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Einstein’s youthful prowess and his later full-blown genius sprang largely from his immense inquisitiveness about the world around him. Throughout his prolific, revolutionary and visionary career he never stopped wondering about the underlying laws that governed the universe. Even at the age of five, he became engrossed in the mysterious workings of a compass given to him by his father. What was the invisible force that tugged at the needle, and why did it always point to the north? The nature of magnetism became a lifelong fascination, typical of Einstein’s insatiable appetite for exploring apparently trivial phenomena.

As Einstein told his biographer Carl Selig: ‘I have no special talents. I am only passionately curious.’ He also noted:‘The important thing is not to stop questioning. Curiosity has its own reason for existing. One cannot help but be in awe when one contemplates the mysteries of eternity, of life, of the marvellous structure of reality. It is enough if one tries to comprehend only a little of this mystery every day.’ The Nobel Laureate Isidor Isaac Rabi reinforced this point: ‘I think physicists are the Peter Pans of the human race. They never grow up and they keep their curiosity.’

In this respect, Einstein had much in common with Galileo. Einstein once wrote:‘We are in the position of a little child entering a huge library, whose walls are covered to the ceiling with books in many different languages.’ Galileo made a similar analogy, but he condensed the entire library of nature into a single grand book and a single language, which his curiosity compelled him to decipher: ‘It is written in the language of mathematics, and its characters are triangles, circles and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these one is wandering about in a dark labyrinth.’

Also linking Galileo and Einstein was a common interest in the principle of relativity. Galileo had discovered the principle of relativity, but it was Einstein who would fully exploit it. Simply stated, Galilean relativity argues that all motion is relative, which means that it is impossible to detect whether or not you are moving without referring to an external reference frame. Galileo stated vividly what he meant by relativity in the Dialogue:

Shut yourself up with a friend in the main cabin below deck on some large ship, and have with you there some flies, butterflies and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how all the little animals fly with equal speed to all sides of the cabin; how the fish swim indifferently in all directions; how the drops fall into the vessel beneath. And, in throwing something to your friend, you need to throw it no more strongly in one direction than another, the distances being equal; and jumping with your feet together, you pass equal spaces in every direction.

When you have observed all these things carefully … have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship moves or stands still.

In other words, as long as you are moving at constant speed in a straight line, there is nothing you can do to measure how fast you are travelling, or indeed to tell whether you are moving at all. This is because everything around you is moving at the same velocity, and all phenomena (e.g. dripping bottles, flying butterflies) happen the same regardless of whether you are moving or stationary. Also, Galileo’s scenario takes place ‘in the main cabin below deck’, so you are isolated, which removes any hope of detecting any relative motion by referring to an external frame of reference. If you isolate yourself in a similar way by sitting with your ears plugged and your eyes shut inside a train on a smooth track, then it is very difficult to tell if the train is racing along at 100 km/h or whether it is still stuck at the station, which is another demonstration of Galilean relativity.

This was one of Galileo’s greatest discoveries, because it helped to convince sceptical astronomers that the Earth does indeed go round the Sun. Anti-Copernican critics had argued that the Earth could not go around the Sun because we would feel this motion as a constant wind or as the ground being pulled from under our feet, and clearly this does not happen. However, Galileo’s principle of relativity explained that we would not sense the Earth’s tremendous velocity through space because everything from the ground to the atmosphere is moving through space at the same speed as we are. A moving Earth is effectively the same environment as the one we would experience if the Earth were static.

In general, Galileo’s theory of relativity stated that you can never tell if you are moving quickly or moving slowly or moving at all. This holds true whether you are isolated on the Earth, or ear-plugged and blinkered on a train, or tucked away below deck on a ship, or cut off from an external reference frame in some other way.

Unaware that Michelson and Morley had disproved the existence of the ether, Einstein used Galileo’s principle of relativity as his bedrock for exploring whether or not the ether existed. In particular, he invoked Galilean relativity in the context of a thought experiment, also known as a gedanken experiment (from the German word for ‘thought’). This is a purely imaginary experiment that is conducted only in the physicist’s head, usually because it involves a procedure that is not in practice achievable in the real world. Although a purely theoretical construct, a thought experiment can often lead to a deep understanding of the real world.

