In Problem 90, you showed that the quantity x 2 + y 2 + z 2 -(ct)

Question:

In Problem 90, you showed that the quantity x² + y² + z² -(ct)² has the same value (0) in both S and S’. Such a quantity is called an invariant. From the results of Problem 89, the quantity p²_x + p²_y + p²_z – (E/c)² must also be an invariant. Show that this quantity has the value -m₀c² in both the S and S’ reference frames.