12.3.4 Einstein's Postulates

Galilean Relativity

• Galilean relativity is the type of relativity we are most 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 m s^–1

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

Diagram showing the difference in velocity of an object in two reference frames

Person C measures the ball to be travelling faster than when measured by Person D

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 (x, y) is the same as the time interval between another frame (x', y')

• However, this is not what happens when we 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, we know that 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 our own reference frame, we are always stationary
• This means in practice, we should not be able to tell whether we are moving or not
  • Someone conducting a physics experiment on a moving train 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, c, 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, you would know whether you 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 

Diagram demonstrating Einstein's postulate of special relativity

Both a moving and stationary observer would measure the same speed of light from the torch