One of the most commonly asked questions about Einstein’s Theory of Relativity
is regarding the twin paradox.
If Adam’s spaceship leaves Earth and travels close to the speed of light,
then when he returns, he will have aged far less than Sarah, who stayed on Earth.
Many people ask why this is not a violation of the fundamental principle
in Einstein’s Theory of Relativity that there is no way to tell
which observer was moving, and which observer was standing still.
Adam and Sarah each think that they are the ones who are standing still,
and that it is the other person who is moving.
When there is no acceleration involved,
each of them will think that the other person's clock is moving slower than their own.
If this were not the case, then it would be possible to tell which of them was moving,
which would violate Einstein’s principle.
For Adam to return back to Earth,
he will eventually need to fire his rockets to turn around.
When he fires his rockets,
Adam will still continue to think that his spaceship is standing still.
However, in order to believe that his spaceship is standing still,
he needs to also believe that there is now a gravitational field present
that is cancelling out the force from his rockets.
Adam will believe that this gravitational field exists everywhere
throughout all of space, and that this gravitational field is causing
the Earth and the rest of the Universe to accelerate towards him.
Gravity affects the flow of time.
Suppose we are in a region of space where
the strength of the gravitational field is the same everywhere.
The amount by which one clock will flow faster than another
will depend on how far apart the two clocks are along the direction of this field.
When Adam fires his rockets to turn around, he is extremely far away from the Earth.
Therefore, Adam will believe that the gravitational field
is causing time on Earth to flow much faster than time on his ship.
It is only during the very brief moment when Adam is firing his rockets
to turn around that he believes this external gravitational field is present.
For the remainder of his return trip after he turns his rockets off,
Adam will again view time on Earth as moving slowly.
Nevertheless, during the very brief moment when he fires his engines,
he sees time on Earth flowing so extremely fast that this far more than compensates
for the fact that he sees time on Earth flowing slowly during the rest of his journey.
This is why Adam will believe that more time has passed for Sarah
than for him when he returns.
But what about when Adam first fired his rockets to take off from earth?
When Adam fired his rockets to take off from Earth,
he also believed that there was a gravitational field present,
causing him to remain still by cancelling out the force from his rockets,
and causing the Earth to accelerate away from him.
However, when Adam is first taking off from Earth,
the distance between his clock and Sarah’s clock is very small.
The amount by which one clock will flow faster than another due to gravity
depends on the distance between the two clocks.
Since Adam’s clock and Sarah’s clock are very close together during takeoff,
gravity’s effects are negligible.
On the other hand, when Adam fires his rockets to turn around,
the distance between his clock and Sarah’s clock is extremely large,
and the effect of gravity on the flow of time is extremely large.
But what about Sarah’s point of view?
From Sarah’s point of view, this external gravitational field never existed.
From her point of view,
Adam’s clock was slower than her clock during the entire voyage,
due to the fact that Adam was moving close to the speed of light.
It is only from Adam’s point of view that
this gravitational field exists when he fires his rockets.
It does not exist from the point of view of people outside his spaceship.
Adam attributes the fact that more time has passed for Sarah
than for him due to the gravitational field and its effect on the flow of time.
Sarah attributes the fact that more time has passed for her
due to the fact that Adam was moving at close to the speed of light.
When Adam returns to Earth, they will both agree that more time has passed for Sarah,
but they will disagree on the reason why.
Both Adam and Sarah will continue to believe that
they were the ones who were standing still during the entire journey.
Einstein’s Theory of Relativity has therefore not been violated.
More information about Einstein’s Theory of Relativity
is available in the other videos on this channel.