explain the null results of Michelson’s experiments. (see Chapter 16) Lorentz’s paper also contained his theories
concerning electromagnetic mass.
Lorentz’s theory disagreed with Abraham’s in several respects. His formula for the electron’s change in mass
depended upon his __Lorentz transformations__ and the resulting contraction
or deformation of the electron.[13] Consequently, Lorentz’s *ad hoc*
magnitudes for the electron’s longitudinal and transverse mass were somewhat
different than Abraham’s theoretical magnitudes. (see Chart 31.1) In his April 1904 paper, Lorentz rationalized
that his magnitudes for electrodynamic mass agreed with Kaufmann’s experimental
results “nearly as well as with those of Abraham.” (Lorentz, 1904c [

In 1905, Einstein’s Special Theory
of Relativity was published. In Section
10 thereof, he sought to determine the magnitude of the __motion__ of the
electron. First, Einstein determined the
equations for the motion and mass of the electron when it was ‘at rest’ in Lange’s
moving inertial reference frame. He then
transformed such equations with Lorentz transformations and his own
transformations for Maxwell’s equations, and inquired “as to the ‘longitudinal’
and the ‘transverse’ mass of the moving electron?” (Einstein, 1905d [Dover, 1952, pp. 61 –
62]) Thereafter, Einstein derived:

Longitudinal mass = m/(√1 – v^{2}/*c*^{2})^{3}

Transverse mass = m/1 – v^{2}/*c*^{2}

(*Id*.

We shall save the discussion and
scrutiny of Einstein’s concept of Relativistic Mass, and the events that
surrounded it, until Chapter 32.[15] The points to be made here are two-fold. First, Einstein utilized the same basic *ad
hoc* and arbitrary concepts and methodologies as Kaufmann, Abraham, Poincaré
and Lorentz used (which would include ether) in order to arrive at his abstract
magnitudes for electromagnetic mass.
Second, Einstein premised his concepts of relativistic mass and
relativistic dynamics on the *ad hoc* concept of electromagnetic mass
(which in reality is __not a mass__ of matter, but only a __resistance__
of the electromagnetic medium), and on Abraham’s *ad hoc* and immeasurable
concept of longitudinal mass.

In 1906, Poincaré published a paper
that attempted to correct and defend several of Lorentz’s concepts related to
the electromagnetic mass. He theorized
that non-electromagnetic forces must be present in order to hold the deformable
electron and its charge together and to maintain their mutual repulsion in an
infinitesimal space. However, such a
theory would appear to contradict the total electromagnetic concept of
mass. If Poincaré’s theory were
accepted, the only way to save the electromagnetic concept of mass would be “to
describe the electron as a structureless point charge” with a radius of
zero. (Jammer, 2000, p. 36) With this scenario, the energy of the
electron’s mass would become infinite.
Jammer concluded that “classical electromagnetic theory has never
resolved this problem.”[16] (*Id*.

“The early enthusiasm with which the theory was met, however, soon diminished, for it became increasingly clear that the electromagnetic theory of mass was unable to carry out successfully the necessary generalizations for the constituents of matter other than electrons.”[17] (Jammer, 1961, p. 152)

**D.
Feynman’s Problems with Electromagnetic Mass**

In his 1964 lecture,
entitled “Electromagnetic Mass,” Feynman applied Special Relativity to
Maxwell’s equations which resulted in the proposition: that a charged particle in an EM field will
have a __momentum__ proportional to its velocity. (Feynman, 1964, pp. 28-1, 28-3) This means that there must be a mass as “the
coefficient between momentum and velocity.”
(*Id*., p. 28-5)

“The momentum in the
field—the electromagnetic momentum—is proportional to *v*. It is just what we should have for a particle
with the mass equal to the coefficient of *v*. We can, therefore, call this coefficient the
electromagnetic mass.” (*Id*., p.
28-3)

The __energy__ of the charged particle in the EM field must also be
proportional to the velocity, “because in the __relativity__ theory they are
different aspects of the same four-vector.”
(*Id*., p. 27-1)

However, when “concepts
of electromagnetic momentum and energy [are] applied to the electron or any
charged particle,” difficulties occur.
(Feynman, 1964, p. 28-1) Even,
“when electromagnetism is joined to quantum mechanics [QED], the difficulties
remain.” (*Id*.*Id*.,
p. 28-4); 2) where does the
[electromagnetic] mass come from” (*Id*., p. 28-3); 3) where does the extra force [of resistance]
come from” (*Id*., p. 28-7); and 4)
how can “the idea of an electron as a simple point charge…be maintained.” (*Id*., p. 28-6)

Feynman attempted to
solve the paradox of the above difficulties with every conceivable theory, but
to no avail. He concluded that
“difficulties associated with” Maxwell’s classical electromagnetics theory were
the cause, and therefore Maxwell’s theory needed to be modified. (Feynman, 1964, p. 28-1) He even attempted to modify Maxwell’s theory,
but again he could not find a solution.
(*Id*., pp. 28-6 through 28-12)

