A Brief History Of Time

The chapter opens with an anecdote of a woman at the lecture of a famous astronomer. She defiantly tells the astronomer that the world is a flat disc carried on the back of a giant turtle and the universe is “turtles all the way down” (1), referencing an ancient myth. Hawking posits how and why a person would now know that this idea is rather silly.

Ancient Greek philosopher Aristotle provided two clear indications that the Earth is round: 1) because its shadow on the full moon during an eclipse is round and 2) because the North Star gets lower in the sky as a person moves south. Greek mariners offered more evidence: They observed that the sails of approaching ships became visible before their hulls. Aristotle believed the Earth was at the center of the universe, and the sun and stars rotated around it. Figure 1.1 (4) illustrates Ptolemy’s model of the universe with the Earth at the center of a set of transparent, concentric spheres, one for each planet and the sun. The outermost sphere contains the stars. Though Ptolemy knew his model was flawed, it was widely accepted and considered compatible with Christian scripture, since the model allowed for the existence of heaven and hell beyond the observable universe.

In 1514, Polish priest and mathematician Nicholas Copernicus proposed a simpler model: Earth and other planets revolve around the sun. However, this model was not taken seriously until nearly a century later, when Italian astronomer Galileo Galilei and German astronomer Johannes Kepler began to support the theory. In 1609, Galileo, using the newly invented telescope, showed that Jupiter had its own orbiting moons, proving the Copernican theory was feasible. Meanwhile, Kepler proved that planetary orbits weren’t circular but elliptical, which corrected the predicted orbits of Copernicus’s theory. Kepler found this disappointing since his theory of planetary motion involved magnetic forces, which necessitate perfectly circular orbits.

In 1687, English polymath Sir Isaac Newton published his Philosophiae Naturalis Principia Mathematica, which Hawking calls “probably the most important single work ever published in the physical sciences” (6). Newton explained elliptical orbits with his theory of gravity, which states that large bodies exert more gravity than small bodies, and close bodies have a stronger pull than faraway ones. This theory made Ptolemy’s celestial sphere model obsolete, introducing the idea of an infinite universe in motion. Because Newton’s theory did not allow for stationary bodies, it was determined that the stars must be distant bodies in motion. Newton believed the universe must be infinite with an infinite number of stars so that there is no central point for the stars to be gravitationally pulled toward. Hawking points out that Newton’s concept of an infinite universe is a common pitfall, and scientists now understand that an infinite, static universe would be impossible. Though it came to be accepted that the universe was not static, there was more effort put into adjusting Newton’s theories than replacing them.  

In 1823, Heinrich Olbers published his arguments for a universe in motion. Olbers pointed out that if the universe were infinite and static, then no matter which direction one looked, there would be an infinite collection of stars, and with that infinite collection of stars would be an infinite collection of light leading to a night sky as bright as the day. Olbers suggested that matter between the stars must absorb this light energy to keep it from brightening the sky. However, if this were the case then the matter absorbing that energy would also heat up and radiate light as well. Therefore, the only thing that could keep the night sky dark was if the stars were not all “turned on” at the same time and therefore their light did not all reach the Earth at the same time. The problem now was figuring out why or how the stars would be “turned on.”        

Before the 20th century, it was widely accepted either that the universe always existed and will continue in perpetuity or that there was a creation event that produced the universe as it exists today. The contemplation of the origins of the universe was traditionally left to philosophers, who tended to believe the former, and the holy men, who tended to believe the latter.

Edwin Hubble’s 1929 discovery that faraway galaxies are receding from Earth’s solar system indicated that the universe is expanding. Logically this means that at some point everything in the universe was closer together. Scientists estimate that about 10 to 20 thousand million years ago, everything in the universe must have been at the same place in one infinitely dense and infinitesimally small mass. This mass exploded outward in the Big Bang, setting the universe into its observable motions. The laws of physics began at that moment, and what happened before this event is observationally irrelevant, since time and space were created at the moment of the Big Bang. Hawking notes that “[a]n expanding universe does not preclude a creator, but it does place limits on when he might have carried out his job!” (11).

Scientific theories must fit the available data and make predictions about new data. Often, a theory is not wholly new but rather a new take on a flawed but promising older theory. For example, Newton’s theory of gravity predicts planetary motions but makes slight errors in the motion of Mercury. Einstein’s theory of relativity matches Mercury’s motion, an important aspect that helped to confirm the new theory. However, the difference is very small when contemplating things as large as the universe, so Newton’s simpler theory usually works just fine and is still used in most situations.

