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tech / sci.physics.relativity / The Twins Inheritance Paradox

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o The Twins Inheritance Paradoxpatdolan

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The Twins Inheritance Paradox

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Date: Wed, 8 Nov 2023 20:58:19 -0800 (PST)
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Subject: The Twins Inheritance Paradox
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 by: patdolan - Thu, 9 Nov 2023 04:58 UTC

Once upon a time there was a kindly old professor of special relativity and his wife who had no children. So they decided to adopt twin baby boys. As the twins grew, one became fiendish whilst the other became goodly. Even so, the professor and his wife loved both of them equally. One day the professor told the twins that he and his wife only had enough wealth to provide an inheritance for just one of them. Therefore the entire estate would go to the twin who outlived the other.

The fiendish twin considered how he might outlive his brother and collect the inheritance. Murder was too risky. He might get caught. Then he remembered what his father, the professor, had taught him about Einstein's theory of special relativity. The fiendish twin thought "According to special relativity, all I need to do is acquire relativistic motion with respect to my inertial twin brother. Then when I return I will have outlived him by years. I will get all the inheritance in a completely legal and lawful manner." So the fiendish twin began to construct a rocket ship for the purpose of taking a 20 year round trip journey near the speed of light.

The goodly twin asked his father why his fiendish brother was building a rocket ship. The professor answered “Your brother has remembered Einstein’s Twins Paradox, my son. He is purposing to outlive you by means of gaining a relativistic velocity whilst you remain inertial. That’s how your twin brother will be able to control your fate from a great distance away out in space.

The goodly twin asked his father “Is there anything I can do to thwart my brother’s fiendish and unfair plan to win your inheritance?”

“Yes” the professor answered. “You can build your own rocket ship and match your twin brother g for g and v for v. When he speeds up, you speed up. When he slows down, you slow down. When he turns around, you turn around. That way you will both age at the exact same rate.”

So off into space the two twins flew, each in their own relativistic rocket ships. After years of exactly mirroring each other’s maneuvers they look at each other through their portholes and saw that they were both aging at exactly the same rate, just like their father told them they would. They realized how futile their relativistic duel had become and they also missed their home back on Earth. So they decided to end their relativistic competition and return to earth together at the same speed. They each pointed their rocket ships towards earth and chose a return velocity of .867c.

As the twins careened towards the clockwork solar system at .867c they marveled as they watched the earth’s orbital velocity fall to only half its normal speed, in accordance with special relativity. But the twins had no clue as to the fiery disaster they were about to bring down upon the earth because their father, the professor, never taught them the Big Ben Paradox. It turned out that the professor, and even Einstein hizself, knew nothing of the Big Ben Paradox.

Remembering his general relativity, the goodly twin suddenly understood the peril in which the twins had placed the earth by traveling at .867c. The earth’s orbital velocity had decreased to only half the value necessary to keep it in stable orbit around the sun. This is because the spacetime curvature (a.k.a. gravitation) in the vicinity of the sun had not decreased at all, in accordance with law of general relativity. The goodly twin realized in the nick of time that the earth would quickly spiral into the sun unless he slowed down his rocket ship. And that is exactly what the goodly twin did and thereby saved the earth.

Meanwhile, the fiendish twin, lusting after his inheritance, continued to race towards the earth at .867c. The fiendish twin then watched in horror as the earth, his inheritance, and everything that he loved was consumed in the nuclear fire of the sun.

Consider now, gentle reader, how both endings to our tale can be true at the same time. And yet this is exactly what the theories of general and special relativity unambiguously state. In the standard twins paradox the traveling twin alters the aging process of the inertial twin by choosing to acquire relativistic velocity. In the twins inheritance paradox one twin saves the earth by giving up his velocity relative to it; while at the same time the other twin chooses to destroy the earth by remaining in relativistic motion with respect to it.


tech / sci.physics.relativity / The Twins Inheritance Paradox

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