3 The Physical Elements of the Special Theory of Relativity
17
of light. The consequence of Einstein’s equivalence of mass and energy is that this
energy, as every other sort of energy, can principally be transformed into any other
form of energy, e.g. into heat. The sum of the energy, as well as sum of the masses
remain constant in any process. It is however a completely different thing to have one
milligram of matter lying on a desk in front of us, or to have the energy of this one
milligram changed into heat energy in our environment. We will give an example to
illustrate this:
We observe a pot containing 200 000 l of water with a temperature of 0
◦ C, and
we then add one milligram of matter to the pot. The pot now contains a total mass
of 200 000, 000 001 kg, with a total energy of E = mc
2
L = 200 000, 000 001 kg · 9 ·
10
16 m
2 s
−2
= 200 000, 000 001 · 9 · 10
16 J.
We will now completely transform the energy of the added milligram into
heat energy. Using Einstein’s equation, we receive the following heat quantity
E = 10
−6 kg · 9 · 10
16 m
2 s
−2
= 9 · 10
10 Nm = 9 · 10
10 J, in other words E = 9 ·
10
10
· 2, 4 · 10
−4 kcal = 2 · 10
7 kcal = 200 000 · 100 kcal.
This amount of energy would be enough to raise the temperature of the 200 000 l
of water from 0
◦ C to its boiling point. The energy needed to raise the temperature
of one litre of water by one degree is calculated as one kcal. (We ignore the fact
that the energy needed to raise the temperature from 1
◦ C to 2
◦ C and from 99
◦ C to
100
◦ C is not quite the same amount). The total sum of the energies and masses of
the 1 milligram, and the 200 000 l stay the same. Special Relativity teaches us that
the mass (the inertia) of the 200 000 l at 100
◦ C is approximately 1 milligram larger
than the mass of 200 000 l (with the same number of molecules) at 0
◦ C.
Every energy possesses an inertial mass; every mass is a carrier of energy.
It is an immediate expression of the equivalence of mass and energy that a moving
mass has to be larger than a static mass. A moving mass possesses not only the energy
of a static mass, but also the kinetic energy of its motion. Let us now compare the
inertial mass m o of a static solid, e.g. our milligram on the desk with the inertial mass
m that the same solid possesses whilst moving with respect to us with the velocity
v. During the process of passing by with the velocity v, we notice that the inertia of
our moving mass has increased, i.e. its resistance against acceleration has increased.
According to Special Relativity, the following equation is valid
m =
m o
1 − v 2 /c
2
L
.
(10)
The moving mass increases.
It follows that an object with a static mass larger than zero can never be accelerated
to the speed of light, even if we increase the forces beyond measure. The speed of
light is the privilege of the speed of light. A particle moving at the speed of light,
e.g. a photon or a neutrino will for an arbitrary observer always retain this speed and
will move with the speed of light throughout all eternity.
17
of light. The consequence of Einstein’s equivalence of mass and energy is that this
energy, as every other sort of energy, can principally be transformed into any other
form of energy, e.g. into heat. The sum of the energy, as well as sum of the masses
remain constant in any process. It is however a completely different thing to have one
milligram of matter lying on a desk in front of us, or to have the energy of this one
milligram changed into heat energy in our environment. We will give an example to
illustrate this:
We observe a pot containing 200 000 l of water with a temperature of 0
◦ C, and
we then add one milligram of matter to the pot. The pot now contains a total mass
of 200 000, 000 001 kg, with a total energy of E = mc
2
L = 200 000, 000 001 kg · 9 ·
10
16 m
2 s
−2
= 200 000, 000 001 · 9 · 10
16 J.
We will now completely transform the energy of the added milligram into
heat energy. Using Einstein’s equation, we receive the following heat quantity
E = 10
−6 kg · 9 · 10
16 m
2 s
−2
= 9 · 10
10 Nm = 9 · 10
10 J, in other words E = 9 ·
10
10
· 2, 4 · 10
−4 kcal = 2 · 10
7 kcal = 200 000 · 100 kcal.
This amount of energy would be enough to raise the temperature of the 200 000 l
of water from 0
◦ C to its boiling point. The energy needed to raise the temperature
of one litre of water by one degree is calculated as one kcal. (We ignore the fact
that the energy needed to raise the temperature from 1
◦ C to 2
◦ C and from 99
◦ C to
100
◦ C is not quite the same amount). The total sum of the energies and masses of
the 1 milligram, and the 200 000 l stay the same. Special Relativity teaches us that
the mass (the inertia) of the 200 000 l at 100
◦ C is approximately 1 milligram larger
than the mass of 200 000 l (with the same number of molecules) at 0
◦ C.
Every energy possesses an inertial mass; every mass is a carrier of energy.
It is an immediate expression of the equivalence of mass and energy that a moving
mass has to be larger than a static mass. A moving mass possesses not only the energy
of a static mass, but also the kinetic energy of its motion. Let us now compare the
inertial mass m o of a static solid, e.g. our milligram on the desk with the inertial mass
m that the same solid possesses whilst moving with respect to us with the velocity
v. During the process of passing by with the velocity v, we notice that the inertia of
our moving mass has increased, i.e. its resistance against acceleration has increased.
According to Special Relativity, the following equation is valid
m =
m o
1 − v 2 /c
2
L
.
(10)
The moving mass increases.
It follows that an object with a static mass larger than zero can never be accelerated
to the speed of light, even if we increase the forces beyond measure. The speed of
light is the privilege of the speed of light. A particle moving at the speed of light,
e.g. a photon or a neutrino will for an arbitrary observer always retain this speed and
will move with the speed of light throughout all eternity.