Time, Space: Special Relativity Simplified

During the spring of 1879, physicists Albert Michelson and Edward Morley conducted multiple experiments that completely revolutionised our perception of light. The result marked the emergence of Einstein’s notable theory of special relativity. Thus, I will provide a brief overview of the scientific developments that precipitated the fact, beginning with the Ancient Greeks.

On the Nature of Sound

Surprisingly, the notion of sound having a finite speed was well-known even in the ancient world. In Aristotle’s Meterology (circa 334BC), he asserted:

“The dry exhalation that gets trapped when the air is in the process of colliding is forcibly ejected as the clouds condense and in its course strikes the surrounding clouds, and the noise caused by the impact is what we call thunder... the ejected wind burns with a fine and gentle fire and it is then what we call lightning, which occurs when the falling wind appears to us to be coloured. Lightning is produced after the impact and so later than thunder, but it appears to us to precede it because we see the flash before we hear the noise."

In fact, much of the wavelike behaviour of sound was well understood: Anaximander suggested that sound required a medium to traverse in, thereby “striking the air next to itself”, and therefore cannot be instantaneous. But it was not until the 1600s that the first attempts at quantitative measurements of the speed of sound were made.

The First Attempts at Understanding Light

Fig 1.1: The Fizeau Method

Almost 300 hundred years later, French physicist Hippolyte Fizeau conducted the first terrestrial experiment to measure the speed of light. This was a task of marked difficulty.

Fizeau shined a light source onto a reflecting mirror, where the light then traverses into the perforations of the toothed wheel (Fig 1.1) and is reflected (through the toothed wheel which must be rotated at the right speed) to the observer as shown in Fig 1.1.

If the number of teeth is given by n and the turns per second is r, and the length between the wheel and the reflecting mirror is L, it is not too difficult to see that the time taken to move one tooth is given by:

1nr=2Lc

where c, the speed of light, was found to be approximately 315,000 km/s. The accuracy of this result was astounding, for it has only roughly 1.0% deviation from our current measurement.

What is relative velocity?

Before beginning our discussion on the Michelson-Morley experiment, we must first expound on this.

Relative motion is perhaps the crux of what special relativity is about. Fundamentally, all motion is relative. Suppose I am on a bus travelling at 60km/h relative to an observer stationary outside, but to me, I am perfectly stationary (it is the observer outside that’s moving in the opposite direction at 60km/h!).

Another example might help, let’s assume two cars are travelling together. Car A is moving at 50km/h, and car B at 70km/h. What is the relative velocity of car B as observed by the driver of car A? It is simply 20km/h. Thus, you can see that the numerical value of motion is only dependent on the frame of reference, i.e. where you measure from.

Michelson-Morley Experiment

Fig 1.2: Michelson-Morley Experiment

Just as in sound waves, which require a medium to traverse in, physicists have long thought of the existence of an “ether”, the medium for which light was postulated to travel through. Michelson-Morley experiment was therefore an attempt to find out the relative velocity between ether and the earth.

It was traditionally thought that just as sound waves travel at a constant velocity through mediums (solid, liquid etc), so does light, but only through ether. Yet, the result of the experiment was astounding, Michelson and Morley detected no such medium, which led to Einstein’s proposition that ether did not exist, and therefore that speed of light is constant everywhere. This began what we now know as the theory of special relativity. (I have linked the mathematical details of the Michelson-Morley experiment below for those interested).

The result completely transcended scientific understanding at the time, precisely because the prior understanding of relative motion became incorrect. Imagine this, suppose a car is travelling with its headlights on, and we want to measure the speed of light from the headlight, we would think it is the speed of light plus the speed of the car. Yet, this is wrong, since the speed of light is always constant.

Thus, through understanding this, physicists Hendrik Lorentz and Albert Einstein derived new equations for relative motion at relativistic speeds (speeds close to speed of light), and it soon became clear how “weird” they were. The products of the computations were concepts known today as “time dilation” and “length contraction”, a stationary observer will perceive that something moving away at very fast speeds is contracting (becoming thinner). And from the perspective of the object moving away, we will find that the stationary observer’s time is moving slower (if you put a clock beside the person).

There is far more to discuss about relating to the concept of special relativity, but they warrant greater mathematical detail. Thus, I have attached relevant information in the further reading section.

Conclusion

Einstein’s ground-breaking discovery of the theory of special relativity completely changed our modern understanding of the nature of light. What was perhaps more impressive about this tour de force was how he continued to improve on it, culminating in the theory of general relativity just a decade later.

Further Reading

https://galileoandeinstein.phys.virginia.edu/lectures/michelson.html

https://galileoandeinstein.phys.virginia.edu/lectures/spec_rel.html

https://www.worldscientific.com/worldscibooks/10.1142/6601

Introduction to Special Relativity by Robert Resnick (1968) (A personal favourite during my academic study)

A First Course in General Relativity by Schutz (1985)

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