Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Kryptid on 19/04/2011 05:24:28
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For the sake of simplicity, let's imagine that the entire Universe is empty except for two objects: Spaceship A and Spaceship B. Spaceship A (including crew, cargo, etc.) has a mass of 10,000 kilograms. Spaceship B is much heavier, at 1,000,000 kilograms.
The crew on Spaceship A are standing still, relative to their own observations. Then they see Spaceship B fly by at 1,000 meters per second. They then attempt to calculate the total energy content of the Universe.
First, they calculate the kinetic energy of Spaceship B:
KESpaceship B = (1/2)mv2
KESpaceship B = (1/2)(1,000,000 kg)(1,000 m/s)2
KESpaceship B = 500,000,000,000 joules
Their own kinetic energy is 0, since they perceive themselves as sitting still.
Then they calculate the energy-mass equivalents of their spaceships:
ESpaceship A = MC2
ESpaceship A = (10,000 kg)(299,792,458 m/s)2
ESpaceship A = 898,755,178,736,817,640,000 joules
ESpaceship B = MC2
ESpaceship B = (1,000,000 kg)(299,792,458 m/s)2
ESpaceship B = 89,875,517,873,681,764,000,000 joules
The total energy of Spaceship B is it's resting mass plus it's kinetic energy:
500,000,000 J + 89,875,517,873,681,764,000,000 J = 89,875,517,873,682,264,000,000 J
The total energy in the Universe is the addition of Spaceship A and Spaceship B:
89,875,517,873,682,264,000,000 J + 898,755,178,736,817,640,000 J = 90,774,273,052,419,081,640,000 J.
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On Spaceship B, however, they think they are the ones who are standing still; they see Spaceship A go by at 1,000 m/s. They calculate Spaceship A's kinetic energy as:
KESpaceship A = (1/2)mv2
KESpaceship A = (1/2)(10,000 kg)(1,000 m/s)2
KESpaceship A = 5,000,000,000 joules
Add it to the rest mass of Spaceship A and you get a total of 898,755,178,741,817,640,000 joules. Add this to the rest mass of Spaceship B (which has no kinetic energy from their own point of view) and you get 90,774,273,052,423,581,640,000 J.
But...90,774,273,052,419,081,640,000 J ≠ 90,774,273,052,423,581,640,000!
Are we to infer that the energy content of a system can be different relative to the observer? Does this not violate the first law of thermodynamics?
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If A and B are truly the only two objects in the universe they cannot know that they are standing still because there is absolutely nothing to measure their velocity against other than the the other spaceship so the result is the sum of the relative kinetic energies of both ships. That is what relativity really means. This concept has nothing to do with Einstein but goes right back to Galileo.
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Right, but I thought that any reference frame is just as valid as any other reference frame? Which would mean that assuming you are still and everything else is moving past you is just as valid as thinking everything else is standing still and you are moving?