In a thought experiment he conducted in 1896, when just sixteen years old, Einstein wondered what would happen if he could travel at the speed of light while holding out a mirror in front of him. In particular, he wondered whether he would be able to see his own reflection. The Victorian theory of the ether pictured it as a static substance that permeated the entire universe. Light was supposedly carried by the ether, so this implied that it travelled at the speed of light (300,000 km/s) relative to the ether. In Einstein’s thought experiment, he, his face and his mirror were also travelling through the ether at the speed of light. Therefore light would try to leave Einstein’s face and try to travel towards the mirror in his hand, but it would never actually leave his face, let alone reach the mirror because everything is moving at the speed of light. If light could not reach the mirror, then it could not be reflected back, and consequently Einstein would not be able to see his own reflection.

This imaginary scenario was shocking because it completely defied Galileo’s principle of relativity, according to which someone travelling at constant velocity should not be able to ascertain whether they are moving quickly, slowly, forwards, backwards – or indeed whether they are moving at all. Einstein’s thought experiment implied that he would know when he was moving at the speed of light because his reflection would vanish.

The boy wonder had conducted a thought experiment based on an ether-filled universe, and the result was paradoxical because it contradicted Galileo’s principle of relativity. Einstein’s thought experiment can be recast in terms of Galileo’s below-deck scenario: the sailor would know if the ship was moving at the speed of light because his reflection would vanish. However, Galileo had firmly declared that the sailor should be unable to tell whether his ship was moving.

Something had to give. Either Galilean relativity was wrong, or Einstein’s thought experiment was fundamentally flawed. In the end, Einstein realised that his thought experiment was at fault because it was based on an ether-filled universe. To resolve the paradox, he concluded that light did not travel at some fixed speed relative to the ether, that light was not carried by the ether, and that the ether did not even exist. Unbeknown to Einstein, this is exactly what Michelson and Morley had already discovered.

You might feel wary of Einstein’s slightly tortuous thought experiment, especially if you view physics as a discipline reliant on real experiments with real equipment and real measurements. Indeed, thought experiments are at the fringe of physics and are not wholly reliable, which is why Michelson and Morley’s real experiment was so important. Nevertheless, Einstein’s thought experiment demonstrated the brilliance of his young mind and, even more importantly, it set him on the road to addressing the implications for a universe devoid of ether and what this meant in terms of the speed of light.

The Victorian notion of the ether had been very comforting, because it provided an adequate enough context for what scientists meant when they talked about the speed of light. Everybody accepted that light travelled at a constant speed, 300,000 km/s, and everybody had assumed that this meant 300,000 km/s relative to the medium in which it travelled, which was thought to be the ether. Everything made sense in the Victorian ether-filled universe. But Michelson, Morley and Einstein had shown that there was no ether. So, if light did not require a medium in which to travel, what did it mean when scientists talked about the speed of light? The speed of light was 300,000 km/s, but relative to what?

Einstein thought about the question intermittently over the next few years. He eventually came up with a solution to the problem, but one that depended heavily on intuition. At first sight his solution seemed nonsensical, yet later he would be proved to be absolutely right. According to Einstein, light travels at a constant velocity of 300,000 km/s relative to the observer. In other words, no matter what our circumstances or how the light is being emitted, each one of us personally measures the same speed of light, which is 300,000 km/s, or 300,000,000 m/s (more accurately, 299,792,458 m/s). This seems absurd because it runs counter to our everyday experience of the velocities of ordinary objects.

