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 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)
3)
Youtube videos
Good
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