And, so. From notes 2, onto the Principle of Relativity (in the restricted sense). This appears to state that natural phenomena run their course following exactly the same general laws in all frames of reference (i.e. same event viewed from different aspects – on the train, standing on the embankment etc), as long as the co-ordinate systems are in uniform motion of translation to one another (no rotation). This seems reasonable; the laws of physics don’t depend on the position in space (ordinarily). But, consider this:
Even then, the experimental data was clear that light always travels in straight lines at the same speed when in a vacuum, regardless of the velocity of the body (e.g. lamp) emitting the light. On the other hand, it is also clear that a person in a railway carriage walking in the direction of travel of the train is travelling faster (when observed from the embankment) than a person in the carriage walking in the opposite direction. However, if that person was holding a lamp, the speed of the light being emitted would be travelling at the same speed (when observed from the embankment) regardless of the direction in which the person holding the lamp was walking in the carriage. This appears to violate the Principle of Relativity (in the restricted sense). Either the Principle is wrong, or the speed of light isn’t always the same??
No, no, no says Einstein. They are both right. Eh? What Einstein then does is to assume they are both right and reason as to what that would imply. In my view, this is the genius. This is the Special Theory of Relativity. Where does this lead? Firstly, consider time (oh, yes). How do you know if two events are simultaneous (e.g. two lightening strikes – useful to consider because each leads to the emission of light)? It is important to avoid assumptions; the definition of ‘simultaneous’ must be linked to measurable factors. In this case, to test for simultaneity, imagine a person standing on the embankment half way between the two lightening strikes. They are equipped with mirrors allowing the two sites that will be struck to be watched at the same time. The person can then verify that the two events happen at the same time. But, if the observer (with the same equipment) is on the train instead, and the train is moving along the line joining the two event sites, then the observer will ‘see’ one of the strikes (the one towards which the train is heading) earlier than the second strike (the one away from which the train is moving). To be sure, the difference is small (as it is light we are talking about), but also real. So, two simultaneous events (as seen from the embankment) are not simultaneous when seen from the moving train.
What??? Exactly. Simultaneity, and hence, time itself, depend on the frame of reference of the observer. Time is not a constant between frames of reference. In the same way, distance between two points on the train is not necessarily the same when measured from the train or from the embankment because the measurement from the embankment requires time to be considered, and this isn’t the same for both frames of reference. Therefore, distance isn’t necessarily the same for both frames of reference either!!!
The constancy of the velocity of light has led to this finding: time and distance are different in different frames of reference. It’s pretty non-intuitive, and pretty difficult to grasp at first. Einstein has thought the unthinkable, and opened up a whole new world with his spanner.