# The Swiveller

Theories and speculations

# How non-local are you?

Relativity and quantum mechanics could sit very easily together if it wasn’t for the issue of locality. What does this mean? Relativity is based on the realisation that time is elastic. This just means that the further you are from the earth’s core the faster time moves. So time travels more quickly at the top of a mountain than it does at the bottom. The difference is tiny even at the top of a mountain, but if you happen to have an atomic clock you can see this difference at a height of just 30cm. In relativity, time is therefore local. In the mathematics that determines quantum physics, this time differential does not exist. In fact, according to some physicists, it is impossible. This is said to mean that quantum physics and relativity are irreconcilable, and that quantum mechanics is ‘non local’. It is quite easy to understand what is meant when we say that time is local in relativity, because it varies locally. But it is much less clear what it means to say that time is ‘non local’ in quantum science. To understand it, we must remember first of all that quantum theory deals with the smallest objects we know about. They can barely be detected, let alone measured, and at that tiny scale any measuring apparatus changes the result of the experiment. Quantum science therefore does not actually attempt measure the speed or position of objects, but calculates the probabilities of their whereabouts. The probability of any event always equals one, or 100%. If you toss a coin 100 times the result will be 50/50, or 49/51 or 48/52 and so on. If you roll a dice a multiple of six times, and add the occurrence of the scores 1-6, you get the same result for the sum probability of the scores, approximately 1/6+1/6+1/6+1/6+1/6+1/6=1. (The proportion may vary like the coin, but the total will always be one. Of course, if you throw the dice only once, the result will still relate to the total event, and the probability of any one number will be 1/6.) It is not hard to see that in this way any one probability sum will always equal one and can only relate to one event. If you measure all the probabilities relating to the position of a particle the same rule will apply, even though there are an infinite number of possible positions. The introduction of an infinite number makes the maths a little complicated to say the least, but the principle holds. All the probabilities of any one event must add up to one. If we are talking about the probable position of a particle, this ‘one’ is a single position. This begins to explain why time in quantum physics might be ‘non local’. The particle is quite clearly to be considered non local before detection in the sense that we don’t actually know where the it is, so we can’t know its position relative to anything, or its speed. The difficulty comes when the particle is detected. If the particle is detected – which is an extremely difficult thing to do – it is then a singularity. What does this mean, and why does it not then have locality? Detecting the particle destroys all the probabilities calculated for the obvious reason that its position becomes momentarily certain. In the language used by scientists, probability collapses. There is a specific temporal; order to this, because of course collapse must follow calculation. Probabilities can’t be destroyed until they are established. This temporal order applies to all collapses in this way, and is not relative to the timing of other events. Detection cannot precede the calculation of probability, because the event, which has happened, was the event being calculated. Collapse is the end. Since the detection is momentary, it is also the beginning of a new set of probabilistic calculations about the subsequent position of the particle. This means that, at the moment of detection it is not relative to anything else, and therefore cannot have difference to anything else, and it also means that calculation and detection have a predefined order. This is why the position of the particle is said to be ‘non-local’. Think of the dice again. Before you threw it, there was only a possible six. Once thrown, probability collapses. If you are staring at a six on a dice, you have a six. It is the result of the throw. Probability doesn’t now come into it. And obviously, you couldn’t have had the six before you threw. But as soon as you go to throw it again the six disappears. Much the same happens with the particle, except that detection is briefer than a flash and the subsequent disappearance beyond anyone’s control. Of course, the dice is not independent of the laws of relativity. But the six ‘exists’ only relative to the probability of its being produced. With regard to the particle, we can say that it too must obey the laws of relativity in so far as it is an object, but that is ‘exists’ in time only while it is detected, and as part of a sequence which is probabilistic.

Although the actual position of the particle may only be detected momentarily in one place at one time, many of its possible positions can be calculated, and these possible positions are very useful. When mapped, they form a field which has wave like characteristics. This field can be used predictively in many ways. It is then tempting to draw an analogy with waves and seas, and understand this probability field as an object. However, because the positions which compose the wave are probabilistic, and therefore only add up to one ‘real’ position, they do not have temporal relativity. This is because they all relate to a single momentary event. This probably means that quantum mechanics and relativity are not incompatible at all. They are just measuring different things, in different ways.