Chapter 2.6 Faster speeds, shorter lengths


Using his two principles, the constancy of the speed of light and relativity, Einstein made a second, astonishing, prediction. As Jill’s spaceship speeds up, earth-bound Jack will find that its length shrinks.
If the spaceship had the shape of a long sausage with fins when it blasted off, at high speeds it will contract lengthwise into the shape of a disc or pancake. As Jill faces forwards out of the window on the ship’s nose, her shoulders will remain the normal distance apart but her belly button will be very close to the skin on her back. This is called length contraction.

For another example, suppose that someone with more money than sense buys a Jaguar on impulse, but returns home to find that the six-metre car will not fit into the three-metre garage. By driving the car at nearly the speed of light towards the open door of the garage, it is actually possible to fit it snugly inside. Of course, the brakes should be applied before hitting the rear wall.

Actually, physicists have found it difficult to confirm length contraction directly. Time aboard a speeding spaceship can be measured by exchanging light or radio signals, but it is harder to measure lengths by pulling alongside the spaceship with a yardstick.

However, length contraction is considered a confirmed effect.

The famous experiments by the Americans Michelson and Morley in 1887 are taken as strong evidence for length contraction. Simply put, they used a long rod moving in the direction of one of its ends.

When they shone a ray of light along the rod and reflected it back to its source, they discovered that the ray took slightly less time for the return trip than expected. Einstein and other physicists concluded that the rod must have shrunk.

Just as with time dilation, these contractions seem strange to us only because we are such slow-moving creatures. The fastest human beings run 100 metres at the Olympics in about ten seconds. If we were many millions of time faster than that, and could flit around the world in a flash, shrinking lengths and slowing times would be an ordinary part of our lives. On Saturday nights, we could become thinner (and dizzy) just by constantly rushing back and forth past our dates. But a professor who paced back and forth in front of the blackboard at near light speed might take hours and hours to finish a lecture.

To summarize, with faster speeds, lengths become shorter in the direction of travel. This can be put more precisely:

Length contraction

Take as a standard a yardstick at rest or moving in a straight line at a constant speed. Other yardsticks moving relatively to this inertial standard will contract in the direction of their travel. That is, the contracted yardsticks will measure only a fraction of the standard yardstick. In fact, the length of all moving objects will contract relative to the standard.

Thus, faster speeds imply shorter lengths.

Length contracts only in the direction of travel: a sausage becomes a pancake, but its diameter remains the same.

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