The author would like to
suggest that perhaps Feynman was looking in the wrong place. In other words, that Einstein’s relativistic
concepts, which defined Feynman’s basic premises, were the culprits. In effect, that: 1) Einstein’s concept of electromagnetic
(relativistic) mass is not a material mass, but rather is only a theoretical
electromagnetic resistance; 2) that
electromagnetic (relativistic) momentum, electromagnetic (relativistic) energy
(if they do exist), and relativistic mass (which is only a variation of electromagnetic
mass) are not proportional to, nor dependant upon, any velocity (see Chapter 31);
and 3) that E = m*c*^{2} is
*inter alia* only a general
approximation of convertibility and not a rigorous formula of equivalence. (Chapter 32)

**E. Conclusions**

Material mass remains an abstract and amorphous concept even though, along with space and time, it should be one of the most fundamental concepts in nature. However, this should not be considered as a revelation, because “the most important and most fruitful concepts are [often] those to which it is impossible to attach a well-established meaning.”[19] (Kramers, 1947, p. 196) Jammer concludes:

“The notion of mass seems to elude all attempts at a fully comprehensive elucidation and a logically as well as scientifically unobjectionable definition…” (Jammer, 1961, pp. 223 – 224)

“One has to admit that
in spite of the concerted effort of physicists and philosophers, mathematicians
and logicians, no final clarification of the concept of mass has been
reached.” (*Id*., p. 224)

[1] Similar words in Hebrew and Egyptian meant substantially the same thing.

[2] The 15^{th}
century concept of ‘impetus’ required the concept of quantity of matter.

[3] Newton
referred to the words ‘body,’ ‘mass’ and ‘matter’ as meaning the same thing,
and he defined its quantity as ‘arising from its density and bulk
conjointly.’ (Newton, *Principia*
[Motte, Vol. 1, p. 1])

[4] In other words, Lavoisier asserted that the same quantity of matter is present after a chemical reaction as was present before such reaction.

[5] Mach’s
definition was equivalent to

[6] In Newtonian mechanics, mass “was a number which was constant, unchanging and invariant with regard to different frames of reference. It only changed when the object itself changed,” i.e. burned. (Goldberg, p. 132)

[7] In other
words, Thompson only conceived of the process “as if” the mass __hypothetically__
increased. (Jammer, 1961, p. 137)

[8] In fact,
Lorentz did describe the effect as ‘electromagnetic inertia.’ (see Goldberg, p. 93) According to Lorentz’s theory of the
electron, electromagnetic inertia was the force exerted by a magnetic field on
the electron in the direction perpendicular to its motion. (*Id*.,
p. 134; see Figure 17.1)

[9] Ether was the fundamental phenomenon of this conceptual view, “charge was the manifestation of forces exerted on the ether,” and mass was the result of the inertia of electric charge moving through various fields. (see Goldberg, p. 133)

[10] Kaufmann was using electrons that were naturally ejected from radium bromide. (Goldberg, p. 134)

[11] Such
interpretation was premised upon

[12] This postulate was critical, because a non-rigid or deformable electron would require other forces to hold it together, which would constitute a contradiction to Abraham’s theory. (Goldberg, pp. 134 – 135)

[13] This effort to remain consistent with the other contraction predictions of his paper resulted in serious problems for his electromagnetic mass theory, which even Poincaré’s heroic rationalizations failed to cure. (Goldberg, p. 136)

[14] This should not be considered as amazing, because Lorentz published his magnitudes in April 1904, the year before Einstein’s Special Theory paper. On the other hand, Einstein’s magnitudes for transverse mass were dramatically different than those of Abraham and Lorentz. (Chart 31.1B)

[15]
Einstein applied his Lorentz transformations to the concept of electromagnetic
mass in order to describe a variable, velocity-dependent concept of mass
(‘relativistic mass’). However, this
concept of relativistic mass was merely a mathematical generalization of the
prior *ad hoc* work of others, and coincidentally its* *magnitudes
only roughly approximate dubious experimental results. Likewise, ‘relativistic dynamics’ depends
upon the validity of relativistic mass and the Lorentz transformations. (see Chapter 31)

[16] Often when theorists are forced to come up with impossible solutions in order to save a theory, this means that the theory is wrong. Such was the case with ‘ether,’ and also with ‘electromagnetic mass.’

[17]
Nevertheless, vestiges of electromagnetic mass live on in certain concepts,
such as Einstein’s relativistic mass, E = m*c*^{2},
quantum mechanics, quantum electrodynamics (QED), quantum field theory,
particle physics, superstring theory, and General Relativity.

[18] The two
theories were the classical theory and Einstein’s relativistic theories “that
mass depended on velocity” and E = m*c*^{2}. (Feynman, 1964, p. 28-4) Feynman also premised this discrepancy upon
dubious conclusions by Lorentz. (*Id*.

[19] In this regard, consider such concepts as: infinity, eternity, creation of the universe, and creation of life.