PDF Summary:A Brief History of Time, by Stephen Hawking

How much do you know about the universe you live in? Thanks to scientific discoveries of the twentieth century, scientists have gained insight into many of nature’s secrets, from the origin of the universe to the nature of space and time. In A Brief History of Time, physicist Stephen Hawking explains these insights for a general audience.

In this guide, we’ll present Hawking’s exposition of modern physics through the lens of five big questions that the book answers: Is reality relative or absolute? Is the future predetermined? How did the universe begin? What is the nature of a black hole? And can you build a time machine? Where applicable, we’ll also examine how Hawking’s assertions and predictions stack up to new data that scientists have collected since the book was published.

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(Shortform note: While the probabilistic nature of quantum theory limits its predictive power, a side benefit is that the study of quantum mechanics has advanced the science of probability and statistics. Mathematicians are just beginning to explore the possibility of adapting methods from quantum mechanics to general statistical modeling, but this is already creating new mathematical tools for statistical analysis.)

3. Quantum Uncertainty Restricts Measurements

We’ve discussed how quantum mechanics limits your ability to predict the future because it’s probabilistic instead of deterministic, but quantum mechanics also limits your ability to measure the present state of the universe because of the uncertainty principle.

As Hawking explains, the uncertainty principle states there is always at least a certain amount of uncertainty in your measurement of the position and velocity of a particle. And uncertainty about the present creates greater uncertainty about the future, because to predict where a particle is likely to go in the future, you need to know where it was at some point in the past or present, and how fast it was going at the time.

To understand how the uncertainty principle works, you need to understand a few things about quantum mechanics. For one thing, as Hawking notes, the basic premise of quantum mechanics is that certain quantities, like energy, are “quantized,” meaning that they can only have certain values, or be incremented by at least a certain minimum value.

(Shortform note: This minimum unit is called a “quantum” of energy, which is where “quantum mechanics” gets its name.)

For another thing, you can only see something if it is reflecting (or otherwise emitting) light. If there’s no light, you won’t be able to see it. But bouncing light off of a subatomic particle will change its velocity. And since energy is quantized, you have to disturb a particle by at least a certain amount to measure it. Thus, there will always be at least a certain amount of uncertainty in your measurement.

Measurement Error Versus Quantum Uncertainty

It is important to distinguish between ordinary measurement uncertainty and quantum uncertainty.

In real life, every measuring device has limited precision. For example, if you measure the length of something with a ruler, your measurement is only as accurate as the marks on the ruler. In general, the better your measuring tools, the less uncertainty there will be in your measurement.

But, the uncertainty principle imposes additional limits on your ability to measure the position and velocity of a particle. So even in the hypothetical case where you had perfect measuring tools, there would still be uncertainty in your measurement, because the light that allows you (or your instruments) to see the particle changes its velocity as you’re trying to measure it.

Question 3: How Did the Universe Begin?

Hawking points out that the origins of the universe have profound philosophical implications. He contrasts the Judeo-Christian belief that God created the universe at some point in the past with the atheistic view that many scientists held in the nineteenth century, namely that the universe was infinite and had always existed.

Hawking recounts that in the twentieth century, new scientific discoveries challenged the theory that the universe had always existed. Based on these discoveries, the “big bang” theory replaced the static universe model. The big bang theory posits that the universe is expanding outward from a point where it came into existence at a finite time in the past.

Let’s take a look at the discoveries that provided evidence for the big bang, and then consider its implications.

Evidence for the Big Bang

The primary piece of evidence that led to the development of the big bang was the discovery that the universe is expanding, which was supported by both theory and observation.

Hawking recounts how, in the 1920s, astronomer Edwin Hubble measured the distance to a number of galaxies and found that they were all moving away from our own. Furthermore, the galaxies that were farther away were moving away faster. This provided direct observational evidence that the universe is expanding.

Hawking also points out that, in hindsight, Hubble’s discovery that the universe is expanding could have been predicted based on general relativity. Einstein recognized this when he first developed the theory of general relativity. But at the time, Hawking explains, the static universe model was so entrenched in the scientific community that Einstein introduced a hypothetical constant into his equations to cancel out the expansion. He called this fudge factor the “cosmological constant.” Hawking recounts that after Hubble’s observations were publicized, Einstein admitted publicly that introducing this hypothetical constant was a mistake.

(Shortform note: Ironically, scientists have recently reintroduced Einstein’s cosmological constant into the theory of general relativity, but with a different value, so that it accelerates the expansion of the universe instead of canceling it out. They’ve done this to explain new observations. Specifically, new measurements indicate that after the big bang, gravity began to slow down the expansion of the universe for a while, but now the expansion rate is speeding up again.)

