Where the Universe Came From: How Einstein's relativity unlocks the past, present and future of the cosmos by New Scientist | eBook

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Where the Universe Came From

How Einstein's Relativity Unlocks the Past, Present and Future of the Cosmos

By Alison George, Stephen Battersby

Nicholas Brealey Publishing

CHAPTER 1

The roots of relativity

In 1915 a patent clerk in Switzerland came up with an idea that transformed our conception of space and time. The clerk was Albert Einstein (1879–1955) and the idea was general relativity. This chapter describes the path that led to his momentous discovery.

A relatively brief history

First, we should get this out of the way: Einstein was not a lone genius. His contribution was immense, but it did not exist in a vacuum.

The story starts when Scottish physicist James Clerk Maxwell (1831–79) achieved one of the great unifications of physics. In the 1860s he took many separate theories of how magnetic and electric fields work, and showed that they could all be described in one set of equations. Then he made a remarkable prediction: the combined fields responsible for electric and magnetic forces could form a type of wave that would travel at the speed of light. By the end of the nineteenth century it was accepted that this was no coincidence: light itself was composed of these 'electromagnetic waves'.

Strangely, the equations said that the waves always travel at an identical speed, regardless of how their source is moving or how fast you as an observer are moving. That didn't seem quite right. If I throw anything forwards from a moving vehicle, it flies faster than if I throw it from a standing start. Why should light be any different?

Based on this logic, people started to look for some kind of variation in the speed of light. The most famous attempt was an experiment in 1887 by the American physicists Albert Michelson (1852–1931) and Edward Morley (1838–1923), who tried to detect light changing its speed as the Earth spins and swings around the Sun. They took a beam of light, split it in two and sent it along two arms at a 90-degree angle – expecting to find slight differences in the time it took to go along each arm, depending on how the set-up was oriented relative to the motion of the Earth. But, however hard they looked, they always found that light moves at the same speed.

In 1895 the Dutch mathematician Hendrik Lorentz (1853–1928) came up with a way to understand the constant speed of light. He developed a set of rules that relate what you see when moving to what you would see when standing still (see Chapter 2). The rules involve what he regarded as a fictional time: if you are moving along at high speed, then you need to use this fictional time, different from the time that would be measured by a normal clock. Using this mathematical trick, everything seems to make sense and the speed of light appears the same for everyone.

Time warp

Five years later, the French scientist Henri Poincaré (1854–1912) wrote an essay ('La mesure du temps') in which he wondered why we thought of time so rigidly. Tellingly, Lorentz thought of warping time as just a mathematical trick – but Poincaré (without referring explicitly to Lorentz) pointed out that in future it might be necessary to abandon the idea of a unique notion of physical time. This was a philosophical leap that helped free Einstein to formulate relativity.

On the subject of philosophy, a second nudge that would influence Einstein's later work came from the Austrian physicist and philosopher Ernst Mach (1838–1916). In his 1883 textbook The Science of Mechanics, Mach asserted that we should never talk about how something is moving in absolute terms – only about how it is moving relative to something else.

Finally, the groundwork was laid for Einstein. In his 1905 paper 'On the electrodynamics of moving bodies', he started with two assumptions: 1 The laws of physics should be the same when we write them relative to any frame of reference moving at constant velocity.

2 We need to take Maxwell's equations seriously – any ray of light moves in any such frame of reference with exactly the same velocity.

About Albert Einstein

Albert Einstein was born in Ulm, south-west Germany, on 14 March 1879, the second child of Hermann Einstein, founder of an electrical engineering company, and his wife Pauline. The family, who were non-observant Ashkenazi Jews, soon moved to Munich where Albert later went to school.

Aged 17, Einstein entered the Swiss Federal Polytechnic School in Zurich, to train as a teacher of physics and mathematics. It was here that he met his fellow student Mileva Maric, whom he married in 1903. In 1987 newly discovered letters between the two revealed that they had a child out of wedlock in 1902, though the fate of this girl is unknown – she may have been adopted or died in infancy. The couple later had two sons, Hans and Eduard, before separating and eventually divorcing in 1919, when he married his cousin Elsa Löwenthal (née Einstein).

After graduating, Einstein spent a frustrating two years trying to secure a teaching position and eventually ended up working at the Swiss Patent Office. It was here, and in his spare time, that he made his early discoveries, including the remarkable series of papers of his annus mirabilis in 1905 (see 'The miraculous year' in Chapter 2). This led to his appointment in 1908 as a lecturer at the University of Bern, Switzerland, which was swiftly followed by a professorship at the University of Zurich. By 1914 he was a professor at the University of Berlin, where he remained for almost two decades until the political situation in Germany changed and the Nazi government began to prohibit Jews from holding teaching positions at universities. In 1933 he gave up his citizenship and emigrated to America, finding refuge at the Institute of Advanced Study in Princeton, New Jersey, where he remained until his retirement.

