I did a thought experiment for myself today to test whether energy is conserved in Lorentz transformations.(adsbygoogle = window.adsbygoogle || []).push({});

I chose to concider three objects lying on a horizontal line. In object 2's rest frame, object 1 has a velocity of 0.600c to the left, and object 3 has a velocity of 0.600c to the right. I let each object have a mass of 1kg.

The total kinetic energy in this system will be [tex]\Sigma E_k=2\cdot (\gamma-1)mc^2=2\cdot 0.25\cdot1kg\cdot c^2=0.5c^2\;[J][/tex]

Now concider the rest frame of object 1. Object 2 now has a velocity of 0.600c to the left and object 3 has a velocity of 0.882c to the left, according to the Lorentz transformation.

The total kinetic energy in this system is now [tex]\Sigma E_k=(\gamma_2-1)mc^2+(\gamma_3-1)mc^2=0.25\cdot 1kg\cdot c^2 + 1.125\cdot 1kg\cdot c^2=1.375c^2\;[J][/tex]

Why does the system have a different energy depending on the reference frame? Am i overlooking something? If energy is not conserved in Lorentz transformations, doesn't that raise the question of which reference frame displays the correct energy, violation the first postulate?

Any help is appreciated.

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# Energy conservation in relativity

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