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A Brief History of Time by Stephen Hawking

14 February, 2021 - 19 min read


I. Brief Summary

Stephen Hawking lays out the history of scientific theories since Nicolaus Copernicus first challenged that the earth was not the center of the universe. This book was highly technical, but Hawking does a wonderful job of using analogies to break down the ideas in an elementary form. The book goes deep into cosmology theories such as relativity, quantum mechanics, uncertainty principle, unified theory, string theory, particle theory, black holes, time travel, thermodynamics, expansion of universe, big bang, singularity and gravity. The book also offers world-class questions from which the theories arises. The primary objective of these scientific theories is to understand the rational governing laws of universe. The work is in progress but Stephen Hawking believes it is probable that we are close to achieving unified theory of universe. This is a masterpiece on scientific writing by Stephen Hawking. A must-read!

II. Big Ideas

  • Edwin Hubble in 1929 made the landmark observation that the distant galaxies are moving rapidly away from us, not matter where you look. This confirmed that the universe is expanding. Hawking explains it further:

    • When we add up all this dark matter, we still get only about one tenth of the amount required to halt the expansion. However, we cannot exclude the possibility that there might be some other form of matter, distributed almost uniformly throughout the universe, that we have not yet detected and that might still raise the average density of the universe up to the critical value needed to halt the expansion.
    • The present evidence therefore suggests that the universe will probably expand forever, but all we can really be sure of is that even if the universe is going to recollapse, it won’t do so for at least another ten thousand million years, since it has already been expanding for at least that long. This should not unduly worry us: by that time, unless we have colonized beyond the Solar System, mankind will long since have died out, extinguished along with our sun!
  • The newtonian theory of gravity states that objects attract each other with a force based on the distance between them. Hawking connects this idea with general relativity introduced by Einstein:

    • This meant that if one moved one of the objects, the force on the other one would change instantaneously. Or in other words, gravitational effects should travel with infinite velocity, instead of at or below the speed of light, as the special theory of relativity required. Einstein made a number of unsuccessful attempts between 1908 and 1914 to find a theory of gravity that was consistent with special relativity. Finally, in 1915, he proposed what we now call the general theory of relativity.
    • Einstein made the revolutionary suggestion that gravity is not a force like other forces, but is a consequence of the fact that space-time is not flat, as had been previously assumed: it is curved, or “warped,” by the distribution of mass and energy in it. Bodies like the earth are not made to move on curved orbits by a force called gravity; instead, they follow the nearest thing to a straight path in a curved space, which is called a geodesic.
    • Our galaxy and other galaxies, however, must contain a large amount of “dark matter” that we cannot see directly, but which we know must be there because of the influence of its gravitational attraction on the orbits of stars in the galaxies.
  • Hawking on quantum theory:

    • In general, quantum mechanics does not predict a single definite result for an observation. Instead, it predicts a number of different possible outcomes and tells us how likely each of these is. Quantum mechanics therefore introduces an unavoidable element of unpredictability or randomness into science.
    • Einstein objected to this very strongly, despite the important role he had played in the development of these ideas. Einstein was awarded the Nobel Prize for his contribution to quantum theory. Nevertheless, Einstein never accepted that the universe was governed by chance; his feelings were summed up in his famous statement “God does not play dice.”
    • The uncertainty principle of quantum mechanics implies that certain pairs of quantities, such as the position and velocity of a particle, cannot both be predicted with complete accuracy.
    • the quantum theory of gravity has opened up a new possibility, in which there would be no boundary to space-time and so there would be no need to specify the behavior at the boundary.
  • Hawking on elementary particles:

    • The word atom means “indivisible” in Greek.
    • Quarks are much smaller than the wavelength of visible light and so do not have any color in the normal sense.
    • The grouping together of atoms to form units called molecules.
    • The phenomenon of interference between particles has been crucial to our understanding of the structure of atoms, the basic units of chemistry and biology and the building blocks out of which we, and everything around us, are made.
    • It also predicted that the electron should have a partner: an antielectron, or positron...We now know that every particle has an antiparticle, with which it can annihilate. (In the case of the force-carrying particles, the antiparticles are the same as the particles themselves.) There could be whole antiworlds and antipeople made out of antiparticles. However, if you meet your antiself, don’t shake hands! You would both vanish in a great flash of light. The question of why there seem to be so many more particles than antiparticles around us is extremely important, and I shall return to it later in the chapter.
  • Hawking explains all 4 forces that would eventually lead to unified theory which arguably is the primary objective of physics today:

