The Principle of Relativity

By the time Einstein was born, it had already been two centuries since physicists had accepted Galileo's principle of inertia. One way of stating this principle is that experiments with material objects don't come out any different due the straight-line, constant-speed motion of the apparatus. For instance, if you toss a ball up in the air while riding in a jet plane, nothing unusual happens; the ball just falls back into your hand. Motion is relative. From your point of view, the jet is standing still while the farms and cities pass by underneath.

The teenage Einstein was suspicious because his professors said light waves obeyed an entirely different set of rules than material objects, and in particular that light did not obey the principle of inertia. They believed that light waves were a vibration of a mysterious substance called the ether, and that the speed of light should be interpreted as a speed relative to this ether. Thus although the cornerstone of the study of matter had for two centuries been the idea that motion is relative, the science of light seemed to contain a concept that a certain frame of reference was in an absolute state of rest with respect to the ether, and was therefore to be preferred over moving frames.

Experiments, however, failed to detect this mysterious ether. Apparently it surrounded everything, and even penetrated inside physical objects; if light was a wave vibrating through the ether, then apparently there was ether inside window glass or the human eye. It was also surprisingly difficult to get a grip on this ether. Light can also travel through a vacuum (as when sunlight comes to the earth through outer space), so ether, it seemed, was immune to vacuum pumps.

Einstein decided that none of this made sense. If the ether was impossible to detect or manipulate, one might as well say it didn't exist at all. If the ether doesn't exist, then what does it mean when our experiments show that light has a certain speed, 3×10⁸ meters per second? What is this speed relative to? Could we, at least in theory, get on the motorcycle of Einstein's teenage daydreams, and travel alongside a beam of light? In this frame of reference, the beam's speed would be zero, but all experiments seemed to show that the speed of light always came out the same, 3 × 10⁸ m/s. Einstein decided that the speed of light was dictated by the laws of physics (the ones concerning electromagnetic induction), so it must be the same in all frames of reference. This put both light and matter on the same footing: both obeyed laws of physics that were the same in all frames of reference.

the principle of relativity

Experiments don't come out different due to the straight-line, constant-speed motion of the apparatus. This includes both light and matter.

This is almost the same as Galileo's principle of inertia, except that we explicitly state that it applies to light as well.

This is hard to swallow. If a dog is running away from me at 5 m/s relative to the sidewalk, and I run after it at 3 m/s, the dog's velocity in my frame of reference is 2 m/s. According to everything we have learned about motion, the dog must have different speeds in the two frames: 5 m/s in the sidewalk's frame and 2 m/s in mine. How, then, can a beam of light have the same speed as seen by someone who is chasing the beam?

c / Albert Michelson, in 1887, the year of the Michelson-Morley experiment.

In fact the strange constancy of the speed of light had already shown up in the now-famous Michelson-Morley experiment of 1887. Michelson and Morley set up a clever apparatus to measure any difference in the speed of light beams traveling east-west and northsouth. The motion of the earth around the sun at 110,000 km/hour (about 0.01% of the speed of light) is to our west during the day. Michelson and Morley believed in the ether hypothesis, so they expected that the speed of light would be a fixed value relative to the ether. As the earth moved through the ether, they thought they would observe an effect on the velocity of light along an east-west line. For instance, if they released a beam of light in a westward direction during the day, they expected that it would move away from them at less than the normal speed because the earth was chasing it through the ether. They were surprised when they found that the expected 0.01% change in the speed of light did not occur.

d / George FitzGerald, 1851- 1901.

Although the Michelson-Morley experiment was nearly two decades in the past by the time Einstein published his first paper on relativity in 1905, he did not even know of the experiment until after submitting the paper.⁴ At this time he was still working at the Swiss patent office, and was isolated from the mainstream of physics.

e / Hendrik Lorentz, 1853-1928.

How did Einstein explain this strange refusal of light waves to obey the usual rules of addition and subtraction of velocities due to relative motion? He had the originality and bravery to suggest a radical solution. He decided that space and time must be stretched and compressed as seen by observers in different frames of reference. Since velocity equals distance divided by time, an appropriate distortion of time and space could cause the speed of light to come out the same in a moving frame. This conclusion could have been reached by the physicists of two generations before, but the attitudes about absolute space and time stated by Newton were so strongly ingrained that such a radical approach didn't occur to anyone before Einstein. In fact, George FitzGerald had suggested that the negative result of the Michelson-Morley experiment could be explained if the earth, and every physical object on its surface, was contracted slightly by the strain of the earth's motion through the ether, and Hendrik Lorentz had worked out the relevant mathematics, but they had not had the crucial insight that this it was space and time themselves that were being distorted, rather than physical objects.⁵

4Actually there is some controversy on this historical point. 5See discussion question F on page 26, and homework problem 12