The Cosmic Microwave Background

As Hawking explains, there was another discovery that helped to establish the big bang theory. Specifically, the big bang theory implies that there was a period of time where the early universe was small, hot, and dense. According to Hawking, physicists calculated that at this stage in its development, the universe would have given off a uniform glow, which should still be detectable in the microwave part of the electromagnetic spectrum.

He also tells how, in the 1960s, astronomers Arno Penzias and Robert Wilson were trying out a very sensitive microwave antenna when they discovered faint, uniform microwave radiation that seemed to come from every direction. This radiation was later dubbed the “cosmic microwave background,” and was exactly what theories predicted the big bang would have produced.

(Shortform note: About the same time that Penzias and Wilson discovered cosmic microwave background radiation, astronomers also discovered a similar background signal in the radio portion of the spectrum. Unlike the microwave background, the radio background is not predicted or explained by the big bang model. Nevertheless, recent measurements have confirmed its existence and revived interest in it. Scientists have not yet determined what causes it.)

Implications of the Big Bang

Hawking had two concerns about the big bang, at least as it was modeled using general relativity.

His first concern was the fine-tuning problem. According to mathematical models, certain physical parameters of the early universe, such as its initial rate of expansion, had to be specified very precisely. If they had been even slightly different, the universe would not have developed in a way that could support human life. To Hawking, this indicated a problem, because it seemed to imply that human life was highly improbable, and yet we observe that human life exists.

His second concern was the singularity. Hawking himself first became famous in the physics community for proving mathematically that, based on the equations of general relativity, the big bang started at a “singularity,” a point where matter, space, and time, are confined to an infinitely small space with infinitely high density. Matter, space, and even time itself came into being at this infinitesimal point, and the universe expanded outward from there. However, reflecting later on his own theoretical proofs, Hawking came to believe that they imply the theory of general relativity is incomplete, not that the universe actually did begin at a singularity. He saw the infinite density of the universe at the singularity as a red flag, because physical quantities are never infinite in real life.

Hawking suggests that a quantum theory of gravity would resolve both his concerns. He expects that it would eliminate the singularity and provide an explanation for the initial parameters of the universe.

(Shortform note: However, a workable theory of quantum gravity has not yet been developed, so Hawking’s expectations have not yet been proven.)

Did Hawking Prove the Existence of God?

Some Christians have used the big bang theory and Hawking’s proof that time had a beginning as an argument for the existence of God and the divine creation of the universe.

Physicists sometimes define time as the dimension in which cause and effect take place, such that causes always come before the effects that they produce. If time itself came into being at some point (an effect), then there must be a cause that exists independent of the space-time of our universe to bring it into existence (cause the effect), because there is no time prior to that for a cause within our universe to trigger the big bang. Anything independent from spacetime would, by definition, be supernatural.

Advocates of this argument also pick up on the fine-tuning of the initial conditions of the universe as evidence that God designed the universe to support human life, rather than seeing the fine-tuning as a problem, as Hawking does.

Question 4: What Is a Black Hole?

Hawking explains that a “black hole” is an object with such strong gravity that its gravity can trap light. And if light can’t escape from a black hole, then nothing can, since general relativity implies that nothing can travel faster than light. He points out that the closer you get to an object, the more its gravity pulls on you. The threshold where light gets trapped forms an imaginary surface around the black hole called the “event horizon.”

(Shortform note: It’s called an “event horizon” because you can’t observe events that happen beyond it. Light from an event has to reach you for you to observe the event, and light that passes inside the event horizon can’t reach you because it can’t escape from the gravity of the black hole.)

Hawking explains that most black holes form from collapsing stars. Normally pressure from nuclear fusion counterbalances a star’s gravity, but if a sufficiently massive star runs out of nuclear fuel, it can undergo runaway gravitational collapse, producing a black hole.

(Shortform note: Nuclear fusion is when the nuclei of two atoms merge to form a new, heavier atomic nucleus. When light atoms like hydrogen and helium combine, this process releases energy. But, for atoms heavier than iron, nuclear fusion actually consumes energy, so a star runs out of energy when all of its lighter elements have been fused into heavier ones.)

Hawking also explains that, although astronomers can’t see black holes, they can observe their effects on stars and other visible objects. He recounts that the first such observation of a black hole was in the Cygnus X-1 system, where a star orbits around an unseen object.

(Shortform note: Since the publication of the book, astronomers have identified many other black holes or likely black-hole candidates.)

Hawking Radiation

Nothing can escape from inside the event horizon of a black hole, but radiation that’s produced just outside the event horizon can escape—and if it originates just outside the event horizon, it would appear to be coming from the black hole itself.

