To understand how gravity affects the flow of time consider the following.
If you are inside a falling box,
you will feel weightless as if there is no gravity present.
On the other hand, if the box is in deep space and it accelerates...
then inside the box, it will look as if everything is falling due to gravity.
In both cases, it will appear to the person inside the box
as if the box is standing still.
One of the fundamental principles of Einstein’s Theory of Relativity is that
there is no way for an observer to tell whether he is moving or standing still.
Suppose that we try to violate this principle by sending pulses
of light from the top of the box to the bottom of the box.
Suppose we measure the time between when the first light pulse leaves
the top of the box, and when the second light pulse leaves the top of the box.
Suppose we also measure the time between when the first light pulse arrives at the
bottom of the box, and when the second light pulse arrives at the bottom of the box.
If the box is standing still,
then the time between the light pulses at the bottom of the box will be
exactly equal to the time between the light pulses at the top of the box.
This will still be true if the box is moving at a constant speed.
But, if the box is accelerating, then the
time between the light pulses at the bottom of the box will now be less
than the time between the light pulses at the top of the box.
Therefore, it appears as if this will allow a person inside the box to tell
whether or not it is moving, thereby violating Einstein’s Theory of Relativity.
However, if we choose to believe that this box is standing still,
then we will also believe that there is a gravitational field present.
This gravitational field affects the rate at which time flows.
It turns out that gravity affects the flow of time in just the right way
to prevent us from ever being able to tell whether or not the box is accelerating.
If we choose to believe that this box is standing still,
then we would also need to believe that there is a gravitational field present.
The gravitational field would cause time at the bottom of the box
to flow slower than time at the top of the box.
This would cause the time between the light pulses at the bottom of the box
to be less than the time between the light pulses at the top of the box.
Therefore, if we believe that the box is standing still, we will get the
exact same results as we would if we believed that the box is accelerating.
The gravitational field exists only from the perspective
of a person who believes that the box is standing still.
The gravitational field does not exist from the perspective of
a person outside who believes that the box is accelerating.
From the perspective of the person outside the box,
the time between the light pulses at the bottom of the box
is less than the time between the light pulses at the top of the box
due to the fact that the box is accelerating.
From the perspective of the person inside the box,
the time between the light pulses at the bottom of the box
is less than the time between the light pulses at the top of the box
due to the effects of gravity on the rate at which time flows.
Although it is for different reasons, in both cases, the time between
the light pulses at the bottom of the box is less
than the time between the light pulses at the top of the box.
Therefore, if we believe that the box is standing still,
we will get the exact same results
as we would if we believe that the box is accelerating.
It is therefore still not possible to tell whether or not the box is moving,
and Einstein’s Theory of Relativity has not been violated.
Suppose we are in a region of space where
the strength of the gravitational field is the same everywhere.
Clocks that are far apart along the direction of the gravitational field
will run at different speeds.
The difference in the rates at which the two clocks run increases
as we increase the distance between the two clocks
along the direction of the gravitational field.
The difference in the rates at which the two clocks run also increases
if we increase the strength of the gravitational field.
Near a black hole,
the strength of the gravitational field is so strong that to outside observers,
time near the back hole almost stops completely.
For more information on the flow of time and Einstein’s Theory of Relativity,
please check out the other videos on this channel.