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