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What is an inertial frame of reference? Suppose in our location we do a variety of experiments and verify fundamental laws of physics. Then we are in an inertial frame of reference! What is more, ANY other frame of reference moving at constant velocity relative to us is ALSO an inertial frame of reference.
What we mainly need from our
discussion of relativity is the correct, general expressions for
things like momentum, kinetic energy, total energy, etc. A
reminder that the energy of a system is a very abstract idea! By
definition, the value of an energy is always arbitrary up to an
additive constant, and the same object observed from different
inertial frames obviously has a totally different kinetic energy
in each frame. This is vitally important in particle physics,
where the largest possible energy needs to be brought into the
system of two colliding particles, in order to find new things.
As a result of the way energy transforms relativistically, high
energy experiments MUST be done in the center-of-momentum frame,
which requires two colliding beams instead of a beam incident on
a fixed target. Otherwise, almost all the beam energy
provided by a particle accelerator is lost. [See pages 124
- 5 in our text.]
