What Is Galilean Relativity?

Galilean relativity states that Newton's laws of motion have the same form in every inertial reference frame. It assumes that time is absolute and relates measurements made by observers moving at constant velocity relative to one another.

This is an HL-only concept in IB Physics topic A.5, Galilean and special relativity.

Suppose reference frame (S') moves at constant velocity $v$ relative to frame $S$ along the positive $x$-direction. If their origins coincide when $t=0$, the Galilean transformations are

$$x'=x-vt$$

and

$$t'=t.$$

The second equation expresses absolute time: both observers assign the same time to every event. Differentiating the position transformation with respect to time gives the Galilean velocity transformation:

$$u'=u-v.$$

The mechanism follows from relative position. During time $t$, the origin of (S') moves a distance (vt) as measured in $S$, so the same event has coordinate (x-vt) in (S'). Because $v$ is constant, differentiating again gives $a'=a$. Therefore, if forces and masses are unchanged, $$ has the same form in both frames.

For example, a passenger walks forward at $2.0\ \text{m s}^{-1}$ inside a train moving at $20\ \text{m s}^{-1}$ relative to the ground. The passenger's velocity relative to the ground is

$$u=u'+v=2.0+20=22\ \text{m s}^{-1}.$$

A common misconception is that Galilean relativity says all observers measure the same velocity. They do not: observers can measure different velocities, but they agree on acceleration and on the form of Newton's laws.

Exam technique: For a Show or Determine question, define the two frames, state the positive direction, and apply the signs consistently. Also recognize the model's limitation: at speeds approaching $c$, Galilean transformations must be replaced by Lorentz transformations from special relativity.