/ Research / Einstein / Relativity / General Results Of The Theory: E=mc2

Section 15

General Results Of The Theory: E=mc2

by Albert Einstein Icon

5 minutes • 980 words

Special Relativity grew out of electrodynamics and optics. It has considerably simplified the theoretical structure*. It has:

simplified the derivation of laws
considerably reduced the number of independent hypotheses which form the basis of theory
- This is much more important

Superphysics Note

We argue that relativity, through Einstein’s field equations, actually made Physics unecessarily complicated

Special Relativity has rendered the Maxwell-Lorentz theory so plausible. I modified Classical mechanics to make it compatible with my Special Relativity. This modification affects only the laws for rapid motions, where the velocities of matter v are near the velocity of light.

Examples are the motions of electrons and ions. For slower motions*, the variations from the laws of classical mechanics are too small to be evident. We shall consider the motion of stars later in General Relativity.

Einstein Con-man

Superphysics Note

Here, Einstein says his theory only works for fast-moving objects. This is false. In reality, it only works for electromagnetic particles. Speed has nothing to do with it. This is proven by the Aharonov-Bohm experiment. Instead, it is the Layer or Element of the particle that decides whether it follows Special Relativity or not. Fast speed or dynamism is a property of Electromagnetism just as slow speed or staticity is a property of the Strong Force.

Relativity says that the kinetic energy of a mass m is no longer given by:

m (v2/2)

Instead, we replace it with:

mc2 / √ (1-(v2/c2))

This expression approaches infinity as the velocity v approaches the velocity of light c*. The velocity must therefore always remain less than c.

Superphysics Note

Here, Einstein imposes c as the supreme judge of all movemements. Newton sourced all movement from ‘Lord God’ (Principia, Book 3). But Einstein sourced all movement from spacetime which is then evidenced by light. But spacetime is based on imagination and so Einstein’s god of motion is really his own imagination using the language of math. This leads to arbitrary shapes of the universe in Section 32.

Its kinetic energy in the form of a series is:

mc2 + m (v2/2) + 3/8 m (v4/c2) + . . .

When v2 / c2 is small compared with unity, the 3rd of these terms is always small in comparison with the 2nd. The last part is alone considered in classical mechanics.

mc2 does not contain the velocity. It is not needed if we are only asking how the energy of a point-mass depends on the velocity. We shall speak of its essential significance later.

Special Relativity is important because it changes our concept of mass. Before Relativity, physics recognised two conservation laws:

the law of the conservation of energy
the law of the conservation of mass

These two fundamental laws appeared independent of each other. Relativity unites them into one law*.

Superphysics Note

This is why the word ‘mass’ is now used for both inertial mass of the Strong Force (Newtonian) measured in grams, and electromagnetic mass of quantum particles measured in electron volts. We fix this by renaming electromagnetic mass as electromagentic potential. In this way, a photon is not a massless particle, but a kinetic particle (non-potential).

Relativity requires that the law of the conservation of energy have a reference to a non-moving viewpoint K and also with respect to every uniformly moving viewpoint K' relative to non-moving K, or, briefly, relative to every “Galileian” system of coordinates.

In contrast to classical mechanics, the Lorentz transformation is the deciding factor in the transition from one such system to another.

Our conclusion matches the fundamental equations of the electrodynamics of Maxwell:

A body moving with the velocity v, which absorbs* an amount of energy E0 as radiation without suffering a change in velocity in the process, has its energy increased as a consequence by an amount E0 / √ 1-(v2c2)

Note

Einstein Note: E0 is the energy taken up, as judged from a coordinate system moving with the body.

The required energy of the body comes out to be

(( m + E0/c2 ) c2) / √1 − (v2/c2)

Thus, the body has the same energy as a body of mass ( m + E0 / c2 ) moving with the velocity v.

Hence: If a body takes up an amount of energy E0, then its inertial mass increases by an amount E0 / c2

The inertial mass of a body is not a constant, but varies according to the change in the energy of the body. The inertial mass of a system of bodies can even be regarded as a measure of its energy.

The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy. This is only valid provided that the system neither takes up nor sends out energy.

The expression for the energy is:

(mc2 + E0) / √ 1-(v2 / c2)

Here, mc2 is nothing but the energy possessed by the body* before it absorbed the energy E0.

Note

*As judged from a co-ordinate system moving with the body.

A direct comparison of this relation with experiment is not possible now because the changes in energy E0 to which we can subject a system are not large enough to make themselves perceptible as a change in the inertial mass of the system.

E0 / c2 is too small compared with the mass m, which was present before the alteration of the energy. This allowed classical mechanics to establish the conservation of mass as a law of independent validity.

The Faraday-Maxwell interpretation of electromagnetic convinced physicists that instantaneous actions at a distance (without an intermediary medium) do not exist under Newton’s law of gravitation.

My theory of relativity, on the other hand, says that action at a distance at the speed of light is always instantaneous as having an infinite velocity. This is because of the fundamental role of the velocity c in my theory.