MATHS READING - THE BEAUTY OF EINSTEIN (I LOST THE WILL TO LIVE)

History may judge 2015 as the year when mankind opened up a completely new window on the universe, exactly a century after Albert Einstein laid the scientific foundations for it. The excitement concerns the possibility of detecting one of nature’s most elusive phenomena – gravitational waves – which could pave the way for a much better understanding of black holes, neutron stars and other violent astronomical systems.

​Several new projects have been launched in the past few months to make gravitational waves the Next Big Thing in astronomy. Rumours have it that one of these – the US’s Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced Ligo) – already “detected something” in September, but the scientists involved remain tight-lipped. Time will tell.

The search for gravitational waves goes back to the dark days of the first world war. In 1915, as Europe was engulfed in carnage, science took a great leap forward. In a series of four lectures delivered at the Prussian Academy of Sciences in Berlin in November and December, Einstein presented a new theory of gravitation, replacing that of Isaac Newton, which had endured for two and half centuries.

Called the general theory of relativity, it has been described as one of the greatest intellectual achievements in history. What makes general relativity distinctive is that it treats gravitation not as a force between bodies such as the sun and the Earth, but as a warping or distortion in the geometry of space and time. This huge conceptual reorientation, plus the sheer mathematical beauty of the theory, ensured that general relativity acquired both a mystique and a fearsome reputation for impenetrability that made Einstein a byword for genius.

But however elegant a scientific theory may be, it is worthless if it cannot predict something new. Einstein did indeed make some predictions, but the distinctive effects he described were truly tiny. One of them is created by the spacewarp near the sun. A star beam passing close to the solar surface will be slightly bent as it traces a path through the curved geometry there. An observer on Earth will see an extremely slight displacement in the position of the star when the sun passes near it in the sky.

The so-called “bending of light effect” was tested by the English astronomer Arthur Eddington in 1919 during a solar eclipse, when the sun’s glare was blotted out, enabling nearby stars to be seen. Eddington’s delicate measurements triumphantly agreed with the predictions of general relativity. It was this experiment more than any other that, almost overnight, transformed Einstein into an international celebrity.

General relativity is based on a system of equations notoriously hard to solve, but shortly after Einstein set out his new theory he produced a particular solution to his equations describing an unusual form of waves that travel across space at the speed of light. Unlike light, however – or any electromagnetic radiation – gravitational waves are literally ripples in the fabric of space-time itself.

What does this enigmatic description mean? In operational terms it is easy to visualise. Because gravitation is a warping of geometry, when a gravitational wave crosses a region of space it stretches distances in one direction and shrinks them in a perpendicular direction, in an oscillating fashion. If such a wave passes through matter – for example, the Earth – it should squash and stretch it periodically, and so set the planet vibrating. Easy to spot, surely?

The trouble is that, once again, the predicted effects are unbelievably small. The basic reason for this feebleness can be traced back to the sheer weakness of gravitation: electricity is a thousand trillion trillion trillion times stronger, which is why electromagnetic waves are commonplace, but gravitational waves were sidelined for decades as a mere curiosity. But in the 1960s a handful of physicists began to wonder whether they could actually be detected in the laboratory. In principle this is very simple: just look for otherwise unexplained tremors in a chunk of matter. In practice it’s not so easy, because the world is filled with noise and vibration.

After experimenting for some years, researchers settled on lasers as the best way to go. By reflecting a laser beam off a mirror, any slight changes in the distance to the mirror caused by the passage of a gravitational wave should show up in the quality of the light. The arrangement is known as an interferometer. The US has two 4km-sized laser interferometer gravitational observatories and Europe has one, Virgo, located near Pisa.

Both Ligo and Virgo operated successfully for several years, but no gravitational waves were detected: not really surprising, given the vibrations being sought are smaller than the size of an atomic nucleus over several kilometres. A striking comparison is that the interferometers need to spot changes equivalent to the width of a human hair in the distance to the nearest star. How likely is it to succeed, and for the substance of those September rumours to be confirmed? If a supernova occurred in our galaxy tomorrow, Advanced Ligo would detect it as a short but intense burst of gravitational waves. But such events are rare and one may not occur this century.

Alternatively, one could observe a pair of neutron stars or black holes – both massive but highly compact objects – in close orbit. As the stars cavort around each other at high speed, they serve as a prolific source of gravitational waves, draining the system of energy. This causes the stars to go into a death spiral, ending in a titanic collision and creating a single black hole. Ligo and Virgo aspire to routinely detect such events far beyond the confines of our own galaxy, the Milky Way, in order to study the fine details of the objects’ violent demise and turbulent aftermath.

The main motivation for gravitational wave detectors, however, is not to test Einstein’s theory one more time, welcome though that would be. Conventional telescopes detect light or radio waves, and satellites have extended the range across the entire electromagnetic spectrum; gravitational observatories, however, would probe an entirely new spectrum, enabling the study of astronomical phenomena, such as neutron star coalescence, that are inaccessible in any other way. And because gravitational waves are so penetrating, they could enable us to peer into regions of space obscured from normal view by gas and dust, such as the environment around supermassive black holes.

Ground-based interferometers are not the only way to study gravitational waves. Ambitious plans are afoot to put an interferometer into space to detect very long waves from much larger astronomical systems such as supermassive black holes. A first step towards Lisa (Laser Interferometer Space Antenna) was taken with last week’s launch of a satellite to test key aspects of the technology.

As always in science, there is potential for a prize as yet unknown. For history has shown that every time the universe is studied with a new type of instrument, unexpected discoveries are made. Gravitational waves are created by any massive rapidly moving objects, from stars and black holes to the big bang itself. With Advanced Ligo up and running, and Advanced Virgo about to launch, it would be highly fitting if the first definitive detection of gravitational waves were to coincide with the centenary of general relativity. The universe is sure to spring surprises: this could yet prove to be Einstein’s greatest gift. (Davies, 2015).
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REFERENCE

Davies, P. (2015) '100 years on, is this Einstein’s greatest gift to human understanding?', The Guardian 7 December [Online]. Available at: http://www.theguardian.com/commentisfree/2015/dec/07/einstein-universe-gravitational-waves-theory-relativity (Accessed 20 January 2016).