91av

LAST month, I answered a reader question about space-time expansion. They wanted to know what space-time is expanding into, given that we scientists tend to analogise with a balloon that is being blown up. As I wrote, this analogy has a flaw because when we blow up a balloon, it is expanding with a room in the background.

In reality, space-time has no background because general relativity is what we call a background independent theory. Which of course invites the question: “What’s that?” The problem is this column has to fit on a single page. I tried to give a short explanation of what background independence means by saying that in relativity, physical reality is the same no matter how we map out the coordinates. My editors, not surprisingly, felt this was insufficient. “But the word count!” I said, while silently agreeing. Then I promised to tackle the question in my next column.

Let’s start with a thought that feels natural: space and time seem absolute in everyday life. Albert Einstein compared this to thinking about a stage on which the drama of the universe unfolds. He said this point of view, advanced by Isaac Newton’s mechanics, construed space as “a giant vessel without walls”. In tandem, time marched forward absolutely and identically for everyone.

Relativity forced a radical revision of our understanding of space. First, taking seriously the experimental result that the speed of light is constant meant that space and time could no longer be thought of separately. Special relativity forced us to see that we were dealing with not space and time, but instead space-time. This theory did share something with the Newtonian perspective: while space and time were no longer absolute, they remained a stage on which events unfolded.

To understand what this means, consider how we measure distance. If you want to frame a painting, you might use a ruler. This ruler never changes shape or size. It is our measurement standard – our metric. There is a mathematical notion of the metric that physically aligns with this idea, and in Newtonian physics and special relativity, this metric never changes in time. Moreover, each point in space-time can be associated with an absolute coordinate location: numbers that tell us where to find it.

Now, imagine if your ruler stretched out when you put it near a more massive object. In other words, how you measure distance depends on where you measure and whether you are near an object that has mass. Your ruler, the metric, now depends on its location in space-time and what is inside of space-time. This was the radical revision in our understanding of space-time necessitated by the merger of special relativity with gravity, which we call general relativity (or “GR”, as physicists call it).

In Einstein’s general relativity the metric was no longer absolute and instead became dynamical: it could change with space and time. The implications this had were profound. It turned out gravity isn’t really a force – it is space-time curvature manifesting like a force, and that curvature is encoded in the metric, the ruler we use to measure distances. General relativity also enforces what we call a dynamical relationship between space-time and its contents. As theoretical physicist John Wheeler said: “Space-time tells matter how to move; matter tells space-time how to… curve.” Space-time curves around massive objects, and that curvature affects how phenomena in space-time can travel in space-time.

To make this more concrete, let’s return to the stage. It is now very weird! It is no longer fixed and unchanging in the background. The very shape of the stage itself depends on whether an actor is on it, where they are on the stage, and what they are doing – for example, if they are rotating, walking across the stage or simply standing still. Their presence shapes the stage and, of course, the shape of the stage will affect how someone or something can move across it. As philosopher Gordon Belot puts it, space-time – the stage – is now one of the actors. Events now happen to space-time too, not just inside of it. This is the meaning of background independence.

Importantly, we can’t see these effects on a real stage because the masses involved are too small for relativistic effects to be visible.

Intuition for background independence becomes clear in another way, too. Remember that the laws of physics are universal, the same throughout space-time. In order to preserve this rule, even while space-time’s geometry can shift, we have to let go of the idea that space-time comes to us with an absolute coordinate system. The structure of space-time is independent of our coordinate background – it is background independent.