Section 16

Experience of Special Relativity

April 2, 2022

Is special relativity supported by experience?

This question is not easily answered as explained by Fizeau’s experiment.

Special Relativity came from the Maxwell-Lorentz theory of electromagnetic phenomena. Thus, everything that supports the electromagnetic theory also supports Special Relativity.

Special Relativity Proven By Starlight

Special Relativity can predict the effects from the light from the fixed stars because the Earth moves relatively to those stars.

One effect is:

  • the apparent position of those stars resulting from the Earth’s motion around the sun (aberration), and
  • the influence of the radial components of the relative motions of the fixed stars with respect to the earth on the colour of their starlight
    • This manifests itself in a slight displacement of the spectral lines of the light from a fixed star, compared with the position of the same spectral lines when they are produced by a terrestrial source of light (Doppler principle).

There are so many experimental arguments in favour of the Maxwell-Lorentz theory that are also in favour of my theory of relativity.

In reality they limit the theoretical possibilities to such an extent, that no other theory than that of Maxwell and Lorentz has been able to hold its own when tested by experience.

But there are two classes of experimental facts hitherto obtained which can be represented in the Maxwell-Lorentz theory only by the introduction of an auxiliary hypothesis, which in itself — i.e. without making use of the theory of relativity — appears extraneous.

Special Relativity Proven By Electrons

Cathode rays and β-rays emitted by radioactive substances are made up of electrons. These have very small inertia but high velocity.

Their motion can be studied exactly by the deflection of these rays under the influence of electric and magnetic fields.

Electro-dynamic theory is unable to give an account of their nature. This is because electrical masses of one sign repel each other. The negative electrical masses in the electron would necessarily be scattered under the influence of their mutual repulsions, unless there are forces of another unknown kind operating between them*.

*General Relativity renders it likely that the electrical masses of an electron are held together by gravitational forces.

If we now assume that the relative distances between the electrical masses constituting the electron remain unchanged during the motion of the electron (rigid connection in the sense of classical mechanics), we arrive at a law of motion of the electron which does not agree with experience.

H. A. Lorentz first introduced the hypothesis that electrons contract in the direction of motion=

 1 - (v2/c2)

This hypothesis gives us a particular law of motion which has been confirmed with great precision in recent years.

My theory of relativity leads to the same law of motion, without needing any special hypothesis on the electron’s structure and behaviour.

We arrived at a similar conclusion in Section 13 in connection with Fizeau’s experiment. My theory of relativity predicted the result without needing to know the the physical nature of the liquid.

Special Relativity Eliminates the Need for the Aether of Space

Can the motion of the earth in space be made perceptible in terrestrial experiments? Section 5 says no.

Before my theory of relativity existed, it was difficult to reconcile this “no” answer. Physicists had inherited prejudices on time and space. They did believed that the Galilei transformation was of prime importance for changing over from one body of reference to another.

The Maxwell-Lorentz equations hold for a non-moving viewpoint K. But they do not hold for a moving viewpoint K' moving uniformly with respect to non-moving K, if we assume that the relations of the Galileian transformation exist between K and K'.

Thus, of all Galileian coordinate systems, movement in non-moving K is physically unique. This implied that=

  • the non-moving K was at rest with a hypothetical æther of space

This motion of the moving K' against the æther was called the “æther-drift” relative to K'. It was dictated by more complicated laws which were supposed to hold relative to the moving K'.

Such an æther-drift was assumed relative to the earth. For a long time, physicists tried to detect the existence of an æther-drift on the earth’s surface.

The Michelson-Morley Experiment

Michelson devised an experiment for this.

  • Two mirrors were arranged on a rigid body so that the reflecting surfaces face each other.
  • If the earth were at rest in the æther, then the light would pass from one mirror to the other and back again in a definite time T
  • If the earth were moving relatively to the æther, then the light would return at a slightly different time T'
    • Moreover, the speed of the aether v would make this time T' is different when the body is moving perpendicularly to the planes of the mirrors from that resulting when the motion is parallel to these planes.

The experiment showed that there was no difference in time. This perplexed physicists.

Lorentz and FitzGerald rescued the theory by assuming that the motion of the Earth relative to the æther produces a contraction of the Earth in the direction of motion. The amount of contraction is just enough to compensate for the difference in time.

Section 12 of my theory of relativity shows that this solution was the right one. However, my theory of relativity has a better solution= there is no such thing as a “specially favoured” (unique) coordinate system that allows the æther-idea. Hence, there can be no æther-drift nor any experiment with which to demonstrate it.

Instead, the contraction of moving bodies comes from the two fundamental principles of my theory without the introduction of particular hypotheses [i.e. the contraction comes from spacetime itself].

The prime factor involved is not the motion in itself, but the motion with respect to the body of reference chosen. Thus=

  • for a coordinate system moving with the earth, the mirror system of Michelson and Morley is not shortened
  • but it is shortened for a coordinate system which is at rest relatively to the sun