Einstein is known not only for his remarkable discoveries. He was also an ardent music lover, a pacifist, a champion of civil rights and a supporter of Zionism. He died of an aneurism in 1955, aged 76, and his ashes were scattered in an unknown location – although his brain was preserved (see later in this chapter).

Relatively special

In a few short pages, Einstein was able to derive a cornucopia of results that we now know as special relativity. Many of these results had appeared before, but now they were unified and given a clear physical interpretation. It was clear, for example, that time dilation is real, not fictional: moving clocks really should slow down. Perhaps because Lorentz and Poincaré had laid so much groundwork, Einstein's 1905 special relativity seems not to have raised too much controversy. Certainly, it did not make anything like the popular impression of his later general theory, which would require over a decade's more work to reach.

One of the first developments towards that goal seemed inauspicious: the Polish-German mathematician Hermann Minkowski (1864–1909) found a neat way of explaining special relativity. He coined the idea of space-time – that space and time are intertwined. You can think about a map of how things unfold in time and space: at the bottom of the map you have the far past, at the top the far future, while left or right mark different places. Minkowski realized that, when you are moving, you point in a different direction in space-time: instead of straight up the page, you tilt to the left or right. Mathematically, it is very much like a rotation that interchanges some of your space for time and some of your time for space. This abstract view correctly generates the results of special relativity in a beautifully streamlined way.

But Einstein recognized that special relativity was limited. It correctly relates different frames of reference only if they are moving at constant velocities. He was also worried about gravity. The best theory of gravity at the time was Newton's. Newton, like Maxwell, was a unifier: he showed that the same force that keeps us glued to the Earth's surface also stops the Moon flying off into space and keeps the Earth orbiting around the Sun. The resulting theory works extremely well, but it involves a kind of instantaneous pull: somehow just the presence of the Earth below exerts a force on us. Even on cosmic scales, you feel the tug of all the galaxies around you at any moment. That doesn't sit comfortably with special relativity, where nothing can travel instantaneously; to make it all fit together, nothing should move faster than the speed of light, not even forces.

The principle of equivalence

Einstein took a first step to bringing gravity into his theory in 1907, by formulating what is now called the principle of equivalence. He pointed out that when you are falling, in some sense there is no gravity. If you look around you, other things that are falling seem motionless – because everything is falling at the same rate. This is what happens on the International Space Station: it's not that the astronauts have escaped Earth's gravitational pull, it's that the space station is constantly falling towards Earth while, say, astronaut Tim Peake was also constantly falling towards Earth at the same rate. (The station never crashes to Earth because it is also moving horizontally at high speed.)

Inspired by Mach's earlier philosophy, Einstein's genius was to take the bold step of insisting that, for any experiment carried out in the microcosm of a space station, the result should be just the same as if gravity simply did not exist. That is the principle of equivalence.

It is bizarre that Einstein's theory of gravity should be based on deep thought about situations where the very force we are talking about disappears. No surprise, then, that it needed a great deal of mathematical development to turn the idea into a theory that could make meaningful predictions. In 1913 Einstein had started to play with Minkowski's idea of space-time as a tool. He found that he could get the right result for how objects move in a gravitational field by assuming that space-time is warped, and that objects try to follow the shortest route through this curved space-time, but he wasn't able to show what makes it curve in the first place.

By now, Einstein was struggling with the maths. For a frenetic few months in 1915 he was corresponding with many different people, in particular the German mathematician David Hilbert (1862–1943). Einstein's and Hilbert's work became so intertwined that it is unclear who exactly wrote down the field equations first. But there is no doubt that Einstein was the driving force. Finally, in November 1915 in his general theory of relativity, he was able to describe how space-time gets curved by the presence of mass, energy and pressure:

Gµv = 8πG/c4 Tµv

There is great richness embedded in these few characters. Within six months of finding the field equations, Einstein was writing papers on gravitational waves, a hundred years before they were finally directly detected (see Chapter 4). Black holes were also predicted shortly after the theory was published (see Chapter 3).

Other consequences took much longer to emerge. In 1949 the Austrian-American mathematician and philosopher Kurt Gödel (1906–78) mounted an attack on relativity. A lover of absurdity, Gödel was able to show that general relativity permitted time travel into the past. This is anathema to physicists: if it is possible to travel back into our own past, what is to stop us changing it? Any science fiction fan will tell you that this is not advisable.

