Hello and welcome back to my blog ‘Physics Talk’.
My previous post was about special relativity, which said that
the laws of physics are equivalent in every frame of reference irrespective of
their speeds and the speed of light in vacuum has a fixed value. One of the
consequences of the Special Relativity is the Time Dilation. It is the
difference in the time measured for the occurrence of an event between two
frames of references. This gave birth to a paradox known as Twin
Paradox.
Twin Paradox is a thought experiment where two twins, suppose
‘A’ and ‘B’, are taken into account (they would have the same age). Consider
that ‘B’ is good in studies and later at the age of 30 he becomes an astronaut.
On the other hand ‘A’ is making his living by doing something on the earth.
Suppose ‘B’ boards a spacecraft on the earth, to go to a distant planet. The
spacecraft moves with speed close to the speed of light. ‘B’ goes to the
distant planet and comes back to the earth. But when he returns one of them
would be younger than the other according to the time dilation phenomenon of
special relativity.
Who do you think would be younger?
From ‘A’s
frame of reference, who is on earth, ‘B’ is moving and he himself is
stationary. Here, the length travelled by ‘B’ in the spacecraft would be less
than what will be measured by ‘A’, due to the length contraction phenomenon of
special relativity. Therefore, in ‘A’s frame of reference, the time taken by ‘B’
for the whole journey would be less than what will be measured by ‘A’.
Therefore, ‘A’ would be older than ‘B’.
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Is it really true?
As frames of references are relative, everybody can consider
themselves to be stationary. As a result, ‘B’ can also claim that he is
stationary and the earth and ‘A’ are moving backward and forward. Therefore in ‘B’s
frame of reference he would be older than ‘A’. But both cannot be younger and
older than the other at the same time. Therefore, one of them must be wrong.
This creates the paradox.
One of the explanation of the
paradox is the role of acceleration. To make the return journey ‘B’ must stop
the spaceship and fire the engines in reverse direction. Therefore, he would
feel the acceleration. This would make his journey non inertial (it is a frame
of reference which is undergoing acceleration with respect to an inertial
frame.). But the special theory of relativity were derived for inertial frames (this
is a frame of reference where net force acting or acceleration is zero) of
references. Hence, ‘A’ would be older than ‘B’.
But this explanation can be
contradicted with the three twin experiment where suppose ‘A’ is on earth, ‘B’
is moving from the earth in spaceship towards some planet ‘M’, and ‘C’ is
moving from planet ‘M’ towards earth in another spaceship. ‘B’ and ‘C’ meet in
between. There they synchronize their clocks and move forward (note: they do
not stop, they synchronize their clocks while moving at the same speed). When ‘C’
would reach the earth, time experienced by him would be less than time measured
by ‘A’ for the whole journey. There is no acceleration here. Therefore,
acceleration cannot be the correct explanation of the paradox.
The most accepted explanation is
that of the role of inertial reference frames. ‘A’, who is on earth is in one
inertial reference frame throughout, while ‘B’ is in two inertial reference
frames as he stops and returns. This is argued to be the explanation for ‘A’
being the stationary observer.
Some also use General Relativity
and Doppler Effect to explain this paradox, but it is not necessary as special
relativity is sufficient to explain this paradox.
