The Essay: Paradoxes provide the keys to unlocking the secrets of the Universe, writes Jim Al-Khalili
The night sky is a profound confirmation of the Big Bang
A paradox is a statement or circular argument that either contradicts itself or leads to a situation that is logically impossible. But there is an important difference between a true logical paradox and mere scientific puzzles. Take the assertion: “This statement is a lie”. The sentence is grammatically correct and appears straightforward. But work through its implications and you soon see it is anything but. In announcing itself to be a lie it is stating that it cannot be a lie, in which case it is true, which is to say that it really is a lie, which means it is not a lie, and so on in an infinite loop. This is a clear paradox that cannot be resolved. More satisfying is when we know there’s a way out.
A veridical paradox is one in which the statement sounds counterintuitive, but which turns out not to be so on more careful consideration, even if this surprising. An example: “Every Scotsman who travels south of the border to England raises the average IQ of both nations”. Impossible? Well, no – albeit more satisfactorily resolved if you happen to be Scottish. The point is this: since all Scotsmen claim to be smarter than all Englishmen, then any one of them surely would enhance the average IQ of England by moving there. But to have left his beloved Scotland in the first place is deemed to be so foolish that he would have to be less intelligent than most Scots, and so will leave behind a slightly higher average IQ.
Many paradoxes in physics are of the veridical type and can, while seeming impossible, turn out to be missing some subtle consideration which knocks out one of the pillars on which the paradox is built and brings the edifice toppling down. But despite having been resolved, many of such scientific paradoxes continue to be referred to as such, partly due to the notoriety they gained at the time of inception (before we had figured out where we were going wrong) and partly because they are a useful tool in helping scientists gain a better understanding of nature.
Take a simple version of the time travel paradox: what if you were to travel back in time and kill your younger self? What happens to the older you? Do you pop out of existence because you stopped yourself from growing older? And if so, and you never did reach the age at which you became a murderous time traveller, who killed the younger you? The older you has the perfect alibi: you never even existed! So if you did not live long enough to reach the point in time when you travel back, then you do not end up killing your younger self, and so you will have survived to travel back in time and kill yourself, so you don’t, and so on. This would appear to be the perfect logical paradox. And yet physicists have not ruled out the possibility, in theory at least, of time travel to the past. But it turns out that this can only be achieved if our universe is but one of many parallel realities, so that multiple versions of history can be acted out.
Some paradoxes will be familiar to many. Take the quantum paradox of Schrödinger’s Cat, in which the unfortunate feline is locked inside a sealed box with poison that is released if triggered by the decay of a radioactive atom. Since the rules of quantum physics state that while we are not observing the atom we are forced to consider it to have both decayed and not decayed at the same time, then the fate of the cat must hang between being dead and alive until we open the box.
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