Question

Suppose you are in a spaceship traveling at 99% of the speed of light past a long, narrow space station. Your direction of travel is parallel to the length of the station. If you measure lengths of objects on the station and also how time is passing on the station, what results will you get?
A) Lengths will appear shorter and time will appear to pass slower.
B) Lengths will appear shorter and time will appear to pass faster.
C) Lengths will appear shorter and time will appear to pass faster.

Answer 1

Answer:

A. Lengths will appear shorter and time will appear to pass slower.  

Explanation:

From theory of relativity, we know that:

L₀ = length of object, measured in stationary frame of reference

L = length of object measured from a frame moving with respect to object, called ‘relativistic length’

v = relativistic speed between observer and the object

c = speed of light

then,

L = L₀ √(1-v²/c² )

Hence, the length of the object decreases with the increase in its relativistic speed "v"

t₀ = time measured by clock at rest with respect to event.

t = time measured by clock in motion relative to the event

v = relativistic speed between observer and the object

c = speed of light

then,

t =  t₀/√(1-v²/c² )

Hence, the time increases with the increase in in relativistic speed and as a result it appears to pass slower.

Hence, the correct option is:

A. Lengths will appear shorter and time will appear to pass slower.  

 

Answer 2

Answer:

B) Lengths will appear shorter and time will appear to pass faster.

Explanation:

This is in line with the laws of relativity.