Einstein was fascinated by this question. It was in fact the question that began to consume him totally towards the end of his life. Once again, now, for modern physicists, it is becoming a consuming question. Can we use this sense of beauty in a physics theory, as a way to develop the ultimate theory ?
The answer is very controversial, but many physicists now answer "Yes ! Indeed, we can !"
This journey we are about to make to discover special and general relativity is one of the early hints that symmetry is an important abstraction for identifying a sense of poetry in a physics theory.
The idea at first appears innocuous. You will be astounded later, as we go along, to find out how it totally overturned traditional thinking.
We want the laws of physics to be the same for all experimenters. It should not matter if you do your experiment on earth or the moon, or anywhere else. We will call the place where you do your observing from a "reference frame". All observers should be lead to the same laws of physics, even if their data appears different from different reference frames.
We will now proceed to formulate this insistence of ours in a mathematical way, so as to study for a variety of phenomena if we do indeed meet our "symmetry of reference frames" requirement.
Motion is relative. In fact the observation of motion (measurement) is a far more complex process than we may at first have imagined. For example, while walking down an aisle in a train your velocity relative to the station will be different depending on whether the train is moving through the station or halted at the station. However, in both cases you would be walking with the same velocity relative to the train. It is clear that the specification of the Frame of Reference with respect to which an observation was made is part of the description of the motion.
Are there different kinds of reference frames? Yes. A frame in which Newton's first law of motion holds identifies an inertial reference frame, when this law does not hold, we have a non-inertial reference frame.
Think about how you would perform an experiment to detect whether you were in an inertial or a non-inertial reference frame.
How many inertial reference frame's are there? The answer is infinitely many. Any reference frame moving with a constant velocity with respect to an inertial reference frame, is itself an inertial reference frame
Think about whether there could ever be an absolute reference frame. Think about whether any one inertial reference frame could be more ``valid'' than any other. Note - This question is not yet settled.
Galilean Relativity specifies the mathematical transformation between inertial reference frames in a way consistent with everyday experience.