Physics is one of those subjects where I can very clearly see the boundaries of my understanding – as soon as we get to quantum physics or Einstein’s theories of relativity I can follow the surface level explanations & analogies, but I’m always aware I don’t understand it on a deeper level. I assume the same is actually true of all subjects at some point – I’m not a genius, and I spread my self-education widely among many subjects rather than deeply delving into one – but for physics I can see the fence. It’s a peculiar sensation.

The three experts who talked about Einstein’s theories of relativity on In Our Time were Ruth Gregory (Durham University), Martin Rees (Astronomer Royal and University of Cambridge) and Roger Penrose (University of Oxford). The programme started with a bit of context: in 1905 Einstein published four papers, including one on Special Relativity. At the time he was working as a clerk in a patent office & was previously unknown as a physicist. Ten years later he published a paper extending Special Relativity into General Relativity.

Prior to Einstein’s theories of relativity the assumption was that there was some sort of objective measure of time in the universe, the same no matter how it was observed. Einstein theorised that the motion of the observer affected the observation of the passage of time – hence relativity. Apparently he later regretted using that word for his theories because it’s been used since to imply that physics is all just subjective & depends on your point of view, but actually there is still an objective physical reality which can be described mathematically & rigorously it’s just that *within the system* the point of view of the observer is important for the observations made.

One of the things that Einstein’s theories grew out of was the observation that the speed of light remains constant no matter what direction you’re travelling in or how fast you’re travelling. This seems to be a paradox. Say you think about driving a car towards or away from another car that’s driving towards you – when you’re travelling towards it, it gets closer to you quicker than if you’re travelling away from it. (I hope that makes sense.) But with light if you’re travelling towards it it appears to be travelling the same speed as it travels if you’re travelling away from it. Einstein’s theory explains how this happens by explaining how time is running differently (I think).

Special Relativity implied that time is another dimension like the spatial dimensions, and Minkowski built on this theory to mathematically describe spacetime. Einstein then used this mathematics as part of his theory of General Relativity. One of the key insights of General Relativity is that spacetime is curved by the presence of mass and this curvature explains why gravity exists. Gregory used an analogy I’ve heard before to describe spacetime & its curvature – thinking of spacetime as being like a four-dimensional version of a two-dimensional rubber sheet. If you have your rubber sheet suspended as a flat horizontal plane and then you put something large like a bowling ball on it, the sheet will be distorted & curved where the ball weighs it down. Then if you roll a marble across it it will accelerate down the slope towards the bowling ball – or if you get your angles and speed right you can make it orbit the bowling ball.

There was some discussion of the twin paradox at two different points in the programme. This is a thought experiment where you have twins one of which remains on Earth, and the other one travels away to a different star system at close to the speed of light, and then returns. When the twins meet again the one that stayed on Earth will be older than the one that went to the stars and back. This is a staple of science fiction, and I think the first time I ran into the idea was in “Time for the Stars” by Robert A. Heinlein which I read when I was at middle school. The first time it was discussed on the programme was in the context of Special Relativity as the way of demonstrating what Einstein is talking about. And they mentioned that this has actually been shown experimentally – by getting a very accurate clock (synchronised with a matching clock) and putting it on a plane and flying it to the other side of the world & back. Then when you compare the two clocks the one that travelled has measured less time than the one that stayed put. Gregory pointed out that the observations demonstrate both the effects of relative motion and the effects of distance from a massive object (the maths needs to take into account that the plane is up in the air while the other clock is on the ground). I had no idea prior to this programme that the effects were measurable on such a *human* scale.

The second time the twin paradox came up was in the context of talking about the geometry of spacetime. Penrose was explaining that with his theories Einstein was trying to explain the universe in geometrical terms. Spacetime is four-dimensional, three dimensions are the familiar spatial ones that can be explained using Euclidean geometry. For the fourth dimension, time, Einstein (and Minkowski?) showed that you could use almost the same geometric rules only needing to reverse a sign – turn a plus to a minus. The way Penrose explained what he meant by this was to use the twin paradox – one twin is moving from event A to event B along a straight line in the time dimension, the other is moving from A to B on a curved line in the time dimension. For the spatial dimensions a curved line is a longer path than a straight line, for the time dimension a curved line is a *shorter* path than a straight line. (And this is what I mean by being able to see the edge of my understanding – I can write that last sentence as a fact and accept it is true, but I don’t understand *why* or *how*.)

I know I’ve missed out various things they discussed but I shall only mention another couple before I finish the post. Firstly there are real world applications of the theories of relativity, it doesn’t just help physicists understand the universe – it’s an important part of the underpinning of how GPS works. The other thing was that Rees was saying that Einstein was in some ways more like an artist than a scientist. By this he meant that for an artist their work is generally unique, if they didn’t exist no-one else would produce the same artworks. But for science generally if one person doesn’t come up with the theory or do the experiment then someone else would not long after. Rees thought (and the other two agreed) that while Special Relativity would probably have been thought of by someone else soon after, General Relativity was such a large jump that if Einstein hadn’t thought of it then we might still have not thought of it.