The Principle of Relativity : The restricted or the Incomplete Sense
Regarding the last section ,I got a complaint from a reader that he didn't understand the last lesson.In this section i will try my best that it comes out to be very simple and straight for the readers. In order to attain the maximum possible clearness, we will take the example of a railway carriage moving uniformly with respect to the embankment. We call its motion uniform translation motion due to its uniform velocity . Let us now suppose that a bullet is fired by a person standing at the embankment. The bullet attains uniform velocity and then undergoes uniform translation motion ,with respect to embankment, after that. When an observer observes the bullet from the railway carriage, he finds that the bullet has some different speed and direction but it travels uniformly with respect to the carriage also. And this is what the logic says. If it is expressed in a more simpler manner then i would say that if a body of mass 'm'(Bullet) travels uniformly in a straight line with respect to a coordinate system K( the embankment ) , and some other coordinate system let us say K'(Railway carriage) also travels uniformly in a straight line with respect to K , Then the mass 'm' also travels in a straight line uniformly with respect to the second coordinate system K', although with a different speed. It follows that If K is a Galilean Coordinate system then K' would also be a Galilean Coordinate System. And all the mechanical laws Galilee - Newton hold good exactly as for K.But it should be kept in mind that there is no rotational motion. This is what the Principle of Relativity states in the restricted sense.
In the earlier time one used to believe that Classical mechanics was very successfully able to represent all the natural phenomenon occurring and there was no need of this principle but as there took development in electrodynamics and optics it became more evident that mechanics can't afford to survive independently.There is a very simple and straight fact put forward in the favor of this principle of relativity.
Let us understand that argument by taking an example.If there is a Galilean coordinate system K( which we take absolutely at rest) and the principle of relativity is not true then for K', which is undergoing uniform translation motion with respect to K, no mechanics law will be applicable directly on K'. If , for instance, our embankment is the system K then our carriage plays the role of the System K'. It is just like the Earth and the Sun. The laws of nature applied on the Earth and some other plane revolving around the Sun would be different and it is a very obvious thing that it is not the true fact. For every planet the mechanics laws are just the same.And it is the simplest fact which supports this principle.
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