Chapter 2.5 The principle of relativity – Space, Time and Einstein

Einstein’s central idea is that there is democracy among all inertial measurements. Any measurement made by a set of rulers and clocks moving at a steady speed in a fixed direction is equally as good as a measurement made by any other set.

Suppose that there are two sets of rulers and clocks moving relatively to each other, and each is measuring the speed of a passing spaceship.

The results of the measurements will differ, but Einstein insists each result may equally claim to be “the” speed of the ship. There is no physical way to show that one speed is more correct than the other.

Suppose that the budget travellers below deck on the ship work hard to discover their speed by doing all sorts of experiments in their cabin. For example, they drop objects and discover that they fall faster and faster the longer they fall. In fact, every second of fall increases their speed by 32 feet per second. This law is the same in the cabin as it would be on shore. That is, even laws of physics are unaffected by the ship’s speed through the river. Thus Einstein’s democracy extends even to laws; they are the same for all observers moving at steady speeds in a fixed direction.

Einstein called this sort of democracy his special principle of relativity: the laws of physics are the same for all observers moving at a steady speed along a straight line. That is, regardless of your relative speed, the laws of physics are the same. As Einstein said: This postulate we call the “special principle of relativity.” The word “special” is meant to intimate that the principle is restricted to the case when the [measuring devices] have a motion of uniform translation . . . and does not extend to the case of non- uniform motion.

What is a law of physics? When we plan a journey by car, we all use the simple law that “distance equals speed multiplied by time”: an average of 90 kilometres an hour for five hours will cover 450 kilometres. Here we have a law that connects three things: distance, speed and time. Each of these can easily be measured with, say, the speedometer of the car, a wristwatch and a good map. This suggests that a law is a relation between measurements. The relation in this law is represented by the italicized words above. In every motion, the relation between distance traversed, speed and time taken will be the same.

Some laws contain constants. For example, when we drop something to the floor, its speed increases by 9.8 metres per second during every second it falls. Thus, in general, a physical law is a relation, involving constants, between measurement results.

Measurements made at different speeds lead to different results.

Birds flying alongside a car sometimes seem to stand still: their measured relative speed is zero. But a pedestrian watching the birds swoop by would disagree, and insist that their relative speed was, say, 40 kilometres per hour. The difference between a speed of zero and 40 kilometres per hour reflects the speed of the measurer. Both the driver and the pedestrian, however, will agree that the distance covered by the birds is given by their speed multiplied by the time taken.

Einstein’s principle of relativity can now be stated more clearly. He says that, while the measurements made by different sets of rulers and clocks will differ and depend on speed, relations between the measurements will be the same for all sets moving inertially. Likewise, any physical constants in laws will be the same. Measurement results are relative; laws are not.

Physics is about relations.

Special relativity is derived from two principles. Both are experimental facts boldly assumed to hold universally. The first says that physical laws are the same for all observers. The second says it is a law that light travels at 300,000 kilometres per second.

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