DERIVATION OF THE PHENOMENON "INERTIA"
As a child, the Nobel Prize-winning physicist Richard Feynman asked his father
why a ball in his toy wagon moved backward whenever he pulled the wagon forward.
His father said that the answer lay in the tendency of moving things to keep moving,
and of stationary things to stay put. "This tendency is called inertia," said
Feynman senior. Then, with uncommon wisdom, he added: "But nobody knows why it is
My question is: what causes inertia, working as a force
opposite to the force by which the particle is influenced?
My answer is: read this page.
In this document, the word mass is frequently used.
The word mass is one of the most diffuse words in science. To the layman, the
concept of "mass" and weight are almost indistinguishable - massive objects are
those that weigh a lot. To the first year physics student, "mass" is weight
divided by a constant factor of 32 here on earth, but then weight is some other
value everywhere else, while mass remains a constant. To the advanced physics
student, "mass" may be all of the above - but it may also vary depending on
velocity, and when the velocity reaches the speed of light (which it can't do)
then it is no longer mass, it has become energy. In this document, the word "mass"
will refer to the thought of "inertial mass", as initially intended by Newton when
he first included it as a component of a classical mathematical equation. In that
form, "mass" is simply a natural resistance to any change in the current state of
motion of any specific part of existence.
The physical cause of inertia
Since I found a new concept determination for energy,
the definition of inertia has to be close because
Mass and energy are like the two sides of a coin. Mass always occurs together with
energy, and energy always together with mass, according to the relation
Energy and mass are like the two sides of a coin. What is this coin?
This coin is the momentum of the luxons! Energy and mass are only different
sides, different aspects of the luxon momentum.
Since energy has been defined by the luxon momentum, mass must be defined by the
luxon momentum, too. As everything consists of luxons, the relation
p = mic or mi = |p| / |c|
is universally true. Thus, instead of mass mi , simply
|p| / |c| can be written.
mi : = | p | / |c |
Inertial mass is the amount of the luxon momentum with the dimension kg.
The common definition of the momentum p:=miv
is, because of the universal validity of p=mic, actually
the definition of mass. Nevertheless, the momentum can be defined with
The rest mass of a photon is zero. Light has its inertial mass only because of its
movement. Here is a mass with movement as the condition for its existence. This
becomes understandable only with the definition of mass by
mi : = |p| / |c|
, because there is no momentum without movement.
Only this definition makes clear, that not the mass of the luxons (which
cannot exist without movement) is the peculiarity, although it seems so extraordinary
to us: What we usually define with "mass" doesn't have to move in order to exist.
The mass of my chair exists, although the chair is only standing in the corner.
The rest mass of a tardyon is a mass which seems to exist without movement.
Actually, the rest mass, too, is based upon movement. The mass of a tardyon
is the sum of the inertial masses of its inner luxons, which move with the velocity
What surprises is the mass of tardyons!
The luxon momentum is the source of all inertia
Much more important for the definition of mass than the clearing of this quantitative
relation is the proof that the luxon momentum is the basic and determining factor
One result of using momentum formulas is that it shows that mass is not a
fundamental property. Momentum is fundamental. [...] A new physical law is
postulated: All known particles are elements of momentum moving at a
. This is the result of extending a quantum theory formula for
massless particles to all particles. The new postulate is known to be true for
photons. They have no mass, move at the speed of light and have momentum. At
first, the new postulate seems to be untrue for particles with a rest mass.
Robert Rutkiewicz: A General Theory of
Particles and Forces
Mass is resistance against acceleration, is inertia against an acting force. A
tardyon has an inertia against an acting force due to its inner luxon momentums,
i.e. against other luxon momentums applied upon it. Its overall movement is the
result of all engaged luxon momentums. The overall momentum of all luxons determines
the velocity of a tardyon.
I assume the case that a tardyon absorbs a luxon and thus is accelerated by it.
In order to calculate the velocity of the tardyon after the acceleration, it is
not at all necessary to handle with masses and forces. It is absolutely enough
to calculate the sum of momentums of all engaged luxons. According to the law of
conservation of momentum, the velocity of the tardyon is unambiguously and
entirely determined by its luxon momentum. The overall momentum of its
luxons determines its velocity.
