A Brief History of Time: From the Big Bang to Black Holes is a popular science book about cosmology, the science of the laws that govern the universe, written by British astrophysicist Stephen Hawking. First published in 1988, it is aimed at a lay audience.
Stephen Hawking is a great narrator who, with his solid knowledge of the recent history of physics, tries to clarify in this book what were the elements that played a key role in the search for the laws that would allow the universe to function. It is not an educational book, but if you are interested in knowing more about the universe that surrounds you and of which we are all a small, very small, infinitesimal part, then this book will tell you what are the discoveries that have profoundly marked the study of the cosmos and of matter.
The cardinal points in this text are the theory of relativity and the uncertainty principle (quantum mechanics), around which all the great physicists and mathematicians of the last century revolved, here evoked in a simple but effective way in the contribution given by each of them. Indeed Hawking seems to have lived at the center of this research process and in this book he becomes its direct witness.
In this book, Hawking describes in a simple way the most commonly accepted theories on the structure, origin, and evolution of the universe. It addresses the concepts of space and time, the elementary particles that make up the universe, and the fundamental forces that govern it. Cosmic phenomena like the Big Bang and black holes are explained, and two major theories are discussed: general relativity and quantum physics. Finally, he evokes the search for a “theory of everything“, capable of describing in a coherent and unified way all the fundamental interactions of the universe.
The book was a great success in bookstores and sold more than 25 million copies. It remained on the Sunday Times bestseller list for over five years and was translated into 35 languages.
In A Brief History of Time, Hawking attempts to explain a wide variety of topics to a lay readership, including the Big Bang, black holes, and cones of light. Its main objective is to give an overview of contemporary cosmology, without resorting to mathematical formalization. In the 1996 and subsequent editions, Hawking questions the possibility of time travel through wormholes as well as the absence of a quantum singularity at the origin of time.
Chapter 1: Our Picture of the Universe
In the first chapter, Hawking evokes the history of astronomical studies, from Aristotle and Ptolemy. Aristotle, contrary to a majority of scholars of his time, thinks that the Earth is round. An idea that comes to him from observing lunar eclipses, which he thinks are caused by the rounded shadow of the Earth, and from the observation that the North Star seems to rise in the sky as the observer moves north. Aristotle also thinks that the Sun and the stars revolve around the Earth in perfect circles, for mystical reasons. Ptolemy, also wondering about the positions and trajectories of the stars, invents a model which graphically formalizes Aristotle’s thought.
If the opposite is accepted today, namely that it is the Earth that revolves around the Sun, it was not until 1609 that the geocentric models of Aristotle and Ptolemy were contradicted. The first person to present a detailed argument in favor of a heliocentric model, that is to say in which the Earth actually revolves around the Sun, was the Polish priest Nicolas Copernicus, in 1514. Slightly less than a century later, Galileo Galileo, an Italian scientist, and Johannes Kepler, a German scientist, observe the displacements of the Moon and the stars and use their observations to prove the theory of N. Copernicus. To formally account for his observations, J. Kepler proposes an elliptical model rather than a circular one. In his 1687 work on gravity, Principia Mathematica, Isaac Newton develops the mathematical equations that support the Copernican theory. The theory of I. Newton also implies that stars, such as the Sun, are not fixed, but rather distant moving objects.
The origin of the universe is the other great subject of astronomy, and it has been extensively debated over the centuries. Early thinkers, like Aristotle, conjectured that the universe is eternal, that it has no beginning or end. Theologians, like Saint Augustine, believe the contrary, that the universe was created at a given moment. Saint Augustine also believes that time is a concept born from the creation of the universe. A millennium later, the German philosopher Immanuel Kant advances the idea that time is infinite.
In 1929, astronomer Edwin Hubble discovered that galaxies were moving apart. Consequently, he thinks, at one time, between 10 and 20 billion years ago, all the galaxies were in an infinitely dense point of space. This discovery shifts the question of the origin of the universe into the realm of science. Today, scientists use two partial theories to explain the evolution of the universe: Albert Einstein‘s theory of general relativity and quantum mechanics. For them, it is a question of formulating a theory of everything that can coherently unify the teachings of these two partial theories and describe, in a convincing manner, the astronomical observations. Hawking is of the opinion that the search for this Theory of Everything, although motivated by an essential human need for logic, order, and intelligibility, is likely to affect the survival of the human species.
