A Brief History of Time

A Brief History of Time

Book Author

Published

September 1998
Pages

213
Greek Publisher

Κάτοπτρο
Category Tags , , , ,

From the Big Bang to Black Holes

What’s it about?

A Brief History of Time (1988) takes a look at both the history of scientific theory and the ideas that form our understanding of the universe today. From big bangs and black holes to the smallest particles in the universe, Hawking offers a clear overview of both the history of the universe and the complex science behind it, all presented in a way that even readers who are being introduced to these ideas for the first time will understand.

About the author

Stephen Hawking, PhD, (1942-2018) was a theoretical physicist, cosmologist and author best known for his work exploring Hawking radiation and Penrose-Hawking theorems. Serving as the Lucasian Professor of Mathematics at the University of Cambridge between 1979 and 2009, Hawking was the recipient of the Presidential Medal of Freedom, an Honorary Fellow at the Royal Society of Arts, and a lifetime member of the Pontifical Academy of Sciences.

Basic Key Ideas

It’s hard to imagine a more arresting and thought-provoking sight than a starry night sky. Something about the twinkle of the cosmos compels us to pause and ponder the deepest mysteries of the universe.

A Brief History of Time will help illuminate these secrets by unlocking the laws which govern the universe. Written in accessible language, it will help even the non-scientifically minded to understand why the universe exists, how it started and what it will look like in the future.

You will also find out about strange phenomena; like black holes which suck everything (well, almost everything) toward them. What’s more, you’ll also discover the secrets of time itself; as these blinks provide the answers to questions like “how fast is time going?” and “how do we know it’s going forwards?”

It’s safe to say that after these blinks, you’ll never view the night sky in quite the same way again.

You’ve probably heard of the theory of gravity or the theory of relativity? But have you ever paused to think what we really mean when we talk about theories?

A theory, in its most basic terms, is a model that accurately explains large groups of observations. Scientists collect data from observations they see in, for example, experiments, and use it to develop explanations of how and why phenomena happen.

For example, Isaac Newton developed the theory of gravity after observing many phenomena, from apples falling from trees to the movements of planets. Using the data he collected he was able to describe gravity in a theory.

Theories have two great benefits:

First, they allow scientists to make definite predictions about future events.

For example, Newton’s theory of gravity allowed scientists to predict the future movements of objects like planets. If you want to know, say, where Mars will be six months from now, it’s possible to predict this precisely using the theory of gravity.  

Second, theories are always disprovable, meaning they’re open to reform if new evidence that doesn’t fit the theory is found.

For example, people once believed in the theory that everything in the universe revolved around the Earth. Galileo disproved this theory when he noticed moons orbit Jupiter; he could therefore show that actually not everything orbit the Earth.

So in effect, a single future observation can always invalidate a theory, no matter how reliable it seems at the moment. This means theories can never be proven correct, and this makes science a constantly evolving process.

Before Isaac Newton, people thought an object’s natural state was at absolute rest. This means that if no force was acting on it, then the object would remain completely still.

In the 1600s, Newton thoroughly disproved this long-held belief. In its place, he introduced a theory which stated that all objects in the universe, instead of being still, were in fact in constant motion.

Newton determined this through his discovery that the planets and stars in the universe were constantly moving in relation to each other. For example, the Earth is constantly orbiting the Sun and the entire solar system is rotating around the galaxy. Therefore, nothing is ever still.

To describe how all objects in the universe move, Newton developed three laws:

The first of Newton’s laws states that all objects will continue moving in a straight line if not acted on by another force. This was demonstrated in an experiment by Galileo in which he rolled balls down a slope. As gravity was the only force acting on the balls, they rolled in a straight line.

Newton’s second law states that an object will speed up at a rate proportional to the force acting on it. For example, a car with a more powerful engine will accelerate faster than one with a less powerful engine. This law also states that the greater the body’s mass, the less a force affects its motion. For example, if there are two cars with the same engine, the heavier car will take longer to accelerate.

Newton’s third law describes gravity. It states that all bodies in the universe attract other bodies with a force proportional to the mass of each object. This means that if you double the mass of one object, the force will be twice as great. If you double one object’s mass and triple the other, the force will be six times as great.

We have seen how Newton’s theory did away with absolute rest and replaced it with the idea that the movement of an object is relative to the movement of something else. Yet, the theory also suggested the speed of an object is relative.

For example, imagine you are reading a book while sitting on a train travelling at 100 mph. How fast are you travelling? Well, to a bystander watching the train speed past, you are travelling at 100 mph. But relative to the book you are reading, your speed is zero mph. So your speed is relative to another object.