The inertia of a tardyon against the acceleration by forces, i.e. luxon momentum
applications, follows directly from the law of conservation of momentum! The
bigger the overall luxon momentum of a tardyon are (thus, the bigger its "mass"
is), the proportionally bigger its inertia against applied forces is,
because the obtained velocity change follows from the sum of all luxon momentum.
Thus, the concept of mass is a special case of the law of conservation of
Tardyon 1 is less accelerated by the same applied momentum than tardyon 2, because
the equilibrium of its inner luxon momentum is changed less by the applied momentum
than the inner momentum equilibrium of tardyon 2. Thus, its inertia is proportional
to the sum of its inner luxon momentum, according to:
before the acceleration
after the acceleration
Tardyon 1 has more luxon momentum than tardyon 2. Therefore, an absorbed luxon
momentum changes its overall momentum and thus its velocity less than the velocity
of tardyon 2. Its inertia is determined exclusively by its luxon momentum.
mi: = p1 /c + p2 /c + p3
/c + ... + pn / c
The inertia of a mass consists of its luxon momentum!
The bigger the mass is, i.e. the bigger the entire luxon momentum with
mi : = p / c
are, the less an applied force (an applied momentum) effects on the overall
momentum, the more inert is the tardyon.
Merely therefore is it impossible to accelerate a
tardyon to the velocity of light or even higher.
But why does it become more and more difficult to accelerate a tardyon, the more
its velocity comes near the velocity of light?
Because an acceleration is an approach to the velocity of light!
The intent to accelerate a tardyon to the velocity of light or faster is like
trying to dye a pot of red paint to white by mixing in white paint. It is impossible.
The paint will always stay a little pink. Only an approach to white can
be obtained, but not a pure white paint.
The definition of mass
My prefered definition of "mass" is the following:
Mass is inertia.
mi is the inertial mass of tardyons and luxons.
This definition is not the standard definition of the word "mass".
Matt Austern wrote:
This is an error. There is an absolute right or wrong!
This question comes up in the context of wondering whether photons are really
"massless," since, after all, they have nonzero energy and energy is equivalent
to mass according to Einstein's equation E=mc2
. The problem is simply
that people are using two different definitions of mass.The overwhelming consensus
among physicists today is to say that photons are massless. However, it is possible
to assign a "relativistic mass" to a photon which depends upon its wavelength.
This is based upon an old usage of the word "mass" which, though not strictly
wrong, is not used much today.
The old definition of mass, called "relativistic mass," assigns a mass to a
particle proportional to its total energy E, and involved the speed of light, c,
in the proportionality constant:
m = E / c2.(1)
This definition gives every object a velocity-dependent mass.
The modern definition assigns every object just one mass, an
invariant quantity that does not depend on velocity.This is given by
m = E_0 / c2, (2)
where E_0 is the total energy of that object at rest.
The first definition is often used in popularizations, and in some
elementary textbooks.It was once used by practicing physicists, but for
the last few decades, the vast majority of physicists have instead used the
second definition.Sometimes people will use the phrase "rest mass," or
"invariant mass," but this is just for emphasis: mass is mass.The
"relativistic mass" is never used at all.(If you see "relativistic mass"
in your first-year physics textbook, complain! There is no reason for books
to teach obsolete terminology.)
Note, by the way, that using the standard definition of mass, the
one given by Eq. (2), the equation "E = m c2
" is not
standard definition, the relation between the mass and energy of an object
can be written as
E = m c2 / sqrt(1 -v2/c2), (3)
E2 = m2 c4+p2 c2,(4)
where v is the object's velocity, and p is its momentum.
In one sense, any definition is just a matter of
convention. In practice, though, physicists now use this definition because
it is much more convenient. The "relativistic mass" of an object is really
just the same as its energy, and there isn't any reason to have another word
for energy: "energy" is a perfectly good word. The mass of an object,
though, is a fundamental and invariant property, and one for which we do
need a word.
There are people who still want to use
relativistic mass and it is not easy to settle an argument
over semantic issues because there is no absolute right or wrong,
just conventions of terminology.
