 Let's try to piece together Stacey's description of the experiment. On her outward journey, she is at rest in the red frame for four years. Earl is moving, so he only ages 3.2 years. For her return journey, she is at rest in the green frame for four years. Earl is moving, so he only ages 3.2 years. Therefore, Stacey might argue that she should end up 8 and Earl 3.2 plus 3.2 equals 6.4 years old. This is the crux of the twin paradox. Each twin considers him or herself at rest and the other moving. Therefore, it would seem, each should find the other twin younger when they reunite. But only one twin can be younger. By symmetry then, the only possible result is they should end up the same age. But there is a subtle point associated with Stacey's jump from the red to the green frame. In the red frame's bookkeeping, Earl is 3.2 years old when this happens. But in the green frame's bookkeeping, Earl is 6.8 years old. If Stacey goes by the reckoning of whichever frame she is currently at rest in, then she would have to conclude that Earl instantly ages 3.6 years when she jumps from the red to the green frame. Now we plot Earl and Stacey's ages according to Stacey's bookkeeping of simultaneous events. Earl's age is on the left, Stacey's on the right, and the line colors correspond to the frames the twins are in. According to Stacey, Earl ages more slowly. But he suddenly gains 3.6 years of age when she changes frames. He then continues to age more slowly. So when they reunite, she is 8 and Earl is 10. Stacey's explanation of the experiment is as follows. Earl was always moving at a speed of 0.6, so his clock always ran slower by a factor of 0.8. Therefore, during each four-year leg of the trip, he aged 3.2 years for a total of 6.4 years. But when I jump frames, he instantly aged 3.6 years. That's why I'm 8, and he's 6.4 plus 3.6 equals 10 years old. The funny thing about this sudden aging explanation is that nobody actually sees this happen. No red or green frame observer will record a video of Earl passing by when he suddenly gets 3.6 years older. We've already animated the complete experiment in the red and green frames, and Earl's age uniformly increases in both. Here the top panel shows the red frame's view of simultaneous events at the time of Stacey's frame jump, and the bottom panel shows the green frames version. It's true that the red frame observers see Earl as 3.2 years old, while the green frame observers see him as 6.8 years old. But these events did not happen at the same time at Earl's location in any frame. In both the red and green frames, they happened 4.5 years apart. It's only in Stacey's reckoning that Earl suddenly ages 3.6 years. And this is a statement about something that happened several light years away that Stacey does not directly observe, that no one directly observes. Yet for Stacey, it has observable consequences. It's her explanation why Earl is older than she is when they reunite, even though she believes he has been aging slower than her during both parts of her journey. Another way to view this is on a space-time diagram. We first plot the blue frame coordinates, and the twin space-time paths. We then ask how old Earl is in the blue frame when Stacey jumps from the red to the green frame. This means, when on Stacey's path through space-time she jumps frames, what is simultaneously happening on Earl's space-time path according to the blue frame observers? To find the answer, we follow a line of constant time, T blue, from Stacey's path to Earl's. We find that Earl is 5 years old. Now we overlay red frame coordinates and ask the question in the red frame. Following a line of constant time, T red, we intersect Earl's path when he is 3.2 years old. Finally, we add the green coordinates and follow a line of constant time, T green, to find that Earl is 6.8 years old. In all three coordinate systems, Earl ages at a uniform rate. But observers in the different frames disagree on how old he is simultaneous with Stacey's jump from the red to the green frame. If Stacey follows red frame bookkeeping before her jump and green frame bookkeeping after, she has to conclude that Earl, who is light years away from her, has suddenly aged 3.6 years. What causes the twins to end up with different ages? Well, this is just how space-time geometry dictates the behavior of clocks moving between two events along different paths. Why do the twins move along different paths? Because one accelerates, and that will be the younger twin. If Stacey accelerates, she will end up younger than Earl. If Earl accelerates, he will end up younger than Stacey. As we did in video 5a, we want to consider what the twins could actually observe about each other in real time. So let's assume each transmits a video of him or herself to the other. Since the signals travel at the speed of light, this introduces a time delay between sending and receiving. So what the twins see is a combination of their aging rates and the communication delay. Since we're simulating a sequence of events that can be seen in real time by a single observer, all reference frames will agree on the results. And we can do our calculations in any reference frame. We'll use the blue frame. First, let's look at transmissions sent by Stacey at one-year intervals. On each leg of her journey, she sends four pulses. On the outward leg, she's moving away from Earl. He finds the pulses are spread out, such that at his location two years pass between reception of each pulse. On the inward leg, he finds the pulses are squeezed together, such that only half a year passes at his location between receptions. Now we animate Earl's observations. On the left, we show Earl's experience of his own age. On the right, we show the age he sees Stacey in the received video. He sees himself age twice as fast as Stacey while she's in the red frame. And he sees Stacey age twice as fast as himself while she's in the green frame. So he sees himself age eight years while Stacey ages four years in the red frame. And he sees himself age two years while Stacey ages four years in the green frame. He ends up ten, and Stacey ends up eight years old when they reunite. Now we animate Earl's transmissions. On her four-year outward journey, Stacey receives two of these. On her four-year inward journey, she receives eight. So in Stacey's observations, she ages twice as fast as Earl while she's in the red frame. And Earl ages twice as fast as her while she's in the green frame. She sees herself age four years in the red frame while Earl ages two. And she sees herself age four years in the green frame while Earl ages eight. She ends up eight, and Earl ends up ten years old when they reunite. So twins can end up with different ages. And this can be precisely described using relativity's model of the workings of space-time geometry. Now admittedly, we might still demand an intuitive explanation of, quote, what's really happening. But that demand emerges from an implicit assumption that our common sense Newtonian model of the world, with absolute time and simultaneity, accurately describes reality under all conditions. Relativity tells us that it does not. Let's consider a very rough analogy. Suppose you live on a flat earth, and you perform the falling experiment. Two travelers, represented by cyan and yellow balls, obey the falling rule during their voyage. When the cyan traveler moves one meter, the yellow traveler also moves one meter, in a direction that maintains a constant distance between them. This causes the travelers to always move along parallel paths. So when they return, they will have the same positions and relative orientation as when they left. Every time you repeat the experiment, you obtain the same result. And this becomes your intuitive understanding about how parallel motion works. But you actually live on a spherical earth. Eventually, you perform the parallel motion experiment over a much, much larger distance. As before, the two travelers always move the same distance and maintain the same distance between them. But the total distance traveled is so great, that Earth's curvature now has a noticeable effect. When the cyan traveler returns to his original position, the yellow traveler does not. And they end up with a very different relative orientation than when they started their journey. Since you have a flat earth world view, this result seems bizarre. You might assume that there must be some, quote, cause of the difference. Maybe one of their measuring rods got stretched, so they didn't actually move in parallel. Otherwise, they would have returned with the same orientation. But, in fact, at every step of their journey, they did move in parallel. This is just how parallel motion works on a curved surface. At high velocities, the geometry of spacetime, as described by relativity, simply does not conform to our intuitive Newtonian view, where everyone experiences the same absolute time. Due to this geometry, when the twins follow different spacetime paths, they experience different elapsed times, and hence end up with different final ages. And that's just how spacetime works.