**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. (see Einstein, *Relativity*, pp. 47, 48;
Chapters 20E, 24 and 27)

__Einstein’s Special Theory of Relativity__: (see Einstein, 1905d [

__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. (see Minkowski,
1908 [

__Einstein’s General Theory of Relativity__: Einstein’s *ad hoc* theory of gravity,
curved space-time, and his application of accelerated motions to light. (see Einstein, 1916 [

__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. (see Chapter 18)