Imagine a schoolboy with a peashooter which always fires peas at 40 m/s. You are leaning against a wall some way down the street from the schoolboy. He fires his peashooter at you, so the pea leaves the peashooter at 40 m/s, it crosses the intervening space at 40 m/s, and when it hits your forehead it certainly feels as if it was moving at 40 m/s. If the schoolboy gets on his bike and cycles towards you at 10 m/s and fires the peashooter again, then the pea still leaves the peashooter at 40 m/s, but it covers the ground at 50 m/s and feels like 50 m/s when it hits you. The extra speed is down to the pea being launched from a moving bicycle. And if you march towards the schoolboy at 4 m/s then the situation gets even worse, because the pea now feels like it is moving at 54 m/s. In summary, you (the observer) perceive a different pea speed depending on a variety of factors.

Einstein believed that light behaved differently. When the boy is not riding his bicycle, then the light from his bicycle lamp strikes you at a speed of 299,792,458 m/s. When the bike is ridden towards you at 10 m/s, then the light from the lamp still strikes you at a speed of 299,792,458 m/s. And even when you start moving towards the bike while it is moving towards you, then the light still strikes you at 299,792,458 m/s. Light, insisted Einstein, travels at a constant velocity relative to the observer. Whoever is measuring the speed of light always comes up with the same answer, whatever the situation. Experiments would later demonstrate that Einstein was correct. The distinction between the behaviour of light and other things, such as peas, is laid out below.

	Your perception of the speed of peas	Your perception of the speed of light
Nobody is moving	40 m/s	299,792,458 m/s
Schoolboy cycles towards you at 10 m/s	50 m/s	299,792,458 m/s
…and you walk towards the boy at 4 m/s	54 m/s	299,792,458 m/s

Einstein was convinced that the speed of light must be constant for the observer because it seemed to be the only way to make sense of his mirror-based thought experiment. We can re-examine the thought experiment according to this new rule for the speed of light. If Einstein, who was the observer in his thought experiment, were to travel at the speed of light, he would nonetheless see the light leaving his face at the speed of light, because it travels relative to the observer. So the light would leave Einstein at the speed of light, and would be reflected back at the speed of light, which means that he would now be able to see his reflection. Exactly the same thing would happen if he were to stand still in front of his bathroom mirror – the light would leave his face at the speed of light and be reflected back at the speed of light, and he would see his reflection. In other words, by assuming that the speed of light was constant relative to the observer, then Einstein would not be able to tell whether he was moving at the speed of light or standing still in his bathroom. This is exactly what Galileo’s principle of relativity required, namely that you have the same experience whether or not you are moving.

The constancy of the speed of light relative to the observer was a striking conclusion, and it continued to dominate Einstein’s thoughts. He was still only a teenager, so it was with the ambition and naivety of youth that he explored the implications of his ideas. Eventually, he would go public and shake the world with his revolutionary ideas, but for the time being he worked in private and continued with his mainstream education.

Crucially, throughout this period of contemplation, Einstein maintained his natural verve, creativity and curiosity, despite the authoritarian nature of his college. He once said: ‘The only thing that interferes with my learning is my education.’ He paid little attention to his lecturers, including the distinguished Hermann Minkowski, who responded by dismissing him as ‘a lazy dog’. Another lecturer, Heinrich Weber, told him: ‘You are a smart boy, Einstein, a very smart boy. But you have one great fault: you do not let yourself be told anything.’ Einstein’s attitude was partly due to Weber’s refusal to teach the latest ideas in physics, which is also the reason why Einstein addressed him as plain Herr Weber, rather than Herr Professor Weber.

As a result of this battle of wills, Weber did not write the letter of recommendation that Einstein required to pursue an academic career. Consequently, Einstein spent the next seven years after graduation as a clerk in the patent office at Berne, Switzerland. As it turned out, this was not such a terrible predicament. Instead of being constrained by the mainstream theories promulgated at the great universities, Einstein could now sit in his office and think about the implications of his teenage thought experiment—exactly the sort of speculative deliberations that Herr Professor Weber would have pooh-poohed. Also, Einstein’s prosaic office job, initially ‘probationary technical expert, third class’, allowed him to squeeze all of his patenting responsibilities into just a few hours each day, leaving him plenty of time to conduct his personal research. Had he been a university academic, he would have wasted day after day dealing with institutional politics, endless administrative chores and burdensome teaching responsibilities. In a letter to a friend, he described his office as ‘that secular cloister, where I hatched my most beautiful ideas’.

