3.11 Relativity

One of our readers recently set a tough challenge. He had heard that if a twin was to travel out into space almost as fast as light itself, she would return younger than her twin who had remained on Earth. Apparently time moves more slowly for people travelling very fast compared to you. Can we explain this?

It’s a tall order, but let’s see if we can at least explain why Einstein saw there had to be changes to the prevailing theory of relativity. Nowhere better to start than our everyday experiences of relative motion. These gave rise to the classical theory of relativity expressed first by Galileo in the 17th century. It was not till 1905 that Albert Einstein recognised that, although this explains our everyday experiences, it only works because the speeds we are accustomed to on Earth are relatively slow.

Classical relativity

In the days when I used to cycle to my science group sessions – when they were live events – I sometimes had some junk to put in a bin I passed: a drinks can, for example. To save the trouble of dismounting I’d release it as I passed by – and sometimes missed. The art was to let it go in advance of reaching the bin, just at the right moment.

The obvious point is that the can was travelling with me on the bike and already had a forward speed before I let it go. You notice this in countless situations, such as a moving pavement at the airport, where by walking on it at your normal pace you overtake people walking on the fixed floor. Clearly, the speed they observe is that of you plus that of whatever you are fixed to: the travellator, in this case. But from the point of view of you on the travellator, you feel you are moving at your normal pace – if you blinded yourself to the surroundings.

Of course the same is true of our very existence on Earth. We might be toddling around at 2 or 3 miles per hour in our daily lives but to a person outside our planet we are hurtling: spinning with the Earth each day and racing around the Sun once a year at 67,000 mph. The whole question of speed depends on your frame of reference. If you’re a passenger on a train and another one passes you in the opposite direction the passengers appear to whizz past at the combined speed of the two trains. On the other hand if a slightly faster train slips past in your direction the passengers appear to be moving very slowly. It’s all relative – hence the name.

The important principle established in the 17th century is that all your actions, all the forces, behave in just the same ways whether you are travelling at high speed, low speed or at rest – but only if the speed is steady. The way we move and interact on the equator – where the land we tread is moving rapidly as the Earth spins – is the same nearer the poles, where it is moving more slowly. In a similar way, a passenger drinking a cup of coffee on a high speed train is going through the same motions as he would at the station café.

This principle of relativity was a starting point for Einstein – physical processes operate in exactly the same way in any frame of reference, whatever its speed – providing it is a steady speed, with no acceleration. That cup of coffee may be speeding along at 100 mph but it is still poured out and drunk the same way (at least until the train brakes suddenly, or the track takes it round a bend, leaving it spilt on your lap).

The dilemma

These simple ideas seemed to work well for our understanding of physics– right up until the middle of the nineteenth century, that is. We understood that when you walk through a train travelling at 100 kilometres per hour at a walking pace of 5kph, your relative speed to someone outside would be 105 kph if you walk forward, or 95 if you walk in the opposite direction. Fine – intuitive.

A problem began to arise when it came to the behaviour, not of physical objects like passengers on train, but of  light – a rapidly moving wave of miniscule electric and magnetic forces. See animation. It’s not intuitive that light has a speed at all. You switch on a light and the room lights up equally everywhere, immediately. It doesn‘t start illuminating nearby first then creep across to other parts, like a wave rippling across a pond. It had been shown as early as the 17th century that light does indeed  travel at a finite speed, but it’s very, very fast: 300,000 kilometers in just one second.

Indeed we now have tangible evidence of this when there’s a delay in radio or TV transmissions or phone calls. The electromagnetic waves that carry the signals (similar to light waves) take their time to reach us.  We now know that light from the Sun takes around eleven minutes to reach us.

The problem was that this speed at which light travels appeared to be a fixed quantity, according to Maxwell’s theory, whatever the frame of reference. It implied that light streaming out from a torch inside a moving train would appear to travel at the same speed whether you were on the train or on the platform as it rushed passed. The speeds of the light and the train don’t add together, as they do when you walk on a travellator. Something was amiss.

A famous experiment, carried out with meticulous precision two decades later, in 1887, aimed to detect the difference in speed between a light beam thrown forward in the direction of the Earth’s motion, compared to one sent out sideways. There was no difference. Theory and experiment now seemed to show that the speed of light is the same in all frames of reference. It wasn’t faster at the equator than the poles. It didn’t move any faster or slower from a torch in a moving train than it would on the platform. And what was true for light also went for all other types of electric and magnetic influence –radio and TV, infra-red and ultraviolet waves, for example. These brute facts forced a reappraisal of the foundations of the classical view of how the world works.

Revolutionary thinking

As you might expect, attempts were made by physicists and mathematicians to work around this problem. One idea was to imagine that all physical objects contracted as they sped up, with the effect only being noticeable near the speed of light (300 million km per second). This strange idea arose from the simple fact that speed is a measure of how much distance is travelled in a given time interval: the number of miles in an hour or kilometers in a second, for example. So if, as it appeared, light doesn’t go any faster to a person outside, when it’s travelling along the carriage of a moving train, perhaps it travelled over a slightly shorter distance or took a bit longer. Either of these changes, or both, could bring the apparent speed back to the fixed value of 300,000 kilometers per second that Maxwell had determined. In other words, perhaps the carriage was a bit shorter or time had slowed down a bit.