According to Hawking, the theory of quantum mechanics predicts that “empty” space is actually full of short-lived particles, or rather pairs of particles and antiparticles that spontaneously appear, only to recombine and annihilate each other. Normally, these “virtual particles” don’t last long enough to be detected. However, if a photon (particle of light) and an antiphoton appear just outside the event horizon of a black hole, and the antiphoton falls into the black hole, while the photon doesn’t, then the photon doesn’t get annihilated. Thus, Hawking predicts that there should be a net flow of antiphotons into a black hole and photons away from the black hole—meaning the black hole will have a faint glow. This glow is called “Hawking radiation.”

(Shortform note: There are at least two ways to explain Hawking radiation. In the book, Hawking describes this phenomenon in terms of particle-antiparticle pairs, but in his original scientific paper, he used an energy-density approach to calculate the radiation produced near a black hole. Some authors have criticized him for explaining it differently in his book than in the original paper because the quantum energy density approach provides additional insights. In particular, the quantum energy fields allow you to calculate the actual amount and distribution of radiation, and it turns out that Hawking radiation is produced not just on the surface of the event horizon, but in a region around the black hole about fifteen times the size of the event horizon.)

Question 5: Can You Build a Time Machine?

Writers of science fiction have long contemplated the idea of a time machine: a device that allows you to travel forward or backward in time to any point in history or the future. You’re already traveling forward through time, but Hawking thinks it's unlikely that you’ll ever be able to go back. He addresses the possibility of backwards time travel from three different angles: general relativity, quantum mechanics, and wormholes.

Time Travel via Speed

As we discussed in Question 1, the theory of relativity implies that as you approach the speed of light, you’ll move faster through space and slower through time. Hawking points out that, extrapolating this principle, if you could travel faster than the speed of light, you would actually travel backwards in time. However, he also points out that, according to the theory of general relativity, nothing can travel faster than light, so nothing can go backwards in time.

Using Time Dilation for Pseudo-Backwards Time Travel

Hawking shows that relativity doesn’t let you literally go back in time, but he doesn’t explicitly discuss the possibility of going back in time relative to someone else, which is clearly possible based on his early explanation of time dilation.

To illustrate this, imagine that you and your sister have both signed up to emigrate to a new colony on a planet that’s a thousand light-years from earth. The two of you board different starships, and blast off at the same time. Your sister’s ship makes the trip at a speed of 99.99995 percent of the speed of light, while your ship only travels at 99.9992 percent of the speed of light.

From Earth’s perspective, the trip takes about a thousand years for each of you, with your ship arriving just a few days after your sister’s ship does. However, during the trip, your sister ages one year, while you age four years. So, if your sister was two years older than you when you left, she’ll be a year younger than you when you arrive. The effect on your relative age is the same as if you’d gone backward in time three years. So, in a sense, you could say you’ve traveled backwards in time relative to your sister.

Time Travel in Quantum Mechanics

Hawking asserts that, according to the theory of quantum mechanics, it is possible for microscopic particles to travel backwards through time. This is because, in quantum mechanics, a particle moving forward through space and time is mathematically equivalent to its corresponding antiparticle moving in the opposite direction through space and time.

(Shortform note: Hawking doesn’t discuss any practical methods of deliberately converting a particle into an antiparticle, much less intentionally sending a subatomic particle back in time. And the fact that you may be mathematically equivalent to a person made up of antimatter moving backwards through space and time doesn’t really give you a way to move backward in time. Thus, we infer that the practical applications of quantum time travel are quite limited.)

Time Travel via Wormholes

Hawking reports that, according to the theory of general relativity, it’s possible for a bridge to form between warped regions of spacetime, potentially creating an alternate pathway between points in time and space. These hypothetical pathways are called “wormholes.” According to Hawking, wormholes might be your best bet for traveling back in time, because, hypothetically, you could travel forward in time as you go through the wormhole, but arrive at a point in the past when you come out the other end.

However, he cautions that this possibility is still quite remote, for two reasons:

1. Hawking asserts that wormholes are extremely unstable. If any mass (such as a person or a vehicle) entered the wormhole, its gravity would affect the curvature of spacetime enough to cause the wormhole to collapse.

(Shortform note: There are ongoing hypothetical studies of wormhole stability. Recently, one team showed that, in their model, it would be possible for tiny particles like photons and electrons to pass through a microscopic wormhole without causing it to collapse.)

2. Hawking explains that wormholes require spacetime to have concave curvature. The presence of a massive body causes convex curvature of space, resulting in gravity, but scientists have never observed concave curvature of space. So, in practice, it may not be possible to create a wormhole in the first place.

(Shortform note: Hawking doesn’t explain why wormholes require spacetime to be concave, but we infer that it’s just a matter of geometry. Think of a physical tunnel. The walls have to be concave for there to be space inside the tunnel. Presumably it works the same with wormholes, except that spacetime itself is curved.)