Time dilation in a Tornado

TIME DILATION IN A TORNADO

INTRODUCTION

Tornado is a fast and violent rotating column of wind. The diameter of tornado varies from 20 to 300 feet and wind speed from 40 to 300 mph depending on the type of tornado. Consider a tornado which rotates at 300 mph and an observer who is stationary with respect to the tornado. According to the Special Theory of Relativity, the tornado’s clock would run slower compared to the observer’s clock. We’ll find the time gained by the tornado relative to the stationary observer.

ASSUMPTIONS

• Earth is a perfect homogeneous sphere.

• The effect of Gravitational time dilation is negligible.

CALCULATION

The wind velocity is,

v = 300 mph = 133.33 m/s

According to the Special Theory of Relativity, the time dilation equation is,

t' = t/γ [s]

t’ – Actual time or Tornado’s time. [s]

t - Proper time or Stationary observer’s time. [s]

γ – Relativistic gamma factor, γ = 1/√ [1-(v/c) ²]

c - Velocity of light [c = 3*10⁸ m/s]

t' = t*√ [1-(v/c) ²]

t' = t*√ [1-1.9752*10^-13]

t' = t*√ [0.999999999999802]

t' = t* 0.999999999999901

CONCLUSION

We can observe that proper and actual time isn’t the same which proves that time dilates on tornado relative to the stationary observer. We’ll consider 2 different t’ values and calculate t value. The larger the t’ the more is the difference between t and t’. Thus in one hour the tornado gains 0.36nanosecond over the observer, so it’ll last for 0.36nanosecond longer before passing out.

Time	t’ [Non-rotating Earth] (s)	t [Rotating Earth] (s)	Difference (s)
1 minute	60	59.9999999999941	0.0000000000059
1 hour	3600	3599.99999999964	0.00000000036