Yet, one major hole developed in Newton’s theory: the speed of light.

The speed of light is constant, not relative. It is always 186,000 miles per second. It doesn’t matter how fast something else is going, the speed of light remains the same.

For example, if that train were speeding towards a beam of light at 100 mph, the speed of light would be 186,000 miles per second. Yet if that train stopped at a red signal, the beam of light would still be 186,000 miles per second. It doesn’t matter who is viewing the light or how quickly they are traveling, its speed will always be the same. 

This fact causes problems for Newton’s theory. How can the speed of something be constant regardless of the state of the observer?

The answer was discovered in the early twentieth century when Albert Einstein postulated his theory of relativity.

The speed of light being constant was problematic for Newton’s theory, because it proved that speed wasn’t always relative. Therefore, scientists needed an updated model that took the speed of light into account.

Albert Einstein developed such a theory, the theory of relativity.

The theory of relativity states that the laws of science are the same for all freely moving observers. This means that no matter what someone’s speed might be, they would observe the same speed of light.

This might seem quite straightforward at first glance, but one of its central suggestions is actually very difficult for many to comprehend; it states that time is relative.

What this means is that because the speed of light doesn’t change for observers moving at different speeds, observers traveling relative to one another would actually measure different times for the same event.

For example, say a flash of light is sent out to two observers: one is travelling toward the light while the other is traveling at a quicker speed in the opposite direction. For both observers, the speed of the light would be the same, even though they are traveling at relatively different speeds and going in different directions.

Unbelievably, this would mean that they each experience the flash event as if it happened at two different times. This is because time is determined by the distance something has traveled divided by its speed. The speed of light is the same for both observers, but as the distance is different, time is relative to each observer.

If both observers carried clocks to record when the pulse of light was emitted, these would confirm two different times for the same event.

So who’s right? Neither observer; time is relative and unique to both observers’ perspectives!

All matter is made up of particles such as electrons or photons. In order to learn more about the universe, scientists want to measure them and study their speed.

However, particles do something very strange when you try to study them. Bizarrely, the more precisely you try to measure the position of a particle, the more uncertain its speed becomes; and the more exactly its speed is measured, the less certain its position becomes! This phenomenon, first discovered in the 1920s, is called the uncertainty principle.

Because of the uncertainty principle, scientists had to use other ways of looking at particles, so they began to look at a particle’s quantum state instead. Quantum state combines many likely possible positions and speeds of a particle.

Since scientists cannot pinpoint a particle’s definite position or velocity, they look at the many likely positions particles might occupy and velocities they might have. As a particle moves about, scientists track all the likely places it could be and determine which of these is the most likely.

To help them determine this, scientists treat particles as if they are waves.

The multitude of different positions that a particle can be in means that they appear like a series of continuous, oscillating waves. Imagine a piece of vibrating string. When it vibrates, the string will arc and dip through peaks and troughs. A particle also behaves like this, although its possible path is a series of such overlapping waves, all happening at once.

Looking at particles like this helps scientists figure out where a particle is most likely to be. The likeliest positions of the particle occur where the arcs and dips on the many waves correspond with each other, and the least likely positions are where they don’t. This is called interference, and it shows which positions and speeds are most probable for the particle wave’s path.

When you view the world around you, you are seeing it in three dimensions, i.e., you can describe any object by its height, width and depth. Yet there is also a fourth dimension, although we ourselves cannot see it: it is time, and it combines with the other three dimensions to form something called space-time.

Scientists use this four-dimensional model of space-time to describe events in the universe. An event is something that occurs at a particular position in space and time. So when calculating an event’s position along with the three-dimensional coordinates, scientists add a fourth coordinate to indicate time.

Scientists have to take time into consideration when determining the position of an event because the theory of relativity states that time is relative. It is therefore an important factor in describing the nature of an event.

An amazing consequence of the combination of space and time is how it changed our conception of gravity.

Gravity is the result of massive objects curving space-time. A huge mass, like that of our sun, curves and actually alters space-time. Think of it like this: Imagine space-time to be a blanket stretched out and held in the air. If you place an object in the middle of the blanket, the blanket will curve and the object will sink a little. This is what massive objects do to space-time.

Other objects then follow these curves in space-time. This is because an object always takes the shortest journey between two points, which is a circular orbit around a larger object. You can see this if you look at that blanket again. If you put a large object like an orange on the blanket and then try to roll a smaller one – say, a marble – past it, the marble will follow the indentation made by the orange. Gravity works in the same way!

