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 3/3 = 1 years. 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 3 × 3 = 9 years. When the journey is finished, the image of the Earth twin has aged by 1 + 9 = 10 years.
The Earth twin sees 9 years of slow (red) images of the ship twin, during which the ship twin ages (in the image) by 9/3 = 3 years. He then sees fast (blue) images for the remaining 1 year until the ship returns. In the fast images, the ship twin ages by 1 × 3 = 3 years. The total aging of the ship twin in the images received by Earth is 3 + 3 = 6 years, so the ship twin returns younger (6 years as opposed to 10 years on Earth).
Read more about this topic: Twin Paradox
Famous quotes containing the words calculation of, calculation, elapsed, time and/or diagram:
““To my thinking” boomed the Professor, begging the question as usual, “the greatest triumph of the human mind was the calculation of Neptune from the observed vagaries of the orbit of Uranus.”
“And yours,” said the P.B.”
—Samuel Beckett (1906–1989)
“Common sense is the measure of the possible; it is composed of experience and prevision; it is calculation appled to life.”
—Henri-Frédéric Amiel (1821–1881)
“... most Southerners of my parents’ era were raised to feel that it wasn’t respectable to be rich. We felt that all patriotic Southerners had lost everything in defense of the South, and sufficient time hadn’t elapsed for respectable rebuilding of financial security in a war- impoverished region.”
—Sarah Patton Boyle, U.S. civil rights activist and author. The Desegregated Heart, part 1, ch. 1 (1962)
“So much of our time is preparation, so much is routine, and so much retrospect, that the pith of each man’s genius contracts itself to a very few hours.”
—Ralph Waldo Emerson (1803–1882)
“If a fish is the movement of water embodied, given shape, then cat is a diagram and pattern of subtle air.”
—Doris Lessing (b. 1919)