Einstein liked to think about things while riding on trains through the Alps. Europeans do not need a Disneyland. They have Switzerland.

Sometimes, Einstein enjoyed bouncing a ball off the ceiling of the train. When the conductor glared at him, he just thought about it quietly to himself. One of the thoughts he had was: how would the ball look to someone outside the train watching him go by? So he drew a picture like the one above.

Let *h* be the height of the passenger car ceiling.
Then to Einstein the ball would seem to go up and back down
the distance of 2 × *h*
while the train moved from point A to point C.
To an observer outside the train, however, the ball would seem to travel
from point A to B, and then down to C.
To the outside observer, the distance the ball traveled would seem longer,
just as the triangle shows.

When taking a trip,
if we multiply our speed by the amount of time our trip takes,
we can calculate the distance we travel.
The formula you probably remember is *d = v×t*,
where *v* is for velocity and *t* is for time elapsed.
(From here on, we will put a Δ
in front of *t* to mean *elapsed* time,
which is the *difference* between two moments on our clock.)
Notice also that the distance the train travels from A to C is
*vΔt*, where *v* is the velocity or speed of the train,
and *Δt* is the elapsed time according to the outside observer.
In our diagram, the distance from A to M is *½vΔt*.

The differences between inside and outside observations is only slight
if the train is moving slowly:

The slower the speed, the less distance from A to C, and therefore from A to M.
When the train stops,
the distances and times of inside and outside observers match.

However, if the train is moving rapidly,
the distance from A to M is greater:

Notice also that while the distance from A to M grows wider,
the distance from M to B shrinks accordingly.

Now replace Einstein with God.
Assume that while God is flying by rapidly from A to C,
he bounces a lightning bolt from his right hand at M to his left hand at B
and back again.
For us standing relatively still,
the round trip distance of the lightning from one hand to the other
(2×*D* = *AB* + *BC*) appears greater
than it is for God (2×*h* = *MB* + *BM*).
A little math shows that the time elapsed on our clocks *Δt*,
as compared to the time elapsed on God's Timex *Δt'*,
is also greater.

By the triangle outlined in red dashes,
we know we can use the Pythagorean theorem to calculate God's time
*Δt'* if we know *Δt*, which is our time.
According to Pythagoras, (MB)² + (AM)² = (AB)².
Or, substituting our measurements,

*h² + (½vΔt)² = D²*.
Using our equations, and a little algebra, let's solve for *Δt*.

Why? Because, from God's point of view, 2*h* = *cΔt'*
is the roundtrip distance the bolt of lightning travels.
Think about it...
For more details, dig up your old Serway *Physics* text,
and read
Chapter 39
.