My all-time favourite scientist was Isaac Newton. Newton was very clever. In fact he was a genius. He discovered lots of interesting and important things. Unfortunately, most of them turned out to be wrong. That doesn’t make him a bad scientist, of course. Finding wrong answers is an important way that science makes progress.
One of the reasons we know that Newton was a genius is that it took a very long time before anyone proved that he was wrong. Around 200 years, in fact. Then Albert Einstein (my second favourite scientist) showed that Newton was wrong, by coming up with some better explanations.
In science, things can get nasty, and Einstein really put the boot into Newton by proving each one of Newton’s theories wrong. In fact, it’s almost as if Einstein’s goal in life was to trash Newton’s achievements.
First, Einstein gave Newton a bloody nose by showing that light wasn’t simply a wave, as Newton had believed – Einstein showed that light can behave like a particle. Secondly, Einstein gave Newton a thorough kicking by disproving Newton’s celebrated Laws of Motion, with his own Special Theory of Relativity. And not yet satisfied with that, Einstein took a baseball bat to Newton’s Universal Theory of Gravitation, replacing it with his General Theory of Relativity.
Poor old Newton. Everything he thought was wrong. Or was it?
The reason why it took 200 years for anyone to think up a better explanation of the universe was that Newton’s laws seemed to work so well. In fact, NASA still uses Newton’s laws to plan spacecraft trajectories like the New Horizons mission to Pluto. But that doesn’t mean Newton’s laws are correct. They work well in certain circumstances (speeds that are slow relative to the speed of light; frames of reference that don’t accelerate too much; gravitational masses that aren’t too big.) In mathematical terms, Newton’s laws are linear approximations to Einstein’s laws.
Newton’s laws are an extremely useful mathematical tool. They even allow us to make calculations of spacecraft journeys. But they don’t describe reality, except in an approximate way. The world doesn’t really work the way Newton thought it did.
There are plenty of similar examples where a simple mathematical rule allows us to make predictions about the world. For instance, I can estimate the volume of an apple by assuming that it’s a sphere. That doesn’t mean that apples are spherical. They have much more interesting shapes, and each one is different. Nevertheless, my simple approximation enables me to estimate the volume of an apple, by measuring its “radius”. I can even estimate the volume of a cow by assuming that cows are spherical – the approximation isn’t as good in this case, but is still reasonable.
It’s the same with Newton’s laws. Newton’s fundamental model is wrong. Mass isn’t a fixed quantity. Space isn’t flat. Time doesn’t move forward at a constant rate. Yet under certain circumstances, assuming that they do is a pretty good approximation.
So Newton was wrong. He didn’t explain how the world works. What he did do was invent some incredibly useful rules that enable us to make detailed calculations of how the world behaves in many cases of interest. He also dismissed a lot of previous misunderstandings. It took a genius to do that, and I don’t want to cast the slightest doubt on his achievements. As I say, Newton’s my favourite all-time scientist.
As for Einstein, he was wrong too. He even knew that he was. The Theory of Relativity doesn’t explain how the universe works either. It’s another approximation, that’s all. Inside a black hole, or in the moments before and after the Big Bang, it all breaks down. What we need next is a theory of quantum gravity. That might be string theory, or loop quantum gravity, or asymptotic safety, or one of many ideas being bounced around the physics world right now.
Of course, these might all be wrong. Eventually some theory will emerge, but even this might be wrong. It may not explain everything.
Ultimately, we have to wonder whether the universe really is mathematical, or if these mathematical theories are all mere approximations of what’s really going on.