The Universe Within (14 page)

Now Einstein just wrote down the equations for energy conservation. The total energy before the emission must equal the energy after it, according to both observers. From these two equations it follows that the atom's kinetic energy after the emission, as seen by the second observer, must equal the atom's kinetic energy before the emission plus the extra energy in the burst of radiation. This equation relates the energy in the burst of radiation to the mass of the atom before and after the emission. And the equation implies that the atom's mass changes by the energy it emits divided by the square of the speed of light. If the atom loses
all
of its mass in this process, and just decays completely into the burst of radiation, the same relation applies. The amount of radiation energy released must be equal to the original mass times the speed of light squared, or
E
=
mc
2
.

Einstein put it this way: “Classical physics introduced two substances: matter and energy. The first had weight, but the second was weightless. In classical physics we had two conservation laws: one for matter, the other for energy. We have already asked whether modern physics still holds this view of two substances and the two conservation laws. The answer is: No. According to the
theory
of relativity, there is no essential distinction between mass and energy. Energy has mass and mass represents energy. Instead of two conservation laws we have only one, that of mass-energy.”
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E
=
mc
2
is a unification. It tells us that mass and energy are two facets of the same thing.

What Einstein's magical little formula tells us is that we are
surrounded
by vast stores of energy. For example, that sachet of sugar you are about to stir into your coffee has a mass energy equivalent to a hundred kilotons of
TNT
— enough to level New York. And of course, his discovery prefigured the development of nuclear physics, which eventually led to nuclear energy and the nuclear bomb.

In Newton's theory, there was no limit to the speed of an object. But in Einstein's theory, nothing travels faster than light. The reason is fundamental: if something
did
travel faster than light, then according to Lorentz's transformations, some observers would see it going backward in time. And that would create all sorts of causality paradoxes.

IN DEVELOPING THE THEORY
of relativity, the next question facing Einstein, which echoed concerns raised by Michael Faraday more than half a century earlier, was whether the force of gravity could really travel faster than light. According to Newton, the gravitational force of attraction exerted by one mass on any other mass acts
instantaneously
— that is, it is felt immediately, right across the universe. As a concrete example, the tides in Earth's oceans are caused by the gravitational attraction of the moon. As the moon orbits Earth, the masses of water in the oceans follow. According to Newton, the moon's gravity is felt instantly. But moonlight takes just over a second to travel from the moon to Earth. Faraday and Einstein both felt it unlikely that the influence of gravity travelled any faster.

In constructing a theory of gravity consistent with relativity, one of the key clues guiding Einstein was something that Galileo had noticed: all objects fall in the same way under gravity, whatever their mass. An object in free fall behaves as if there is no gravity, as we know from the weightlessness that astronauts experience in space: an astronaut and her space capsule fall together. This behaviour suggested to Einstein that gravity was not the property of an object, but was instead a property of spacetime.

What then is gravity? Gravity is replaced, in Einstein's theory, by the bending of space and time caused by matter. Earth, for example, distorts the space­time around it, like a bowling ball sitting in the centre of a trampoline. If you roll marbles inwards, the curved surface of the trampoline will cause them to orbit the bowling ball, just as the moon orbits Earth. As the physicist John Wheeler would later put it, “Matter tells spacetime how to curve, and spacetime tells matter how to move.”
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After ten years of trying, in 1916 Einstein finally discovered his famous equation — now called Einstein's equation — according to which the curvature of space­time is determined by the matter contained within it. He used the mathematical description of curved space invented by the German mathematician Bernhard Riemann in the 1850s. Before Riemann, a curved surface, such as a sphere, had always been thought of as embedded within higher dimensions. But Riemann showed how to define the key concepts in geometry, like straight lines and angles, intrinsically within the curved surface, without referring to anything outside it. This discovery was very important, because it allowed one to imagine that the universe was curved, without it having to be embedded inside anything else.

Einstein's new theory, which he called “general relativity,” brought our view of the universe much closer to that of the ancient Greeks: the universe as a vital, dynamic entity with a delicate balance between its elements — space, time, and matter. Einstein altered our view of the cosmos, from the inert stage I had envisaged as a child to a changeable arena that could curve or expand.

In welcoming Einstein to London, the celebrated playwright George Bernard Shaw told a jokey story about how a young professor — Albert Einstein — had demolished the Newtonian picture of the world. Upon learning that Newton's gravity was no more, people asked him: “But what about the straight line? If there is no gravitation, why do not the heavenly bodies travel in a straight line right out of the universe?” And, Shaw continues, “The professor said, ‘Why should they? That is not the way the world is made. The world is not a British rectilinear world. It is a curvilinear world, and the heavenly bodies go in curves because that is the natural way for them to go.' And at last the whole Newtonian universe crumbled up and vanished, and it was succeeded by the Einsteinian universe.”
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In the early days Max Born described Einstein's
theory
of general relativity thus: “The theory appeared to me then, and it still does, the greatest feat of human thinking about nature, the most amazing combination of philosophical penetration, physical intuition, and mathematical skill. But its connections with experience were slender. It appealed to me like a great work of art to be admired from a distance.”
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Today, Born's statement is no longer true. Einstein's younger successors applied his theory to the cosmos and found it to work like a charm. Today, general relativity is cosmology's workhorse, and almost every observation we make of the universe — whether from the Hubble Telescope or giant radio arrays or X-ray or microwave satellites — relies on Einstein's theory for its interpretation.

General relativity is not an easy subject. As an undergraduate, I trudged my way through a famously massive textbook on the subject called
Gravitation,
which weighs 2.5 kilograms. It was a quixotic attempt — while the subject is conceptually simple, its equations are notoriously difficult. After six months of trying, I decided instead to take a course. That made it all so much easier. Physics, like many other things, is best learned in person. Seeing someone else do it makes you feel you can do it too.