These years as a patent clerk would prove to be one of the most fruitful periods of his intellectual life. At the same time, it was a highly emotional time for the maturing genius. In 1902, Einstein experienced the deepest shock of his entire life when his father fell fatally ill. On his deathbed, Hermann Einstein gave Albert his blessing to marry Mileva Marić, unaware that the couple already had a daughter, Lieserl. In fact, historians were also unaware of Albert and Mileva’s daughter until they were given access to Einstein’s personal correspondence in the late 1980s. It emerged that Mileva had returned to her native Serbia to give birth, and as soon as Einstein heard the news of their daughter’s arrival he wrote to Mileva: ‘Is she healthy and does she already cry properly? What kind of little eyes does she have? Who of us two does she resemble more? Who is giving her milk? Is she hungry? And is she completely bald? I love her so much and I do not even know her yet!… She certainly can cry already, but will learn to laugh only much later. Therein lies a deep truth.’ Albert would never hear his daughter cry or watch her laugh. The couple could not risk the social disgrace of having an illegitimate daughter, and Lieserl was put up for adoption in Serbia.

Albert and Mileva were married in 1903, and their first son, Hans Albert, was born the next year. In 1905, while juggling the responsibilities of fatherhood and his obligations as a patent clerk, Einstein finally managed to crystallise his thoughts about the universe. His theoretical research climaxed in a burst of scientific papers which appeared in the journal Annalen der Physik. In one paper, he analysed a phenomenon known as Brownian motion and thereby presented a brilliant argument to support the theory that matter is composed of atoms and molecules. In another paper, he showed that a well-established phenomenon called the photoelectric effect could be fully explained using the newly developed theory of quantum physics. Not surprisingly, this paper went on to win Einstein a Nobel prize.

The third paper, however, was even more brilliant. It summarised Einstein’s thoughts over the previous decade on the speed of light and its constancy relative to the observer. The paper created an entirely new foundation for physics and would ultimately lay the ground rules for studying the universe. It was not so much the constancy of the speed of light itself that was so important, but the consequences that Einstein predicted. The repercussions were mind-boggling, even to Einstein himself. He was still a young man, barely twenty-six years old when he published his research, and he had experienced periods of enormous self-doubt as he worked towards what has become known as his special theory of relativity: ‘I must confess that at the very beginning when the special theory of relativity began to germinate in me, I was visited by all sorts of nervous conflicts. When young I used to go away for weeks in a state of confusion, as one who at the time had yet to overcome the state of stupefaction in his first encounter with such questions.’

Figure 21 Albert Einstein pictured in 1905, the year he published his special theory of relativity and established his reputation.

One of the most amazing outcomes of Einstein’s special theory of relativity is that our familiar notion of time is fundamentally wrong. Scientists and non-scientists had always pictured time as the progression of some kind of universal clock that ticked relentlessly, a cosmic heartbeat, a benchmark against which all other clocks could be set. Time would therefore be the same for everybody, because we would all live by the same universal clock: the same pendulum would swing at the same rate today and tomorrow, in London or in Sydney, for you and for me. Time was assumed to be absolute, regular and universal. No, said Einstein: time is flexible, stretchable and personal, so your time may be different from my time. In particular, a clock moving relative to you ticks more slowly than a static clock alongside you. So if you were on a moving train and I was standing on a station platform looking at your watch as you whizzed by, then I would perceive your watch to be running more slowly than my own watch.

This seems impossible, but for Einstein it was logically unavoidable. What follows in the next few paragraphs is a brief explanation of why time is personal to the observer and depends on the travelling speed of the clock being observed. Although there is a small amount of mathematics, the formulas are quite simple, and if you can follow the logic then you will understand exactly why special relativity forces us to change our view of the world. However, if you do skip the mathematics or get stuck, then don’t worry, because the most important points will be summarised when the mathematics is complete.

