Space & Time

maxresdefaultSpacetime is a new and unique substance in physics. It has 4 dimensions: 3 in space and 1 in time. Yet it is much more than just a taping together of time and space. This article will examine, in basic terms, its nature and implications for cosmology.

Space is, on the whole, intuitive. Its 3 dimensions can all be given in kilometres, and they are interchangeable. If a map tells you to go 2 km North and 2 km East, you will know that it doesn’t matter in which direction you go first. And for a shortcut you might instead go North-East.UntitledNow add a time dimension, let’s say that your train leaves in 20 minutes. Is there any way of adding this dimension to the diagram above? Not really. Our intuition doesn’t allow time and space to be co-represented, let alone reconciled. 1 metre and 1 minute are not just two different things but two different kinds of things. However, in General Relativity, distance and time are, in a sense, interchangeable. This is a drastic step, and not simply an addendum, for each dimension now represents something different than before; x is no longer Newton’s x, since it relates to time in a way that the length of a football pitch intuitively does not. Yet Einstein’s idea has been vindicated, and precisely by its most absurd predictions. Gravitational lensing, the idea that light is deflected in a gravitational field despite having no mass, was observed in 1979, and as recently as 2016 gravitational waves were found, emitted by orbiting masses pulling on the fabric of spacetime like ripples on a pond. Where our intuition falls short, Einstein’s relativistic spacetime triumphs.

Having established therefore what it is not, what actually is spacetime? In basic terms, spacetime is the substance of which the Universe is made and through which everything in it moves. It is no longer a stage on which events happen but instead a key player helping to shape the scene. Spacetime tells matter how to move and matter tells spacetime how to curve. This relationship is formalised in Einstein’s Field Equations, where the left-hand side describes curvature and the right-hand side matter.2

Untitled 10This may appear to be only 1 equation, but it is in fact 10. The subscripts μ and v (pronounced ‘mew’ and ‘new’) each take the values of x, y, z and t. One term so far left undefined is Λ (capital lambda). This is the cosmological constant, which Einstein introduced in 1917 and later called his ‘biggest blunder’. His motivation for inserting it was that, earlier in 1917, the astronomer Vesto Slipher had observed interstellar redshift, a clue that the Universe might be expanding. Einstein’s equations didn’t allow for this. In fact they described a cosmos dominated by gravity and doomed to collapse back on itself with nothing to provide resistance, let alone expansion. The cosmological constant was costless and perhaps face-saving, hence his later regrets, but he turned out in fact to be correct. Λ has now been measured to be ~10⁻²⁵ kg m⁻³, and physically it represents the dark energy opposing gravity and causing the Universe to expand.

But what exactly is expanding? Cosmology is changed utterly by the introduction of spacetime. The Big Bang is normally visualised as an inflating balloon, but this is a gross misrepresentation. It is spacetime – not space – that is expanding; that new and unfamiliar substance. Whereas a balloon expands in x, y and z, spacetime expands in x, y, z and t, and as we’ve seen those first three dimensions aren’t the same as before. A balloon cannot travel faster than the speed of light, yet spacetime can. The reason we are limited to an observable Universe is because the fabric on which the rest of it lies carries it away from us faster than c. Indeed, spacetime is a very different kind of creature than the space with which we are familiar. And we should be careful not to oversimplify it. ‘What is it expanding into?’ is a very good question for the high school teacher’s 3-dimensional balloon, but is – it turns out – nonsensical when applied to a 4-dimensional Universe. For the time being the great cosmological questions remain unanswered, but it is worth noting that the questions themselves have changed.

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