Imagine that I am showing you a cube, and the face I am showing you is red. Now suppose I rotate it so the face is no longer visible. Do you think it is still red? Of course you do. And if I put a ball inside a box, do you still think the ball exists, even when you can’t see it? When did we get such faith in the existence of things that we can’t see? Probably from the age of around a few months old, according to research on developmental psychology. Babies younger than a few months appear unable to deduce the continued existence of an object hidden from sight, even if they observe the object while it is being hidden; babies lack a sense of “object permanence“. As we get older, we learn to believe in the existence of things that we can’t directly see. True, we don’t all believe in God, but most of us believe that our feet are still there after we put our shoes on.
In fact, scientific progress has gradually been acclimatising us to the real existence of things that we can’t directly see. It is all too easy to forget that, before Einstein blew our minds with general relativity, he first had to get humanity on board with a more basic idea: atoms. That’s right, the idea that things were made up of atoms was still quite controversial at the time that Einstein published his groundbreaking work on Brownian motion, supporting the idea that things are made of tiny particles. Forgetting this contribution of Einstein is a bit like thanking your math teacher for teaching you advanced calculus, while forgetting to mention that moments earlier he rescued you from the jungle, gave you a bath and taught you how to read and write.
Atoms, along with germs, the electromagnetic field, and extra-marital affairs are just one of those things that we accept as being real, even though we typically can’t see them without the aid of microscopes or private investigators. This trained and inbuilt tendency to believe in the persistence of objects and properties even when we can’t see them partially explains why quantum mechanics has been causing generations of theoretical physicists to have mental breakdowns and revert to childhood. You see, quantum mechanics tells us that the properties of some objects just don’t seem to exist until you look at them.
To explain what I mean, imagine that cube again. Suppose that we label the edges of the cube from one to eight, and we play this little game: you tell me which edge of the cube you want to look at, and I show you that edge of the cube, with its two adjacent faces. Now, imagine that no matter which edge you choose to look at, you always see one face that is red and the other face blue. While this might not be surprising to a small baby, it might occur to you after a moment’s thought that there is no possible way to paint a normal cube with two colours such that every edge connects faces of different colours. It is an impossible cube!
The only way an adult could make sense of this phenomenon would be to try and imagine the faces of the cube changing colour when they are not being observed, perhaps using some kind of hidden mechanism. But to an infant that is not bounded by silly ideas of object permanence, there is nothing particularly strange about this cube. It doesn’t make sense to the child to ask what the colour is of parts of the cube that they cannot see. They don’t exist.
Of course, while it makes a cute picture (the wisdom of children and all that), we should not pretend that the child’s lack of object permanence represents actual wisdom. It is no help to anyone to subscribe to a philosophy that physical properties pop in and out of existence willy-nilly, without any rules connecting them. Indeed, it is rather fortunate that we do believe in the reality of things not visible to the eye, or else sanitation and modern medicine might not have arisen (then again, nor would the atom bomb). But it is interesting that the path of wisdom seems to lead us into a world that looks more like a child’s wonderland than the dull realm of the senses. The cube I just described is not just a loose analogy, but can in fact be simulated using real quantum particles, like electrons, in the laboratory. Measuring which way the electron spins in a magnetic field is just like observing the colours on the faces of the impossible cube.
How do we then progress to a `childlike wisdom’ in this confusing universe of impossible electrons, without completely reverting back to childhood? Perhaps the trick is to remember that properties do not belong to objects, but to the relationships between objects. In order to measure the colour of the cube, we must shine light on it and collect the reflected light. This exchange of light crosses the boundary between the observer and the system — it connects us to the cube in an intimate way. Perhaps the nature of this connection is such that we cannot say what the colours of the cube’s faces are without also saying whether the observer is bound to it from one angle, or another angle, by the light.
This trick, of shifting our attention from properties of objects to properties of relations, is exactly what happens in relativity. There, we cannot ask how fast a car is moving, but only how fast it is moving relative to our own car, or to the road, or to some other object or observer. Nor can we ask what time it is — it is different times for different observers, and we can only measure time as a relative property of a system to a particular clock. This latter observation inspired Salvador Dali to paint `The Persistence of Memory’, his famous painting of the melting clocks:
According to Dali, someone once asked him why his clocks were limp, to which he replied:
“Limp or hard — that is not important. The important thing is that they keep the right time.”
If the clocks are all melting, how are we to know which one keeps the right time? Dali’s enigmatic and characteristically flippant answer makes sense if we allow the clocks to all be right, relative to their separate conditions of melting. If we could un-melt one clock and re-melt it into the same shape as another, we should expect their times to match — similarly, relativistic observers need not keep the same time, but should they transform themselves into the same frame of reference, their clocks must tick together. The `right’ time is defined by the condition that all the different times agree with each other under the right circumstances, namely, when the observers coincide.
The same insight is still waiting to happen in quantum mechanics. Somehow, deep down, we all know that the properties we should be talking about are not the ever-shifting colours of the faces of the cube, the spins of the electrons, nor the abstract wave-functions we write down, which seem to jump around as we measure them from one angle to the next. What we seek is a hidden structure that lies behind the consistent relationships between observers and objects. What is it that makes the outcome of one measurement always match up with the outcome of another, far away in space and time? When two observers measure different parts of the same ever-shifting and melting system, they must still agree on the probabilities of certain events when they come together again later on. Maybe, if we can see quantum systems through a child’s eyes, we will have a chance of glimpsing the overarching structure that keeps the relations between objects marching in lock-step, even as the individual properties of objects themselves dissolve away. But for the moment we are still mesmerised by those spinning faces of the cube, frustratingly unable to see past them, wondering if they are still really there every time they flicker in and out of our view.