Time dilation in TGV train

TIME DILATION IN TGV

INTRODUCTION

TGV [Train a grande vitesse] is a high speed train in France. The TGV has a top speed of 323.75 mph, Consider an observer in TGV who travels from Paris to suburbs and another observer who is stationary with respect to the TGV. According to the Special Theory of Relativity, the TGV’s clock would run slower compared to the observer’s clock. We’ll find the time gained by the TGV relative to the stationary observer.

ASSUMPTION

The effect of Gravitational time dilation is negligible.

CALCULATION

The TGV’s velocity is,

v = 323.75 mph = 143.88 m/s

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

t' = t/γ [s]

t’ – Actual time or TGV’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*√ [1-2.3*10^-13]

t' = t*√ [0.99999999999977]

t' = t* 0.999999999999885

CONCLUSION

We can observe that proper and actual time isn’t the same which proves that time dilates on TGV relative to the stationary observer. We’ll consider 3 different t’ values and calculate t value. The larger the t’ the more is the difference between t and t’. Thus the TGV gains 0.41nanosecond in 1 hour and 2.1nanosecond in 5 hours over the stationary observer.

Time	t’ [Stationary observer] (s)	t [Observer in TGV] (s)	Difference (s)
1 minute	60	59.9999999999931	0.0000000000069
1 hour	3600	3599.99999999959	0.00000000041
5 hours	18000	17999.9999999979	0.0000000021