**Experiment 4****:** Super Einstein is flying through space with
his twin brother, Murray, who is 186,000 miles behind him. Every time he
wants to make an acceleration of 10 mph, he uses a flashlight to signal
his brother so that they will accelerate together and stay the same distance
apart.

From Einstein's perspective, he and his brother are 186,000 miles apart, and by letting 1 second pass on his clock before accelerating, he allows the light to reach his brother right at the moment of acceleration. As a result, from Einstein's point of view he and his brother accelerate together and remain a constant 186,000 miles apart. This is what Einstein sees, but if we are standing still with respect to Einstein and his brother, then what will we see?

__Answer__: From our perspective, two things happen. First, we say
that the beam of light has less than 186,000 miles to travel since his brother
is traveling toward it. Second, we are going to see Einstein's clock as
running slow. Thus, for two reasons we are going to see Einstein's brother
get the signal to accelerate before a full second has passed on Einstein's
clock and he begins his own acceleration. Hence, the distance between Einstein
and his brother gets shorter. However, if we stop our analysis at this point,
then we are going to wind up with a contradiction, because if Einstein and
his brother keep accelerating, and if we keep seeing his brother accelerate
first, then eventually distance between them will become so small that Murray
will run into Einstein. However, from Einstein's perspective, he and his
brother stay a constant 186,000 miles apart! How can we resolve this seeming
contradiction? Only by making a very bizarre assumption. In order to keep
Murray from running into his brother __the shortening of the distance between
Einstein and his brother must be compensated for by a contraction of length
in a direction parallel to the direction in which Einstein and his brother
are moving__! In other words, from our point of view, Einstein and his
brother are getting shorter so that some distance always remains between
them in spite of their accelerations.

In the next experiment we will derive a formula that will show us by just how much lengths contract.