Time dilation in a maglev train

TIME DILATION IN A MAGLEV TRAIN

INTRODUCTION

Maglev is an acronym for Magnetic Levitation. The principle of magnetic levitation is that when two wires carry current in opposite direction, they produce a magnetic field which repels each other. This creates a friction free surface. Trains working on the principle of magnetic levitation are referred to as Maglev trains. A Maglev train can move as fast as 381.25 mph. Consider an observer in a Maglev train and another observer who is stationary with respect to the Maglev train. According to the Special Theory of Relativity, the Maglev train’s clock would run slower compared to the stationary observer’s clock. We’ll find the time gained by the Maglev train relative to the stationary observer.

ASSUMPTION

The effect of Gravitational time dilation is negligible.

CALCULATION

The Maglev velocity is,

v = 381.25 mph = 169.44 m/s

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

t' = t/γ [s]

t’ – Actual time or Maglev train’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*√ [1-3.189*10^-13]

t' = t*√ [0.999999999999681]

t' = t* 0.999999999999841

CONCLUSION

We can observe that proper and actual time isn’t the same which proves that time dilates on Maglev train 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 Maglev train gains 0.57nanosecond in one hour and 2.9nanosecond in 5 hours over the stationary observer.

Time	t’ [Stationary observer] (s)	t [Observer in Maglev] (s)	Difference (s)
1 minute	60	59.9999999999905	0.0000000000095
1 hour	3600	3599.99999999943	0.00000000057
5 hours	18000	17999.9999999971	0.0000000029