8 The end of time?
Until now, general relativity has been spoken of in glowing terms. It accounts for the motions of celestial bodies better than Newton’s theories. It has passed every test that physicists have devised to try to prove it wrong. But inside the event horizon, this theory is running out of space.
At the centre of a black hole, general relativity predicts that the entire mass of the collapsed star will be compressed into a mathematical point – a ‘singularity’. Density will become infinite as will the curvature of space. Physicists don’t like quantities becoming infinite, so what does this mean? Has something gone wrong with general relativity?
So far, this week has only considered general relativity and ignored quantum mechanics, which you met in Week 3. Each of these theories has its own realm. General relativity is important for very large masses; quantum mechanics is important at very small sizes. But what happens when a very large mass has a very small size? We don’t yet have a theory of ‘quantum gravity’ that would tell us what happens when general relativity and quantum mechanics clash, though there have been a number of contenders. For that reason, we cannot say what really happens at the centre of a black hole. But we can make some estimates on where and when such a theory might be necessary.
Theoretical physicists have estimated a distance, the Planck length – you came across this in Week 3 – at which general relativity must break down. It’s very roughly where the Schwarzschild radius of an object becomes equal to its quantum wavelength and is about 1.6 × 10-35 metres. The time it takes light to travel that distance, the Planck time, is about 5 × 10-44 seconds.
The Planck length and the Planck time represent fundamental limits on our knowledge of space and time. It doesn’t really make sense to talk about distances shorter than the Planck length, or times shorter than the Planck time. So, we ultimately don’t know – and for the time being we cannot know – what happens when an astronaut falling into a black hole encounters the singularity at the centre. But if you are already spaghettified, that probably won’t matter much to you.