The Twin Paradox vs. Contact

     The movie Contact makes an effort to display a realistic representation of the Twin Paradox, but the fundamental concept of time dilation was displayed incorrectly. The time dilation in the twin paradox is a result of the point of view of a stationary observer seeing a clock move slower as it moves with a constant velocity past them. This can be portrayed in the diagram below:

     Keep in mind that light in a vacuum will always travel at the speed of light [c], which represents the second postulate of special relativity. The second section of the illustration above represents the actual motion of a photon in both a moving inertia frame and a stationary inertia frame. The third section of the illustration represents what a stationary observer would see as the clock moves by them at a constant velocity. Notice how the distance that the photon actually travels (2d) is shorter than the distance that the stationary observer sees. To the stationary observer, the photon travels a longer distance at the same velocity [c], which causes the period of each oscillation to appear greater to the stationary observer; according to special relativity, someone holding the moving light clock could say the same thing about the stationary light clock, since there is no possible way of truly defining which reference frame is moving. The stationary observer has evidence that the second clock was moving slower, but the second clock has evidence that it was the first clock that was moving slower. This is the paradox, since they are both actually right.
     Now that there is a basic understanding of this nontrivial concept, lets analyze the portayal of it in the movie. After Dr. Eleanor traveled through various wormholes along her journey, she claimed

"Because of the effects of relativity what I experienced as a period of approximately eighteen hours passed almost instantaneously on Earth.",

     Assuming that Dr. Eleanor was in an inertial, non-accelerating reference frame the entire time, this is opposite to what we just discussed. Had the movie correctly portrayed this paradox, the observers on Earth would have said that they actually passed time quicker than Eleanor did on her spacecraft. 
     Also, there is another scene in the movie where a woman goes into the spacecraft and sees that the duration of the flight that the spacecraft measured was eighteen hours. This doesn't violate the Twin Paradox specifically, but violates the concepts involved. Remember, the light clock in both scenarios ticks at the same pace, so the elapsed time recorded by the stationary observer and Dr. Eleanor would actually be the same, it is only the apparent movement of time that one inertial frame witnesses in the other frame that creates the paradox. 
     
     
     
     











Comments

  1. Your last paragraph seems to confuse the issue. The key is that *all* clocks in a given reference frame will see time pass in the same way, while clocks in *different* frames need not observe time passing the same. However, the shortest time interval that anyone can observe is the proper time, measured by an observer in the frame with the clock. Ellie and her recorder measured proper time.

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