Consider two identical cars, each travelling at a constant velocity v towards each other. Suppose that they crash, and to simplify things, let’s not consider any rebound. Then the energy of each is kinetic in nature and so the energy of the crash is given by
Ok. That’s a nice way to show the energy of the collision goes up with the square of velocity.
Now, according to the principle of relativity this should be an identical situation if you consider it from the reference frame of one of the cars. In that case, the car you are looking at has a velocity of 0, while the other car has a velocity of 2v. Now the total energy of the crash looks like
So. Why the discrepancy?