General relativity is the currently favourable model of space and time, whereas quantum mechanics deals with the stuff, matter if you like, which appears in space and time.
Quantum theory is a really quite extraordinary subject because it does have a profoundly challenging conceptual background, yet also its incredibly useful. I mean the whole modern world works because of quantum mechanics. Every electronic device we have in the house, in the lab, everywhere, is based on quantum theory.
So its amazing actually that a subject that is so profoundly mystical almost is also so useful.
At school a physics master lent me a book. I just opened it at random and I saw an equation. It was written down, and this equation was somehow very fundamental. It described how things were. And I was astonished. It was just a string of Greek symbols. There were some I didn’t recognise at all. There was a letter h with a bar through it. You see it was all very mystical and there were hats over things like that. The whole thing was extraordinary.
That’s when it suddenly hit me. How can it be that you can describe the world in some depth with strings of letters. And it absolutely fascinated me that idea. That’s when the idea of actually becoming a theoretical physicist first started in my mind.
The second thing that happened that really triggered me into doing theoretical physics was when I was in my gap year with the GPO [General Post Office] and one lunchtime with nothing much to do I wandered up into the library and took a book off the shelf at random. It turned out to be a book by David Bohm, a very well-known physicist, on quantum theory. I opened the book and I realised that it was the same strings of letters and things that I’d seen only much more developed than this previous book, and that’s when I finally decided ‘I’ve got to do this, I’ve got to understand this, it’s so profound.’
The fascination in theoretical physics is always the same really. It’s this strange business that mathematics can describe the world. You can make predictions with mathematics on how things are going to happen and it actually works, the universe works, it’s out there, it’s real, it works. That’s incredible I think.
I used to think from time to time about why did we use the mathematics that we did to talk about space and time. Basically we use real numbers. But why do we do that?
In ordinary mathematics a statement is either true or false and also things either exist or they don’t exist. But apparently in Topos Theory it is the case you can have statements that are partly true and what’s even more extraordinary mathematical entities that can partially exist and partly not exist. That degree of partial existence is actually specified in a very precise logical mathematical way. And it suddenly hit me ‘Wow, that’s quantum theory. There’s got to be a way to use Topos Theory in quantum theory’. I was so excited I couldn’t sleep that night at all.
One of the reasons for doing this Topos Theory wasn’t just to do quantum theory and general relativity. It was to try and find out a different way of doing theoretical physics altogether. And it does actually give you that. It does give you a different framework, a much bigger framework for discussing or applying maths to physics than existed before.
You have mathematics which takes you, as it were, from one type of experiment to another, and it predicts a relation between the two experiments. But in between, there’s like a path, a mathematical path that goes from one to the other. If you ask ‘what does that path mean?’, there’s no answer, it’s just there in the mathematics. It’s where mathematics gets to places where human reasoning can’t. And that’s one of the fascinations of theoretical physics actually, it’s that mathematics has this extraordinary ability not just to describe the world but to take you beyond the current understanding and suggest new ideas which turn out to be correct.
As far as my best work is concerned, it’s this stuff on Topos Theory. I think I had a genuinely original idea and I can tell you original ideas are very rare actually in science.
It’s a very abstract way of earning a living, I have to say.