### Roger Penrose on Mathematical Physics

I’m Roger Penrose Emeritus Rouse Ball

Professor of Mathematics at the University of Oxford The subject of Physics very much depends

on mathematics and we have extremely good equations, theories to describe vast

ranges of physical activity I mean, how particles move, how bodies move going

back to Newton most of what we know about the dynamics of bodies including

how the planets move and so on to very good approximation came from

Newton’s ideas and that’s very mathematical theory you need to

know, see planets are attracted by each other gravitationally by an inverse square law

and this makes the planets move around the Sun in ellipsis and that kind

of thing which was first step in understanding the movements of the

heavenly bodies, but it’s also modern mathematical physics we accept all that

except it’s got modified by Einstein in particular, when motions get very large,

when you want extreme accuracy or when gravitational fields get very strong, you

have to worry about Einstein’s theory of gravity, which is a much more complicated

theory although very beautiful one it describes the motion of planets not just

by force attracting bodies to each other but by the fact that the whole

space and time sort of fit together into a four dimensional structure, and Einstein has equations which tell us how that behaves. Very difficult to work out

in practice but important if you want to know certain things, like, well

we know now that, for example, that there are things called black holes where gravity get so

strong that things collapse into this hole in a sense

where nothing can escape from and our galaxy, the Milky Way galaxy the stars which you see, which look like almost a sort of a milky background to the sky and across the sky. The center is the Sagittarius, there is a place where there lives a black hole,

which is about four million times the mass of the Sun, and people can see stars

they can track stars going around it and ok you don’t see them move just like

that, but over a period of weeks you can actually see the movements, and this is

something which tells us there is this very very concentrated object as I say

about 4 million times the mass of the Sun at the center of the galaxy. So that’s

an example of the sort of thing you can do with mathematical physics,

understanding the general principles which tell us how things move. I’ve

talked about gravity, but in other areas too. Electromagnetic effects, Maxwelll the great Scottish mathematical physicist James Clerk Maxwell who well a lot of the equations of electricity and

magnetism were known, but they were incomplete, and Maxwell by theoretical

reasons realized there must be another term in it and the whole thing fitted

together in what we now call Maxwell’s equations Maxwell’s equations not only

tell you how electricity and magnetism work but they tell us how light works. That was a fantastic realization which came about from Maxwell’s equations, he

realized that electric and magnetic fields when they oscillate will push

each other along through space at the speed of light, and so he postulated that

light was electric and magnetic fields pushing each other along because he

worked out that it’d be the speed of light and that’s what light

was that was fantastic achievement And it also requires the nuclear power

drill, which is going to be quite a challenging thing to put on another planet