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### S3. Galilean Relativity

Relativity was there long before Einstein. Here we discuss about the Galilean principle of relativity.

During the Galileo’s time the common held believe about nature of the motion was that of the $Aristotelian$ philosophy;

It claimed the following as the basis of motion observed,
• all objects on Earth, being imperfect, will naturally slow down,
• that in a vacuum(if existed), infinite speeds would ensue,
• and that perfect celestial bodies must move in circles.

But, did the object really slowed down naturally? Or that in the vacuum, was there no constraint to the speed of an object? Or ??....These were the question Galileo wanted to understand.

The basis of his understanding on the motion of an objects can be understood from the following thought experiment,

Imagine a person inside a ship which is sailing on a perfectly smooth lake at constant speed. This passeneger is in the ship's windowless hull and, despite it being a fine day, is engaged in doing mechanical experiments (such as studying the behavior of pendula and the trajectories of falling bodies). A simple question one can ask of this researcher is whether she can determine that the ship is moving (with respect to the lake shore) without going on deck or looking out a porthole.

Since the ship is moving at constant speed and direction, she will not feel the motion of the ship. Still one might wonder whether the experiments being done in the ship's hull will give some indication of the its motion. Based on his experiments Galileo concluded that this is in fact impossible: all mechanical experiments done inside a ship moving at constant speed in a constant direction would give precisely the same results as similar experiments done on shore.

He therefore, concluded that observer in a house by the shore and another in the ship will not be able to determine that the ship is moving by comparing the results of experiments done inside the house and ship. In order to determine motion these observers must look at each other. It is important to note that this is true only if the ship is sailing at constant speed and direction, should it speed up, slow down or turn, the researcher inside can tell that the ship is moving. For example, if the ship turns you can see all things hanging from the roof (such as a lamp) tilting with respect to the floor.

Generalizing these observations Galileo postulated his relativity hypothesis:

 any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments
This is in contrary to the notion of the Aristotelian principle, that there exists a natural frame of reference relative to which the objects naturally slowed down.

In the above statement Galileo makes it clear that the choice of the reference frame was indeed crucial to determining the motion of an object. i.e.“the concept of the velocity is not absolute”.

This means that velocity can only be measured in reference to some object(s), and that the result of this measurement changes if we decide to measure the velocity with respect to a different reference point(s). Imagine an observer travelling inside a windowless spaceship moving away from the sun at constant velocity. Galileo asserted that there are no mechanical experiments that can be made inside the rocket that will tell the occupants that the rocket is moving . The question are we moving'' has no meaning unless we specify a reference frame (are we moving with respect to that star'' is meaningful). This fact, formulated in the 1600's remains very true today and is one of the cornerstones of Einstein's theories of relativity.