A Brief History of Time

A Brief History of Time

by

Stephen Hawking

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A Brief History of Time: Chapter 6 Summary & Analysis

Summary
Analysis
John Wheeler came up with the name black hole in 1969 to describe an idea that had been around for around 200 years. In Newton’s time, people argued whether light was a particle or a wave, and how gravity would therefore affect it. Under quantum mechanics, scientists know it is both. Gravity will affect light the same way it does all other particles. Roemer showed that light has a specific speed, rather just traveling infinitely fast, so gravity could have  significant effects on light’s movement.
Hawking provides a catch up summary here, focusing more on those concepts directly relevant to the black holes he is preparing the reader to consider. As seen already with other concepts, the idea of black holes were around far before the scientific knowledge to back them up, let alone the technology to detect them. Humanity’s curiosity about black holes had not died out before an approach was devised to understand them.
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John Michell’s paper in 1783 first suggested the idea of black holes, though he did not use the name. He said that any star that was big and dense enough would have such a strong gravitational pull that light could not escape it. We cannot see them, but we should be able to detect them due to their gravitational effects. Laplace made a similar suggestion at a similar time, but wrote it out of later editions of his book. Perhaps the idea was too ridiculous.
Laplace’s back tracking on the idea of black holes demonstrates the challenges facing the theory, as one of its own proponents lost heart awaiting proof. Nevertheless, the idea has survived since the late 1700s, reflecting the staying power of logical suggestions, regardless of their difficulties in gaining immediate mass acceptance.
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But one cannot compare light to other matter that gravity drags in, like a cannonball falling back to earth. Light travels at a fixed speed in one direction. Einstein’s general relativity helped to explain this, although it took decades for the relevance to be applied to black holes and massive stars.
Gradually, more theories were established that could support the reasoning behind and offer further exploration of the idea of black holes. Again, Hawking emphasizes the slow build up behind establishing black holes as a valid theory, one dependent on the many discoveries made previous. Scientific understanding is a process dependent on sustained curiosity and on each interconnecting link in the chain, for now.
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A star forms when a large volume of gas begins to collapse in on itself under its own gravity—usually it is mostly hydrogen. The increasing number of atomic collisions taking place as the gas contracts causes it to heat up. Soon, it there is so much energy, the atoms fuse instead to create helium. This massive energy creates the star’s shine. It also creates pressure, which offsets the gravity, and halts the star’s contraction. Eventually, however, the star will run out of fuel. This happens more quickly the bigger the star is, as it requires higher energy and pressure to offset its higher gravitational pull. When it does run out of fuel, it will begin to contract again.
As black holes are born from stars, Hawking first gives the reader a thorough, and fascinating grounding in a star’s lifecycle. For the most part, stars spend their life in an existential balancing act. As a massive cloud of burning gas, the star faces the contracting pull of its gravity on the one hand, and the outward pressure of its colliding particles on the other. But this stage cannot last forever, as a star’s fuel is finite, so eventually the star’s own gravity will overpower its pressure, and the contracting phase will begin again.
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While sailing to England in 1928 to work with Sir Arthur Eddington, one of the only people who understood general relativity at the time, Subrahmanyan Chandrasekhar worked out how big a star needed to be to support itself against its own gravity after using up all its fuel. According to the Pauli exclusion principle, matter cannot be in exactly the same place, so nearby particles will repel each other, driving a star’s expansion. This can balance against the star’s gravity, just as its heat did in an earlier stage.
Familiar with stars’ balancing act lifestyle, Chandrasekhar dug a little deeper and found the boundary at which a star’s mass determines its fate. Below the so-called Chandrasekhar limit, after collapsing for a while, the star will again find stability at a smaller size because of the way particles cannot be in the exact same place, giving it structure.
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But the Pauli exclusion principle only helps to a certain extent, as particles’ speed is limited to the speed of light, as light must travel faster than everything else. After a certain point, if the star is dense enough, its gravity will outweigh its expanding force. The Chandrasekhar limit states a star one and a half times the mass of our sun will not be able to sustain itself against its own gravity at this stage. Russian scientist Lev Davidovich Landau made a similar discovery at the same time. Stars smaller than the Chandrasekhar limit will become white dwarves, supported by the Pauli exclusion principle between electrons—the electrons repel each other, giving the object structure rather than collapsing. Landau also showed that stars supported by the exclusion principle acting between protons and neutrons would become neutron stars, which are much smaller and denser than white dwarves.
If a star is above the Chandrasekhar limit, this exclusion principle of particles repelling each other is not as strong as the force of the star’s own gravity, as the bigger its mass, the stronger its gravity. But smaller stars can balance this out. They can become a white dwarf (a small, cold but still glowing and stable star that has used up its nuclear fuel), because of the repulsion between the electrons in the star, according to the exclusion principle. Or, smaller stars can become neutron stars after collapsing, which are instead supported by the repelling force between the star’s protons and neutrons. The fact that Landau made a similar discovery at the same time as Chandrasekhar shows the inevitable progress science will make, as one discovery provides the impetus for the next. Humanity’s innate inquisitiveness spurs it onto each subsequent breakthrough.
