Special relativity

Special relativity is the first of the modern theories of physics and the template for all the problems that followed.

It is best understood in relation to its origins, which are detailed here.

The key finding in physics at the end of the nineteenth century was that the aether model for light and electromagnetism had failed. That model, and the reasons it was strongly established by the mid-nineteenth century are detailed here. The reasons for its rejection are detailed here. The reasons why that rejection was premature are detailed here.

Without a background medium it was necessary to abandon the search for a mechanistic explanation for light and electromagnetism. Light still had all the properties that are normally associated with a wave, namely reflection, refraction, interference and diffraction, but no medium that would make the standard wave explanations for these phenomena work.

Physics therefore adopted two principles, the first specific to special relativity, the other more general.

The general principle adopted was that it was no longer appropriate to require mechanistic explanations for fundamental phenomena. The problems with this are detailed here.

## The principle of relativity

The specific principle was the principle of relativity. It was stated by Poincaré as:

‘The impossibility of experimentally demonstrating the absolute motion of the Earth appears to be a general law of Nature; it is reasonable to assume the existence of this law, which we shall call the relativity postulate, and to assume that it is universally valid.’^{i}.

Einstein adopted this principle as follows:

‘Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. … We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies.’^{ii}.

## Components of the theory

There are two aspects of the principle of relativity as expressed in 1905.

The first is clearly stated in each version, that it is impossible to discover the ‘absolute motion of the Earth’ (Poincaré), or, a bit more cautiously, that it is impossible to identify a frame of reference that has ‘properties corresponding to the idea of absolute rest.’ (Einstein)

The second is that, in the popular phrase, ‘everything is relative’. This was encapsulated in Einstein’s frequently repeated witticism ‘What time is this station leaving the train?’

We will examine more recent observations here and ask whether these support either version.

The Einstein version includes a statement about the constancy of the speed of light. Note that it was the observed constancy of the speed of light for different observers, inferred from the Michelson-Morley experiment, that led directly to leading theorists such as Lorentz and Poincaré considering the relativity principle in the first place, several years ahead of Einstein.

An important component of the modern version of the special theory of relativity is the observation that physical laws are the same in different inertial frames. This is a very important observation theoretically, but also practically, as it allows us to drink tea on an aeroplane and to examine universal physical laws in a laboratory that is in complex motion.

We will examine if it is indeed equivalent to the relativity principle here.

The final component of the theory is the Lorentz transformation. This is required to make relativity work as mathematics; otherwise, if we chase after light, it would appear to slow down, like cars in adjacent lanes on a motorway. Therefore, in relativity, we have to add and subtract velocities in a more complex, Lorentzian way.

## The Lorentz transformation

The Lorentz transformation predates Einstein by several years.

The transformation is derived from several different starting points: Lorentz used it for electrodynamics; even earlier, Waldemar Voigt derived it from the Doppler effect; Einstein and Poincaré used it to make the other components of relativity work together consistently; and modern relativity derives it from a spacetime diagram, also called a Minkowski diagram; it is also essential to physical laws being the same in different inertial frames.

There is a simple mathematical reason why the same formula can be found in different situations, and it is explained here.

Although the Lorentz transformation is an essential part of each of these phenomena, this does not mean that these are all the same phenomenon, and must be considered together. For example, Lorentz and the Irish physicist George Fitzgerald independently suggested a physical basis for the transformation, which would then explain the Michelson-Morley result and the relativism of physical laws without the need for the relativity principle.

## What it does

The Lorentz transformation is used to explain why the Michelson-Morley experiment was unable to detect any changes to the velocity of light even when the Earth was travelling in entirely different directions at different parts of its orbit.

It is used to explain the observed relativism of physical laws.

It is used to calculate the differences in the speed of ticking of atomic clocks when in relative motion.

It is used to calculate the apparent increase in mass of particles in particle accelerators as they require ever increasing force to accelerate them further as they approach light speed.

It is also, therefore, used to explain that light speed is a limiting speed for accelerated matter.

## Summary

The special theory of relativity contains the following elements:

The impossibility of identifying a preferred frame of reference

‘Everything is relative’

The constancy of the speed of light

The relativity of physical law

The Lorentz transformation.

We will examine here which of these elements are supported by observation and which are contradicted.

Return to top of page

i. Henri Poincaré, The dynamics of the Electron, Rend. Del Circ. Mat. Di Palermo 21(1906), 129; translation in C.W. Kilmister, Special Theory of Relativity (Pergamon Press, 1970) 145.

ii. A Einstein - Annalen der Physik 17 (1905) 891; translation in C.W. Kilmister, Special Theory of Relativity (Pergamon Press, 1970) 187.