Chapter 2: Space and Time
Before G. Galileo and I. Newton, it was widely accepted that Aristotle was correct in conjecturing that objects were at rest until some force set them in motion. Newton proves the opposite by using the experiments of G. Galileo to design his three laws of motion. He also formulates a universal law of gravitation, which explains the movement of stellar bodies. In the Aristotelian tradition, a physical event takes place at a given point in space. Newton proves the contrary: each object is in motion relative to the others, and it is impossible to assign each an absolute position of rest.
Both Aristotle and Newton believe that time is absolute, outside of space. A belief that does not allow them to explain the behavior of objects moving at a speed close to or equal to the speed of light. The speed of light was first measured in 1676 by Danish astronomer Ole Rømer, who observed that the time it took for light to come from Jupiter’s moons depended on their respective distances from Earth. Hence it is established that the speed of light is very high but effectively finite. However, scientists run into a problem when they try to establish that light always travels at the same speed. They then imagine a substance, called ether, a subtle fluid supposed to fill the space beyond the Earth’s atmosphere and supposed to explain the absolute value of the speed of luminous phenomena.
Since the ether theory failed to systematically explain the speed of light phenomena, Einstein proposed in 1905 to abandon the idea of the ether and, with it, the idea that time is absolute. The French mathematician Henri Poincaré has the same intuition. This idea of Einstein is called the theory of relativity: it encompasses and supplants the theory of universal gravitation of Newton, limited to small speeds, relative to the speed of light, and weak gravitational fields.
According to the theory of relativity, the laws of physics remain invariant, and the speed of light remains constant regardless of the Galilean reference frame – or frame in uniform translation – in which it is observed. It implies, in particular, that time is not an absolute notion and that it can expand, that is to say, that the time elapsed between two events can be experienced differently by two observers, either because of their relative velocities with respect to each other, or because of their respective positions in the gravitational field. Schematically, time passes more slowly for the observer who moves at a speed close to or equal to that of light, compared to one who is stationary; analogously, time passes more slowly for the observer located near an extraordinarily massive object, compared to one located in a weak gravitational field. S. Hawking illustrates this principle by using the paradox of the twins.
A fundamental notion of the theory of relativity, the cone of light makes it possible to describe the light events observed, by distinguishing between a past event, a future event, and an inaccessible event in the past or in the future. The upper part of the light cone represents where the light will propagate from the event, the future, and the lower part represents where the light was before the event, the past. The center represents the event itself.
Chapter 3: The Expanding Universe
In the third chapter, Hawking addresses the issue of the expansion of the universe, and the phenomenon is explained through the evocation of the Doppler effect. The Doppler effect occurs when an object approaches or moves away from another: it is characterized by a shift between the frequency of a wave measured at its emission and at its reception when the distance between the sender and receiver varies over time.
In the context of astronomical observations, the effect is applied to light emitted by stars and observed on Earth. In this case, the Doppler effect manifests itself either as a redshift or as a blueshift. The redshift occurs when the luminous object considered moves away from the observer, while the blueshift occurs when it approaches him. In practice, in the case of a redshift, the wavelength of the observed light increases as the emitting object moves away, so that the visible light shifts towards the red end and infrared of the electromagnetic spectrum. Conversely, the blue shift means that the wavelength decreases (and the frequency increases), and therefore indicates that the object is getting closer.
Hubble having observed a redshift in the light emitted by many stars in the universe, concludes that these stars are moving away from us and that the universe is expanding. The idea of expansion assumes that the observable universe originated from an extremely dense and hot phase, named Big Bang, from which it expanded.
