Advent calendar door #16: What is space?
Space is the stage on which physics happens. If you are the lucky owner of a smartphone you can easily find out where on this stage you are right now, in global coordinates readily understood by any other GPS device on the planet. And once you start to move, the change in those coordinates describes your journey. Space itself has nothing to do with it: it could not care less about where you, or anything else in it, happens to be. And it would still be there even if everything else suddenly vanished.
This is how we learn to think of space at school — a rigid box in which things happen — and it is hard to imagine it otherwise. Yet the idea only became mainstream recently, in historical terms, with Newton's Principia Mathematica published in 1687. "Absolute, true, and mathematical space remains similar and immovable without relation to anything external," he wrote.
Newton did not claim he could prove that physical space was really like that. "He was aware that [his statement] was just a hypothesis," says Francesca Vidotto, a theoretical physicist at the Radboud University Nijmegen. "But the assumption is so powerful, it allowed Newton to construct his mechanics; we can construct bridges, we can go to space and even outer space. Newton's assumption was so successful that people forgot it was only a hypothesis." Because of its power Newton's pronouncement pretty much put a lid on centuries' worth of philosophical debate on whether this abstract and relation-less space, this void, could actually exist in nature.
The maths that has grown from Newton's assumption, and which has given us bridges and spacecraft, is based on another idea that chimes with our intuition: that space is continuous. In theory you could zoom in on it to any level you like without seeing it break up into pixels or fall apart in some other strange way.
Yet from another point of view, the idea of continuity is itself pretty mind-boggling. A continuous piece of line, no matter how short, is made up of infinitely many individual points. There are so many points you could not even label them 1,2,3, ... as you could label an infinitely long queue of people if you had an infinite amount of time. A continuous line gives you an uncountable infinity, something inherently larger than an infinite amount of discrete objects. So assuming that space is continuous means admitting that you can hold a frighteningly large infinity in the palm of your hand.
"Suppose you hold your fingers ten centimetres apart," argues George Ellis, a cosmologist and mathematician at the University of Cape Town. "If you believe that there is a [continuous] line of points between those fingers, then you believe that there is an uncountable infinity of points between your fingers. That's completely unreasonable. I believe that that's a mathematical idea that does not correspond to physics."
So what, then, is space really like? Find out by continuing to read this article here.