According to Einstein’s Theory of Relativity, Sarah will see
the length of this train as shorter due to the fact that from her perspective,
the train is moving at close to the speed of light.
From Sarah’s point of view, the train has shrunk,
and the train is shorter than the tunnel.
From Adam’s perspective, the train is standing still,
and it is the rest of the Earth which is moving in the opposite direction.
Therefore, from Adam’s perspective, the train is still at its normal length,
and it is the length of the rest of the Earth which has become shorter.
According to Einstein’s Theory of Relativity, both points of view are equally valid.
Suppose that this train passes through a tunnel.
Suppose that while the train is inside the tunnel,
we briefly close the doors at the entrance and exit of the tunnel.
From Sarah’s point of view, the train has shrunk,
and the train is shorter than the tunnel.
From Adam’s point of view, the tunnel has shrunk,
and the tunnel is shorter than the train.
Although Adam and Sarah can disagree about whether it is
the tunnel or the train that has shrunk, they must agree on
whether or not the doors hit the train when they tried to close.
So, if Sarah sees that the doors did not hit the train when they closed,
Adam must also see that the doors did not hit the train.
But how is this possible, when Adam sees the tunnel as being shorter than the train?
The answer is that according to Einstein’s theory of relativity, different observers
can disagree about whether or not two events happened at the same time.
From Sarah’s point of view,
the doors at the entrance and the exit of the tunnel closed at the same time.
From Adam’s point of view, the doors did not close at the same time.
Therefore, Adam will see that the train passed through the tunnel
without being hit by the doors, even though, from his perspective
the tunnel is shorter than the train.
Now let us consider a different scenario.
This time, the doors close and never reopen,
thereby permanently trapping the train inside the tunnel.
Since Sarah sees the full length of the train completely trapped inside the tunnel,
Adam must therefore see the same thing.
But how is this possible?
The answer lies in the fact that the train is not a rigid body.
That is, it can not be thought of as a single solid rectangle.
Instead, we need to think of it as many separate rectangles
that are tied together through flexible connections.
If the train were a single solid rectangle,
then when we applied a force on one side of the train,
the force would be immediately felt on the other side the train.
However, this would mean that we sent a signal instantaneously
from one side of the rectangle to the other, which would violate
Einstein’s principle that no information can travel faster than the speed of light.
On the other hand, if we think of the train as many separate rectangles,
then when we apply a force to one side of the train,
the other side of the rectangle will not know about it until much later,
and hence the signal has not travelled faster than the speed of light.
If we assume that the doors to the tunnel are unbreakable,
then when the train hits the closed door at the tunnel’s exit,
the front of the train will stop first,
while the back of the train will initially keep moving at the same speed as before,
and stop much later.
In this way, once both doors are closed,
both Adam and Sarah will agree that the train is trapped inside the tunnel.
Note: This is shown from the frame of reference that continues to move at a constant velocity relative to the Earth, even after the train is at rest relative to the Earth.
Now let us consider yet another scenario.
This time, instead of a train in a tunnel,
we have a train trying to cross a bridge with a section of the bridge missing.
From Sarah’s point of view, the train is much shorter than
the section of the missing bridge, and will therefore fall through the hole.
From Adam’s point of view, the hole is much shorter than the train.
However, since Sarah saw the train fall through the hole,
Adam must also see the train fall through the hole.
This is possible if we again remember that the train is not a rigid object, and must
be thought of as many rectangles that are connected through flexible connections.
Therefore, Adam will see each section of the train fall through the hole as shown.
In this way, Adam and Sarah will both agree that the train has fallen
through the hole without violating Einstein’s Theory of Relativity.
Much more information about Einstein’s Theory of Relativity
is available in the other videos on this channel.