Einstein's Postulates (AQA A Level Physics): Revision Note

Einstein's postulates

Galilean relativity

• Galilean relativity is the type of relativity most people are familiar with

• At everyday speeds, an object's speed in one frame of reference may be different in another frame of reference

  • This is because the velocity, position and time of an event appear differently from different reference frames

• For example:

  • Person D is on a skateboard travelling at 4 m s^–1 when they throw a ball in a straight line at a constant velocity of 2 m s^–1

  • Person C is a stationary observer of the event

    • In Person D's reference frame, the ball is travelling at 2 m s^–1

    • In Person C's reference frame, the ball is travelling at $4+2=6\mathrm{m}{\mathrm{s}}^{-1}$

• So the speed of the ball depends on the reference frame

When does Galilean relativity stop working?

• Galilean relativity states that Newton's laws of motion are the same in all inertial reference frames

  • Therefore, space and time are treated as fixed and absolute

  • This means the time interval between two events in one frame $\left(x,y\right)$ is the same as the time interval between another frame $\left(x\text{'},y\text{'}\right)$

• However, this is not what happens when speeds are close to the speed of light

  • Space and time become relative, meaning, the length of an object or a time interval depends on the frame of reference

• Velocity addition works with speeds much lower than the speed of light ($c$)

• It doesn't work for objects travelling closer to the speed of light

  • According to Galilean relativity, if a rocket ship travels at $0.7c$ and releases a probe directly in front of it at $0.5c$, a stationary observer would view this at $0.7c+0.5c=1.2c$

  • However, nothing can travel faster than the speed of light, so this is not possible

• Einstein proposed two postulates of special relativity

The first postulate of relativity

• Einstein's first postulate of special relativity states:

The laws of physics are the same in all inertial frames of reference

• In a person's own reference frame, they are always stationary

• This means in practice, they should not be able to tell whether they are moving or not

  • Someone conducting a physics experiment on a train moving at a constant velocity versus on a stationary platform should produce the exact same results

The second postulate of relativity

• Einstein's second postulate of special relativity states:

The speed of light in a vacuum is the same in all inertial frames of reference

• Two different observers will always measure the speed of light to be the same value, $c$ in their reference frame

  • It makes no difference whether they are travelling or not

  • If it did, they would know whether they are moving, which counteracts the first postulate

• For example, a runner holding a flashlight in front of them will measure the speed of the light as $c$

  • However, someone stationary observing the runner will also see the speed of light as $c$ and not $c$ + the velocity of the runner

• This only works for the speed of light, not any other speed