images; the ship twin sees the Earth twin age by different amounts in the red and blue shifted images. Calculation of elapsed time from the Doppler diagram The twin on the ship sees low frequency (red) images for 3 years. During that time, he would see the Earth twin in the image grow older by . He then sees high frequency (blue) images during the back trip of 3 years. During that time, he would see the Earth twin in the image grow older by When the journey is finished, the image of the Earth twin has aged by The Earth twin sees 9 years of slow (red) images of the ship twin, during which the ship twin ages (in the image) by He then sees fast (blue) images for the remaining 1 year until the ship returns. In the fast images, the ship twin ages by The total aging of the ship twin in the images received by Earth is , so the ship twin returns younger (6 years as opposed to 10 years on Earth). The distinction between what they see and what they calculate To avoid confusion, note the distinction between what each twin sees and what each would calculate. Each sees an image of his twin which he knows originated at a previous time and which he knows is Doppler shifted. He does not take the elapsed time in the image as the age of his twin now. If he wants to calculate when his twin was the age shown in the image (i.e. how old he himself was then), he has to determine how far away his twin was when the signal was emitted—in other words, he has to consider simultaneity for a distant event. If he wants to calculate how fast his twin was aging when the image was transmitted, he adjusts for the Doppler shift. For example, when he receives high frequency images (showing his twin aging rapidly) with frequency , he does not conclude that the twin was aging that rapidly when the image was generated, any more than he concludes that the siren of an ambulance is emitting the frequency he hears. He knows that the Doppler effect has increased the image frequency by the factor 1 / (1 − v/c). Therefore, he calculates that his twin was aging at the rate of when the image was emitted. A similar calculation