Hawking explains that the ultimate goal of physical science is to understand a single theory that describes and explains the entire universe. Most scientists separate this goal into two primary objectives. One objective is to explain the universe’s present and predict the universe’s future. The second objective is to explain the initial state of the universe. Most science focuses on smaller parts of the whole to come up with accurate partial theories that could then fit together into a larger theory.

Two universally accepted partial theories explaining the universe exist, and Hawking calls them the “great intellectual achievements of the first half of [the 20th] century” (11). However, the two theories are not consistent when compared to one another so they can’t both be accurate. The general theory of relativity describes the large-scale aspects of the universe, such as gravity, planets, and huge distances. Quantum mechanics describes the small-scale aspects of the universe, such as atoms and sub-atomic particles. The primary goal of physics is to find a theory that will combine the two theories into a single unified theory: the quantum theory of gravity.

Hawking concedes that the pursuit of a unified theory may seem unnecessary. After all, through these partial theories scientists have developed nuclear power and microelectronics, and having a unified theory may not make much difference in the survival of humankind. However, he argues that “[h]umanity’s deepest desire for knowledge is justification enough for our continuing quest” (13).

Before Galileo and Newton, most scientists understood the laws of motion in the universe through Aristotle’s lens. Aristotle declared that bodies at rest tend to stay at rest unless acted upon by a force, and that heavier objects fall to the ground faster than lighter ones. He believed the laws of the universe could be figured out with pure reason and that observation is not necessary. Galileo contradicted Aristotelian tradition by finding that bodies in motion stay in motion unless acted on, and that large balls roll downhill at the same rate as small balls, indicating that objects fall at the same rate regardless of their size. Some objects appear to fall slower than others—like a feather versus a lead weight—because of the effect of air resistance, another force acting opposite to gravity. Much later, an astronaut on the moon confirmed Galileo’s observations by dropping a piece of iron and a feather. Because there’s no air on the moon to slow the feather, it hit the ground at the same time as the iron. Galileo’s discoveries changed physics and proved effective science depends on experiments as well as reason.

Newton expanded on Galileo’s work in his laws of motion. Newton’s first law of motion states that a body at rest will remain at rest and a body in motion will stay in motion, maintaining a straight line unless acted on by a force. Newton’s second law illustrates what happens when a force does act on a body, which is that the body will either accelerate or slow down at a rate proportional to the force enacted upon it. The change in motion will depend on the mass of the body as well as the strength of the force. Hawking provides the classic example of a car and its engine: “The more powerful the engine, the greater the acceleration, but the heavier the car the smaller the acceleration for the same engine” (18).

Newton developed laws to define gravity. Each body attracts other bodies with a force (gravity) proportionate to its mass. If the mass of one object is increased or decreased, then the force of gravity it exerts on another body will also increase or decrease proportionately. This helps make sense of why objects of different weights fall at the same rate—though the pull of gravity may be greater on heavier objects, it also requires more force to set heavier objects into motion, canceling out the additional pull of gravity. Gravity also gets weaker with distance. If two objects become twice as far apart, then they will exert one-fourth of their previous gravitational force on each other. This explains the shape and consistency of planetary orbits and why planets do not fall into one another or spiral out into space.

Aristotle believed in a state of absolute rest that a body would exist in if no force acted upon it, but Newton’s laws indicate that there is no absolute rest, since an object can always be considered as in motion in relation to another object. In other words, one could equally say that a train is at rest while the Earth rotates under it as one could say the train is traveling around the Earth. From the perspective of someone bouncing a ball on the train, it appears that the ball hits the same place on the floor twice, but from the perspective of someone outside the train, the ball would appear to have hit the ground at two different spots a few yards apart. These two perspectives indicate that there is no way to give an absolute position in space, and therefore there is no body at absolute rest. This idea was troubling for Newton because of his strong faith in an absolute God, and he refused to believe what his laws indicated.

Newton did believe that the time between two events could be measured objectively and that all observers from all perspectives would record the same amount of time passing. This idea turned out to be inaccurate and needed to be altered, especially at velocities near the speed of light. In 1676, Danish astronomer Ole Christensen Roemer showed that Jupiter’s moons disappeared behind the planet at different times depending on whether the Earth was closer to Jupiter or farther away in its orbit. Roemer reasoned that light takes time to get from one place to another, and he reckoned its speed at 140,000 miles a second. Though this was later corrected to 186,000 miles a second, Hawking finds Roemer’s calculations impressive since they were made over a decade before Newton’s seminal publication.

