special relativity
The equation explained
In wordsThe place of the clock in the resting system equals its velocity times the time of the resting system.OverviewWhere the clock is. It sits at the origin of the moving system, and that origin travels at the velocity v, so in the resting system the clock's position is the velocity times the time.Full explanationThe second of the two equations that hold for this clock, and the one that makes it this clock rather than any point of space. The clock was placed at the coordinate origin of the moving system, and section 3 set that origin travelling along the X-axis of the resting system with the velocity , the two origins having coincided at the start. So in the resting system the clock's coordinate at any time is the velocity times the time. Substituting it into the transformation is what turns a relation holding at every place into a statement about one travelling clock.Every stepThe moving system's origin starts where the resting system's origin is and travels at the constant velocity , so after a time of the resting system it has covered : the printed line.Also