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limits of Newtonian mechanics in an appropriate regime, where dissipation
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and friction are central. (Coffee cups do come to a stop, after all.) In the
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same way, it’s possible to understand why it’s so useful to refer to causes and
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effects in our everyday experience, even if they’re not present in the underly-
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ing equations. There are many different useful stories we have to tell about
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reality to get along in the world.
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What Determines What Will Happen?
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Isaac Newton, the most influential scientist of all time, was a very reli-
gious man. His views were undoubtedly heterodox by the standards of
his childhood Anglican faith; he rejected the Trinity, and wrote nu-
merous works on prophesy and biblical interpretation, with chapter titles
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such as “Of the power of the eleventh horn of Daniel’s fourth Beast, to
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change times and laws.” He couldn’t rely on an argument for God’s exis-
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tence along the lines of Aristotle’s unmoved mover. His own work seemed
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to depict a universe moving perfectly well under its own power, but as he
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pointed out in the “General Scholium” (an essay appended to later editions
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of his masterwork, Principia Mathematica), someone had to set it all up:
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This most excellently contrived System of the Sun, and Plan-
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ets, and Comets, could not have its Origin from any other than
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from the wise Conduct and Dominion of an intelligent and
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powerful Being.
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Elsewhere, Newton seemed to imply that the mutual perturbations of the
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planets on one another would gradually cause the system to get out of
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whack, at which point God would intervene to set things back in order.
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Pierre- Simon Laplace, a French physicist and mathematician born a cen-
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tury after Newton, thought differently. Scholars debate over his true reli-
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gious views, which seem to have vacillated between deism (God created the
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world, but did not subsequently intervene in its operation) and outright
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atheism. Laplace is the one who, when asked by Emperor Napoleón why
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God didn’t appear in his book on celestial mechanics, purportedly replied,
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“I had no need of that hypothesis.” Whatever his ultimate beliefs, it seems
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that Laplace held steadfastly against the idea of a Creator who would ever
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directly interfere in the motions of the world.
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Pierre- Simon Marquis de Laplace, 1749– 1827.
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Laplace was one of the first thinkers to truly understand classical
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(Newtonian) mechanics, deep in his bones— better than Newton himself.
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Someone was bound to do it. Science progresses, and we learn more and
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more about our best theories; there are many physicists today who under-
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stand relativity better than Einstein, or quantum mechanics better than
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Schrödinger or Heisenberg. Laplace tackled problems from the stability of
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the solar system to the foundations of probability, routinely inventing the
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required new mathematics along the way. He suggested that Newtonian
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gravity could be thought of as a field theory, positing a “gravitational poten-34
tial field” that filled all of space, thereby resolving Newton’s puzzlement
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about actions at a distance between faraway bodies.
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Perhaps Laplace’s greatest contribution to our understanding of me-
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chanics was not a technical or mathematical advance, but a philosophical
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one. He realized that there was a simple answer to the question “What
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determines what will happen next?” And the answer is “The state of the
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universe right now.”
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There’s a worry that this result threatens the existence of human agency,
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our ability to make choices about what to do next. As we’ll see, that’s not
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really an issue of physics, but one of description: What is the best way we
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have to talk about human beings? When we talk about simple Newtonian
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systems, like the planets moving through the solar system, determinism is
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part of the picture. When we talk about enormously more complex things
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like people, there’s no way for us to have enough information to make iron-
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clad predictions. Our best theories of people, presented on their own terms
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and without reference to underlying particles and forces, leave plenty of
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room for human choice.
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The world, according to classical physics, is not fundamentally teleological.
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What happens next is not influenced by any future goals or final causes
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toward which it might be working. Nor is it fundamentally historical; to
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know the future— in principle— requires only precise knowledge of the
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present moment, not any additional knowledge of the past. Indeed, the en-
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tirety of both the past and future history ar
e utterly determined by the
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present. The universe is resolutely focused on the current moment; it
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marches forward, instant to instant, under the grip of unbreakable physical
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laws, with no heed paid to its glorious accomplishments or to its hopeful
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prospects. Much later, the biologist Ernst Haeckel would dub this view-
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point dysteleology, though the term is so ungainly that it never really
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caught on.
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In modern parlance, Laplace was pointing out that the universe is some-
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thing like a computer. You enter an input (the state of the universe right
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now), it does a calculation (the laws of physics) and gives you an output (the
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state of the universe one moment later). Similar ideas had previously been
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suggested by Gottfried Wilhelm Leibniz and Roger Boscovich, and were
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prefigured over two millennia earlier by Ajivika, a heterodox school of an-
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cient Indian philosophy. Since computers hadn’t been invented yet, Laplace
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imagined a “vast intellect” that knew the positions and velocities of all the
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particles in the universe, and understood all the forces they were subject
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to, and had sufficient computational power to apply Newton’s laws of mo-
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tion. In that case, as he put it, “for such an intellect nothing would be
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uncertain, and the future just like the past would be present before its eyes.”
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His contemporaries immediately judged “vast intellect” to be too boring,
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and renamed it Laplace’s Demon.
