Principle of relativity

A Principle is an idea that is taken as fundamentally true. Principles play somewhat the role of axioms in logic and mathematics, or more loosely, as foundations or guides on which to build beliefs or theories^[1]. The "Principle of Relativity" is one of these.

Various "Principles of Relativity" have been assumed in belief systems and disciplines throughout history. The belief (or definition) that any law of nature should be the same in all circumstances is one of the most common. But this sense is not always the case as in, q.v.,

• Linguistic relativity
• Moral relativism
• Factual relativism
• Cultural relativism
• Aesthetic relativism

The only common thread may be that the term "relativity" occurs in each. Also see Relativism^[2]. This article discusses the scientific uses of the term.

In the sciences, the "Principle of Relativity" is most commonly used in physics in the first sense above, as an axiom and a guide. It combines two superficially contradictory notions:

• Different observers may see the same events differently
• Laws should be universal, and the same for all observers.

The apparent contradiction is resolved by treating the last notion as a definition of what can be a physical law. Thus, anything the observers see differently, is not a physical law, but is incidental to the observer. Whatever remains constant for different observers is a candidate for a physical law. This principle is most useful in dynamics and kinematics, the descriptions of forces and the motion of bodies. The term "relative" in this context refers to the fact that measurements are always relative to an observer, and the "universal" suggests there may be rules relating the measurements of any observer to those of any other.

Theoretical physics attempts to describe observations as models. These are usually systems of equations that predict how the measured data will change from one instant to the next, depending on zero or more free parameters. A simple example of a model is Galileo's law of falling bodies. Measurements made by a single observer are relative to that observer, and use arbitrary coordinate systems selected by the observer.

The form the model takes depends strongly on the observer's coordinate system.

For example, if an observer uses Cartesian coordinates, the path of a falling body has a simple form; but if the observer is contrary and uses, say, ellipsoidal coordinates which change with time, measurements of the same path will be described by a much more complicated expression. Fortunately the mathematical rules for switching between coordinate systems are inherent in their definitions. This applies to all possible coordinates, including those in arbitrary relative motion.

But the idea that laws must look the same to all observers in any coordinate system imposes a symmetry on the laws. According to a mathematical result called Noether's theorem ^{[3] [4]}, any continuous symmetry will also imply a corresponding conservation law ^[5].

As an example, if a law is the same for observers at different times, energy must be conserved. In this light, relativity principles make testable predictions about how nature behaves.

The ideas behind the principle of relativity have been around since Galileo. By the mid nineteenth century, the idea was widespread, especially in the context of electromagnetism, but the term was only formalized in 1904 by Poincaré:

“Il semble que cette impossibilité de démontrer le mouvement absolu soit une loi générale de la nature; je l’appellerai le principe de relativité.”^[6][7]

There have been several main areas of physics where a version of the Principle of Relativity was used, with different assumptions about what is constant. In particular Einstein formulated it for the special case of uniform motion,^[8]

Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.

This defines an inertial frame of reference.

The special principle of relativity is used in both Newtonian mechanics and the theory of special relativity. Its influence in the latter is so strong that Max Planck named the theory after the principle.^[9]

In the general case there is no restriction on the relative motion of the coordinate systems; In classical physics, fictitious forces are used to describe acceleration in non-inertial reference frames. General Relativity eliminates the need for such ad-hoc inventions, although they are still very useful in ordinary circumstances.