Professor Malcolm Longair,
astrophysicist & cosmologist
In answer to the question, ‘what is time?’ I find two statements by eminent relativists useful. First, David Finkelstein’s: ‘Time is just one goddamn thing after another’. This is much deeper than it looks since it means that there is a time-ordering of events, an arrow of time. There are a number of these – the thermo-dynamic arrow of time, the electromagnetic arrow of time and the cosmological arrow of time.
Hermann Bondi’s definition was: ‘Time is what I measure on my watch…’. This is also much deeper than it seems since it states that all we need is something which keeps a regular beat or pulse – a clockwork watch, the frequency of an atomic oscillator, or the motion of the Earth about the Sun.
What comes as a surprise is that the rate at which clocks are observed to run depends upon our motion and the gravitational field in which they are located. The speed of light is not additive in the same way as in classical Newtonian physics. If you are on a moving walkway and you run along it, you add the speeds together to find your speed over the ground. Light does not behave like that. The speed of light is absolute.
We should not think of space and time as being separate entities. According to Einstein’s special theory of relativity, we live in four-dimensional space-time. Getting from one point to another in four-dimensional spacetime depends upon the path you take through it. This leads to the ‘Twin Paradox’, according to which my twin, who goes on a return journey to the Moon, comes back younger than me – a phenomenon confirmed by many experiments. We also needed to reformulate the laws of motion in four-dimensional space-time and this lead directly to E = mc2.
All the laws of physics build special relativity into their theoretical foundations, with the exception of gravity. It took Einstein eight years to understand how to incorporate the concepts of four-dimensional spacetime into his general theory of relativity. Now, the rate at which clocks are observed to run depends upon where they are located in a gravitational field. The satellite-based GPS system, which tells you precisely where you are on your mobile phone, includes general relativistic corrections – without them, you could be out by 200 km.
General relativity also predicts the existence of black holes, singularities in space-time. The circumstantial astronomical evidence for these objects in the nuclei of galaxies was compelling but finally, in 2015, came the discovery of the gravitational radiation pulse, or ‘chirp’, from the coalescence of two 30 solar mass black holes. These ripples in spacetime were precisely predicted by Einstein a century earlier.
But we need to be careful. Consider matter falling radially into a black hole. There are now three times which need to be distinguished. Observer A far away from the black hole keeps a track of time – this acts as a reference coordinate time. A stationary observer B at some point along the trajectory of the infalling matter is observed by A to measure a different time since observer B is located in a stronger gravitational field. The clock is observed to run slower than A’s clock. At a particular radius known as the Schwarzschild radius close to the black hole, the observed time is slowed down so much that it appears to come to a stop – equivalently, light from that radius is red-shifted to infinite wavelength. But, what about the unfortunate observer C who is travelling with the material falling into the black hole? He/she measures a third time and collapses into the space-time singularity in the black hole in a finite time.
New physics will be required to cope with time-scales on which spacetime itself needs to be quantised. This is expected to occur on the Planck time-scale which is about 10-43 seconds. Watch this space-time…
‘It was Einstein who recognised we live in four-dimensional space-time.’
music broadcaster & author
As Malcolm writes, scientists have only recently been able to detect the gravitational waves that are the infinitesimal echo of the big bang, and the very beginning of time in our universe – or at least this phase of our universe, or whichever theory of cosmic teleology you happen to subscribe to. But in music, we’ve been able to hear the effects of changing musical gravity on time for centuries. And the music you’ll hear in the London Sinfonietta’s concert in March is a cross-section through arguably the most profoundly destabilising gravitational wave – or rather, anti-gravitational wave – that shook musical history in the decades around the turn of the 20th century.
In their different ways, composers across the world – Debussy, Schoenberg, Berg, Webern, Stravinsky, Ives and Cowell, among others – unmoored music from the conventions of musical gravity and temporal flow, creating an Einsteinian vision of musical relativity as opposed to the Newtonian rationality of music’s process in earlier centuries, where resolution was the imperative. And however diverse their innovations were, disrupting and renewing every aspect of musical discourse – the harmonic atomisation and suspension, the ‘air from another planet’, that Schoenberg’s Second Quartet breathes, or the transformation of instrumental colour into structure in Debussy’s Preludes, or the warped mechanical repetitions of the rhythms in Stravinsky’s Three Pieces – they share the same essential effect, which is a transformation of how music works in time. In music like Webern’s songs, time feels as if it moves in circles and cycles, or it creates the sense that a moment has been held into eternity: like taking a breath, and never exhaling.
In this strange and wondrous interzone where clock-time is stopped, or made to spin faster, or in which different speeds are layered on top of one another, composers can make limitlessly imaginative experiences. Our programme will reveal some of these miraculous musical timemachines, alongside demonstrations of the scientific discoveries that were emerging at exactly the same time.
Bach, the Universe & Everything - The End of Enchantment?
Bach, the Universe & Everything - Stepping on to the Cosmic Path
Bach, the Universe & Everything - View From the Pale Blue Dot
Bach, the Universe & Everything - Astronomy and Poetry
Bach, the Universe & Everything - Just as the Snow Falls
Bach, the Universe & Everything - The Best of Times