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It’s convenient to say “one moment later,” but for Newton and Laplace,
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and to the best of our current understanding in theoretical physics, the flow
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of time is continuous rather than discrete. That’s no problem at all; this is a
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job for calculus, which Newton and Leibniz invented for just this reason.
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By the “state” of the universe, or any subsystem thereof, we mean the posi-
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tion and the velocity of every particle within it. The velocity is just the rate
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of change (the derivative) of the position as time passes; the laws of physics
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provide us with the acceleration, which is the rate of change of the velocity.
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Together, you give me the state of the universe at one time, and I can use
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the laws of physics to integrate forward (or backward) and get the state of
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the universe at any other time.
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We’re using the language of classical mechanics— particles, forces— but
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the idea is much more powerful and general. Laplace introduced the idea of
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“fields” as a centrally important concept in physics, and the notion became
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entrenched with the work of Michael Faraday and James Clerk Maxwell on
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electricity and magnetism in the nineteenth century. Unlike a particle,
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which has a position in space, a field has a value at every single point in
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space— that’s just what a field is. But we can treat that field value like a
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“position,” and its rate of change as a “velocity,” and the whole Laplacian
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thought experiment goes through undisturbed. The same is true for Ein-
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stein’s general theory of relativity, or Schrödinger’s equation in quantum
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mechanics, or modern speculations such as superstring theory. Since the
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days of Laplace, every serious attempt at understanding the behavior of the
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universe at a deep level has included the feature that the past and future are
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determined by the present state of the system. (One possible exception is
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the collapse of the wave function in quantum mechanics, which we’ll dis-
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cuss at greater length in chapter 20.)
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This principle goes by a simple, if potentially misleading, name: conser-
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vation of information. Just as conservation of momentum implies that the
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universe can just keep on moving, without any unmoved mover behind the
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scenes, conservation of information implies that each moment contains
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precisely the right amount of information to determine every other
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moment.
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The term “information” here requires caution, because scientists use the
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same word to mean different things in different contexts. Sometimes “in-
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formation” refers to the knowledge you actually have about a state of affairs.
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Other times, it means the information that is readily accessible, embodied
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in what the system macroscopically looks like (whether you are looking
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at it and have the information or not). We are using a third possible defini-
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tion, what we might call the “microscopic” information: the complete spec-
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ification of the state of the system, everything you could possibly know
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about it. When speaking of information being conserved, we mean literally
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all of it.
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These two conservation laws, of momentum and information, imply a
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sea change in our best fundamental ontology. The old Aristotelian view was
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comfortable and, in a sense, personal. When things moved, there were mov-
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ers; when things happened, there were causes. The Laplacian view— one
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that continues to hold in science to this day— is based on patterns, not on
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natures and purposes. If this certain thing happens, we know this other
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thing will necessarily follow thereafter, with the sequence described by the
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laws of physics. Why is it that way? Because that’s the pattern we observe.
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Laplace’s Demon is a thought experiment, not one we’re going to reproduce
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in the lab. Realistically, there never will be and never can be an intelligence
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vast and knowledgeable enough to predict the future of the universe from
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its present state. If you sit down and think about what such a computer
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would have to be like, you eventually realize it would essentially need to be
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as big and powerful as the universe itself. To simulate the entire universe
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with good accuracy, you basically have to be the universe. So our concern
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here isn’t one of practical engineering; it’s not going to happen.
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Our interest is a matter of principle: the fact that the current state of the
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universe determines its future, not that we can imagine taking advantage
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of that fact to make predictions. This feature, determinism, rubs some
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people the wrong way. It’s worth taking a careful look at its limitations and
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prospects.
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Classical mechanics, the system of equations studied by Newton and
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Laplace, isn’t perfectly deterministic. There are examples of cases where a
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unique outcome cannot be predicted from the current state of the system.
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This doesn’t bother most people, since cases like this are extremely rare—
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they are essentially infinitely unlikely among the set of all possible things a
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system could be doing. They are artificial and fun to think about, but not
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of great import to what happens in the messy world around us.
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A more popular objection to determinism is the phenomenon of chaos.
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The ominous name obscures its simple nature: in many kinds of systems,
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very tiny amounts of imprecision in our knowledge of the initial state of
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that system can lead to very large variations in where it eventually ends up.
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As far as determinism is concerned, however, the existence of chaos could
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not possibly be more irrelevant. Laplace’s point was always that perfect in-
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formation leads to perfect prediction. Chaos theory says that slightly im-
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perfect information leads to very imperfect prediction. True, and it doesn’t
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change the picture the slightest bit. Nobody in their right mind was ever
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under the impression that we would be able to use Laplace’s reasoning to
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build a useful prediction- making device; the thought experiment was al-
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ways a matter of principle, not one of practice.
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The real issue with classical mechanics is that it’s not how the world
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works. These days we know better: quantum mechanics, which came along
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in the early twentieth century, is an entirely different ontology. There are
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no “positions” and “velocities” in quantum mechanics; there is only “the
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