Chapter 4: The Uncertainty Principle
The uncertainty principle, or indeterminacy theorem, is the principle that it is impossible to know both the position and the velocity or momentum of a particle. To determine the position of a particle, scientists illuminate it. The higher the frequency of light used, the more accurately the position of the observed particle can be determined, and the less accurate the measurement of its momentum. Conversely, the lower the frequency of the light used, the less accurately the position can be determined, and the more accurately the measurement of its momentum. In other words, the indeterminacy theorem states, unlike classical mechanics, that for a given particle, it is impossible to simultaneously know its exact position and velocity according to a proportionality formula.
First presented in 1927 by German physicist Werner Heisenberg, the indeterminacy theorem is based on the idea of wave-particle duality whereby a given physical object can sometimes exhibit wave properties and sometimes corpuscle properties. The consequence is that the manifestation of these properties does not depend only on the object studied in isolation, but also on all the measuring equipment used. Light is a good example: it is both wave-like, hence the concept of wavelength, and particle-like, as evidenced by photons.
As it demonstrates the inadequacy of the classical concepts of “corpuscles” or “waves” to describe the behavior of quantum objects, wave-particle duality is a fundamental concept of quantum physics.
Chapter 5: Elementary Particles and Forces of Nature
An elementary particle is the smallest known element, a constituent corpuscle of all observable matter and energy, the internal structure of which scientists do not know. A quark is an elementary particle, and there are six “flavors” of it: Down quark, Up quark, Strange quark, Charm quark, Bottom or Beauty quark, and Top or Truth quark, the most massive of them. Each quark has a quantum number, called a “color charge“, so it can be “red”, “green”, or “blue”. In total, there are therefore 18 varieties of quarks to which correspond 18 varieties of antiquarks with opposite magnetic charges and moments. Compounds of quarks are called “hadrons”.
Each particle has what is called a “spin“, an angular momentum of its own that tells us what it looks like from different angles. For example, a spin 0 particle looks the same from all angles, while a spin 1 particle looks different from each angle – like a single arrow – and a spin 2 particle has the same appearance when it is turned 180°, like a double arrow. There are two types of particles in the universe: those with zero or full spin (0, 1, or 2), and those with half-full spin (½). Particles that have half-integer spin obey the Pauli exclusion principle: in a considered system, two particles of spin ½ cannot be simultaneously in the same quantum state, that is, they cannot have the same position or the same speed. Without Pauli’s exclusion principle, the universe would be a gigantic formless cosmic soup.
Particles with spin 0, 1, or 2 carry force from one particle to another. Thus the photon, of spin 1, is the mediating particle of the electromagnetic interaction, responsible for the cohesion and stability of any chemical structure, atom, or molecule, whatever its complexity. In other words, when two electrically charged particles interact, this interaction translates from a quantum point of view to an exchange of photons. In the same way, the graviton, of spin 2, is the mediating particle of gravitation, responsible for the attraction of massive bodies between them.
Besides the electromagnetic interaction and gravitation, there are two other fundamental forces: the weak nuclear interaction and the strong nuclear interaction. The weak nuclear interaction, transported by heavy bosons, is responsible for beta radioactivity; the strong nuclear interaction, transported by the gluon, is responsible for the cohesion of all the hadrons, that is to say, all the particles composed of quarks, which makes it indirectly responsible for the cohesion of the atomic nuclei, the small, dense region at the center of the atom consisting of protons and neutrons.
One of the challenges of contemporary theoretical physics is to achieve a Grand Unified Theory (GUT), namely a model that can describe in a unified and coherent way the electromagnetism, the nuclear interaction weak and the strong nuclear interaction, in the form of a single fundamental force. The unification within the same theoretical model of a GUT and the last fundamental force, gravitation, would be a Theory of Everything (TOE); the idea being that building a GUT would open the way to a TOE.
Chapter 6: Black Holes
A black hole is a celestial object so compact that the intensity of its gravitational field prevents any form of matter or radiation from escaping from it. It is black in the sense that it does not emit or reflect any light to the distant observer, making it literally invisible. Black holes are stars that have collapsed on themselves in a point, a singularity, and whose gravity is so strong that it sucks everything in its gravitational field, including, therefore, light radiation. Only very massive stars, whose mass is at least one and a half times that of the Sun, such as supergiants, are large enough to become black holes. This critical mass is called the “Chandrasekhar limit”, named after the Indian scientist who made this discovery. Below this limit, the collapsing star does not become a black hole, but a different, smaller type of star. The boundary of a black hole is called the event horizon. An object inside the event horizon will never escape from the black hole.
