The Elegant Universe - Brian Greene [19]
The Effect on Time: Part I
With minimal effort, we can make use of the constancy of the speed of light to show that the familiar everyday conception of time is plain wrong. Imagine that the leaders of two warring nations, sitting at opposite ends of a long negotiating table, have just concluded an agreement for a cease-fire, but neither wants to sign the accord before the other. The secretary-general of the United Nations comes up with a brilliant resolution. A light bulb, initially turned off, will be placed midway between the two presidents. When it is turned on, the light it emits will reach each of the presidents simultaneously, since they are equidistant from the bulb. Each president agrees to sign a copy of the accord when he or she sees the light. The plan is carried out and the agreement is signed to the satisfaction of both sides.
Flushed with success, the secretary-general makes use of the same approach with two other embattled nations that have also reached a peace agreement. The only difference is that the presidents involved in this negotiation are sitting at opposite ends of a table inside a train traveling along at constant velocity. Fittingly, the president of Forwardland is facing in the direction of the train's motion while the president of Backwardland is facing in the opposite direction. Familiar with the fact that the laws of physics take precisely the same form regardless of one's state of motion so long as this motion is unchanging, the secretary-general takes no heed of this difference, and carries out the light bulb–initiated signing ceremony as before. Both presidents sign the agreement, and along with their entourage of advisers, celebrate the end of hostilities.
Just then, word arrives that fighting has broken out between people from each country who had been watching the signing ceremony from the platform outside the moving train. All those on the negotiation train are dismayed to hear that the reason for the renewed hostilities is the claim by people from Forwardland that they have been duped, as their president signed the agreement before the president of Backwardland. As everyone on the train—from both sides—agrees that the accord was signed simultaneously, how can it be that the outside observers watching the ceremony think otherwise?
Let's consider in more detail the perspective of an observer on the platform. Initially the bulb on the train is dark, and then at a particular moment it illuminates, sending beams of light speeding toward both presidents. From the perspective of a person on the platform, the president of Forwardland is heading toward the emitted light while the president of Backwardland is retreating. This means, to the platform observers, that the light beam does not have to travel as far to reach the president of Forwardland, who moves toward the approaching light, as it does to reach the president of Backwardland, who moves away from it. This is not a statement about the speed of the light as it travels toward the two presidents—we have already noted that regardless of the state of motion of the source or the observer, the speed of light is always the same. Instead, we are describing only how far, from the vantage point of the platform observers, the initial flash of light must travel to reach each of the presidents. Since this distance is less for the president of Forwardland than it is for the president of Backwardland, and since the speed of light toward each is the same, the light will