PX156 - J3 - relativistic invariants

for collisions, the reference frames will differ

so, predictions and measurements will need to be translated by lorentz transformations

use only quantities that are invariant, ie: same value in every inertial reference frame

special relativity is based on invariance of some quantities:

• speed of light
• space-time interval
  • suppose there are two events, $A(x_A,y_A,z_A,c{t}_A)$ and $B(x_B,y_B,z_B,c{t}_B)$
  • space-time interval, $I$, has the same value in every frame, where:
  $$I=(x_A-x_B{)}^2+(y_A-y_B{)}^2+(z_A-z_B{)}^2-c^2(t_A-t_B{)}^2$$
• $E^2-p^2{c}^2=m^2{c}^4$

cannot talk about the same things in different frames

use invariants to connect reference frames