Chapter 7: Black Holes Ain’t So Black
Hawking realizes over the course of his work that the event horizon of a black hole can only grow, and in no case shrink. It grows when a celestial object is sucked into the black hole, and the merger of two black holes produces an event horizon that is at least equal in size to the sum of those of the two original black holes.
The study of black holes is linked to the notion of entropy, namely, the thermodynamic quantity expressing the degree of disorder of matter. The second law of thermodynamics states that any transformation of a thermodynamic system takes place with an increase in global entropy including the entropy of the system and the external environment. In other words, the degree of disorder of matter in a given system, for example, the universe, necessarily increases as it changes. However, by throwing objects into a black hole, it becomes possible to decrease the entropy of the universe, which is a violation of the second law of thermodynamics, therefore impossible. The relationship between a black hole’s entropy and the size of its event horizon was first studied by Jacob Bekenstein and later elucidated by Hawking, whose calculations suggest that black holes actually emit radiation.
The Bekenstein–Hawking formula resolves the paradox by stating that a black hole’s entropy increases as it absorbs an object, and its increase in entropy is always greater than that of the absorbed object. In the same way, the entropy of a black hole tends to fall when this one radiates, because this radiation is accompanied by a loss of energy and consequently by a reduction in the size of the black hole. However, the entropy of the radiation emitted by the black hole is seven times greater than the entropy lost by the black hole. Thus, whatever the process envisaged involving one or more black holes, the total entropy, the sum of the ordinary entropy and that of the black holes, always increases over time.
Chapter 8: The Origin and Fate of the Universe
Most scientists agree that the expansion of the universe begins with the Big Bang. The dominant model is that of the “Hot Big Bang“, in virtue of which, as the universe expands, it cools or, which is the same thing, the universe was hotter when it was denser. And honestly, there is no serious competitor model to the Big Bang.
Hawking wonders what the universe could have been if it were different from ours, the one described by the model of the “Hot Big Bang”. For example, a faster inflationary phase than that experienced by our universe would not have been conducive to the same arrangements of matter, therefore to the appearance of life on Earth.
Chapter 9: The Arrow of Time
The ninth chapter is dedicated to the time dimension, and why it seems to be unidirectional. This impression is intimately linked to the three arrows of time.
The first arrow of time is the thermodynamic arrow: the universal disorder necessarily increases as time passes, which is why the shards of a broken vase never come together to reform an intact vase. This is a law from all eternity.
The second arrow of time is the psychological arrow: our perception of time is itself unidirectional, which is why we remember the past, but not the future. According to Hawking, our brain’s measurement of time is based on the perception of the increase in universal disorder, for lack of ever witnessing the reverse (the shards coming together to form a vase). Therefore, the psychological arrow of time interpenetrates the thermodynamic arrow.
The third arrow of time is the cosmological arrow: the observable universe is expanding, not contracting. Hawking thinks that our conception of the first two arrows of time is only possible because the universe was initially extremely ordered. It is only because the universe is expanding that disorder increases, which is why the cosmological arrow of time is consistent with the thermodynamic arrow.
However, if the universe is indeed a finite but boundless, boundaryless space, the theory predicts that a contraction will follow the expansion. However, it is unimaginable that from this breaking point time goes backward, while the universe would return to an extremely ordered state.
Asked why human beings have the impression that the three arrows of time point in the same direction, Hawking postulates that it is because they exist in the expansion phase of the universe. According to him, no form of intelligent life, let alone human life, could have existed in a phase of universal contraction, and the expansionary phase of the universe is only conducive to intelligent life thanks to the thermodynamic arrow. Hawking calls this theory the “weak anthropic principle”.
Chapter 10: Wormholes and Time Travel
Many physicists have attempted to devise possible methods by which humans with advanced technology may be able to travel faster than the speed of light, or travel backward in time, as a lot of science fiction can testify.