During their lifetimes, stars need enormous amounts of energy to produce heat and light. Yet, this energy doesn’t last forever; eventually it runs out, leaving the star to die.

What happens to a star when it dies depends on its size. When a very large star runs out of energy, something spectacular is created: a black hole.

A black hole occurs because the gravitational field of most massive stars is so strong. While the star is alive, it is able to use its energy to keep itself from collapsing. But when the star runs out of energy, it can no longer overcome the gravity and its decaying body collapses in on itself. Everything is pulled inwards toward an infinitely dense, spherical point called a singularity.

This singularity is the black hole.

When a black hole forms, space-time is curved so steeply by its gravity that even light bends along it.

Not only does a black hole pull in everything nearby, it also prevents anything that crosses a certain boundary around it from escaping again: this point of no return is called the event horizon, and not even light, which travels faster than anything else in the universe, can escape back over it.

This raises a question: if a black hole absorbs light and anything else that crosses its event horizon, how can we know they are there?

Scientists search for black holes by looking for their gravitational effect on the universe and for the X-rays produced by their interaction with orbiting stars.

For example, scientists look for stars orbiting dark and massive objects that could be black holes.

They also look for the X-rays and other waves that are commonly produced by matter when it is being sucked in and torn up by a black hole. There is even a source of radio and infrared waves at the center of our galaxy that could be a supermassive black hole.

If the gravitational pull of a black hole is so strong that not even light can escape it, then you’d think nothing else could escape either.

But you’d be wrong. In fact, black holes must release something; otherwise they’d break the second law of thermodynamics.

The universal second law of thermodynamics states that entropy, the tendency toward greater disorder, always increases. And as entropy increases, so must temperature. An example of this is the way a fire-poker, after being in a fire, glows red-hot and releases radiation as heat.

According to the second law, since black holes suck in disordered energy from the universe, the entropy of the black hole should also increase. And with this increase in entropy, black holes should have to let heat escape.

The escape of heat is possible because, although nothing that has passed a black hole’s event horizon can escape, virtual pairs of particles and antiparticles near the event horizon conserve the second law of thermodynamics. Virtual particles are particles that cannot be detected but whose effects can be measured. One of the partners in the pair has positive energy and the other has negative energy.

In a black hole, gravitation is so strong it can suck the negative particle into the black hole and in doing so give its particle partner enough energy to possibly escape into the universe and be emitted as heat. This allows the black hole to emit radiation, and thus follow the second law of thermodynamics.

The amount of positive radiation emitted is balanced by the negative particles being sucked into the black hole. This inward flow of negative particles can reduce the black hole’s mass until eventually it evaporates and dies. And if its mass becomes small enough, the black hole will most likely end in a massive final explosion, as large as millions of H-bombs.

Imagine a scenario where the universe began to contract and time started running backward. What would that be like? Perhaps clocks would run backward and the course of history would reverse. Scientists haven’t completely ruled it out, but there are three strong indicators that suggest time only moves forward.

The first indicator showing that the passage of time goes from past to future is the thermodynamic arrow of time. According to the second law of thermodynamics, entropy – the disorder of a closed system – tends to increase with time. This means that time can be measured by the tendency of disorder to increase.

For example, if a cup rolls off a table and breaks, it has become less ordered, and its entropy has increased. Since a broken cup would never spontaneously reassemble and increase its order, we see that time is only going forward.

The broken cup and the thermodynamic arrow of time are also aspects of the second indicator of forward time: the psychological arrow of time, which is dictated by memory. After that cup has broken, you can remember it being on the table; but before this, when it was still on the table, you can’t “recall” it’s future position on the floor.

The third indicator, the cosmological arrow of time, refers to the expansion of the universe, and this also follows along our perception of the thermodynamic arrow of time. This is because as the universe expands, entropy increases.

If the disorder in the universe were to reach its maximum point then the universe could start contracting, reversing the cosmological arrow of time. However, we wouldn’t know about it because intelligent beings can only exist as disorder increases. This is because we rely on the process of entropy to break down our food into energy.

Therefore, as long as we’re around, we will observe the cosmological arrow of time as going forward.

What kinds of forces are at work in the universe?

Most people will have heard about only one: gravity, the force that attracts objects to one another and which is experienced in the way that Earth’s gravity pulls us to its surface.

However, most people are unaware that there are actually three additional forces that act on the smallest particles.

