Jim Al-Khalili was on Radio 4 a little while ago talking about quantum physics and his new Time project. He was being asked why, in quantum physics, time does not exist, and responded by describing the way we divide quantum physics from ‘normal’ thinking. The question was, “Is there some threshold at which matter starts to be subjected to the laws of time?” He replied, “That’s what’s called the quantum classical boundary, the ‘classical’, that means the everyday world, of us beings made up of trillions of atoms, so where is that boundary and how does that transition take place?” Quantum physics suggests that the ‘laws of time’ do not apply when we try to observe things that are too small to see, and as Professor Al-Khalili says there is assumed to be a boundary somewhere between the way Quantum physicists have to think about events and the way we ‘normally’ think about them, according to the laws of relativity. What Professor Al-Khalili means by the ‘everyday world’ is the visible world, in which time is generally regarded as described by the law of relativity. According to this, time is ‘local’, which means that time varies according to locality. Time travels at a slightly different speed at the top of a mountain, compared to the bottom. In quantum physics, which deals with particles that are too small to see, time does not appear to behave like this, and is therefore said to be ‘non local’.

So why do large objects move through time differently to small objects? To answer this question, let’s imagine a medium size cardboard box at the Amazon distribution centre, waiting to be used and dispatched. We can locate it easily in two or three dimensions, in the distribution centre, and we can describe it in three – it has length, width and height, although not a lot of the third since at present it’s flat packed. Our conventional way of imagining this box is that we will then observe it through time, as it is opened, filled and dispatched to Wherever, and then sent for recycling and maybe returned in a flat pack to Amazon. We may not be sure how long this process would take, but we don’t have any difficulty with the idea that is is a measurable process that will take a finite time which we can measure on a clock according to the rules of relativity (which in this case means that the life time of the box will pass at a constant and predictable and therefore measurable speed). Time is therefore the fourth dimension of the box’s location. Simple.

It is perhaps not so simple, though. The process I have described, and therefore the measurement, would in reality only be valid if we could actually observe the box for the whole of the process. Under examination our assumptions quickly fall apart. Of course, the box will never simply be recycled back into an Amazon box. It may be recycled with many other boxes into many different objects, and each Amazon box may in turn be constructed of card made from many different sources. To make matters worse, right now, we are not observing a box. We are looking at a computer screen and imagining it, so it is not ‘local’ to us at all. Even right now, in the present, imagining a box also involves imagining – or calculating – how its story might unfold over time, and obviously this is a speculative exercise. In this sense, the box is just like a sub-atomic particle we can’t see. We don’t know where it came from, have only a vague notion of where it is now and have no idea where it will be in the future. We might know that there is an Amazon warehouse that contains boxes but most of us couldn’t point to it on a map, even though we might be quite confident in talking about the box that is sitting on a shelf inside it. To pile uncertainty upon uncertainty, so far as the box itself is concerned, the order that may fill it has not arrived. And even if it has, and we discover its ‘destination’, that’s not its destination at all because it will probably be recycled and will continue in some form we don’t yet know (and will never know) to exist. We can only talk about where it will be in terms of probability, and clearly as time goes on the probabilities of its whereabouts widen to the infinite. Equally, if we travel in our experiment in the opposite way, to the past, we don’t know where the box has been either. There is no record of what our box was recycled from. So we have as little idea of the box’s past as we do of its future. We are only certain of the box’s present (and even that, if plausible, is imaginary). The past is as much a mystery as the future, and if we really want to work it out our only means is probability.

Now lets make this a little more real. Let’s say a book has just arrived in a clearly observable Amazon box. Let’s allow ourselves to forget that the event itself is imaginary for a moment, and consider the event, “Box is made of card”. In order to calculate any idea of how this happened we need to estimate the the origin of the box, the time and place of its making, and all the possible card items used in the recycling of the card at the time the box was made, all the potential items from which the card was recycled, and all the potential things it might have been recycled into. Then we might be able to estimate the probability of any card items being made into this box and becoming this event. If we did this complex and difficult task, we would get an unimaginably large set of probabilities relating to the possible constituents of the box. Each probability would be a tiny fraction and all the tiny fractions would then add up to this one event, “card is made into Amazon box” which, as it sits before us, represents one single event. This adding up to one event is the crucial point, quite literally, because the box before us exists in a present point in time, which, if perceived, succeeds all possibilities (the card from with the card that made the box is recycled), and then precedes all further possibilities (for instance, those addressing the question “What will the box now become?). So in this instance of the Amazon box, time only exists as a kind of marker between sets of past and future probabilities. Time is defined only by the event. Relativity and the local measurement of time are quite irrelevant.