· · ·

THE DISCOVERY OF GENERAL
relativity, and its implication that spacetime was not rigid, raised a question: what is the universe doing on the very largest scales, and how is it affected by all the matter and energy within it? Like everyone else at the time, when Einstein started to think about cosmology, he assumed the universe was static and eternal. But immediately a paradox arose. Ordinary matter attracts other ordinary matter under gravity, and a static universe would just collapse under its own weight. So Einstein came up with a fix. He introduced another, simpler form of energy that he called the “cosmological term.” Its main properties are that it is absolutely uniform in spacetime, and it looks exactly the same to any observer. The best way to visualize the cosmological term is as a kind of perfectly elastic, stretchy substance, like a giant sponge filling space. It has a “tension,” or negative pressure, meaning that as you stretch it out it stores up energy just like an elastic band. But no matter how much you stretch it, its properties do not change — you just get more of it.

At first, a negative pressure sounds like exactly what you don't want holding up the universe. It would suck things inward and cause a collapse. However, as we described earlier, the expansion of the universe is not like ordinary physics. It is not an explosion: it is the expansion of space. And it turns out that the effect of a negative pressure, in the Einstein equations, is exactly the opposite of what you might expect. Its gravity is
repulsive
and causes the size of the universe to blow up. (This effect of repulsive gravity is the same one that Guth used in his theory of inflation.)

So Einstein made his mathematical model of the universe stand still by balancing the attractive gravity of the ordinary matter against the repulsive gravity of his cosmological term. The model was a failure. As noticed by the English astrophysicist Arthur Eddington, the arrangement is unstable. If the universe decreased a little in size, the density of the ordinary matter would rise and its attraction would grow, causing the universe to collapse. Likewise, if the universe grew a little in size, the matter would be diluted and the cosmological term's repulsion would win, blowing the universe up.

It would fall to two very unusual people to see what Einstein could not: that his theory describes an expanding universe.

THE FIRST WAS ALEXANDER
Friedmann, a gifted young Russian mathematical physicist who had been decorated as a pilot in the First World War. Due to the war and the Russian Revolution that followed it, news of Einstein's theory of general relativity did not reach St. Petersburg, where Friedmann worked, until around 1920. Nevertheless, within two years, Friedmann was able to publish a remarkable paper that went well beyond Einstein. Like Einstein, Friedmann assumed the universe, including ordinary matter and the cosmological term, to be uniform across space and in all directions. However, unlike Einstein, he did not assume that the universe was static. He allowed it to change in size, in accordance with Einstein's equation.

What he discovered was that Einstein's static universe was completely untypical. Most mathematical solutions to Einstein's equations described a universe which was expanding or collapsing. Einstein reacted quickly, claiming Friedmann had made mathematical errors. However, within a few months, he acknowledged that Friedmann's results were correct. But he continued to believe they were of exclusively mathematical interest, and would not match the real universe. Remember, at the time of these discussions, very little was known from observations. Astronomers were still debating whether our own Milky Way was the only galaxy in the universe, or whether the patchy clouds called “nebulae,” seen outside its plane, were distant galaxies.

Einstein's reason for disliking Friedmann's evolving universe solutions was that they all had singularities. Tracing an expanding universe backward in time, or a collapsing universe forward in time, you would typically find that at some moment all of space would shrink to a point and its matter density would become infinite. All the laws of physics would fail at such an event, which we call a “cosmic singularity.”

Friedmann nevertheless wondered what would happen if you followed the universe through a singularity and out the other side. For example, in some models he studied, the universe underwent cycles of expansion followed by collapse. Mathematically, Friedmann found he could continue the evolution through the singularity and out into another cycle of expansion and collapse. This idea was again prescient, as we will discuss later.

Today, Friedmann's mathematical description of the expansion of the universe provides the cornerstone of all of modern cosmology. Observations have confirmed its predictions in great detail. But Friedmann never saw his work vindicated. In the summer of 1925, he made a record-breaking ascent in a balloon, riding to 7,400 metres, higher than the highest mountain in all Russia. Not long afterwards, he became ill with typhoid and died in hospital.

TWO YEARS LATER, UNAWARE
of Friedmann's work, a Belgian Jesuit, Abbé Georges Lemaître, was also considering an evolving universe. Lemaître added a new component: radiation. He noticed that the radiation would slow the expansion of the universe. He also realized that the expansion would stretch out the wavelength of electromagnetic waves travelling through space, causing the light emitted from distant stars and galaxies to redden as it travelled towards us. The U.S. astronomer Edwin Hubble had already published data showing a reddening of the starlight from distant galaxies. Lemaître interpreted Hubble's data to imply that the universe must be expanding. And if he traced the expansion back in time, billions of years into our past, he found the size of the universe reached zero: it must have started at a singularity.

Once more, Einstein resisted this conclusion. When he met Lemaître in Brussels later that year, he said, “Your calculations are correct, but your grasp of physics is abominable.”
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However, he was once more forced to retract. In 1929, Hubble's observations confirmed the reddening effect in detail and were quickly recognized as confirming Lemaître's predictions. Still, many physicists resisted. As Eddington would say, the notion of a beginning of the world was “repugnant.”
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Lemaître continued to pursue his ideas, trying to replace the singular “beginning” of spacetime with a quantum phase. What he had in mind was to use quantum theory to prevent a singularity at the beginning of the universe, just as Bohr had quantized the orbits of electrons in atoms to prevent them from falling into the nucleus. In a 1931 article in
Nature
, Lemaître stated: “If the world has begun with a single quantum, the notions of space and time would altogether fail to have any meaning at the beginning: they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.”
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Lemaître called his hypothesis “the Primeval Atom,” and as we'll see, it prefigured the ideas of the 1980s.