Galilean Relativity: Volume-2

Galilean Transformation

Galileo Galilei

The theories that deals with relativity are mainly -

• Special Theory of Relativity (1905)
• General Theory of Relativity (1915)

Yet these two theories draw their foundation from the Galilean Relativity. The concept that is borrowed by Einstein is the principle of Inertial Frame.

          The Galilean Transformation deals with the relative motion of the two bodies that move with a velocity negligible to that of light (assigned a value c). To analyze this consider a situation wherein two bodies, let us say two trains, are moving in the same direction (say, towards geographical north). For our analysis, let the velocity of train A be 30 mph and of train B be 20 mph. Now by the Galilean Transformation the relative velocity of train A with respect to train B is 10 mph (30 mph - 20 mph) towards geographical north while the relative velocity of train B with respect to train A is 10 mph (20 mph - 30 mph) towards geographical south.

          Let us say in a subsequent situation, that a man in train A gets up from his seat and moves in the direction of motion of the train i.e. geographical north, with a velocity of 32 mph with respect to the ground. In this case the relative velocity of the man with respect to train B will be 12 mph (32 mph - 20 mph) towards geographical north while with respect to train A it will be 2 mph (32 mph - 30 mph).

          Now in the same situation let us consider the man to walk in a direction opposite to that of the train's motion and with a velocity of 32 mph. This time the relative velocity of the man with respect to train B will be 52 mph (32 mph + 20 mph) however with respect to train A it is 62 mph (32 mph + 30 mph).

Note: It may seem weird that the relative velocity of man with respect to the ground is 32 mph which is greater than the velocity of either of the trains but this is perfectly alright because the man is in contact (sitting) with the train so his velocity with respect to the ground is already 30 mph, an additional walk lets say of 2 mph will result in the mentioned value, 32 mph.