But this solution didn’t work. What was needed, as happens very occasionally in science, was  a complete revolution in our understanding, not just a re-hash of previous thinking. Albert Einstein, a young unknown patent clerk at the time, saw this. He famously used his imagination to develop new thinking (his so-called “thought experiments”). He says, for example that at the age of sixteen, while still a schoolboy, he imagined pursuing a beam of light and reaching the same speed as the light. He imagined it would be like looking out of a train window at another train passing at almost the same speed. Neither would appear to be moving. A light beam would appear to be static rather than the wave of rapidly oscillating electric and magnetic influences that it was understood to be. This could not be right.

He saw that the unexpected consequences of both theory and experiment could only be explained by reimagining what we mean by distance and time – the two components of speed. The stark reality was that our very notions of distance and time had to be altered to account for what happens when thing go extremely fast relative to one another. More precisely, he saw that our measurement of a given distance or of an interval of time would be different if we were moving compared to someone else who was moving at a different speed (or stationary). These measurements would have to be relative, not absolute. I would only see your kilometer as the same as my kilometer, if we were both moving at the same speed (or at rest). If we are moving relative to one another your meter and your second are different to mine.

This extraordinary idea runs counter to our most basic intuitions and shatters our understanding of the physical world at a fundamental level. Of course, we don’t notice this at all in our everyday lives because the effect is only noticeable at unimaginably fast speeds – something approaching a billion kilometers per hour. At everyday speeds – say 100 kph – a one meter ruler moving past you would appear to be just 0.00000000000001 of a meter shorter than it would if you were travelling with it. Undetectable.

Einstein’s Theory of Special Relativity provides a formula for working out how distances are shorter when you look at something moving relative to you. It also provides a formula for how time intervals lengthen. In the case of the twins that launched this story, it was the slowing down of time that gave the traveller the age advantage. Although you need maths to prove it fully, here’s an intuitive way of seeing why time must slow down when you observe actions in a frame of reference that is moving relative to you.

In this diagram, a person “A”  is travelling along at high speed compared to her companion “B” who remains stationary outside. Imagine a beam of light shooting up from the floor to the ceiling of the compartment “A” is travelling in and bouncing back again, from a mirror. She would see the light simply shooting up and down from floor to ceiling and back (if it weren’t so fast).

If she could measure it, she would note that it took a certain time to do so  – extremely short, of course. But her companion on the outside, “B”, would see it differently. She would see that the light beam had traversed a longer path (in yellow and green) because the vehicle itself had moved on while the light was travelling. But light, unlike other things, would not be travelling any faster even though it was in a moving carriage – all light in any frame moves at the same steady speed. So, for her, outside the carriage, the light must have taken longer to travel to the ceiling and back again, to cover the extra distance of the yellow line.  

Now to get a feel for how time must pass more slowly in these circumstances, let’s imagine the light to come repeatedly from something like a flashing digital clock or a lighthouse. Let’s say it flashed once a second from the point of view of the traveller. The interval between flashes as seen by the person outside would be longer. What took a second inside the moving compartment would have taken longer for the person outside.

In the ordinary circumstances of our lives this effect is, of course, negligible. However fast we manage to travel in practice, it’s very much less than the speed of light. The yellow path in the diagram would be indistinguishable from the straight up and down path seen by the traveller.  So our clocks (and everything else) would run at the same speed as far as we are able to detect in everyday activity. However, this tiny discrepancy has now been detected and measured in special experiments designed to test the theory. In 1971, and on several occasions since, extremely sensitive atomic clocks have been placed aboard planes flying at several hundred kilometers per hour. They have found differences of tens or hundreds of nanoseconds (just tenths of millionths of a second), tiny intervals of time, but sufficient to confirm Einstein’s formula.

So, time moves more slowly when you observe it in a moving thing. This gave rise to the very bizarre thought concerning twins and space travel that launched this story. If one twin travelled at extremely high speed out into space then returned, time would have moved more slowly for that person, as seen by the twin who remained on Earth. This is indeed the case.

In fact the pilot and scientists who travelled in the experimental plane carrying an atomic clock would have been a few nanoseconds younger than had they remained on Earth.

It’s not only ticking clocks that are affected by this relativistic effect. There’s nothing special about clocks – all physical changes take place in time and follow the same logic. Biological processes are no exception. Heartbeat, breathing, digestion all would take place more slowly for the travelling twin, compared to the Earth-bound one. She would have aged less.

More generally

Einstein knew when he published this theory at the tender age of twenty six, that he had only considered the relative motion of things if they were travelling at steady speed relative to one another. He realised he would need to go on to develop a more general theory to embrace situations where things were speeding up or slowing down relative to one another. This insight opens up an even greater assault on our “common sense” intuitions. But given that one theory of relativity is enough to take in at a sitting, we’ll leave that to a future date.

© Andrew Morris 30th October 2020