The Special Theory of Relativity, Part 1 – Time and Distance – Richard Jones

Einstein’s Special Theory of Relativity was presented to the world in 1905. It had its origins in Scottish physicist J Clerk Maxwell’s work on the propagation of light. From experimental laws of electricity and magnetism he used mathematics to derive a formula for the speed of light which made no mention of what that speed might be relative to.

An idea developed that there must be a physical medium involved which was given the name ether (not the anaesthetic!). The Earth in its orbit, six months apart on opposite sides of the Sun, must be travelling through the ether in opposite directions. American physicist Albert Michelson developed an optical interferometer capable of detecting tiny differences that this would cause in the travel times of two orthogonal light beams. The Michelson-Morley experiment as it became known, detected no difference and this was arguably the most important negative result in the history of scientific experiment.

Einstein gave no citations nor references in his publications, helping to build for himself the reputation of a genius whose brain conjured Special Relativity out of pure thought. This was not so. Galileo in 1632 stated that the laws of motion are the same in all inertial frames of reference and that the concept of absolute motion is meaningless. Inertial means frames where these is no acceleration, change of direction nor rotation. Hendrik Lorentz in 1889 proposed relativistic time dilation for fast moving objects. In 1900, Henri Poincaré described the momentum of particles in an electric field with the equation E = M c 2 . In 1904, he formulated the Principle of Relativity according to which the laws of physical phenomena must be the same for a stationary observer as for an observer carried along in a uniform motion of translation; so that we have not and cannot have any means of discerning whether or not we are carried along in such a motion.

Astronomical observations demonstrate that light travels at a constant speed relative to all inertial observers. This is reinforced by the Principle of Causality which hints that no material object nor information can be transmitted at a speed greater than that of light.

Einstein’s genius was to take all these inexplicable observations and obscure theoretical ideas and construct a meaningful and all-encompassing theory from them. He was not a top-ranking mathematician but his outstanding gift was to develop “thought experiments” which made it possible for many people to understand the entirely unfamiliar consequences of the constancy of the speed of light and the Principle of Relativity. He realised that if the speed of light is constant for all observers, since speed = distance / time, then distance and time are different for different observers. In particular, there is no simultaneity of time for different observers. If Observer A see Event 1 happening before Event 2, Observer B could see Event 2 before Event 1.

Two other consequences were described in this first talk on Special Relativity: Time Dilation and Length Contraction. They only happen at “relativistic speeds”, that is speeds that are a substantial fraction of the speed of light. When A observes the time measured by B’s clock, A sees B’s time run more slowly than his or her own. B’s time is stretched or dilated. B watching A will see the same thing for A – that has to be since we have the same laws for all.

The dilated time compared to “Proper Time” is described by:

t’ = ϒ Δt

Where t’ is dilated time, t is proper time v is velocity and c the speed of light. Gamma is the Lorentz Factor and is always greater than one. It approaches infinity at the speed of light.

The Length Contraction formula relates Contracted Length to Proper Length:

L’ = L/ϒ

Time Dilation was first confirmed by Ives and Stilwell in 1938 in a very difficult experimental measurement of the Relativistic Doppler Effect. In recent decades, observations of unstable sub-atomic particles called muons show that they survive longer at high speed than they do when at rest relative to us. For us, we see muons’ time slow down. If muons had wrist watches, they would see their time run normally but they travel further than muonic expectations would otherwise suggest because their path through space is much shortened. These are not optical illusions but real effects that have in over one hundred years been shown to follow Einstein’s predictions exactly and to have no other accepted physical explanation. They also have remarkable implications for future long-distance space travel.