MEMO 24.3
The Various Different Concepts and Definitions of “Relativity”

Relative Motions:  All motions are relative  (Einstein, Relativity, p. 67).

Galileo’s Relativity:  Equivalent inertial motions of a material body permit empirically covariant mechanical accelerations on it and a sense of rest for an observer on such body, so that the state of motion of the body cannot be detected by such observer  (Chapter 5).

Lange’s Relativity:  Relative inertial motions can theoretically exist between two different abstract frames of reference (coordinate systems)  (Chapter 13).

Galilean Translational Relativity:  One-to-one Galilean transformation equations mathematically translate a theoretical mechanics experiment and its accelerations from one frame of reference (coordinate system) to another, and they describe and measure such acceleration with coordinates as viewed by an observer in each spatially separated inertial reference frame  (Chapter 14).  This mathematical “carbon copy” type of relativity is sometimes misdescribed as “Galilean Relativity.”

Lorentz’s Relativity:  Space and time coordinates are transformed between inertial reference frames by radical Lorentz transformation equations in such a way that any relative velocity is eliminated and a theoretical velocity dependent contraction of matter is mathematically produced relative to the stationary ether  (Chapter 16).

Poincaré’s Principle of Relativity:  The laws of physics should be the same for an observer absolutely at rest in the stationary ether or for an observer moving in uniform translation relative to the stationary ether, so that either observer would have no way to detect from such laws whether or not he is moving relative to the stationary ether.  The Lorentz transformation equations mathematically described Poincaré’s Principle of Relativity and were embedded in Poincaré’s Principle of Relativity  (Chapter 16).

Einstein’s Principle of Relativity:  The laws of physics are mathematically covariant (they have the same algebraic form) in all inertial reference frames (coordinate systems) that are related by Lorentz transformation equations, and thus such laws are invariant with respect to Lorentz transformations  (Einstein, Relativity, pp. 47, 48; Chapters 20E, 24 and 27).

Einstein’s Special Theory of Relativity:  (Einstein, 1905d [Dover, 1952, pp. 37 – 65]; and part II of this treatise).

Minkowski’s Space-time:  Minkowski’s ad hoc mathematical and geometrical theory of space and time, which used Einstein’s and Lorentz’s theories as its models  (Minkowski, 1908 [Dover, 1952, pp. 75 – 91]; our Chapter 33).

Einstein’s General Theory of Relativity:  Einstein’s ad hoc theory of gravity, curved space-time, and his application of accelerated motions to light  (Einstein, 1916 [Dover, 1952, pp. 111 – 164]; our Chapter 40).

The Universal Principle:  The laws of nature are the same with respect to any material body or observer, regardless of its position, time or states of motion  (Chapter 18).