In Aristotle's physics, the Earth was at the center of the universe and so provided an absolute reference for the location of everything else that exists. This absolute notion of space also included Aristotle's "Prime Mover." Additionally, the Prime Mover was in a state of absolute rest, i.e. motionless, and served to give an absolute reference of time.
The notion of absolute space and absolute rest was set aside by Galileo, who established a principle of relativity. In his Dialogue Concerning the Two Chief World Systems, Galileo wrote:
...have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.
This is the first formulation of The Principle of Relativity. In other words, "the mechanical laws of physics are the same for every observer moving uniformly with constant speed in a straight line". Such an observer who "moves uniformly with constant speed in a straight line" (i.e., "moves with constant velocity") is a special type of observer: called an "Inertial" Observer. (From now on, we use "inertial" instead of "moves with constant velocity")
So, we can restate Galileo's Principle of Relativity:
The mechanical laws of physics are the same for every inertial observer. By observing the outcome of mechanical experiments, one cannot distinguish a state of rest from a state of constant velocity.
What impact does this concept have on our perception of the universe? Suppose two different inertial observers see the same two events happen in sequence, like a glass being bumped off a table top that later hits the floor and breaks. [Event 1: Glass being bumped. Event 2: Glass breaking.] They each measure how long it takes the glass to fall (i.e. the time interval between the events) and the height it fell from (the distance between the events). Now, they compare their measurements. Did they get the same values?
According to Aristotle, for whom time and space were absolute, the answer would have to be yes. But, when the experiment is actually done, the answer is no (as long as the two observers have some relative speed between them).
According to Galileo's relativity, everyone agrees on the time when they see things happen (absolute time) but not necessarily on the distance between them (relative space).
Observer A sees the two events at x1, t1 and x2, t2. Observer B (moving with speed v relative to Observer A) sees the same two events at:
[To see how this works in practice, try investigating the "spacetime" diagram of Galilean systems. . .]
Still, Galileo's principle says that simultaneous events have the same distance between them according to all inertial observers. In our everyday world, Galileo's answer is usually good.
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