Chapter 1. The principle of relativity Section 1. Velocity of propagation of interaction

To describe processes, we need coordinates and clocks These define a “system of reference.”

If a free body (F ext = 0) moves at constant velocity v in a particular reference system K, then K is an inertial reference system. K V

If a reference system K’ moves uniformly relative to an inertial reference system K, then K’ is inertial, too. K K’ V

Principle of relativity: All laws of nature are identical in all inertial reference systems (experiment!) The equations expressing laws are invariant (same form) under transformation of coordinates and time.

Newtonian Mechanics: Interactions are described by potential energy. This assumes instantaneous propagation. If the source of an electric force moves or changes, a test charge feels it with no delay - F

Experiment: There always is a delay. Velocity of propagation is finite. If finite, it must have a maximum value. A consequence is that motion of particles cannot exceed this maximum. Maximum is called the “signal velocity.”

Signal velocity must be the same in all inertial reference systems. By principle of relativity, if there is a maximum propagation velocity in one inertial reference system K, it must have the same value in any other inertial reference system K’. Signal velocity is a universal constant = “c”.

Principle of relativity + finite signal velocity = Principle of relativity of Einstein Relativistic Mechanics

The transition from relativistic to classical mechanics is effected in formulas by setting c -> 0 c -> infinity c-> x cm/s 1 2 3

The transition from relativistic to classical mechanics is effected in formulas by setting c -> 0 c -> infinity c-> x cm/s

Distance is already relative in classical mechanics. Spatial relations depend on reference system. Two non-simultaneous events can occur at the same place or at different places depending on the system. K K’ V

Time is absolute in classical mechanics. The interval of time between two events is the same in all systems. Velocity of composite motion = vector sum of individual velocities. This universal law of classical mechanics if applied to propagation of interactions would mean the signal velocity should depend on the reference system. Contradicts Einstein relativity principle. This is confirmed by Michelson experiment: No dependence of light velocity on direction of earth’s motion.

K K’ V Time cannot be absolute in relativisitic mechanics. Events simultaneous in one system K’ will not be in a different system K.

Two inertial reference systems, K’ moves relative to K along X (X’). Two signals start from A simultaneously. Both signals travel at c. They reach points B and C, equidistant from A, simultaneously in K’. B A C K K’ X’ Z’ Y’ Y Z X V

The two events, which are simultaneous in K’, are not simultaneous in K. In K, both signals also travel at c. But B moves towards source while C moves away. Signal arrives at B earlier than at C in K system. B A C K K’ X’ Z’ Y’ Y Z X V

An “EVENT” occurring in a material particle is defined by 3 spatial coordinates of the particle and the time of the occurrence. The time of occurrence is different in different inertial reference systems, and is not absolute. Events are “WORLD POINTS” in 4-dimensional space with x,y,z,t axes.

Which statement is not true? All physical laws have the same form in all inertial reference systems. The maximum possible signal velocity is the same in all reference systems. The signal velocity depends on the motion of the observer

Which statement is not true? All physical laws have the same form in all inertial reference systems. The maximum possible signal velocity is the same in all reference systems. The signal velocity depends on the motion of the observer.