Nearly 200 years later, James Clerk Maxwell unified the existing partial theories of electricity and magnetism to establish the electromagnetic spectrum, which includes the spectrum of visible light. The electromagnetic spectrum is divided up by wave frequency, which is measured from the peak of one particle wave to the peak of the next. Radio waves are about a meter apart while microwaves are a few centimeters apart, and the distance between waves of visible light is measured in millionths of a centimeter. X-rays and gamma rays are even shorter.

Since Newton established that there is no absolute rest, but Maxwell’s theory predicted that light traveled at specific speeds, there needed to be something against which light’s movement could be compared. Scientists hypothesized that light makes waves in a mysterious material they called the ether. They expected that light would travel faster if a viewer were traveling toward the light source and slower if the observer were moving away from it. In 1887, Albert Michelson and Edward Morley compared the speed of light in the direction of Earth’s rotation to the speed of light perpendicular (at right angles) to the Earth’s rotation. They proved that light approaches every observer at the same speed. Several attempts were made to explain why, but in 1905, Albert Einstein demonstrated that there’s no need for an ether if one accepts that absolute time does not exist and that time warps at high speeds. This warping makes light travel at the same speed no matter who measures it or from where. Thus, the laws of physics behave the same for all observers at all speeds, but their sense of time shifts.

Einstein’s theory is called the theory of relativity, and the fundamental hypothesis is that all the laws of physics should remain consistent for all observers regardless of their rate of movement. This idea unified Newton’s laws with Maxwell’s theory and Michelson and Morley’s observations on the speed of light. Though fairly simple, Einstein’s work had profound consequences for the field of physics. Relativity shows that mass and energy are equivalent, which is shown in the famous equation of E=mc^2, which means the energy of an object in motion adds to its mass, so the faster an object moves, the more energy is required, which makes acceleration increasingly difficult as the object moves faster. Hawking describes how an object traveling at 10% of the speed of light would increase in mass by 0.5%, while an object traveling at 90% of the speed of light increases to over double its mass at rest. The relationship is exponential: As the object approaches the speed of light, its mass increases at a faster and faster rate, as does the energy to move it. By the time the object reaches light speed, the amount of energy needed to move it would be infinite because its mass would be infinite. Nothing, then, can travel at the speed of light except light itself, or any other wave with no inherent mass to start with.

Another consequence of relativity is that absolute time no longer exists. Because speed is determined by dividing distance by time, the constant speed of light requires time to vary with distance. Space and time thus are connected, and “[w]e must accept that time is not completely separate from and independent of space, but is combined with it to form an object called space-time” (23).

To deal with time as a dimension connected to space, scientists construct a “space-time diagram” (22). These are graphs with a vertical axis on the left side that shows time going upward from bottom to top, and a horizontal axis at the bottom that shows distance getting longer from left to right. Figure 2.2 (27), shows Earth’s sun traveling upward on a vertical line through time for 4.5 years. To its right is a nearby star, Alpha Centauri, which also travels upward for 4.5 years. A ray of light leaves the sun at its starting position at the bottom of the graph and travels diagonally, up and to the right, until it strikes Alpha Centauri at the upper end of that star’s travel through time. This is how long it takes our sun’s light to reach that star. The distance between the sun and Alpha Centauri, as shown by the horizontal axis, is about 24 trillion miles. This is the distance the light travels during its 4.5-year journey from the sun to Alpha Centauri.

The behavior of light can be illustrated using a stone being dropped into a pond to create ripples. Figure 2.3 (27) shows that the expanding ripples can be graphed in two dimensions as a cone: the tip of the cone is the dropped stone plunging downward, and the other end, a wide circle, shows the width, in distance, that the water ripples have spread on the surface. The cone gets both longer and wider as time passes. This same concept applies to a bulb that emits light into space.  

In 1915, after several failed attempts, Einstein found a new gravitational theory consistent with special relativity by reasoning that gravity is not like other forces and is actually a consequence of space-time’s multi-dimensional nature. Because space-time is not flat, it warps space, so large bodies, like suns and planets, cause space to curve around them. Objects moving past get caught on the curve and curl around the big objects. With this inclusion of a reconciled gravitational theory, this unified theory became known as the theory of general relativity. General relativity predicts planetary orbital paths around the sun that are almost the same as those predicted by Newton’s law of gravity. The most noticeable difference is the orbit of Mercury, which lies closest to the sun: Its orbit shifts slightly in ways not expected by Newton but predicted by Einstein and confirmed by astronomers.