The first is electromagnetic force, which can be observed in everyday life when a magnet sticks to a refrigerator or when you recharge your cell phone. It acts on all particles with electric charges, such as electrons and quarks.

Electromagnetic force, like the north and south poles on a magnet, can be attractive or repulsive: positively charged particles attract negative particles and push away other positive particles, and vice versa. This force is much stronger than gravity and dominates at the small level of the atom. For example, electromagnetic force causes an electron to orbit around the atom’s nucleus.

The second is weak nuclear force, which acts on all the particles that make up matter and which causes radioactivity. This force is called “weak” because the particles that carry it can only exert force at short distances.

At higher energies, the strength of weak nuclear force increases until it matches that of electromagnetic force.

The third is strong nuclear force, which binds protons and neutrons in the nucleus of an atom, and binds the smaller quarks within protons and neutrons. In contrast to electromagnetic force and weak nuclear force, strong nuclear force gets weaker at higher energies.

At a very high energy called grand unification energy, electromagnetic force and weak nuclear force get stronger and strong nuclear force gets weaker. At that point, all three forces reach equal strength and become different aspects of a single force: a force that might have played a role in the creation the universe.

Most scientists believe that time began with the big bang – the moment when the universe went from an infinitely dense state to a rapidly expanding entity which is still growing today.

Scientists, however, don’t exactly know how this big bang occurred, although a number of theories have been proposed to explain how this huge expansion might have happened.

The most widely accepted theory of the universe’s beginning is the hot big bang model.

In this model, the universe started with zero size and was infinitely hot and dense. During the big bang, it expanded, and as it grew its temperature cooled as its heat was spread. In the first few hours of this expansion, most of the elements in the universe today were created.

As the universe continued to expand, gravity caused denser regions of the expanding matter to start rotating, creating galaxies. Within these newly forming galaxies, clouds of hydrogen and helium gases collapsed. Their colliding atoms caused nuclear fusion reactions, which created stars.

When these stars later died and collapsed, they created huge stellar explosions that ejected more elements into the universe. This provided the material for the birth of new stars and planets.

Although this is the generally accepted version of the big bang and the birth of time, its not the only model.

Another model is the inflationary model. This model proposes that the energy of the early universe was so enormously high that the strengths of the strong nuclear force, weak nuclear force and electromagnetic force were equal.

As the universe expanded, however, the three forces took on different strengths very quickly. As the forces split, an enormous amount of energy was released. This would have had an anti-gravitational effect, causing the universe to expand rapidly, and at an increasing rate.

In their desire to understand and describe the universe, scientists have developed two major theories. The first is general relativity, which concentrates on a very large phenomenon in the universe: gravity. The second is quantum physics, which describes some of the smallest known objects in the universe: particles smaller than atoms.

While both theories provide great insights, there are big differences in what is predicted with the equations of quantum physics, and what is predicted and observed with general relativity. This means that currently there is no way of combining them together to make one complete unified theory of everything.

One issue that prevents the two theories being brought together is that many of the equations scientists use in quantum physics result in seemingly impossible infinite values. For example, according to the equations, the curve of space-time would be infinite, something observations have shown to be false.

To cancel out these infinities, scientists try to introduce other infinities into the equation. Unfortunately, this keeps scientists from being able to predict accurately. As a result, instead of using the equations from quantum physics to predict events, the events themselves have to be added and the equations tweaked to make them fit!

A second, similar problem is that quantum theory suggests that all the empty space in the universe is made up of virtual pairs of particles and antiparticles.

However, the existence of these virtual pairs causes difficulties for general relativity.

Since there is an infinite amount of empty space in the universe, the energy of these pairs would have to have infinite energy.

This is problematic because Einstein’s famous equation E=mc2 suggests that the mass of an object is equal to its energy. So the infinite energy of these virtual particles would mean that they would also have infinite mass. And if there were infinite mass, then the whole universe would collapse under the intense gravitational pull and become a single black hole.

The main message in these blinks:

Many people are put off physics because they see it as an impenetrable  world of lengthy equations and complex theories. And, to a certain extent, this is true. But the complexity of physics shouldn’t stop us non-experts from learning how and why the universe works.

There are a number of rules and laws that help us understand the mysteries of the universe around us. Rules and laws that most of us can comprehend. And once we understand them, we can begin to see the universe in a new light.

SECOND REVIEW FROM SHORTFORM

About Book

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.

1-Page Summary

Science has profound implications for philosophy and everyday life because science describes and predicts how the universe works. To make the discoveries and implications of modern science more accessible to everyone, renowned physicist Stephen Hawking described the principles of modern physics for a general audience in A Brief History of Time.

