Big Bang. Simon Singh

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.

       The Gravity Battle: Newton v. Einstein

      Einstein’s ideas were so iconoclastic that it took time for mainstream scientists to welcome this deskbound civil servant into their community. Although he published his special theory of relativity in 1905, it was not until 1908 that he received his first junior academic post at Berne University. Between 1905 and 1908, Einstein continued to work at the patent office in Berne, where he was promoted to ‘technical expert, second class’ and given the time to push ahead with his effort to extend the power and remit of his theory of relativity.

      The special theory of relativity is