To understand the impact of the special theory of relativity on the concept of time, let us consider an inventor, Alice, and her very unusual clock. All clocks require a ticker, something with a regular beat that can be used to count time, such as a swinging pendulum in a grandfather clock or a constant dripping in a water-clock. In Alice’s clock, the ticker is a pulse of light that is reflected between two parallel mirrors 1.8 metres apart, as shown in Figure 22(a). The reflections are ideal for keeping time, because the speed of light is constant and so the clock will be highly accurate. The speed of light is 300,000,000 m/s (which can be written as 3 × 10⁸m/s), so if one tick is defined as the time for the light pulse to travel from one mirror to the other and back again, then Alice sees that the time between ticks is

Alice takes her clock inside a train carriage, which moves at a constant velocity down a straight track. She sees that the duration for each tick remains the same—remember, everything should remain the same because Galileo’s principle of relativity says that it should be impossible for her to tell whether she is stationary or moving by studying objects that are travelling with her.

Meanwhile, Alice’s friend Bob is standing on a station platform as her train whizzes past at 80% of the speed of light, which is 2.4 X 10⁸m/s (this is an express train in the most extreme sense of the word). Bob can see Alice and her clock through a large window in her carriage, and from his point of view the light pulse traces out an angled path, as shown in Figure 22(b). He sees the light pulse as following its usual up-and-down motion, but for him it is also moving sideways, along with the train.

In other words, in between leaving the lower mirror and arriving at the upper mirror, the clock has moved forward, so the light has to follow a longer diagonal path. In fact, from Bob’s perspective, the train has moved forward 2.4 metres by the time the pulse has reached the upper mirror, which leads to a diagonal path length of 3.0 metres, so the light pulse has to cover 6.0 metres (up and down) between ticks. Because, according to Einstein, the speed of light is constant for any observer, for Bob the time between ticks must be longer because the light pulse travels at the same speed but has farther to travel. Bob’s perception of the time between ticks is easy to calculate:

Figure 22 The following scenario demonstrates one of the main consequences of Einstein’s special theory of relativity. Alice is inside her railway carriage with her mirror-clock, which ’ticks’ regularly as the light pulse is reflected between the two mirrors. Diagram (a) shows the situation from Alice’s perspective. The carriage is moving at 80% of the speed of light, but the clock is not moving relative to Alice, so she sees it behaving quite normally and ticking at the same rate as it always has.

Diagram (b) shows the same situation (Alice and her clock) from Bob’s perspective. The carriage is moving at 80% of the speed of light, so Bob sees the light pulse follow a diagonal path. Because the speed of light is constant for any observer, Bob perceives that it takes longer for the light pulse to follow the longer diagonal path, so he thinks that Alice’s clock is ticking more slowly than Alice herself perceives the ticking.

It is at this point that the reality of time begins to look extremely bizarre and slightly disturbing. Alice and Bob meet up and compare notes. Bob says that he saw Alice’s mirror-clock ticking once every 2.0 x 10^-8s, whereas Alice maintains that her clock was ticking once every 1.2 × 10^-8s. As far as Alice is concerned, her clock was running perfectly normally. Alice and Bob may have been staring at the same clock, but they perceived the ticking of time to be passing at different rates.

Einstein devised a formula that described how time changes for Bob compared to Alice under every circumstance:

It says that the time intervals observed by Bob are different from those observed by Alice, depending on Alice’s velocity (v_A) relative to Bob and the speed of light (c). If we insert the numbers appropriate to the case described above, then we can see how the formula works:

Einstein once quipped: ‘Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. That’s relativity.’ But the theory of special relativity was no joke. Einstein’s mathematical formula described exactly how any observer would genuinely perceive time to slow down when looking at a moving clock, a phenomenon known as time dilation. This seems so utterly perverse that it raises four immediate questions:

1. Why don’t we ever notice this peculiar effect?

The extent of the time dilation depends on the speed of the clock or object in question compared with the speed of light. In the above example the time dilation is significant because Alice’s carriage is travelling at 80% of the speed of light, which is 240,000,000 m/s. However, if the carriage were travelling at a more reasonable speed of 100 m/s (360km/h), then Bob’s perception of Alice’s clock would be almost the same as her own. Plugging the appropriate numbers into Einstein’s equation would show that the difference in their perception of time would be just one part in a trillion. In other words, it is impossible for humans to detect the everyday effects of time dilation.

