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.