Newtonian physics

In pre-Einstein 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.

v' = v - u (the velocity of a particle from the perspective of S' is slower by u than from the perspective of S)
a' = a (the acceleration of a particle remains the same regardless of reference frame)
F' = F (since F = ma) (the force on a particle remains the same regardless of reference frame; see Newton's law)
the speed of light is not a constant
the form of Maxwell's equations is not preserved in different reference frames

Details

Consider two reference frames, one of which is traveling at a relative speed of u to the other. For example, for a car passing another car at a relative speed of 10 km/h, u is 10 km/h.

Two reference frames S and S', with S' traveling at a relative speed of u to S; an event has space-time coordinates of (x,y,z,t) in S and (x',y',z',t') in S'.

The space-time coordinates of an event in Galilean-Newtonian 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 space-time coordinates in reference frames differing by a relative speed of u in the x direction (let x = ut when x' = 0) is:

x' = x - ut

y' = y

z' = z

t' = t

The set of formulas defines a group transformation known as the Galilean transformation (informally, the Galilean transform).

Velocity

In pre-Einstein relativity velocities are directly additive and subtractive. For example, if one car traveling at 60 km/h passes another car traveling at 50 km/h, from the perspective of the car it passes it is traveling at 60-50 = 10 km/h.

Mathematically, if we define the velocity of the second reference frame in our previous discussion above as the vector u = ux (x being the x-dimensional unit vector), following the above formulas gives us:

v' = v - u

as we would expect.