The concept of Time Dilation is pretty easy to understand, here’s how
How beautiful it is to think and wonder about the meaning and fascinating prediction of physics using mathematical equations. It doesn’t even give us the meaning but provides a sense of weirdness and complication that our universe possesses. Among the many beautiful equations, the equation of time dilation is one of the fascinating equations which was discovered by Einstein in 1905 in his groundbreaking theory of Special Relativity.
The beauty of physics and mathematics is that if we understand and feel every letter and symbol in the equation, then we can create such if we know the basic idea of the problem.
Einstein proved that Time is not linear with his discoveries of Special Relativity in 1905. He imagined a train moving at the speed of light and two lightings striking 100 meters apart. From his perspective of standing at the station, two lighting strikes simultaneously. But when he imagines himself in the train moving at light speed there is time elapsed between two striking. Then how can the same event have different time intervals in different situations? Then he found that time is different for everyone, it depends on the frame of reference. Time passes slower for someone moving near the speed of light.
The equation of time dilation can be easily understood through high school algebra. Here, sections are made for easier understanding. Let’s dive into the equation.
Fig(I): It shows a light particle moving at light speed ‘c’ covering the distance of (L) when it is at rest.
Fig (II): It shows a light particle moving at light speed ‘c’ covering a distance of (D) when it is in motion moving at velocity (v).
In ∆CAB
sinϴ=L/D Or, D=L/sinϴ (….1)
cosϴ=v/c (….2)
We have,
At rest
Distance=L
Velocity =c
At motion
Distance=D=L/sinϴ (from 1)
Velocity=c
Elapsed time in motion (∆t’) =D/(c )=(L/sinϴ)/C {since, v=d/t}
Elapsed time in rest (∆t) = L/C
Time Dilation=∆t’/∆t= Υ=(Elapsed time in motion)/(Elapsed time in rest)
Υ=[(L/sinϴ )/c)/(L/c ) ] (from 1 and 2)
Υ=1/sinϴ
Υ=1/√(1-v²/c² ) {Since, sin² θ+cos² θ=1}
Thus, (∆t’ )/∆t =1/√(1-v²/c² )
which is the required equation of time dilation.
Conclusion: The faster we move through space, the slower we move in time, and vice-versa.I
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