24 Nov 1905, Einstein’s ‘miracle year’ (JOHN HIGGS) | Part B’
Relativity showed that we lived in a stranger, more complex universe where space and time were no longer fixed, but could be stretched by mass and motion. This was a universe of black holes and warped space-time that seemed to have little in common with the everyday world in which we live. Relativity is often presented in ways that make it appear incomprehensible, but the core idea at its heart can be grasped surprisingly easily.
Imagine the deepest, darkest, emptiest chunk of space possible, far removed from stars, planets or any other influence. In this deep void imagine that you are floating, snug and warm in a space suit. Importantly, imagine that you are not moving.
Then imagine that a cup of tea comes slowly floating past, and eventually disappears into the distance.
At first glance, this scenario sounds reasonable. Newton’s First Law says that an object will continue to remain at rest, or will move in a straight line at a constant velocity, unless some external force acts on it. Clearly, this is a perfect description of the behaviour of both you and the cup of tea.
But how could we say that you were at rest? Einstein would ask. How do we know that it’s not the cup of tea that’s at rest, and you that are moving past it? Both situations would appear identical from your point of view. And also, from the point of view of the cup of tea.
Galileo was told in the 1630s that it wasn’t possible the earth was going around the sun, because we on earth do not feel like we are moving. But Galileo knew that if you were moving smoothly, without accelerating or decelerating, and if there were no visible or audible clues to movement, then you would not be aware of your motion. He argued that you cannot claim to be ‘at rest’, because it is impossible to tell the difference between a moving object and a stationary one without some form of external reference to compare it against.
This may sound like a dubious, pedantic point. Surely, you might think, you are either moving or not moving, even if there’s nothing else around. How could anyone claim that the statement ‘you are at rest’ is absurd or meaningless?
Instinctively we feel that we or the tea must be moving – or not – against some form of definitive ‘background’. But if there is a definitive background, what could it be?
In our everyday lives the solid ground beneath our feet is a point of reference that we unconsciously judge everything by. Living with such a clear fixed point makes it hard to imagine one not existing. But how fixed is the ground? We have known that continents are slowly moving since the acceptance of plate tectonics in the 1960s. If we are seeking a fixed point, it is not the land that we stand on.
Could we instead define our position with the very centre of the earth? This isn’t fixed either, because the earth is moving around the sun at over 100,000 km/h. Or perhaps we can define the sun as our fixed point? The sun is moving at 220 km/s around the centre of the Milky Way galaxy. The Milky Way, in turn is moving at 552 km/s, relative to the rest of the universe.
What of the universe itself? As a last-ditch and somewhat extreme attempt to locate a fixed point, could we not declare the centre of the universe to be our omphalos? The answer, once more, is no. There is no ‘centre of the universe’, as we will see later, but for now we can also reject the idea for being ridiculously impractical.
So how can we say anything definite about our position, or that of the cup of tea? There may not be a real ‘fixed point’ which we can use, but we are still free to project our own frames of reference wherever we like. We can create a reference frame centred on ourselves, for example, which allows us to say that the tea is moving relative to us. Or we can create one centred on the tea, which would mean that we were moving relative to the cup. What we can’t do is say that one of these frames of reference is correct or more valid than the other. To say that the tea moved past us would be to declare our innate, tea-ist prejudice.
There is an apt example of how one frame of reference is no more valid than another in Einstein’s 1917 book, Relativity. In the original German-language edition, he used Potsdamer Platz in Berlin as the frame of reference in one example. When the book was translated into English, this was changed to Trafalgar Square in London. By the time the book was out of copyright and made available online as an eBook, this had been changed to Times Square in New York because, in the opinion of the editor, ‘this is the most well known/ identifiable location to English speakers in the present day.’ What is important about the reference point, in other words, is that it has been defined as the reference point.
Practically, it could be anywhere. The first step towards understanding relativity, then, is to accept this: a statement of position is only meaningful when it has been defined along with its frame of reference. We can choose whatever frame of reference we like, but we can’t say that it has more validity than any other.
With that in mind, let us return to Zurich in 1914.
Einstein gets on a steam train in Zurich and travels to Berlin. He is leaving his wife Marić and their two surviving children in order to begin a new life with his cousin, who will later become his second wife. Imagine that the train travels in a straight line at a constant speed of 100 km/h, and that at one point he stands, holds a sausage at head height, and drops it on the floor.
This raises two questions: how far does the sausage fall, and why is he leaving his wife? Of these two questions Einstein would have found the first one to be the most interesting, so this is what we will focus on. Let us say he holds the sausage up to a height of five feet above the train floor and drops it. It lands, as you would expect, near to his scuffed shoes, directly below his raised hand. We can say that it has fallen five feet exactly. As we have just seen, such a statement only makes sense when the frame of reference is defined. Here we take Einstein’s frame of reference, that of the inside of the train carriage, and we can say that relative to that, the sausage fell five feet.