Einstein–Rosen bridges, the “wormholes“, were hypothesized early in the history of general relativity research. They would appear identical to black holes from the outside, but matter which entered would be relocated to a different location in spacetime, potentially in a distant region of space, or even backward in time.
However, later research demonstrated that such a wormhole, even if it was possible for it to form in the first place, would not allow any material to pass through before turning back into a regular black hole. The only way that a wormhole could theoretically remain open, and thus allow faster-than-light travel or time travel, would require the existence of exotic matter with negative energy density, which violates the energy conditions of general relativity. As such, almost all physicists agree that faster-than-light travel and travel backward in time are not possible.
Hawking also describes his own “chronology protection conjecture“, which provides a more formal explanation for why faster-than-light travel and backward in time travel are almost certainly impossible.
Chapter 11: The Unification of Physics
Physicists have, throughout history, produced partial theories describing a limited number of phenomena, but without managing to build a theory of everything. Regarding the discovery of such a theory in the near future, Hawking is cautiously optimistic. It should, if necessary, overcome the fundamental contradiction between the classical theory of gravitation and the indeterminacy theorem specific to quantum mechanics. Most attempts in this direction have led to absurd conclusions about infinitely massive particles or infinitely small universes. In 1976, however, an interesting theory of supergravity was proposed as a solution to the problem. However, too difficult to prove mathematically, it was quickly abandoned. In 1984, another type of theory gained popularity: these were the so-called “string” theories, which considered that elementary objects were not particles, but rather two-dimensional strings. These string theories claim to better explain the existence of certain particles than the theory of supergravity. However, instead of a four-dimensional spacetime, they assume that the universe could have 10, 11, or even 26 dimensions. These additional dimensions would not be perceptible to humans because they are too tightly curved. String theories allow us to think of the existence of these imperceptible additional dimensions in certain regions of the universe, without excluding that they may be salient in others. Curiously, the theories of strings and supergravity arrive at substantially equivalent results, as if they were respectively approximations of one and the same theory. Nowadays, supergravity theory is considered an effective theory of string theories.
It is on the basis of this research that Hawking foresees three scenarios:
- there is a Theory of Everything that we will eventually discover;
- there is an infinity of theories that overlap and describe the universe more and more precisely;
- there is no Theory of Everything.
This third possibility is circumvented by admitting the limits set by the uncertainty principle. The second scenario more or less describes the historical development of physical science, with the emergence of partial theories of ever-greater probative value. Hawking thinks that this dynamic of refinement will meet its own limits in the 21st century and that it is ultimately the study, in the laboratory, of the primordial universe, which will make it possible to build a unified theory. In his mind, such a theory would not necessarily be proven, but at least already mathematically coherent, and his predictions would, for their part, agree with our observations.
Chapter 12: Conclusion
In this final chapter, Hawking summarises the efforts made by humans throughout their history to understand the Universe and their place in it. Starting from the belief in anthropomorphic spirits controlling nature, followed by the recognition of regular patterns in nature, and finally with the scientific advancement in recent centuries, the inner workings of the universe have become far better understood. He recalls the suggestion of the nineteenth-century French mathematician Laplace that the Universe’s structure and evolution could eventually be precisely explained by a set of laws whose origin is left in God’s domain. However, Hawking states that the uncertainty principle introduced by the quantum theory in the twentieth century has set limits to the predictive accuracy of future laws to be discovered.
Hawking comments that historically, the study of cosmology (the study of the origin, evolution, and end of Earth and the Universe as a whole) has been primarily motivated by a search for philosophical and religious insights, for instance, to better understand the nature of God, or even whether God exists at all. However, for Hawking, most scientists today who work on these theories approach them with mathematical calculation and empirical observation, rather than asking such philosophical questions. In his mind, the increasingly technical nature of these theories has caused modern cosmology to become increasingly divorced from philosophical discussion. Hawking nonetheless expresses hope that one day everybody would talk about these theories in order to understand the true origin and nature of the Universe, and accomplish “the ultimate triumph of human reasoning”.