* Sagittarius A* is pronounced ‘Sagittarius A-star’.
† 1 Astronomical Unit is (approximately) equal to the distance of the Earth from the Sun.
‡ The speed of light is 299,792,458 metres per second.
§ By ‘gravitational radius’ they mean the Schwarzschild radius.
¶ The temperature of the cosmic microwave background radiation today is 2.725 degrees Celsius above absolute zero.
2
Unifying Space and Time
‘The word “distance” by itself does not belong in a book on general relativity. The word “time” by itself does not belong in a book on general relativity.’
Edwin F. Taylor, John Archibald Wheeler and Edmund Bertschinger12
Black holes are perfect for learning about physics because understanding them requires pretty much all of it. Don Page begins his exhaustive ‘inexhaustive review of Hawking radiation’ with the sentence: ‘Black holes are perhaps the most perfectly thermal objects in the universe, and yet their thermal properties are not fully understood.’13 Thermodynamics is one of the cornerstones of physics, dealing with familiar concepts such as temperature and energy, and a possibly less-familiar concept, entropy. Thus, we will need to learn some thermodynamics. Stephen Hawking’s seminal paper ‘Particle Creation by Black Holes’ begins: ‘In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies …’14 Thus, we will need to learn some quantum mechanics. And, of course, there is Einstein’s General Theory of Relativity, wherein, as Misner, Thorne and Wheeler write in their great (in quality and in mass) textbook Gravitation, ‘… the reader is transported to the land of black holes, and encounters colonies of static limits, ergospheres, and horizons – behind whose veils are hidden gaping, ferocious singularities’.15 This is the land we will explore first.
We learn at school that gravity is a rather mundane thing – the force between everyday objects; you can’t jump too high from the surface of the Earth because there is a force that pulls you back down to the ground. In 1687, Isaac Newton formalised this idea and published it in The Principia Mathematica. Newton’s theory works well in most situations, allowing us to calculate the trajectories of spacecraft to the Moon and beyond, and at first sight has nothing to say about space and time at all. Newton did, however, assume two properties of space and time in formulating the theory. He assumed that time is universaclass="underline" if everyone in the Universe carries a perfect clock and all the clocks were synchronised sometime in the past, they will all read the same time in the future. Newton put it more poetically: ‘Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external …’ He also assumed that space is absolute: a great arena within which we live out our lives. ‘Absolute space, in its own nature, without regard to anything external, remains always similar and immovable … Absolute motion is the translation of a body from one absolute place into another.’ These assumptions sound like common sense – so much so that it’s a testament to Newton’s genius that he even noticed he’d made them. His true genius is revealed when we discover that his care was prescient because both assumptions are wrong. The Universe is not constructed this way, and as the foundations of the theory crumble, so must the theory itself. Einstein’s General Theory of Relativity is the replacement, describing a Universe in which distances in space and the rate at which time ticks depend on an observer’s proximity to stars and planets and black holes or even on their route to the shops and back.
It is an experimental fact that the passage of time varies from place to place and depends on how fast things move relative to each other. In a wonderfully simple experiment, carried out in 1971, Joseph C. Hafele and Richard E. Keating bought round-the-world airline tickets for themselves and four high-precision atomic clocks. In their own carefully chosen words: ‘In science, relevant experimental facts supersede theoretical arguments. In an attempt to throw some empirical light on the question of whether macroscopic clocks record time in accordance with the conventional interpretation of Einstein’s relativity theory, we flew four caesium beam atomic clocks around the world on commercial jet flights, first eastward, then westward. Then we compared the time they recorded during each trip with the corresponding time recorded by the reference atomic time scale at the US Naval Observatory. As was expected from theoretical predictions, the flying clocks lost time (aged slower) during the eastward trip and gained time (aged faster) during the westward trip.’16 The eastward clocks lost 59 nanoseconds and the westward clocks gained 273 nanoseconds.* These are tiny time differences over such a long journey, but they are not zero and, most importantly, the experimental observations agree with the mathematical calculations performed using Einstein’s theory. The Hafele–Keating paper finishes in a similarly concise fashion: ‘In any event, there seems to be little basis for further arguments about whether clocks will indicate the same time after a round trip, for we find that they do not.’ And there we have it – a remarkable and highly unexpected feature of our Universe that relativity theory is designed to describe: time is not what it seems.
Space is not what it seems either: in a further affront to common sense, the distance between two points in space is not something everyone will agree upon. Hold your fingers apart in front of you. Who would dare say that the distance between your fingertips depends on the point of view? Einstein would. This is also a well-verified experimental fact. The Large Hadron Collider at CERN is the world’s most powerful particle accelerator. The giant machine’s job is to make protons travel around its underground tunnel at 99.999999 per cent the speed of light, before smashing them together. The purpose is to explore the structure of matter and the forces of Nature that animate our world. The LHC is 27 kilometres in circumference from the point of view of someone standing on the ground in Geneva, marvelling at this great engineering achievement. From the point of view of the protons orbiting around the ring, the circumference is 4 metres.
Einstein didn’t know about atomic clocks or airliners or the Large Hadron Collider in 1905, and no experiments had been performed that challenged Newton’s pictures of absolute space and universal time. Why, then, did Einstein decide to invent a new picture? The answer is that he realised there is a fundamental clash between Newton’s seventeenth-century theory of gravitation and James Clerk Maxwell’s nineteenth-century theory of electricity and magnetism.
The clash concerns the way the speed of light appears in Maxwell’s theory. The theory, which is based on experimental observations carried out by Michael Faraday, André-Marie Ampère and others throughout the nineteenth century, states that light is an electromagnetic wave that travels through the vacuum of empty space at a fixed speed: 299,792,458 metres per second. According to the theory, the speed of a beam of light is always this precise number, no matter how the person that measures it moves relative to the source of the light. That’s a very strange prediction, and not the way most other things in Nature behave.
The fastest ball ever bowled in international cricket, at the time of writing, was by Shoaib Akhtar for Pakistan against England in Cape Town in 2003. Nick Knight, opening for England, played a textbook defensive stroke to square leg, rounding off a maiden over for Akhtar. The ball travelled down the wicket at 100.2 mph.† If Akhtar had instead bowled the ball from a Grumman F14 Tomcat travelling at 600 mph directly towards Knight, then the ball would have reached the batsman at 600 + 100.2 = 700.2 mph, and he may not have guided it to square leg. This is not true for light. If, rather than the cricket ball, a laser beam had been sent towards Knight from the F14 Tomcat, the light would still have reached him at the speed of light (not the speed of light + 600 mph).