In the frame of reference,

PHYSICS · Multi-part · A Level · Physics · Turning points in physics · Turning points in physics

Problem

S

, the two ends of a table are located at the coordinates

x_1

and

x_2

such that the proper length of the table,

L = x_2 - x_1

. An observer in the frame of reference,

S'

, moving with a speed,

v

, relative to

S

measures, at the same time, the coordinates of the ends of the table to be at

x_1'

and

x_2'

such that the length of the table measured in

S'

L' = x_2' - x_1'

. (1) Using the Lorentz transformations, show that

L = \gamma (x_2' - x_1')

. (2) Hence, show that

L' = \frac{L}{\gamma}

. (3) Suggest why this phenomenon is called *length contraction*.