Space, Time and Einstein
J. B. Kennedy
PART I – Einstein’s revolution
The lazy ship
When Einstein published his ideas about time dilation in 1905, he limited his predictions to a special case: to special sorts of measure- ments. As mentioned above, special relativity is special because it is limited to special cases. To understand these important limitations, we must consider some simple facts about motion.
Suppose a ship is sailing very smoothly down a wide river at a constant speed and in a fixed direction. Suppose some budget travellers have cabins below deck without windows, and so cannot see the river banks sliding slowly by the ship. When they wake up in the morning such passengers will not be able to tell whether the ship is moving or standing still. In fact, no observation or experiment performed within the cabin can measure the ship’s motion: without looking outside steady speeds are undetectable and unmeasurable.
This is very peculiar. If the passengers are really moving, they should be able to discover it without looking elsewhere. Philosophers and scientists discussed this riddle so often that they gave steady motion a special name: Inertial motion: Motion at a constant speed along a straight line. “Inertial” comes from the Latin word for inactive, sluggish or lazy.
Thus, during inertial motion the ship is lazy in the sense that it just keeps doing what it was doing: it does not change speed or direction.
The opposite of inertial motion is accelerated motion, and that is easy to detect. For example, when a car accelerates, the passengers are pushed back against their seats. If the ship were to slow down or speed up, the passengers below deck might spill their coffee and would immediately conclude that the ship’s speed was changing. The word “acceleration” is used to mean a change in speed or in direction (or both). Thus, steering a car to the left without touching the accelerator pedal is also an acceleration in this sense.
Distances and durations are measured with rulers and clocks.
Einstein limited his special theory to the case where the rulers and clocks used in measurements were at rest or moving inertially. In short, the special theory applies only to “inertial measurements”. The object that is measured may be accelerating – it may be turning loops or flapping up and down – but the measuring devices must be resting or moving steadily.
We can now state Einstein’s claims about time dilation more precisely:
Time dilation: Take as a standard a clock that is at rest or moving inertially. Other clocks moving relative to the standard will have longer hours (i.e. “dilated hours”). Furthermore, all physical processes moving relative to the standard clock will take longer than if they were at rest relative to the standard.
That is, it will take more than an hour on the inertial, standard clock for an hour to pass on a clock moving relative to it or, for example, for a moving video player on the spaceship to show an hour-long programme. (The special theory can be applied to accelerating measuring devices by using approximations. If the period of acceleration is divided into short intervals, the device can be treated as moving inertially during each interval. By adding the changes during each of these intervals together, the change during the entire acceleration can be approximated. But, strictly speaking, the special theory applies only to measurements made by devices moving at constant speeds in a straight line.)