While Stephen Hawking was busy writing his surprise bestseller A Brief History of Time, he was advised by a sagacious editor to shy away from using any mathematical equations; each one, the editor said, would halve his readership. Though unable to resist including one or two, Hawking largely followed this advice, and my recent effort to understand Einstein’s dauntingly capitalised masterwork, the General Theory of Relativity, has only increased my admiration for that editor.
Image: Wikimedia Commons
Grappling with mathematics
If it matters, I was actually quite good at maths at school, and could smugly ‘multiply out’ every bracket in sight and feel satisfyingly accomplished. But I was soon given reason to believe that my innate talent for this kind of thing did not extend much further than that. It is no coincidence that I ended up studying biology at university; I have seen otherwise bright life sciences students whinny and whimper at the sight of a logarithm. And so it was with some hesitation that, when I saw the flurry of articles accompanying the 100th anniversary of Einstein’s 1915 theory of gravity, I made a deliberate and concerted effort to obtain at least a conceptual understanding of what the theory is all about.
I had already read and enjoyed Walter Isaacson’s brilliant biography of Albert Einstein, and could marvel at his ability to transmute difficult theoretical ideas into windowpane prose, while being guilty of reading the scientific passages slightly more hurriedly than is wise. I was, I confess, more interested in Einstein’s small but decisive role in the creation of the atomic bomb, and in his hectic love life, than I was in the minutiae of the elusive trajectories of photons.
Newton and Einstein
Wikipedia is almost considered a swear word in most academic circles, but it is actually incredibly useful for science subjects, even if only as a source of further references. Case in point: it has a page, titled ‘Introduction to general relativity’ and aimed at non-specialists. More precisely, ‘non-technical introduction’ is the encouraging phrase used. It largely manages to live up to this description, and takes us through a mostly equation-less tour of the history of Einstein’s theory.
As with the majority of the articles and sources that I looked at, it begins with Newton. As I understand it, his theory of gravity worked perfectly well at the level of apples and humans, but problems arose at the stupefying distances of stars and solar systems. The main issue is that Newton didn’t know the nature of this force; gravity was presumed to act immediately, or instantaneously. This was called into doubt after it was established that nothing could travel faster than light. Newton himself was perhaps too preoccupied with scrutinising the Bible for apocalyptic references, and with searching for the philosopher’s stone, to lose much sleep over it.
The article deals in depth with Einstein’s fondness for thought experiments; his idea of fun was to sit in an armchair and imagine what would happen if you were inside a free-falling lift. It also explains how and why Einstein’s 1905 theory of Special Relativity, which among other things helped to fuse space and time, giving spacetime, struggled to incorporate acceleration and gravity. Only toward the end of the article, which contains frightful references to a ‘Schwarzschild solution’ and some monster called the ‘Friedmann–Lemaître–Robertson–Walker metric,’ did it completely lose me. But when I dared to briefly glance at a few lecture notes on the subject, I realised how much of an understatement ‘non-technical introduction’ is.
It is often said (mostly by mathematicians themselves) that mathematics is a language in and of itself; it is the language of the universe. I can appreciate that my inability to speak it severely hinders my appreciation of the General Theory, and that the Newtonian dimensions of my mammalian brain mean that the even more mathematically-dense theory of Quantum Mechanics remains a mystery to me. Fortunately, I am in good company; as Richard Feynman may or may not have said, “If you think you understand quantum mechanics, you don’t understand quantum mechanics.”
I had initially hoped that this happy dictum would also apply to relativity, allowing me to contentedly wallow in (inevitable and universal!) misunderstanding. Sadly, this appears not to be the case.
I have until now resisted giving a summary of what the General Theory actually says, because I don’t want to give the impression that I understand more than I do. I can admit, however, that the most useful learning material I found was a Radio 4 clip specifically aimed at six year olds. In it, physicist Chris Smith uses a trampoline analogy to explain the theory to children. The trampoline represents spacetime, and a large mass in the centre of the trampoline represents, say, the Sun.
The presence of that mass manipulates the fabric of the trampoline; spacetime becomes curved in the presence of mass. Any other small mass placed on the trampoline is going to roll down toward the centre. Hence, gravity! This was Einstein’s big insight. The falling of an apple to Earth and the orbit of that same Earth around the Sun is all neatly explained by the dent that a mass causes in a trampoline, and without a single ‘Schwarzschild solution’ in sight.
This may not seem like much, but it’s actually quite an impressive elucidation, and is made all the more so by the fact that it can clearly be understood by young children.
We are often told that Einstein’s theory is science’s beautiful answer to Shakespeare’s tragedies and Mozart’s symphonies; the summit of human intellectual achievement. The fundamental language in which it is codified may be inaccessible to most of us, but I’m sure that Einstein, with his famous love of un-mathematical thought experiments, would agree that thinking about a trampoline can go a long way.
Do you understand Einstein’s theory of General Relativity? Let us know in the comments below!