Author: Gaurav Dar (202.54.26.---)
Date: 07-20-04 08:10
I was also struck and stupefied by the same doubt as yours at one time. I have a way of clearing your doubt. Read on.
Simultaneity example was this: Light flashes as two ends equally far from an observer on the embankment and the train. Observer on the embankment views the light flashes to be simultaneous. Since the train is rushing towards one of the light flashes the signal from that light flash, according to Einstein, will reach the observer on train earlier than the other light flash. Therefore, according to the train observer the two lights did not flash simultaneously.
The doubt was this: Speed of light is 'c' according to the person on the embankment as well as the person on the train. Hence, it should take equal times to reach the observer (located midway between the light bolts) irrespective of the frame of reference (whether the embankment or the train). If the two flashes are simultaneous in one frame they should hence be simultaneous in the other frame too, contradicting Einstein. Is Einstein's reasoning wrong. Ofcourse not. SOmething is wrong with our way of looking at it.
Clarification of the doubt: Instead of flashing lights lets throw a ball each from the two ends at the same speed. If the two balls reach the observer on the embankment at the same time, then they must have been thrown simultaneously. However, it should be clear that the two balls will not reach the observer on the train simultaneously. The two balls had equal speeds relative to the embankment, but they do not have equal speeds relative to the train. This can be found by a simple measurement by a person on the train. That is why, even though the two balls reach the person on the train at different times he can easily conclude that the two balls must have started at different times. Hence, if the two balls were thrown simultaneously relative to the embankment they were also thrown simultaneously relative to the train. ALL THIS IS CLASSICAL NOTION.
Whats different about the light example that makes simultaneity relative whereas in the ball example simultaneity is absolute. To start off in the ball example the two balls reach the person on the train at different times because the train is rushing towards one of the ball and away from the other ball. Exactly the same thing happens in the case of light. However, in the ball example the person on the train concludes that the two balls were thrown simultaneously even though they reached him at the same time. Thats because the speed of the two balls relative to him are unequal. However, in the light example if light from the two ends reaches the observer at different instants he must conclude that they also started off from the two ends at different instants. Thats because the speed of light from the two ends are equal (the speed of two balls were not) relative to the train (which is also equal to its speed relative to the embankment). It is this difference that makes makes the two events (light flashes from the two ends) non-simultaneous on one frame even though they are simultaneous in another frame.
If there any lopholes in the argument, find them ! I can find none.
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