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:

KE_{Spaceship B} = (1/2)mv^{2}

KE_{Spaceship B} = (1/2)(1,000,000 kg)(1,000 m/s)^{2}

KE_{Spaceship 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:

E_{Spaceship A} = MC^{2}

E_{Spaceship A} = (10,000 kg)(299,792,458 m/s)^{2}

E_{Spaceship A} = 898,755,178,736,817,640,000 joules

E_{Spaceship B} = MC^{2}

E_{Spaceship B} = (1,000,000 kg)(299,792,458 m/s)^{2}

E_{Spaceship 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:

KE_{Spaceship A} = (1/2)mv^{2}

KE_{Spaceship A} = (1/2)(10,000 kg)(1,000 m/s)^{2}

KE_{Spaceship 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?