Question

The Twin Paradox In this discussion you are going to post some of your results from the "Interstellar Travel" exercise, which explores the impact of special relativity. Special relativity is one of those results of modern physics that has fairly surprising implications, yet which rests on solid experimental grounds (GPS satellites actually have to correct for the effects of time dilation to work properly). Consider the student dialog in question 8 from the exercise: Student 1: I will also be 70* years old. Because I was going in one direction on the way out and the other direction on the way back, the effect will reverse itself on the way home and time will start passing more rapidly for me than for my friend. Student 2: My friend must see the same thing happening for me as I see happening for them, because I can say they were first moving away from me and then moving towards me at a high speed. This must mean we are the same age. Student 3: I am only 40 years old, I am 30* years younger than my friend. It took me 44 years divided by 3.2 or 14 years to make the round trip. The gamma factor depends only on relative speed, not on direction. Write a post explaining which student you agreed with, if any, and why or why not. Then write about your reaction to this exercise overall and to special relativity. What puzzles you about it? Does it help or hurt the case for interstellar travel? Respond to a class mate's post with a correction, disagreement, appreciation of a good argument, or commiseration.

Answer 1

The third student is right. The gamma factor depends only on the velocity. Thus he is right.

Student 1 is wrong because the change in direction doesn't reverse the effect. That is it doesn't makes you older.

Student 2 is wrong because his argument violates the special theory of relativity.

The paradox is explained as follows. Based on the fact that the earthbound twin is at rest in the same inertial frame throughout the journey, while the travelling twin is not: in the simplest version of the thought-experiment, the travelling twin switches at the midpoint of the trip from being at rest in an inertial frame which moves in one direction (away from the Earth) to being at rest in an inertial frame which moves in the opposite direction (towards the Earth). In this approach, determining which observer switches frames and which does not is crucial. Although both twins can legitimately claim that they are at rest in their own frame, only the traveling twin experiences acceleration when the spaceship engines are turned on. This acceleration, measurable with an accelerometer, makes his rest frame temporarily non-inertial. This reveals a crucial asymmetry between the twins's perspectives: although we can predict the aging difference from both perspectives, we need to use different methods to obtain correct results.

For a moment-by-moment understanding of how the time difference between the twins unfolds, one must understand that in special relativity there is no concept of absolute present. For different inertial frames there are different sets of events that are simultaneous in that frame. This relativity of simultaneity means that switching from one inertial frame to another requires an adjustment in what slice through spacetime counts as the "present". In the spacetime diagram on the right, drawn for the reference frame of the Earth-based twin, that twin's world line coincides with the vertical axis (his position is constant in space, moving only in time). On the first leg of the trip, the second twin moves to the right and on the second leg, back to the left. Blue lines show the planes of simultaneity for the traveling twin during the first leg of the journey; red lines, during the second leg. Just before turnaround, the traveling twin calculates the age of the Earth-based twin by measuring the interval along the vertical axis from the origin to the upper blue line. Just after turnaround, if he recalculates, he will measure the interval from the origin to the lower red line. In a sense, during the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps over a large segment of the world line of the Earth-based twin. When one transfers from the outgoing inertial frame to the incoming inertial frame there is a jump discontinuity in the age of the Earth-based twin.