Imagine a universe in which all that exists are three balls(one red, one blue, and one yellow). Each ball has a mass of 1kg. The red and blue balls are at rest with respect to each other, but are moving with respect to the yellow ball. From a reference frame in which the yellow ball is at rest, the red ball and the blue ball are moving and thus have kinetic energy. Now, let's move our reference frame to one in which the blue ball is at rest. The red ball at rest relative to the blue ball, so has no kinetic energy(and neither does the blue ball). The yellow ball, however, is moving and thus has kinetic energy. The red ball has more energy in the reference frame of the yellow ball than it does in the reference frame of the blue ball. Thus energy is dependent on the reference frame and is not conserved from frame to frame. Mass, however is the same in every frame of reference. If we consider the three balls as a system and use the same reference frames, we get different values for the total energy of the system.
As stated, each ball has a mass of 1kg. In the reference frame where the red and blue balls are at rest, the yellow ball is observed to be moving at 100m/s with respect to the red and blue balls. In the reference frame where the yellow ball is at rest, the red and blue balls are each observed to be traveling at 100m/s with respect to the yellow ball.
How much [acr=Kinetic Energy]KE[/acr] does this universe have?