Light also gets deflected by the warping of space around large objects. As the Earth revolves around the sun, some stars seem to disappear behind the sun. However, during solar eclipses, astronomers have shown that the hidden star’s light rays sometimes get bent around the sun so that the star appears to be next to the sun when it’s still behind it. This proves that Einstein’s general theory of relativity is correct. This theory also suggests that the deeper one goes into a gravity field, the slower time becomes. Thus, someone on the Earth, closer to the planet’s gravitational center, ages slightly slower than an astronaut in orbit above the surface. Likewise, someone traveling in a spaceship at close to the speed of light will age much more slowly than those who remain on Earth.

Einstein’s revelation that neither time nor space is absolute drastically changed perception of the universe. The static, infinite universe was replaced by a dynamic, finite universe that was created at some point and will possibly end.

In the night sky are numerous points of light. The brightest of these are neighboring planets—Venus, Mars, Jupiter, and Saturn—and most of the rest are stars. Though the stars appear to be fixed, many of them exhibit small changes in position relative to one another. The ones that change position the most are those that are closest to Earth, and because these stars shift against a background of other stars, their distances from Earth can be determined by comparing them to each other. Ancient astronomers hypothesized that the stars could clump together—as in the Milky Way—if most of the stars were arranged along a disc-like area. It wasn’t until 1924, when Edwin Hubble showed that the Milky Way is just one of many galaxies, that it became accepted that Earth exists in what is now called a spiral galaxy.

To prove that there are other galaxies containing vast numbers of stars clumped together with huge empty spaces between them, Hubble needed to determine their distance from Earth. These galaxies are so far away that they do not appear to move at all from Earth’s perspective, so Hubble used indirect measuring. The apparent brightness of a star as it is perceived on Earth encompasses both the star’s actual luminosity (how much light it radiates) and the star’s distance (closer stars appear brighter, even if they emit less total light—are less luminous—than a further star). If a star’s luminosity and its apparent brightness on Earth are known, its distance can be calculated. Hubble noted that many types of nearby stars had the same luminosity, deducing that those same types of stars would have the same luminosity in another galaxy. He calculated the distance between Earth and nine other galaxies with similar stars by using the stars’ luminosity and apparent brightness to find their distances.

Stars appear as points of light with no shape or distinct size, but often have color. Newton discovered that light will separate into its component parts, or refract, when passed through a prism, creating a rainbow; each color has a different wavelength. He dubbed these component parts the spectrum. Astronomers noticed that stars in faraway galaxies emitted spectra that were redder (and shorter in wavelength)relative to their distance from Earth. This is called the Doppler effect: If an object is stationary, then the frequency of the waves it emits will remain the same, but as it moves relative to the observer, the wave frequency will increase as something moves toward the observer and decrease as it moves away. With sound, the pitch will move up as something moves toward us and down as it moves away (think of a car driving past). Prior to Hubble’s work, most people believed the galaxies were moving at random in comparison to earth. Hubble’s careful catalog of galaxies found that the vast majority of galaxies experienced a red shift, indicating a decrease in light wavelength that meant they must be moving away from the Earth. In 1929, Hubble also determined that the further away a galaxy is, the faster it moves away from Earth. This indicates an expanding universe and “was one of the great intellectual revolutions of the twentieth century” (41).

Hawking finds it curious that no one thought of an expanding universe before, since a static universe would have contracted via the force of gravity, according to Newton’s laws. Even Einstein believed in the static universe so strongly that he adjusted his calculations to accommodate a kind of anti-gravity; he felt that the universe had an innate tendency to expand, but this cosmological constant kept this expansion in check. Many other scientists looked for solutions to why the universe remained static despite general relativity’s suggestion that it isn’t. A few years before Hubble’s work, Russian physicist and mathematician Alexander Friedmann theorized that the universe should look the same in any direction from any point of observation. Hawkins feels that this predicts Hubble’s discovery.

In 1965, Friedmann’s assumptions were confirmed when Robert Wilson and Arno Penzias of Bell Telephone Laboratories tested a new microwave detector and found that, no matter where they pointed it, they picked up the same small microwave noise (Microwaves are electromagnetic waves like light waves, but they are longer than visible light). They deduced that the microwaves likely originate beyond the Milky Way. This consistent microwave signal verifies Friedmann’s first assumption, though the universe is only identical on average; it can appear to have variations on very small scales, just as the near objects in the night sky (like the planets in our solar system) look different from different directions on the earth, but the clusters of galaxies beyond our own look the same from wherever they are observed. Tiny variations in the microwave background noise were detected by the Cosmic Background Explorer (COBE) satellite in 1992. These variations become critical in the discussion of black holes and the origins of the universe in Chapter 8.

