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The past, present and future of general relativity

A century ago, on 25 November 1915, Albert Einstein first announced his general theory of relativity, a cornerstone of cosmology and the key to understanding some of the most dramatic objects in the universe.

To mark this anniversary, Roger Highfield, co-author of a book on Einstein, Harry Cliff, curator of an Einstein exhibit, and double-Oscar winner Paul Franklin, who put Einstein’s equations to work in the movie Interstellar, shared their thoughts.

The birth of general relativity 

By Dr Roger Highfield  

Governing the universe on the largest scales, general relativity stands with quantum mechanics, which reigns on the smallest scales, as a foundation stone of modern physics and will be celebrated over the next few weeks by events worldwide.

Albert Einstein first presented his complete general theory of relativity to the Prussian Academy on November 25, 1915, and it was published—in four short pages— on December 2 that same year (Zur allgemeinen Relativatstheorie, Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin, 831-839).

Albert Einstein, author of the special and general theories of relativity in 1912. Image: ETH-Bibliothek Zürich, Bildarchiv / Fotograf: Langhans, J. F.

Albert Einstein, author of the special and general theories of relativity in 1912. Image: ETH-Bibliothek Zürich, Bildarchiv / Fotograf: Langhans, J. F.

But the genesis of general relativity stretches back to 1905 when, at the age of 26, Einstein proposed his special theory of relativity to reconcile the laws of electromagnetic radiation with the physics of moving bodies developed by Galileo Galilei and Newton. Special relativity posits that the speed of light is always the same, irrespective of the motion of the person who measures it. Special relativity also implies that space and time are intertwined to a degree never previously imagined.

Starting in 1907, Einstein began trying to broaden special relativity to include gravity. His first advance came when he was working in a patent office in Bern, Switzerland and an idea occurred to him:

If a man falls freely, he would not feel his weight… This simple thought experiment… led me to the theory of gravity.

He realised that there is a deep relationship between systems affected by gravity and those that are accelerating.

Then in 1908, Einstein’s former teacher Hermann Minkowski repackaged relativity in a neater mathematical form that dealt with space and time as an inseparable whole, called ‘space-time’. The next step was to find a new language to describe this four-dimensional landscape.

Einstein turned for guidance to Marcel Grossmann, the same friend whose lecture notes he had cribbed years before as a student. ‘Grossmann, you must help me, or else I’ll go crazy’ he wrote.

Grossmann acted as Einstein’s guide through the jungles of non-Euclidean geometry, where space is curved so that parallel lines do not exist and the three angles of a triangle do not add up to 180 degrees. Einstein needed a mathematical tool that would allow him to deal with this exotic geometry. In 1913, he and Grossmann published a paper in which they began this programme, using what is called tensor calculus.

As Einstein struggled in Berlin in 1915 to complete the extension of relativity, he increasingly cut himself off from the outside world. Letters were far less likely to be answered than to be impaled on a large meat hook and later burnt. The work was most intense in mid to late November, when Einstein wrote to almost no one, aside from David Hilbert, the great German mathematician, whose work on gravity ran remarkably close to his own.

In November, came Einstein’s epiphany. He revealed to the world that he could now explain an astronomical puzzle — a variation in the orbit of Mercury around the Sun that had perplexed scientists since it was first reported in 1859.

Success showed that, after eight years of groping for the truth about gravity, he had provided a new and profound glimpse of the workings of the universe. His latter-day colleague Abraham Pais has described this as possibly the strongest emotional experience of Einstein’s life. It was certainly a rapturous one. Einstein reported having had heart palpitations and feeling as if something inside him had snapped. ‘I was beside myself with ecstasy for days,’ he told Paul Ehrenfest, the theoretical physicist.

Einstein showed that gravity was not a force from one body acting on another, but a property of space-time itself. Massive objects such as black holes create distortions in the space-time around them, and these four-dimensional curves act as pathways for smaller objects to follow, rather as a ball bearing follows the line of least resistance over a hilly two-dimensional surface.

His exertions left him exhausted. In December 1915 Einstein wrote to his old friend Michele Besso that he was ‘satisfied but rather done in’.

 

General relativity today

By Dr Harry Cliff

A century after its birth, general relativity is still science’s ultimate tool for understanding the cosmos. It underpins our modern cosmological theories, allowing scientists to study the birth, evolution and ultimate fate of the universe. It describes the most extreme objects in nature, from the supermassive black holes that lurk at the centres of galaxies to violent collisions between neutron stars. Astronomers have even used general relativity’s predictions of how massive bodies bend light rays to map clouds of invisible dark matter that thread vast clusters of galaxies.

General relativity was so ahead of its time in 1915 that it took decades to explore many of its consequences. Physicists including Roger Penrose and Stephen Hawking only began to make progress in understanding black holes in the 1960s and 70s, and the prediction of general relativity that the rotation of the Earth should drag space and time along with it has still to be confirmed by observation.