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When a star is above the Chandrasekhar limit it faces serious problems when running out of fuel. It might explode, losing the mass required to remain stable. If it doesn’t explode, it will become a black hole and ultimately collapse to infinite density. That shocked Eddington but, when Chandrasekhar won the Nobel Prize years later, it was in part for this work.
Eddington opposed Chandrasekhar’s finding because it did not fit with his understanding of the general theory of relativity, and as he considered himself the only person since Einstein to understand it, this was most likely hard for him to accept. Indeed, Einstein himself disagreed with the idea of stars collapsing to a point. Facing such opposition, Chandrasekhar shelved the theory, but its validity held out, and years later was recognized by the highest award in the scientific community.
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Related Quotes
In 1939, American scientist Robert Oppenheimer, took the idea further, though his theories couldn’t be proven with technology in his day. Essentially, his work states that stars’ gravitational pull changes light’s path through space-time. Finally, the light is pulled so strongly, it cannot escape. As light moves faster than anything else, nothing else can escape either. This area of no return is a black hole, the boundary of which is called its event horizon.
Oppenheimer provided the next logical step from the work preceding his own, especially relating to Michell’s seminal suggestion that observers would not be able to see such black holes directly. Oppenheimer’s work only gained recognition when telescopes became strong enough to provide observational support. Valid theories can survive the test of time, but ultimately must agree with observation to be accepted. 
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Because time is relative, what happens at a black hole will look different to different observers, such as someone on the surface of the star versus someone at a distance. If an astronaut sent signals to the distant observer on a spaceship every second until the star contracted past the critical radius at which nothing could escape, at 11 a.m., the last signal before 11 a.m. would take an infinite time to arrive because it would not be able to escape the gravitational pull. In fact, each previous signal would take longer and longer to arrive, and the light of the star would appear redder and redder. Finally, at 11 a.m., the star would not allow light to escape at all, and it would appear as a black hole. But the distant observer’s spaceship would still orbit the black hole and feel its gravitational affects.
Light from collapsing stars will appear redder and redder as the gravitational force strengthens. This is because light loses more energy escaping the star’s surface as the gravity strengthens, lengthening the light’s wavelength, which appears to the human eye as red light. Signals will also seem to take longer to arrive as the star’s gravity strengthens as the star contracts. Eventually, escape will become impossible, for light, signals, and the astronaut. Given that escape is impossible, scientists can only imagine what black holes would look like on the inside.
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Because gravity is strongest at the star’s surface, the difference in gravity between the astronaut’s head and feet would stretch and then tear him or her apart as the star reached its critical radius. Large regions like galaxies can collapse in similar ways.
If someone were brave and inquisitive enough to want to go see a black hole for themselves, they would not be able to anyway, as they would be torn to shreds before the star hit the critical radius after which it becomes a black hole. Perhaps they are better left imagining.
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Penrose and Hawking showed in the late 1960s that there must be a singularity of infinite density and space-time curvature at the center of a black hole. This is similar to the beginning of time at the big bang, but is the end of time for that star, and anything else caught up in it. The laws of science break down in a singularity, but observers outside would not be affected, as nothing can escape from the black hole. Penrose called this notion that breakdowns of science are always hidden from view the cosmic censorship theory.
Penrose’s cosmic censorship theory could be said to follow similar logic to the anthropic principle, in the sense that humans cannot see breakdowns in the laws of physics, or else they would be caught up in that same breakdown and die. Thus it is logical that humans cannot continue to experience time (i.e. live) if witnessing that breakdown. Therefore humans continuing to exist will wonder why they cannot personally witness breakdowns in physics.
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Some options available within general relativity let the astronaut escape through a wormhole, to appear somewhere else in the universe. But these would be unstable and unpredictable, probably destroying the astronaut in the process. The stronger cosmic censorship theory states the singularity is always in the astronaut’s future, as his time ends with it, so singularities are always at the beginning or end of time, as the laws of science break down at singularities, and with them, the concept of time. A black hole’s event horizon could be considered a one-way membrane, allowing things in, but not out. Anything that falls in will soon meet the end of time.
General relativity offers a set of equations from which various scientists extrapolate varying solutions. Some of these potential applications include ruptures in space-time that would allow short cuts to other sides of the universe, paths known as wormholes. Also like the anthropic principle, Penrose’s cosmic censorship has a stronger version.
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General relativity states that moving objects give off gravitational waves, which bend space-time. These waves carry energy away from the object producing them. Slowly, these objects lose energy as the waves take energy away from them, just like how the earth will eventually fall into the sun and become stationary.