Meanwhile, American physicists Bob Dicke and Jim Peebles worked on an idea suggested by George Gamow, one of Friedmann’s former students. Gamow believed that the beginning of the universe was white-hot and extremely dense. Dicke and Peebles hypothesized that this light would be observable since it would be just getting to Earth, but would be so red-shifted that it would be made of invisible microwaves. When Wilson and Penzias heard about Dicke and Peebles’ intention to look for this light from the beginning of the universe, they realized that the microwave noise must be exactly that. Wilson and Penzias won the 1978 Nobel Prize for their discovery, though Hawking feels Dicke, Peebles, and Gamow were cheated.

Hawking points out that, while it is tempting to imagine the Earth at the center of the universe, there is nothing inherently special about its location. He offers the analogy of a balloon with spots painted on it: As the balloon expands, the spots move apart from each other with no spot being considered at the center, and the farther apart the spots, the faster they move away from one another. Three models fit these assumptions. The model Friedmann found is that the universe expands slowly enough that gravity will slow the expansion, stop it, and then contract. In this model, space is both finite and boundless. A second model suggests gravity has just enough force to slow the expansion down a bit. In this model, the universe eventually reaches a steady speed, though it never stops expanding and therefore becomes infinite. In the third model, the universe expands just rapidly enough that gravity doesn’t cause it to collapse back in on itself. In this case, the galaxy is still infinite; the distance between galaxies grows slower and slower but never quite stops.

The speed at which the universe expands has been estimated at between 5% and 10% every thousand million years. The density of the universe is less well understood, including estimated “black matter,” which scientists believe must be present because of gravitation effects on galactic bodies. When all the matter in the known universe is added up, there is still insufficient mass to stop the universe from expanding. Hawking concedes that there may be some other form of matter not yet detected, but current knowledge indicates the universe will likely expand indefinitely.

Friedmann’s predictions imply that the entire universe was once contracted into a single point, called the singularity. At that point, the density of the universe would have been infinite and so would the curvature of space-time. Since current methods cannot predict what happened before the Big Bang, nor would any information about what happened before allow for predictions of what happened after, it is assumed that time began at the moment of the Big Bang. This idea can be uncomfortable since it suggests divine intervention; the Catholic Church declared the Big Bang model in accordance with Scripture.

In the late 1940s, an alternate idea, the “steady state theory” (49), proposed that as the universe expands, new galaxies form to fill in the gaps. Astronomers found, though, that faraway galaxies emit radio signals different from nearby ones, which suggests that the universe has evolved over time. Meanwhile, the discovery of the microwave background radiation showed that the early universe was denser. Since steady state theory simply doesn’t account for these facts, it was no longer considered valid.

Another theory proposed in 1963 suggests that the universe contracted in the past but not into a singularity. Since Friedmann’s estimates only showed the galaxies moving directly away from each other, this suggests all the galaxies were once in the same place, but in real-world observations, the galaxies also exhibit sideways motion, so the Big Bang is not a foregone conclusion. Instead, this new theory hypothesized that expansion is the result of a previous contraction in which galaxies did not collide but swung past each other and re-expanded. By 1970, studies showed this theory was less likely than the Big Bang and it was withdrawn. The work was still valuable in that it established that a Big Bang was possible according to general relativity, though it did now define if “general relativity predict[s] that our universe should have a big bang” (50).

In 1965, physicist Roger Penrose proposed that when a star collapses due to its own gravity, both its surface and volume must collapse to zero size, condensing into a singularity contained within a black hole. Hawking suggested in his PhD thesis that, if Friedmann’s infinite-space model of the universe is accurate, Penrose’s theory also points to the universe beginning as a singularity. In 1970, Hawking and Penrose proved together that the big gang singularity must have occurred as long as the current theory of general relativity holds and that current estimates of the amount of matter in the universe are mostly correct.

After exploring the problem through quantum mechanics, which did not exist when Hawking wrote his thesis, Hawking now concludes that there probably wasn’t a big bang. Hawking promises to explain how quantum mechanics reveal that general relativity is only a partial theory, complicating everything learned about our universe over the last century.