Now, all this speculation comes about because we can’t always see the actual box. But it arises quite regardless of the size of the box. The case I have described would be the same whether the box was the size of a house or the size of a particle.

So you can see that, even in the case of quite large visible objects, the division between how we apply time to objects we can possibly see and objects we possibly can’t is a matter of probability, not a matter of physical size or time measurement. We have no absolute idea of the box. We don’t know where the box came from or where it will go, nor in each case how long it took, and we almost certainly won’t glimpse it for more than an hour or two of its entire life, if that. You cannot have ‘normal’ relativistic ideas about how time affects objects unless you can observe them, and clearly the box is mostly beyond observation. Now, it might be objected that the fact that it is ‘observable’ makes a quantum difference because ‘somebody’ can always see it. It is true that this is ‘possibly’ a difference, but the fact that this is not certainly a difference puts us in the same position as we were before. We don’t know who will see it, for how long or where, or indeed who they will be or where they are. We are imagining the box and now we are imagining its observers too, and both are subject to probability. We know that observation will change it in the same way as it changes the particle, by locating it, but, like the particle, as soon as the observer looks away it will vanish again into probabilistic existence. Neither the box, nor the event nor the observation are dependable. Our only ‘objective’ idea is of time, because we can imagine the time before observation and the time after observation. If the observation is imaginary, then we imagine the time before and after imagination. But, weirdly, these two things are the same. In both cases there is no ‘real box’, only a real instance in which it is appears in our consciousness. All that observation tells us is that, if we glimpse it, the box came from somewhere and is going somewhere. We know that for certain.

This is all contrary to our assumptions. A box is a box. But we can see that, objectively, its existence is far more complex. It has come out of an infinite set of probabilities which relate to its previous form and existence. And as soon as we throw it away we throw it back into that infinite probabilistic world. Compared to those two huge infinite spaces our glimpse of it is insignificant and tiny. Here, in this short piece of speculation, where there is clearly no box, we have no way of locating it anywhere, except by imagining it.

So what this little thought experiment shows us is that the ‘classical boundary’, which Professor Al-Kalili mentions, is probably imaginary, and it is as subject to probability in relation to a cardboard box as it is in relation to the smallest sub atomic particle. There is no practical difference. This is really interesting, I believe, because it suggests that the science of very small things is actually very closely related to the science of very big things and may in fact not work in a different way at all. It calls into question many of the assumptions we make about the ‘existence’ of larger objects, and it suggests, that, if we can’t actually see them, we might treat them in a way which is not at all dissimilar to the way quantum physicists treat tiny objects. It suggests there is no “quantum classical boundary” at all. This is as important a philosophical conclusion as a scientific one, because it has immediate consequences for many of the ideas we have about the world we live in and the way we are conscious in it, and it shows us why imagination plays such a huge part in our existence. Our box is a speculation. All the guesses we might make about it (if we could be bothered to make them) would ‘collapse’ at the moment we actually see it, just as our guesses about the position of a particle collapse if the particle is detected. And then, as we turn away, they would ‘reappear’ in our imagination. Thinking about a simple cardboard box in this way can therefore call into question the whole concept of relative time on which our normal ‘large scale’ idea of local objects is based. It also calls into question the assumptions we make very easily about our powers of observation and objectivity. And it suggests that we might be seriously underestimating the powers of imagination to negotiate a probabilistic existence. I have written a longer and much more detailed paper about the difficulties inherent in objectifying probabilities in quantum physics, and the implications for interpretation, which you can find here.