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?

Question 1: Is Reality Relative or Absolute?

Science is founded on the assumption that reality works the same for everyone: If two scientists conduct exactly the same experiment, they should get the same results. Ironically, this principle has driven scientists to the conclusion that many things—including motion, position, time, and weight—are relative to the observer.

Motion Is Relative

Hawking explains that motion is relative to the observer, because there is no absolute reference frame.

To illustrate this concept, imagine you’re sitting in a boat on a body of water. Looking into the water, you see a fish swim by. Relative to your frame of reference, the fish is moving at a certain speed. But an observer on land might disagree. Let’s say the body of water is a river, and the fish is holding a constant position, relative to the river bottom, while your boat drifts by. So is the fish moving or staying in the same place? In an absolute sense, we can’t tell. Relative to your boat, the fish is moving. Relative to the earth, the fish is stationary. But of course the earth is also moving, relative to the sun, so the fish is moving relative to the sun. And the sun is moving, relative to the galaxy, and so on.

(Shortform note: One familiar scenario where the relativity of speed becomes important is driving a car. To avoid collisions, you have to keep track of the motion of other cars relative to your own. You also have to keep track of your speed relative to the road, since posted speed limits are implicitly specified relative to the road. To maintain a constant following distance behind another car, you have to adjust your speed to be zero relative to the other car.)

Time Is Relative

In the same way that the motion of objects is relative to the observer, Hawking argues that different observers may measure time differently. Hawking explains that, in particular, time appears to slow down for entities that are moving very fast. This is because of the relationship between time, speed, and distance, and the fact that everyone who accurately measures the speed of light gets the same result. He notes that this is true regardless of their particular reference frame, because the laws of physics are consistent for all observers.

(Shortform note: When Hawking refers to “the speed of light,” technically he’s referring to the speed of light in a vacuum. Light slows down slightly when it travels through materials like water or glass. This is what causes refraction of light, where the change in speed at the boundary between two materials causes the light to bend.)

For example, imagine two kids playing laser tag on a starship that is traveling at the speed of light. As they fire pulses of light back and forth, from opposite sides of the ship, an observer on the ship measures the distance that the light travels and finds it equal to the width of the ship. But if you’re outside the ship, you would see the light traveling a greater distance. Specifically, the distance would be the hypotenuse of a right triangle, with one leg equal to the width of the ship, and the other equal to the distance the ship traveled while the light was moving across it. Since you perceive the light traveling a greater distance (at the same speed) than the people on the starship, you must also perceive more time elapsing during the event than they do.

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Relativity

When time progresses at a different rate for one person than another, scientists call this “time dilation.” As Hawking points out, Albert Einstein developed his theories of relativity as a mathematical model for predicting the motion of objects, even at speeds where time dilation becomes significant. (Earlier theories of motion didn’t account for time dilation.)

As Hawking recounts, Einstein introduced his theory of relativity in two phases: first, special relativity and then general relativity. Let’s discuss each of these theories in turn.

(Shortform note: “Special relativity” is “special” because it only works in situations where there is no gravity or acceleration. Physics problems with no gravity or acceleration are simpler, and constitute a “special case,” where a relatively simple theory of relativity can be applied.)

As Hawking recounts, when Einstein developed his theory of special relativity he ignored gravity and acceleration to make the mathematical derivation simpler. This allowed him to publish his theory quickly and gain support for it. Then he developed his theory of general relativity as a more generalized version of the theory, which could account for gravity and acceleration as well.

Hawking notes that the key idea that allowed Einstein to complete the theory of general relativity was his realization that gravity could be viewed as the curvature of space itself. In other words, general relativity is based on the principle that mass actually causes space to warp, such that the shortest distance between two points is an arc segment, rather than a straight line.

Testing General Relativity

Initially, Einstein’s theory of general relativity was somewhat controversial, and so it was subjected to even more testing than most theories. So far, the test results support the theory.

Since general relativity is a theory of motion and gravity, most tests of the theory involve using it to predict the motion of astronomical bodies like planets, stars, and black holes (we’ll discuss black holes more in Question 5), and comparing these predictions with observations.

The first widely-publicized test of general relativity came in 1915, when Einstein used his theory to predict the orbit of the planet Mercury. He predicted that the orbit would be slightly different from what Newtonian Mechanics predicted—and he was right.

