I have been reading Matt Brown’s Everything You know about Science is Wrong. Silly title aside it is the expected mix of short essays about some common and not-so-common misconceptions people may have about different bits of science. Naturally, like QI, some of the revelations about ‘what you think is wrong’ only work if you read the question in a very specific way, but that doesn’t really matter if the information presented is at least interesting.
One of the short chapters is on the four dimensional universe. Now I would guess that most people with a passing interest in physics would be familiar with some of the various ideas that go by the name of string theory. In particular that all string theories only ‘work’ in many more than four dimensions. In fact it is yet to be seen if anything much can be made of string theory even in ten or twenty-six dimensions, but so far more than four has always been a necessary ingredient. For those of you wondering, the four dimensions that might be expected of our universe are the three space dimensions and time. String theory has been one attempt since the early 1980s to combine the two big 20th century theories, the first being quantum mechanics and the standard model of particle physics, and the second being Einstein’s general theory of relativity. The first of these describes how things behave on a very small scale, and very accurately too. The latter is all about gravity and the large scale universe. These do not agree and so far all attempts to bring them together have not got very far. To do so is one of the outstanding great problems of modern physics.
In the book Matt Brown writes that in fact the world has more than four dimensions, unlike what you think you know, fitting into his overall theme. Now I have several problems with what is written there. Firstly it is far from clear that the claims for high dimensional universes made by the various forms of string theory are true. There is not a single piece of experimental evidence for it, and nor is there anything approaching a coherent theory which could be argued in its favour. More than four dimensions is just a requirement of these particular ideas. But these ideas are far from anything like a solid theory. As they do not yet predict anything, even any of the things we already know, they can hardly be used in favour of even more exotic ideas. They could turn out to be true, and they could not. The best we can say at the moment is that it looks like the universe has four dimensions, but it could perhaps be more.
Now this perhaps one could just let slide, after all string theory is interesting so why not use this as the excuse to put a mention in the book. The book is after all clearly not meant to be a careful exposition of the current state of science! It is a fun book about some things you may or may not have realised about physics, biology, chemistry, and so on.
The second issue arises when he starts to explain what these dimensions are. This part of the chapter is just bizarre. The explanation of dimensions five and six seem to be a confusion with the idea of the many worlds interpretation of quantum mechanics. (Itself an incoherent idea in my opinion, but let’s save that for another time.) Dimension seven is then apparently the multiverse, or one version of it, i.e. many different universes with slightly different set-ups. The eighth dimension is another version of this. Now already there is a very simple mathematical problem here. Brown introduces two extra dimensions, but claims that they describe every possible permutation of the four fundamental forces. Clearly that is more than two dimensions! It would be as many dimensions as there were free parameters in the theories to change, which is something we do not in fact know. His final tenth dimension is supposed to be all of the previous ones together, which just suggests that he does not in fact know what a dimension is.
Now in fact in string theory the extra dimensions are nothing so exotic, nor could they be. What is described in the book is completely mathematically and physically incoherent. Instead the extra dimensions are assumed to be just like the usual three space dimensions but rolled up very small so one can not notice them, see the figure below. As an example imagine a two dimensional plane like a piece of paper. One can use the usual two Cartesian coordinates x and y to describe any point on the paper, and in that sense it is two dimensional. Now if you roll up the paper along one direction, it is still two dimensional. However you can roll it up so tight os that you can barely notice one direction and it will look essentially one dimensional. That is the usual idea behind the extra dimensions.
Or maybe I just missed a joke…
A two dimensional sheet rolled up to something a bit more like one dimension.