8Special relativity

IA Dynamics and Relativity

8 Special relativity

When particles move Extremely Fast

TM

, Newtonian Dynamics becomes inaccu-

rate and is replaced by Einstein’s Special Theory of Relativity (1905).

Its effects are noticeable only when particles approach to the speed of light,

c = 299 792 458 m s

−1

≈ 3 × 10

8

m s

−1

This is really fast.

The Special Theory of Relativity rests on the following postulate:

The laws of physics are the same in all inertial frames

This is the principle of relativity familiar to Galileo. Galilean relativity mentioned

in the first chapter satisfies this postulate for dynamics. People then thought

that Galilean relativity is what the world obeys. However, it turns out that

there is a whole family of solutions that satisfy the postulate (for dynamics),

and Galilean relativity is just one of them.

This is not a problem (yet), since Galilean relativity seems so intuitive, and

we might as well take it to be the true one. However, it turns out that solving

Maxwell’s equations of electromagnetism gives an explicit value of the speed of

light,

c

. This is independent of the frame of reference. So the speed of light must

be the same in every inertial frame.

This is not compatible with Galilean relativity.

Consider the two inertial frames

S

and

S

0

, moving with relative velocity

v

.

Then if light has velocity

c

in

S

, then Galilean relativity predicts it has velocity

c − v in S

0

, which is wrong.

Therefore, we need to find a different solution to the principle of relativity

that preserves the speed of light.