Wormholes and more

Gödel's example required the whole universe to be spinning, which it is not (as far as we can tell). But in 1988, the physicists Mike Morris and Kip Thorne found another route to time travel. They showed that wormholes – short cuts from one part of space-time to another – could, in principle, be opened if an exotic type of energy could be produced by an advanced civilization. Once open, they can be used to zip across space and time. While the prospects are remote, time travel is seemingly permitted by Einstein's equations; this still provokes plenty of heated discussion between physicists.

In the meantime, there is plenty to be working on. It has only recently become possible to solve Einstein's equations on computers, which has opened up a whole new way of exploring the bizarre behaviour of black holes and other exotic objects. Combined with the detection of gravitational waves, we finally seem to be getting to grips with the theory and its implications – a process that has taken a hundred years. But we must remember that the richness of relativity tells us not only about the genius of Einstein but of his predecessors, his contemporaries and the many people who have worked to figure out what it all means.

'The most lucid, not to mention entertaining, proponent of Einstein's ideas has always been Einstein himself.'

Stephen Hawking, A Stubbornly Persistent Illusion (2008)

Einstein in his own words

In 2010 Albert Einstein's original handwritten manuscript 'The Foundation of the Generalized Theory of Relativity' was put on display for the first time in its entirety at Israel's Academy of Sciences and Humanities in Jerusalem.

Einstein wrote the 46-page paper in 1916 – three years before the theory's first major confirmation of general relativity during an eclipse. The paper mentions the potential test of the theory, as well as its prediction for the perihelion of Mercury's orbit, which had, until general relativity, remained an anomaly. He also commented in the paper that it remained 'an open question whether the theory of the electromagnetic field in conjunction with that of the gravitational field furnishes a sufficient basis for the theory of matter or not'.

Writing in 1916, Einstein didn't yet know of the two other forces that would have to be taken into account – the weak and strong nuclear forces – but his question was profound and remains an open one today. Legions of physicists are trying to answer a similar question, as they seek to unite general relativity with quantum mechanics in an ultimate theory of everything.

There's a particular thrill that comes from reading Einstein in his own words (digitized versions of this paper and others can be found online). His unique philosophical style is at times deceptively simple, full of useful thought experiments and always questioning even our most basic assumptions about reality. In 1921 he was awarded the Nobel Prize in physics for his 'services to theoretical physics, and especially for his discovery of the law of the photoelectric effect'.

The light bends

How did Einstein's theory hold up to real-world tests?

The theory of relativity is often considered a triumph of pure intellect, one of the most elegant of fundamental physical theories. But elegance and intellect mean nothing in physics if they don't match our observations of nature.

For more than 200 years, Newton's theory of gravity had passed this test with flying colours. At its core was the law of universal gravitation: the force of gravity between any two objects is proportional to each of their masses and inversely proportional to the square of their distance apart. Newton's law was used to predict the motion of planets in our solar system with remarkable accuracy. Such was its power that in 1846 the French astronomer Urbain Le Verrier (1811–77) used it to predict the existence of Neptune.

There was only one case where Newton's theory did not give the right answer. Le Verrier found that Mercury's orbit drifted by a tiny amount – less than one-hundredth of a degree over a century – relative to what would be expected from Newton's theory. This puzzling discrepancy remained until 1916, when Einstein showed that his general theory of relativity would lead to the observed drift in Mercury's orbit. General relativity passed its first test almost immediately.

Einstein also predicted that a massive object such as the Sun should distort the path of light: in effect, the curved geometry of space should act as a lens and focus the light (see Figure 1.3). (In fact, Newton's theory also predicts that light will curve, but only half as much as in general relativity.)

Lucky eclipse

On 11 August 1999, the skies above Albert Einstein's birthplace in the city of Ulm in Germany darkened as the Moon eclipsed the Sun. It was a fitting tribute to the man who transformed our picture of the natural world – and an unlikely one, too. Although a total eclipse occurs roughly every 18 months somewhere in the world, at a given location the gap between successive eclipses is about 350 years. What were the chances, then, that the greatest scientist of the twentieth century should be commemorated by the last total eclipse of the millennium? But perhaps we should not be too surprised about the coincidence; for Einstein, eclipses have always been lucky.

(Continues...)

Excerpted from Where the Universe Came From by Alison George, Stephen Battersby. Copyright © 2017 New Scientist. Excerpted by permission of Nicholas Brealey Publishing.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Where the Universe Came From: How Einstein's relativity unlocks the past, present and future of the cosmos

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How Einstein's Relativity Unlocks the Past, Present and Future of the Cosmos

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