Objects cannot emit energy in the form of gravity infinitely. Emitting energy saps energy from the object, which will eventually run out. Energy always has to be accounted for, as determined by physicists’ ever more specific calculations.
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This process is too slow to see in the earth, but in a system called PSR 1913 + 16, two neutron stars are orbiting each other. J. H. Taylor and R. A. Hulse won the Nobel Prize for this discovery in 1993. Just before the stars finally collide in 300 million years, they will be orbiting each other so quickly our current technology would pick up the gravitational waves.
From proposing the idea of black holes, to refining the theory, to determining the alternative outcomes of a collapsing star (here a neutron star), to actually finding them in the night’s sky, humanity’s continued pursuit of knowledge is slowly but surely unlocking the mysteries of the universe.
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The collapse of a star is much more rapid, and what the final stationary form of a black hole would look like was an open question. Werner Israel revolutionized views on black holes by showing that non-rotating black holes would be spherical. Any two black holes of the same size would be identical. One could use Karl Schwarzschild’s solutions to general relativity equations to describe them.
Hawking presents science as an ongoing line of open questions. In this case, the question is how to describe the unseeable. Yet, physicists have found a way, thanks to the predictable outcomes of the laws they have discovered.
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Isreal thought this meant only a perfectly spherical star could become a black hole, meaning there were no black holes in reality. But Penrose and Wheeler said a non-rotating star’s gravitational waves during its collapse would make it spherical. In 1963, Roy Kerr extended this to rotating black holes too. Brandon Carter helped to prove Kerr’s and Schwarzschild’s solutions in 1970 by showing if a rotating black hole had an axis of symmetry, its size and shape depend only on its mass and rate of rotation. Hawking helped to prove this for stationary rotating black holes. David Robinson later used their work to prove the Kerr solution, showing that black holes settle into a stationary, rotating but not pulsating state after collapse. This means a star of any shape or chemical make up could become a black hole, meaning there could be many of them.
Here Hawking shows how the scientific community comes together to solve problems, by expanding on, challenging, and improving each other’s work. Through this collaborative approach, in which any theory can be thrown out at any instant in favor of a more accurate one, humanity’s knowledge of the inner workings of black holes (which cannot even be seen) has gradually been streamlined and distilled into a form that the layman can grasp.
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Black holes were proposed before they were found. In 1962, Maarten Schmidt found what is now called a quasar, a whole region of a galaxy falling in on itself. In 1967, Jocelyn Bell-Burnell and her supervisor Anthony Hewish found a pulsar, which is a rotating neutron star. It was the first of its kind of be found, and held out hope for black hole believers. Although, at first they thought they might have found alien signals.
Hawking emphasizes explicitly a fact that has simmered under the surface of his narration throughout the chapter: the idea that black holes started life as a suggestion based on no direct, observable evidence. Nevertheless, the math held out, and in the 1960s the scientific community gained its long-awaited first signs of reassurance.
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Finding something that we cannot see seems impossible. But Michell suggested in 1783 we can measure a black hole’s gravitational effects on the material around it. There are examples of systems where stars orbit some unseen source of gravity. In one case, the minimum mass of the unseen object is far above the Chandrasekhar limit, meaning it is not a white dwarf or neutron star. It is most likely a black hole.
Here, Hawking expands on what, for now, might be the best available proof of black holes, given they cannot be directly seen. As with virtual particles, scientists can deduce the laws of physics based even on what cannot directly be seen, but only indirectly detected. Only the most curious creatures would have patience for this.
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More black holes have been found since, and given the age of the universe, there could be more than the observable stars in the sky. The extra mass would explain why the Milky Way, earth’s galaxy, rotates. There could also be a very large black hole at the center of the galaxy. Even larger ones could lie at the center of quasars. Objects orbiting such massive black holes would lose matter and energy into it, causing the black holes to rotate in the same direction as the matter orbits it, creating a magnetic field. This would create jets of particles.
With greater confidence that such objects as black holes do actually exist, cosmologists can make better judgments about what they observe in the universe. Black holes might not be viewable, but they do have a visible effect on the matter around them due to their mass and gravitational pull. Astonomers can now factor this into their calculations, driving humanity’s scientific progress along further.
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There could also be much smaller black holes, with a smaller amount of matter compressed by large external pressure, probably in the heat of the early universe. This would be because the early universe was not uniform—areas of higher density would cause such black holes, as well as the clumping of galaxies. Whether such “primordial” black holes exist depend on the state of the early universe—meaning if scientists can find them, they can determine the state of the early universe.
Finding “primordial” black holes, if they exist, as well as determining some of their properties, could tell physicists about the state of the early universe. Each discovery, theory, or even suggestion leads to the next big question. No wonder Hawking argues that only when humans know everything will they feel satisfied.
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