What other frames of reference could we use? Imagine there is a mouse on the railway track, and that the train rumbles safely over the mouse as Einstein drops his sausage. How far would the sausage fall if we use this mouse as a point of reference? The sausage still starts in Einstein’s hand and lands by his feet. But, as far as the mouse is concerned, Einstein and the sausage are also moving over him during the sausage’s fall. During the period between Einstein letting go of the sausage and it hitting the floor, it will have moved a certain distance along the track. The position of his feet when the sausage lands is further down the track than the position of the hand at the moment it was dropped.
The sausage has still fallen five feet downwards, relative to the mouse, but it has also travelled a certain distance in the direction the train is travelling in. If you were to measure the distance taken by the sausage between the hand and the floor, relative to the mouse, its path would be at an angle rather than pointing straight down, and that means it would have travelled further than five feet.
This is, instinctively, something of a shock. The distance that the sausage moves changes when it is measured from different frames of reference.
How can non-mathematicians understand Einstein’s mathematical world, which he called space-time? We are trapped in the reference frames that we use to understand our regular world, and we are unable to escape to his higher mathematical perspective where their contradictions melt away. Our best hope is to look downwards at a more constrained perspective that we can understand, and use that as an analogy for imagining space-time.
Imagine a flat, two-dimensional world where there is length and breadth but no height. The Victorian teacher Edwin Abbott Abbott wrote a wonderful novella about such a place, which he called Flatland. Even if you are not familiar with this book, you can picture such a world easily by holding a piece of paper in front of you and imagining that things lived in it.
If this piece of paper were a world populated by little flat beings, as in Abbott’s story, they would not be aware of you holding the paper. They could not comprehend our three-dimensional world, having no concept of ‘up’. If you were to bend and flex the paper they would not notice, for they have no understanding of the dimension in which these changes are taking place. It would all seem reassuringly flat to them.
Now imagine that you roll the paper into a tube. Our little flat friends will still not realise anything has happened. But they will be surprised when they discover that, if they walk in one direction for long enough, they no longer reach the end of the world but instead arrive back where they started. If their two-dimensional world is shaped like a tube or a globe, like the skin of a football, how could these people explain those bewildering journeys that do not end? It took mankind long enough to accept that we live on a round planet even though we possessed footballs and had the advantage of understanding the concept of globes, yet these flat critters don’t even have the idea of globes to give them a clue. They will need to wait until there comes among them a flat equivalent of Einstein, who would use strange arcane mathematics to argue that their flat world must exist in a higher-dimensional universe, where some three-dimensional swine was bending the flat world for their own unknowable reasons. The other flat critters would find all this bewildering, but given time they will discover that their measurements, experiments and regular long walks fit Flat Einstein’s predictions. They would then be confronted with the realisation that there is a higher dimension after all, regardless of how ludicrous this might seem or how impossible it is to imagine.
We are in a similar position to these flat creatures. We have measurements and data that can only be explained by the mathematics of space-time, yet space-time remains incomprehensible to the majority of us. This is not helped by the glee with which scientists describe the stranger aspects of relativity instead of explaining what it is and how it relates to the world we know. Most people will have heard the example of how, should a distant observer see you fall into a black hole, you would appear to take an infinite amount of time to fall even though you yourself thought you fell quickly. Physicists love that sort of stuff. Befuddlement thrills them, but not everyone benefits from being befuddled.
It is true that space-time is a deeply weird place from a human perspective, where time behaves like any other dimension and concepts such as ‘future’ and ‘past’ do not apply as we normally understand them. But the beauty of space-time is that, once understood, it removes strangeness, not creates it. All sorts of anomalous measurements, such as the orbit of Mercury or the way light bends around massive stars, lose their mystery and contradictions. The incident where the cup of tea may or may not pass you in deep space becomes perfectly clear and uncontroversial. Nothing is at rest, unless it is defined as being so.
General Relativity made Einstein a global celebrity.
He made an immediate impression on the public, thanks to press photographs of his unkempt hair, crumpled clothes and kind, smiling eyes. The idea of a ‘funny little man’ from the European continent with a mind that could see what others could not was a likeable archetype, one which Agatha Christie put to good use when she created Poirot in 1920. The fact that Einstein was a German Jew only added to the interest.
The reception of Einstein and relativity shows a world more interested in the man than his ideas. Many writers took an almost gleeful pleasure in their failure to understand his theories, and the idea that relativity was impossible for normal people to comprehend soon took hold. Contemporary press reports claimed that there were only twelve people in the world who could understand it. When Einstein visited Washington in 1921 the Senate felt the need to debate his theory, with a number of Senators arguing that it was incomprehensible. President Harding was happy to admit that he didn’t understand it. Chaim Weizmann, later the first President of Israel, accompanied Einstein on an Atlantic crossing. ‘During the crossing Einstein explained relativity to me every day,’ he remarked, ‘and by the time we arrived I was fully convinced that he really understands it.’
Stranger Than We Can Imagine