- Galilean Transformation – v’ = v +- V – cannot be applied to light
- If (x1 , t1) and (x2,t2) are two events in K, and (x1’,t1’) and (x2’,t2’) are their co-ordinates in K’, then (x2 –x1) / (t2 – t1) = (x2’ – x1’) / (t2’ – t1’) –> strange , but true

Solving problems with two inertial observers moving relative to each other

Consider the ‘at rest’ observer. For her, the time,length etc. are all ‘proper’ time. The ‘moving’

### Length Contraction – Does an object ACTUALLY shrink ?

No.

Explanation 1 – Using 4-vectors – The length is simply one part of a 4-vector – just as a 3-D book will cast a different shadow based on its orientation, just so, the meter rod will cast a different ‘projection’ depending on the orientation of the moving observer.

Explanation 2 – Using Relativity of Simultaniety

To measure the length of an object we must know the space-time coordinates of the point of it’s beginning and the point of it’s end at the same moment and form this information we can measure the length .

In the case of a moving object the idea of

the same momentis not valid due to the Relativity of simultaneity .

For an observer who is in the frame of the moving object the idea of at the same moment is valid , she measures the length of the object as the same length she would have measured before moving . But for an observer who is in a stationary frame outside the moving object the idea of at the same moment is not valid, he measures the length of the object as shorter than the length he would have measured before moving .

### TimeLike, SpaceLike and LightLike

TimeLike means that events A and B occur such that their time ordering is preserved. That is – if Observer O measure A to occur before B, so does observer O’ . This also means that an object can travel from A to B at v < c.

Note that just because time ORDERING is preserved, does not mean that the events are considered simultaneous by O and O’.

SpaceLike means that an object would have to travel at v > c to go from A to B.