A model of a black hole, used by Stephen Hawking at a Royal Society soiree in the 1970s. It will be displayed in the upcoming exhibition, Einstein’s Legacy. Image: Science Museum

A model of a black hole, used by Stephen Hawking at a Royal Society soiree in the 1970s. It will be displayed in the upcoming exhibition, Einstein’s Legacy. Image: Science Museum

But the most highly anticipated test today of general relativity is the detection of gravitational waves, ripples in the fabric of space-time created by the acceleration of massive bodies. Observing these ripples would give astronomers a new window on the universe, allowing them to study exotic objects like black holes and to peer further back towards the Big Bang than is possible using light-based astronomy.

The trouble is that gravitational waves are incredibly weak, and require huge and extremely sensitive instruments to detect. The $620 million Laser Interferometer Gravitational Wave Observatory (LIGO) in the USA offers the best hope to observe them in the near future.

LIGO’s L-shaped observatories work by beaming lasers down two 4km arms at right angles to one another. If a gravitational wave passes by it will cause the two arms to shrink and expand by tiny but different amounts, about a 10,000th of the width of a proton. This is then detected as a tiny shift in the arrival time of the laser light’s peaks and troughs, creating what is known as an interference pattern.

Although LIGO has not spotted any gravitational waves yet, it has recently been upgraded and should soon be able to detect ripples in space-time produced by collisions between neutron stars in distant galaxies up to around 650 million light-years from Earth. If gravitational waves are seen in the next few years, it will mark the beginning of an exciting new age of astronomy and of our understanding of Einstein’s greatest contribution to science.

 

The future of general relativity

By Paul Franklin, co-funder of Double negative

The plot of Interstellar, Christopher Nolan’s sci-fi epic, spins around Gargantua a super-massive black hole, simulated in unprecedented detail for the film. Black holes had long been the subject of speculation among astronomers going back to the 18th century – a region of space from which nothing, not even light, can escape – but it was general relativity that first allowed scientists to explore the physics underpinning them. Over the last few decades black holes have become a regular feature of science fiction, but we’ve become used to looking at fanciful and, frankly, inaccurate representations of them – we were determined to change that.

Interstellar's supermassive black hole, Gargantua. Credit: Warner Bros. Entertainment Inc. and Paramount Pictures Corporation

Interstellar’s black hole. Credit: Warner Bros. Entertainment Inc. and Paramount Pictures Corporation

For Chris Nolan it was essential to embed real science into the story and then see where it would take us. Relativity allowed us to explore the story possibilities offered by time dilation – through which clocks can tick at different rates for different characters depending on where they are in the universe – and the extraordinary power of Einstein’s equations allowed us to visualise Gargantua, the super-massive black hole that features in the film, and in unprecedented detail.

Gargantua was realised through a unique collaboration between Kip Thorne, The Feynman Professor of Theoretical Physics Emeritus at CalTech in Pasadena, California, and Double Negative’s research and development team, headed up by Chief Scientist Oliver James. Kip is a leading expert on general relativity and the inspiration for Sir Michael Caine’s character in the film.

Together, Kip, Oliver and our R&D team developed a new suite of software tools to model one of general relativity’s most famous predictions, that the path of a light beam can curve as it passes through gravitationally-warped space. The result was a super-accurate model of the “gravitational lens” around Gargantua which, through the simulation of trillions of light beams, created the stunning images seen in the film – when you see the “waterfall of fire” in the accretion disc cascading around Gargantua you are looking directly at the visual results of Einstein’s ground-breaking work.

Interstellar also deals with the concept of travel through hypothetical tunnels in space-time connecting distant parts of the universe, also predicted by Einstein’s general theory of relativity.  Work in the 1930s by Einstein and Nathan Rosen in Princeton revealed a solution of the general relativity equations that describes a bridge between two places/times (regions of what scientists call space-time).

This so called ‘Einstein-Rosen bridge’ – what we now call a wormhole – could pave the way to the possibility of moving colossal distances across the universe, and even open the door to a form of time travel. Wormholes are among the subjects tackled in The Science of Interstellar, a book written by Kip to accompany Chris’s movie.

One unexpected – and hugely satisfying – outcome of our work on Interstellar was that the requirement of creating Gargantua and the wormhole at such a high level of resolution had revealed some interesting new discoveries about the complex warping of space-time produced by such intense gravity. As a result we were able to publish scientific papers (see here and here), including one in the Journal of Classical and Quantum Gravity, featuring our findings.

Interstellar pushes cinematic imagery into new and uncharted territory – there is no better way to enjoy the film and its depiction of the astonishing reality of general relativity than to see it in true 70mm large format film in the Science Museum’s wonderful IMAX cinema – the biggest canvas available to filmmakers today!

Discover more about Albert Einsteins lasting influence on science and society in Einsteins Legacy, an exhibit marking the centenary of the general theory of relativity, which opens at the Science Museum on 25 November 2015. 

Roger Highfields contribution is extracted from his book The Private Lives of Albert Einstein (Faber, 1993), written with Paul Carter.

Written by Roger Highfield