In preEinstein relativity (known as Galilean relativity[?]), time is considered an absolute in all reference frames.
From this assumption, the following consequences can be derived about the perspective of an event in two reference frames, S and S', where S' is traveling at a relative speed of u to S.
Two reference frames S and S', with S' traveling at a relative speed of u to S; an event has spacetime coordinates of (x,y,z,t) in S and (x',y',z',t') in S'.
The spacetime coordinates of an event in GalileanNewtonian relativity[?] are governed by the set of formulas which defines a group transformation known as the Galilean transformation:
Assuming time is considered an absolute in all reference frames, the relationship between spacetime coordinates in reference frames differing by a relative speed of u in the x direction (let x = ut when x' = 0) is:
The set of formulas defines a group transformation known as the Galilean transformation (informally, the Galilean transform).
Mathematically, if we define the velocity of the second reference frame in our previous discussion above as the vector u = ux (x being the xdimensional unit vector), following the above formulas gives us:
as we would expect.
See also: special relativity.
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