    • The first category is the gravitational force. This force is universal, that is, every particle feels the force of gravity, according to its mass or energy. Gravity is the weakest of the four forces by a long way...This has no mass of its own, so the force that it carries is long range.
    • The next category is the electromagnetic force, which interacts with electrically charged particles like electrons and quarks, but not with uncharged particles such as gravitons. It is much stronger than the gravitational force: the electromagnetic force between two electrons is about a million million million million million million million (1 with forty-two zeros after it) times bigger than the gravitational force.
    • The third category is called the weak nuclear force, which is responsible for radioactivity and which acts on all matter particles of spin ½, but not on particles of spin 0, 1, or 2, such as photons and gravitons. similarly. The effect is rather like the behavior of a roulette ball on a roulette wheel. At high energies (when the wheel is spun quickly) the ball behaves in essentially only one way—it rolls round and round. But as the wheel slows, the energy of the ball decreases, and eventually the ball drops into one of the thirty-seven slots in the wheel.
    • The fourth category is the strong nuclear force, which holds the quarks together in the proton and neutron, and holds the protons and neutrons together in the nucleus of an atom. It is believed that this force is carried by another spin-1 particle, called the gluon, which interacts only with itself and with the quarks. The strong nuclear force has a curious property called confinement: it always binds particles together into combinations that have no color.
  • Hawking on a lifecycle of a star:

    • To understand how a black hole might be formed, we first need an understanding of the life cycle of a star. A star is formed when a large amount of gas (mostly hydrogen) starts to collapse in on itself due to its gravitational attraction. As it contracts, the atoms of the gas collide with each other more and more frequently and at greater and greater speeds—the gas heats up. Eventually, the gas will be so hot that when the hydrogen atoms collide they no longer bounce off each other, but instead coalesce to form helium. The heat released in this reaction, which is like a controlled hydrogen bomb explosion, is what makes the star shine. This additional heat also increases the pressure of the gas until it is sufficient to balance the gravitational attraction, and the gas stops contracting. It is a bit like a balloon—there is a balance between the pressure of the air inside, which is trying to make the balloon expand, and the tension in the rubber, which is trying to make the balloon smaller. Stars will remain stable like this for a long time, with heat from the nuclear reactions balancing the gravitational attraction. Eventually, however, the star will run out of its hydrogen and other nuclear fuels. Paradoxically, the more fuel a star starts off with, the sooner it runs out. This is because the more massive the star is, the hotter it needs to be to balance its gravitational attraction. And the hotter it is, the faster it will use up its fuel. Our sun has probably got enough fuel for another five thousand million years or so, but more massive stars can use up their fuel in as little as one hundred million years, much less than the age of the universe. When a star runs out of fuel, it starts to cool off and so to contract.
  • Hawking on singularity, space-time & black holes:

    • A space-time in which events have imaginary values of the time coordinate is said to be Euclidean, after the ancient Greek Euclid, who founded the study of the geometry of two-dimensional surfaces. What we now call Euclidean space-time is very similar except that it has four dimensions instead of two. In Euclidean space-time there is no difference between the time direction and directions in space. On the other hand, in real space-time, in which events are labeled by ordinary, real values of the time coordinate, it is easy to tell the difference—the time direction at all points lies within the light cone, and space directions lie outside.
    • ...what the singularity theorems really indicate is that the gravitational field becomes so strong that quantum gravitational effects become important: classical theory is no longer a good description of the universe.
    • According to the singularity theorems of classical general relativity, there would still have been a big bang singularity.
    • ...anthropic principle, which can be paraphrased as “We see the universe the way it is because we exist.”
    • Einstein’s general theory of relativity, on its own, predicted that space-time began at the big bang singularity and would come to an end either at the big crunch singularity (if the whole universe recollapsed), or at a singularity inside a black hole (if a local region, such as a star, were to collapse).
    • The existence of radiation from black holes seems to imply that gravitational collapse is not as final and irreversible as we once thought. If an astronaut falls into a black hole, its mass will increase, but eventually the energy equivalent of that extra mass will be returned to the universe in the form of radiation. Thus, in a sense, the astronaut will be “recycled.”
    • A precise statement of this idea is known as the second law of thermodynamics. It states that the entropy of an isolated system always increases, and that when two systems are joined together, the entropy of the combined system is greater than the sum of the entropies of the individual systems.
    • General relativity predicts that heavy objects that are moving will cause the emission of gravitational waves, ripples in the curvature of space that travel at the speed of light. These are similar to light waves, which are ripples of the electromagnetic field, but they are much harder to detect.
    • In order to understand what you would see if you were watching a star collapse to form a black hole, one has to remember that in the theory of relativity there is no absolute time. Each observer has his own measure of time. The time for someone on a star will be different from that for someone at a distance, because of the gravitational field of the star.
    • The gravitational field of the star changes the paths of light rays in space-time from what they would have been had the star not been present.
    • As the star contracts, the gravitational field at its surface gets stronger and the light cones get bent inward more. This makes it more difficult for light from the star to escape, and the light appears dimmer and redder to an observer at a distance. Eventually, when the star has shrunk to a certain critical radius, the gravitational field at the surface becomes so strong that the light cones are bent inward so much that light can no longer escape.
    • According to the theory of relativity, nothing can travel faster than light. Thus if light cannot escape, neither can anything else; everything is dragged back by the gravitational field. So one has a set of events, a region of space-time, from which it is not possible to escape to reach a distant observer. This region is what we now call a black hole. Its boundary is called the event horizon and it coincides with the paths of light rays that just fail to escape from the black hole.
    • Einstein’s general theory of relativity seems to govern the large-scale structure of the universe. It is what is called a classical theory; that is, it does not take account of the uncertainty principle of quantum mechanics, as it should for consistency with other theories. The reason that this does not lead to any discrepancy with observation is that all the gravitational fields that we normally experience are very weak. However, the singularity theorems discussed earlier indicate that the gravitational field should get very strong in at least two situations, black holes and the big bang.
    • In such strong fields the effects of quantum mechanics should be important. Thus, in a sense, classical general relativity, by predicting points of infinite density, predicts its own downfall, just as classical (that is, nonquantum) mechanics predicted its downfall by suggesting that atoms should collapse to infinite density.
    • We do not yet have a complete consistent theory that unifies general relativity and quantum mechanics, but we do know a number of the features it should have.
    • This might suggest that the so-called imaginary time is really the real time, and that what we call real time is just a figment of our imaginations. In real time, the universe has a beginning and an end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real is just an idea that we invent to help us describe what we think the universe is like.
    • The increase of disorder or entropy with time is one example of what is called an arrow of time, something that distinguishes the past from the future, giving a direction to time. There are at least three different arrows of time. First, there is the thermodynamic arrow of time, the direction of time in which disorder or entropy increases. Then, there is the psychological arrow of time. This is the direction in which we feel time passes, the direction in which we remember the past but not the future. Finally, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting.
  • Hawking on unified theory:

    • We want to make sense of what we see around us and to ask: What is the nature of the universe? What is our place in it and where did it and we come from? Why is it the way it is?
    • A complete, consistent, unified theory is only the first step: our goal is a complete understanding of the events around us, and of our own existence.
    • ...we have, as yet, had little success in predicting human behavior from mathematical equations!
    • In Newton’s time it was possible for an educated person to have a grasp of the whole of human knowledge, at least in outline. But since then, the pace of the development of science has made this impossible. Because theories are always being changed to account for new observations, they are never properly digested or simplified so that ordinary people can understand them. You have to be a specialist, and even then you can only hope to have a proper grasp of a small proportion of the scientific theories. Further, the rate of progress is so rapid that what one learns at school or university is always a bit out of date. Only a few people can keep up with the rapidly advancing frontier of knowledge, and they have to devote their whole time to it and specialize in a small area...Seventy years ago, if Eddington is to be believed, only two people understood the general theory of relativity. Nowadays tens of thousands of university graduates do, and many millions of people are at least familiar with the idea.
    • ...we could never be quite sure that we had indeed found the correct theory, since theories can’t be proved. But if the theory was mathematically consistent and always gave predictions that agreed with observations, we could be reasonably confident that it was the right one.
    • I think that there is a good chance that the study of the early universe and the requirements of mathematical consistency will lead us to a complete unified theory within the lifetime of some of us who are around today, always presuming we don’t blow ourselves up first.
    • We might indeed expect to find several new layers of structure more basic than the quarks and electrons that we now regard as “elementary” particles.
    • With the advent of quantum mechanics, we have come to recognize that events cannot be predicted with complete accuracy but that there is always a degree of uncertainty.
    • The main difficulty in finding a theory that unifies gravity with the other forces is that general relativity is a “classical” theory; that is, it does not incorporate the uncertainty principle of quantum mechanics...A necessary first step, therefore, is to combine general relativity with the uncertainty principle.
    • We don’t yet have a complete and consistent theory that combines quantum mechanics and gravity. However, we are fairly certain of some features that such a unified theory should have. One is that it should incorporate Feynman’s proposal to formulate quantum theory in terms of a sum over histories.
    • ...any model that described the whole universe in detail would be much too complicated mathematically for us to be able to calculate exact predictions. One therefore has to make simplifying assumptions and approximations—and even then, the problem of extracting predictions remains a formidable one.

III. Quotes

  • Equations are more important to me, because politics is for the present, but an equation is something for eternity. — Albert Einstein
  • How much choice did God have in constructing the universe? — Albert Einstein
  • Up to now, most scientists have been too occupied with the development of new theories that describe what the universe is to ask the question why. On the other hand, the people whose business it is to ask why, the philosophers, have not been able to keep up with the advance of scientific theories.
  • Why does the universe go to all the bother of existing? Is the unified theory so compelling that it brings about its own existence? Or does it need a creator, and, if so, does he have any other effect on the universe? And who created him?
  • In this book I have given special prominence to the laws that govern gravity, because it is gravity that shapes the large-scale structure of the universe, even though it is the weakest of the four categories of forces.
  • But can there really be such a unified theory? Or are we perhaps just chasing a mirage?
  • Moreover, Einstein refused to believe in the reality of quantum mechanics, despite the important role he had played in its development.
  • Thus the possibility of time travel remains open. But I’m not going to bet on it. My opponent might have the unfair advantage of knowing the future.
  • Where does this difference between the past and the future come from? Why do we remember the past but not the future?
  • One possible answer is to say that God chose the initial configuration of the universe for reasons that we cannot hope to understand.
  • Does the universe in fact have a beginning or an end? And if so, what are they like?
  • The number of black holes may well be greater even than the number of visible stars, which totals about a hundred thousand million in our galaxy alone.
  • In other words, the singularity would always lie in his future and never in his past.
  • A consistent theory of how gravity affects light did not come along until Einstein proposed general relativity in 1915.
  • So the question is: what are the truly elementary particles, the basic building blocks from which everything is made?
  • As Richard Feynman once observed, “We are lucky to live in an age in which we are still making discoveries….The age in which we live is the age in which we are discovering the fundamental laws of nature.”
  • Questions about our origins were once regarded as the territory of philosophers and theologians. But gradually the answers have been provided by science; speculations have been replaced by hard facts.
  • It would bring to an end a long and glorious chapter in the history of humanity’s intellectual struggle to understand the universe.
  • Energy is a bit like money: if you have a positive balance, you can distribute it in various ways, but according to the classical laws that were believed at the beginning of the century, you weren’t allowed to be overdrawn. So these classical laws would have ruled out any possibility of time travel.