I can`t agree with this definition of "mass". I prefer the old Definition
of the word mass. It is the same simple reason why I don`t like the definition of
an aether or absolute resting space:
Resting space doesn`t exist. There is not such a thing in nature!
Resting mass doesn`t exist. There is not such a thing in nature!
This is no conventions of terminology!
"Rest mass" is only a word and not a physical reality at all !
Mass (mi) is inertia .
A particle will 'show' inertia (slowness, resistance) against changes to its
velocity in relation to an inertial system, i.e. against acceleration. This
property was introduced in Newton's 2nd law as inertial mass, mi .
mi is the proportionality factor between the acceleration and the
resulting force on the particle. Thus Newton's 2nd law:
where is the acceleration
and the resulting force.
I`m only interested in this definition of mass as inertial
mass mi .
Mass is inertia. The "relativistic mass" of an object is not really
just the same as its energy.
Energy is not inertia!
Why is the concept of "(resting) mass"a pseudo-explanation?
According to the principle of relativity, no reference system is privileged, thus
the "(rest) mass mo in the "resting " system is not privileged either.
The standard definition of mass is in contradiction to the special theory of relativity.
The (rest) mass of a body is no explanation for the cause why it moves with
a velocity below the velocity of light, but the simple description that it does
so. The inertial mass mi of a body is called its (rest) mass
mo, if it is at rest in relation to the observer. The "rest mass" is
only a word for this, not an explanation. "Rest mass" is not a physical
characteristic at all, as the electric field or the temperature are.
But this is believed. This nonsense originates formulations as:
"This particle moves with a velocity below the velocity of light, because it has
a (rest) mass".
This is wrong. Right is:
We designate a part of its inertial mass as its "rest mass", because it
moves with a velocity below the velocity of light. In exactly this case it is
possible to rest with relation to it. The fact that a particle moves with a velocity
below the velocity of light, is the only reason for assigning a rest mass
to it. We do not have any other criterion for the existence of rest mass.
A number can be divided by two not for the cause that it is even but the other
way round: It is called "even" because it can be divided by two. Thus
it follows that all even numbers can be divided by two. But their being
"even" is no "explanation" for the fact that they can
be divided by two.
In the same way, the rest mass is no explanation for the fact that particles move
with a velocity below the velocity of light!
The resting of an particle is an attribute of the particle and not an
attribute of its mass!
The formulas of the special theories of relativity, however, are still contradicting
their own axiom of the principle of relativity, because they use the concept of
a rest mass mo. Of course, the moved
mass m' ( mi ) and the rest mass
mo are absolutely equal. This follows already from the
principle of relativity. But in this case the theory has to put up formulas
which do not need the mass mo.
Merely the luxon theory is able to overcome the contradiction of the theory
of relativity between the basic axiom (principle of relativity: All inertial
systems are equal) and formalism (in the formulas the rest mass mo is
In the luxon theory, this is no problem at all, because the entire mass of a body
is the sum of its luxons inertial mass. Not a trace of the independent form of
matter "rest mass". The reference system which is at rest with relation
to the body is in no way privileged before other inertial systems.
These, too, regard the mass of the body as the sum of the mass of its inner luxons
which move with the velocity of light!
Rest mass is no independent form of mass, but a form of luxon (inertial) mass.
This comprehension already follows from the principle of relativity. According to
the principle of relativity, no reference system is privileged, thus the
"rest mass" in the "resting " system is not privileged either.
The rest mass of a body is no form of energy as its chemical, electrical or thermal
energy. The rest mass is not converted to light energy as it is in case of a battery,
which converts chemical energy into electrical energy. Every type of energy
which is stored by a body increases its rest mass. The temperature of a body rises
together with its weight. The thermal energy of a body is not "converted" to its
rest mass. Because its thermal energy keeps existing inside!
Because of this it is a big mistake to simply designate the rest
mass of a body as its "mass". This mistake, unfortunately, is
very common and is the origin of many
misunderstandings. After all, luxons have inertial
mass, but no rest mass.
All energy resists to changes of movement; all energy acts like matter; a piece
of iron is heavier when it is red hot than when it is cold; the radiation crossing
the universe, as, for example, solar radiation, contains energy and thus, mass;
the sun and all stars loose mass with their radiation.
(Einstein/Infeld 1956, page 134