Question

What is Galilean-Newton Relativity? can you explain it fully, and give me an example problem with the answer.

Answer 1

Galilean - Newton relativity states that the laws of motion are the same in all inertial frames. Inertial frames means those which are not accelerating.

Galileo Galilei first described this principle in 1632 using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary. The fact that the Earth orbits around the sun at approximately 30 km/s offers a somewhat more dramatic example, though it is technically not an inertial reference frame.

Specifically, the term Galilean - Newton relativity today usually refers to this principle as applied to Newtonian mechanics—that is, Newton’s laws hold in all inertial frames. In this context it is sometimes called Newtonian relativity. Among the axioms from Newton’s theory are:

• There exists an absolute space in which Newton’s laws are true. An inertial frame is a reference frame in relative uniform motion to absolute space.
• All inertial frames share a universal (or absolute) time.
• Albert Einstein’s central insight in formulating special relativity was that, for full consistency with electromagnetism, mechanics must also be revised such that Lorentz invariance (introduced later) replaces Galilean relativity.
• Example : Suppose a ball is thrown horizontally by a passenger in a moving train. If the the passenger measures the speed of the ball v_b , and the speed of the train is v_t, then what is the speed of the ball to an observer standing in the platform?
• Solution : Speed of the ball to the outside observer = v_t + v_b
• Galilean - Newton Relativity is proved here. Newtonian laws of motion are same in all inertial frames.