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TIME DILATION



TIME DILATION: A review of The Twin Paradox


“Time and space are modes by which we think and not conditions in which we live”
-Albert Einstein

Time measurement began with the invention of Sundials as early as 1500 B.C. Till now humans have defined time by a set of rules which seemed convenient to them. Several Concepts have been surrounding this physical quantity since then. We shall take a look at one of those concepts named “TIME DILATION”.

 
Time dilation is a famous phenomenon featured in various sci-fi movies including the popular one, Interstellar. It may be defined as the difference in the elapsed time between two clocks because they have a relative velocity between them.

A simple thought experiment which can validate this is the twin paradox which shows that time passes at relative speeds when relative velocities are involved. Here, two twins (X and Y) are taken - Y flies in space at nearly the speed of light (90%) to an object 9 light-years away while X remains on earth. Theoretically, it is seen that, when Y returns from space, he is aged only by a few years while X is aged by a large number of years.
 The example can be explained  as follows:


Let us assume that the time needed to bring the spaceship back towards earth is negligible. Y argues that time moves slowly for X while X states the opposite. So who is actually correct?
X has 0 acceleration and hence remains in the same inertial frame.
Yon, the other hand has a non-zero proper acceleration as he makes a turn and decelerates to a stop. Thus he has two inertial frames of references, one while moving away from earth and the other while moving towards it. Time dilation should be used in a single frame of reference. Hence, Y’s result is wrong.
Thus, here there are three segments to the process:
1)       X and Y are at the origin.
2)       Y is nearly 9 light-years away (Measured from X’s frame)
3)       Y returns back to origin.

According to the calculations of X,


we use a gamma factor which comes out to be 1/0.436. (Gamma)

 For the segment 2,
 time passed for X = 9/0.9=10yrs
                            
time passed for Y = 10x(Gamma) =4.36 years
For segment 2 to 3 their time ticks by another 10 and 4.36 yrs respectively.

Thus when they are back at the origin, X has aged 20 yrs but Y is 8.72 years. This will be the correct answer as he calculates from a single inertial frame of reference. Thus, Y’s assumptions will be wrong as he is using two frames of reference for his calculations (as stated earlier).

An example of this effect was also studied by NASA on the twin astronauts Scott Kelly and Mark Kelly. Scott Kelly stated after returning from space, "I came back from space younger than my twin."

Albert Einstein’s theory of Special Relativity has been verified with unprecedented accuracy. Experiments with the help of the particle accelerator in Germany has also proved the dilation effect with great accuracy.



 
Space and time are still one of the most intriguing and complex problems faced in the field of science. This paradox is one of the different attempts taken to understand the mysterious nature of the physical quantity “TIME”.

Saptasya Mukhopadhyay
Ritwick Banerjea
Department of Chemical Engineering (HIT-K).

Sources -
1)       A Brief History of Time ( S. Hawking)
2)       einstein-online.info
3)       Youtube videos
4)       scientificamerican.com
5)       www.nasa.gov.in

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