TIME
DILATION IN A CAR
Consider a car moving of mass one ton, length 2.5m
moving at a velocity of 100kmph [62mph] or [27.77m/s]. According to the theory of Special
Relativity, the car will undergo changes in length, mass and time. The length
contracts while time and mass increase. The change in length and mass is highly
negligible, but the change in time is considerable over a period of time.
Let the time
measured outside the car by an observer be TS = 10minutes
[600second]
The clock
inside the car will move faster than the observer’s clock. The time inside the
car is given by,
T’
= γ*T
Where, T’ - Time inside car (s)
T – Proper time (s)
γ – Relativistic gamma factor
γ = 1/√[1-(v/c)2]
c – Speed of light 3 x 108 m/s
v – Velocity of
car [27.77 m/s]
Substituting
all values in the above equation, we get the time inside the car to be
T’ = 600.000000000002 s
The difference between both times T’ – T =
2picosecond
Thus for every
10minutes the clock inside the car runs 2picosecond faster that the observer’s
clock. For 5hours the car gains 0.1nanosecond over the observer’s clock.