More recently, general relativity has been tested using LIGO, the Laser Interferometer Gravitational Observatory, which detects gravity waves. General relativity predicts that since gravity is the curvature of space, massive objects moving through space should create ripples in spacetime. These ripples are called gravity waves. The heavier the objects and the faster they move, the more gravity waves they produce. Researchers at LIGO have observed gravity waves from colliding black holes and have found them to be consistent with what general relativity predicts.

Mass Is Relative

We’ve discussed how time is relative to speed (if you’re moving very fast, relative to someone else, you perceive less time passing than they do), and we’ve discussed how Einstein developed his theories of relativity to model this phenomenon. As Hawking explains, it turns out that the theories of relativity also imply that mass is relative to speed and time is relative to gravity. Specifically, Hawking explains that, as an object accelerates to speeds closer and closer to the speed of light, its mass increases, such that it can never actually reach the speed of light.

Alternative Explanation

Experimental data from particle accelerators conclusively demonstrates that, as the speed of a particle increases, the energy required to further increase its speed also increases, just as the theory of relativity predicts.

However, some scientists have argued that this is not because the mass of the particle increases. Instead, it’s because the forces used to accelerate the particle (typically electromagnetic forces) travel at the speed of light, and so the force they apply to the particle decreases as its speed approaches their own speed.

To illustrate this principle, imagine a sailboat. When you first hoist the sails and catch the wind, the force of the wind against the sails is strong, and the boat accelerates. However, as the speed of the boat starts to approach the speed of the wind, the wind no longer pushes on the sails as hard, and the acceleration of the boat tapers off. If the sailboat could go the same speed as the wind, then the wind would no longer apply any force to the sails.

Question 2: Is the Future Predetermined?

As we have seen, scientific theories allow us to model the behavior of objects and predict their behavior. Hawking points out that if you could formulate a unified theory of physics and if you knew the exact state of the entire universe at any point in time, you could use that theory to predict the state of the universe at any other time.

This would make human free will an illusion, since you could calculate everyone’s future actions. Hawking refers to this as “scientific determinism.” However, he also discusses three limitations of scientific determinism:

1. There Is No Unifying Theory (Yet)

Hawking asserts that the ultimate goal of science is to develop a “unifying theory” that can be applied in any context. Scientists have made progress towards this goal, but have not yet achieved it. Instead, scientists currently use two major theories: general relativity and quantum mechanics.

Hawking points out that general relativity works well for modeling the motion of stars and other macroscopic objects (objects big enough to see without a microscope), but relativity does not accurately model the behavior of subatomic particles. Instead, subatomic particles exhibit a variety of behaviors that can only be modeled using quantum mechanics.

As Hawking explains, quantum mechanics accurately models subatomic particles, but quantum mechanics doesn’t allow for modeling gravitational interactions or macroscopic objects. This is because the mass of subatomic particles is too small for scientists to measure their gravitational interactions. And you can’t simply add more particles to make them easier to measure, because, according to Hawking, the calculations quickly become prohibitively complex as the number of particles increases.

(Shortform note: Astrophysicist Paul Sutter offers a slightly different explanation for the incompatibility of quantum mechanics and gravity. He explains that, when calculating particle interactions in quantum mechanics, scientists assume that space is Euclidean (not curved) and is not affected by the particles. But general relativity assumes that the presence of mass causes space to warp, creating gravity. If you try to incorporate curved space into quantum mechanics, that adds a whole new dimension of complexity, making the math problem insoluble.)

Is Thermodynamics the Unifying Theory?

Hawking asserts that no one has yet come up with a complete theory that incorporates both quantum mechanics and general relativity. However, in 2011, Pharis E. Williams published a book on “Dynamic Theory,” which allegedly provides a simple yet powerful way to unify quantum mechanics and general relativity.

The essence of Williams’s approach was to generalize the first and second laws of thermodynamics in five dimensions: three dimensions of space, one of time, and one of mass. Williams shows how, if you make certain simplifying assumptions, this set of equations reduces to the equations of quantum mechanics, while if you make different simplifying assumptions, they reduce to the equations of general relativity. If you don’t assume either special case and keep all the terms in Williams’s model, then it appears to provide a unifying theory that’s universally applicable. However, Williams’s theory has yet to be rigorously tested.

2. Quantum Mechanics Is Not Deterministic

Hawking explains that quantum mechanics imposes another limitation of scientific determinism because solutions to quantum mechanics problems are probabilistic, not deterministic. In other words, if you model the motion of a particle with quantum mechanics, you get a probability map, showing you where the particle is most likely to go, and where it is less likely to go.

(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.)

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