- #1
GregAshmore
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In figure 3-1 (page 63) of Taylor and Wheeler's Spacetime Physics, the observer on the train determines that the lightning strikes are not simultaneous because the flashes do not reach her simultaneously.
I see two problems with this.
1. The narrative in figure 3-1 contradicts the text in section 2.7 (pg 39): "Location and time of each event is recorded by the clock nearest to that event." The time of the lighting strike at the front of the train should be recorded by a clock at the front of the train. Likewise, the time of the strike at the rear of the train should be recorded by a clock at the rear of the train. The procedure used in figure 30-1 will lead to incorrect results, as stated in 2.7: "We do not permit the observer to report on widely separated events that he himself views by eye. The reason: The travel time of light."
2. The claim that the observer on the train will see the front flash first is based on a view from the embankment. There is no assurance that the view from inside the train will match the view from the embankment--indeed the exercise is intended to determine whether this is so. For comparison, consider the scene proposed by Menzel in his derivation of the equation of special relativity. A flash of light occurs at the instant a rocket ship (or train) passes a point on Earth. The sphere of the light has two apparent centers: One center (for the observer on earth) is at the point on Earth where the emission was observed; the other center (for the observer on the rocket) is at the point on the rocket where the emission was observed. Of course, these two centers separate with the velocity of the rocket ship. By this reasoning, the two light flashes on the train will reach the observer in the center of the train simultaneously.
Comments?
I see two problems with this.
1. The narrative in figure 3-1 contradicts the text in section 2.7 (pg 39): "Location and time of each event is recorded by the clock nearest to that event." The time of the lighting strike at the front of the train should be recorded by a clock at the front of the train. Likewise, the time of the strike at the rear of the train should be recorded by a clock at the rear of the train. The procedure used in figure 30-1 will lead to incorrect results, as stated in 2.7: "We do not permit the observer to report on widely separated events that he himself views by eye. The reason: The travel time of light."
2. The claim that the observer on the train will see the front flash first is based on a view from the embankment. There is no assurance that the view from inside the train will match the view from the embankment--indeed the exercise is intended to determine whether this is so. For comparison, consider the scene proposed by Menzel in his derivation of the equation of special relativity. A flash of light occurs at the instant a rocket ship (or train) passes a point on Earth. The sphere of the light has two apparent centers: One center (for the observer on earth) is at the point on Earth where the emission was observed; the other center (for the observer on the rocket) is at the point on the rocket where the emission was observed. Of course, these two centers separate with the velocity of the rocket ship. By this reasoning, the two light flashes on the train will reach the observer in the center of the train simultaneously.
Comments?