2. Is this difference in time real?

Yes, it is very real. There are numerous pieces of sophisticated hi-tech gadgetry that have to take into account time dilation in order to work properly. The Global Positioning System (GPS), which relies on satellites to pinpoint locations for devices such as car navigation systems, can function accurately only because it takes into account the effects of special relativity. These effects are significant because the GPS satellites travel at very high speeds and they make use of high-precision timings.

3. Does Einstein’s special theory of relativity apply only to clocks relying on light pulses?

The theory applies to all clocks and, indeed, to all phenomena. This is because light actually determines the interactions that take place at the atomic level. Therefore all the atomic interactions taking place in the carriage slow down from Bob’s point of view. He cannot view these individual atomic interactions, but he can view the combined effect of this atomic slowing-down. As well as seeing Alice’s mirror-clock ticking more slowly, Bob would see her waving to him more slowly as she passed by; she would blink and think more slowly, and even her heartbeat would slow down. Everything would be similarly affected by the same degree of time dilation.

4. Why can’t Alice use the slowing of her clock and her own movements to prove that she is moving?

All the peculiar effects described above are as observed by Bob from outside the moving train. As far as Alice is concerned, everything inside the train is perfectly normal, because neither her clock nor anything else in her carriage is moving relative to herself. Zero relative motion means zero time dilation. We should not be surprised that there is no time dilation, because if Alice noticed any change in her immediate surroundings as a result of her carriage’s motion, it would contravene Galileo’s principle of relativity. However, if Alice looked at Bob as she whizzed past him, it would appear to her that it was Bob and his environment that was undergoing time dilation, because he is moving relative to her.

The special theory of relativity impacts on other aspects of physics in equally staggering ways. Einstein showed that as Alice approaches, Bob perceives that she contracts along her direction of motion. In other words, if Alice is 2 m tall and 25 cm from front to back, and she is facing the front of the train as it approaches Bob, then he will see her as still 2 m tall but only 15 cm from front to back. She appears to be thinner. This is nothing as trivial as a perspective-based illusion, but is in fact a reality in Bob’s view of distance and space. It is a consequence of the same sort of reasoning that showed that Bob observes Alice’s clock ticking more slowly.

So, as well as assaulting traditional notions of time, special relativity was forcing physicists to reconsider their rock-solid notion of space. Instead of time and space being constant and universal, they were flexible and personal. It is not surprising that Einstein himself, as he developed his theory, sometimes found it difficult to trust his own logic and conclusions. ‘The argument is amusing and seductive,’ he said, ‘but for all I know, the Lord might be laughing over it and leading me around by the nose.’

Nevertheless, Einstein overcame his doubts and continued to pursue the logic of his equations. After his research was published, scholars were forced to acknowledge that a lone patent clerk had made one of the most important discoveries in the history of physics. Max Planck, the father of quantum theory, said of Einstein: ‘If [relativity] should prove to be correct, as I expect it will, he will be considered the Copernicus of the twentieth century.’

Einstein’s predictions of time dilation and length contraction were all confirmed by experiments in due course. His special theory of relativity alone would have been enough to make him one of the most brilliant physicists of the twentieth century, providing as it did a radical overhaul of Victorian physics, but Einstein’s stature was set to reach even greater heights.

Soon after publishing his 1905 papers, he set to work on a programme of research that was even more ambitious. To put it into context, Einstein once called his special theory of relativity ‘child’s play’ compared with what came after it. The rewards, however, would be well worth the effort. His next great discovery would reveal how the universe behaved on the grandest scale and provide cosmologists with the tools they needed to address the most fundamental questions imaginable.