17 September 2013

Counting dimensions

High energy theorists are split in two camps. One camp believes that space and time have ten, eleven or twelve dimensions. The other camp believes that there are two or three dimensions, not four. Reading the arxiv preprints, we can see each camp presenting arguments for its respective view.

A normal person might say that the battle is futile, because no experiments will ever verify either camp. In the past, some experiments have been proposed, but they all had flawed premises. No experimental test seems possible, so that the camps will go on discussing.

But why will they continue? Both camps claim that there is a minimum experimental length in nature. That is bizarre. A minimum length means that there is no way to measure the number of dimensions. Dimensions only exist if lengths can be as tiny as imaginable.

So these theorists fight about something that cannot ever be measured. Isn't that sad?


  1. Clara, I remembered something about this from Schiller's volume 6 of Motion Mountain. I forgot what he said, so I had to have a little re-read. He says at the minimum length scale, you cannot perform the experiments to determine the dimensions of space.

    Makes sense to me :)

    I wonder if the best number of dimensions to suppose depends upon what you are trying to calculate. Use four, say, but if using four won't give you an answer, try using two or ten or whatever. Choose the model in which the problem has its simplest expression.

    And somebody says, 'Yes but how many dimensions really?'. Do we answer, 'There is no really exactly. Such ideology just gives you blinkers.'?

  2. If there are four limit laws -- maximum speed, maximum force, minimum action, and minimum entropy -- then physical reality should be four-dimensional. But then if you try to determine those limits exactly, you come up against a problem: roughly you cannot imagine an experiment to determine one of the limits to a better accuracy than the minimum amount of time compared to the age of the universe.

    But if the limits are only knowable approximately, then the dimensions are only approximate. So how many dimensions exactly? No answer.

    How many dimensions in practice? Four obviously. You only need look around. Did I go wrong?