The Big Picture
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n 1971, viewers watching live TV got to see Apollo 15 astronaut David
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Scott perform a fun demonstration. Near the end of an extravehicular
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moon walk, Scott held up a hammer and a feather, then proceeded to
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let go of them simultaneously. Both objects, under the gentle pull of the
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moon’s gravity, fell to the ground, landing at precisely the same time.
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That’s not what would have happened here on Earth, unless you
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were practicing your spacesuit drills in one of NASA’s giant vacuum
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chambers. Under ordinary circumstances, air resistance would greatly slow
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the fall of the feather, while the hammer would be largely unaffected.
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But in the vacuum on the moon’s surface, their trajectories were indistin-
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guishable.
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Scott had confirmed an important insight put forward by Galileo Gali-
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lei back in the late sixteenth century: the natural motion of all objects is to
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fall in the same way under the influence of gravity, and it is only friction
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caused by air that makes heavier objects seem to fall faster than lighter ones
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in our everyday experience. And a good thing too. As mission controller Joe
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Allen put it, this experimental result was “predicted by well- established
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theory, but a result nonetheless reassuring considering both the number of
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viewers that witnessed the experiment, and the fact that the homeward
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journey was based critically on the validity of the particular theory being
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tested.”
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The story is told that Galileo performed a version of the experiment
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himself, dropping balls of different weights (but comparable air resistance)
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from the top of the Leaning Tower of Pisa. Galileo doesn’t seem to have
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claimed that he did this, but it was later asserted by his pupil Vincenzo
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Viviani in a biography of his master.
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The Leaning Tower of Pisa.
(Courtesy of W. Lloyd MacKenzie)
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The experiment we know Galileo actually performed was an easier one
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to construct and control: he rolled balls of different masses down inclined
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planes. He was able to show that the balls accelerated in a uniform fashion,
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by an amount that depended on the angle of the plane but not on the
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masses of the balls. He then suggested that if we could trust this result all
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the way to planes that were inclined absolutely perpendicular to the floor,
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that would be exactly like dropping objects straight down, without a plane
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there at all. Therefore, he concluded, all masses would fall in a uniform way
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under the force of gravity, if it weren’t for the influence of air resistance.
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More important than this specific finding is the underlying message it
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conveys: we can learn about the natural motion of objects by imagining we
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can get rid of various nuisance effects, such as friction and air resistance,
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and then perhaps recovering more realistic kinds of motion by putting
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those effects back in later.
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That is no small insight. It is arguably the biggest idea in the history of
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physics.
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Physics is, by far, the simplest science. It doesn’t seem that way, because
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we know so much about it, and the required knowledge often seems esoteric
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and technical. But it is blessed by this amazing feature: we can very often
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make ludicrous simplifications— frictionless surfaces, perfectly spherical
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bodies— ignoring all manner of ancillary effects, and nevertheless get re-
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sults that are unreasonably good. For most interesting problems in other
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sciences, from biology to psychology to economics, if you modeled one tiny
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aspect of a system while pretending all the others didn’t exist, you would
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just end up getting nonsense. (Which doesn’t stop people from trying.)
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This enormous, paradigm- shifting idea— in idealized situations where
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friction and dissipation can be ignored, physics becomes simple— was in
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large part responsible for helping to establish an equally influential, argu-
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ably more world- shattering concept: conservation of momentum. It might
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not sound like a principle of such dramatic import, but momentum is at the
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very heart of a shift in how we view the world, from an ancient cosmos of
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causes and purposes to a modern one of patterns and laws.
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Before Galileo and others revolutionized the study of motion in the six-
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teenth and seventeenth centuries, Aristotle had long reigned as the leading
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thinker on the subject. Aristotle’s view of physics was resolutely teleologi-
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cal: he thought of objects as having a natural state of being, and processes
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as being directed toward a goal. Famously, he suggested that we could dis-
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tinguish between four different kinds of “causes,” although “kinds of expla-
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nation” might be a better translation of what he had in mind. The four
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kinds were material cause, the stuff of which an object is made; formal
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cause, the essential property that makes an object what it is; efficient cause, 32
the thing that brings the object about (closest to our informal notion of
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“cause”); and final cause, the purpose for which an object exists. Under-
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standing why things change and move and behave the way they do comes
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down to putting them in the context of these causes.
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For Aristotle, the nature of an object determines how it moves. Of the
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four classical elements, earth and water tend to fall to lower elevations,
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whereas air and fire tend to rise. An object can be in its natural state of rest
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or motion, where it will tend to remain until a “violent motion” causes it to
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change, after which it will return.
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Consider a coffee cup sitting at rest on a table. It is in its natural state, in
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this case at rest. (Unless we were to pull the table out from beneath it, in
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which case it would naturally fall, but let’s not do that.) Now imagine we
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exert a violent motion, pushing the cup across the table. As we push it, it
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moves; when we stop, it returns to its natural state of rest. In order to keep
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it moving, we would have to keep pushing on it. As Aristotle says, “Every-
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thing that is in motion must be moved by something.”
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This is manifestly how coffee cups do behave in the real world. The dif-
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ference between Galileo and Aristotle wasn’t that one was saying true
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things and the other was saying false things; it’s that the things Galileo
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chose to focus on turned out to be a useful basis for a more rigorous and
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complete understanding of phenomena beyond the original set of examples,
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in a way that Aristotle’s did not.
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In the sixth century, John Philoponus, a philosopher and theologian
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living in Egypt, began the journey from Aristotle to our present under-
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standing of motion. He suggested that we should think of a motive power
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or “impetus,” which was imparted to a body by the initial act of pushing,
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and kept the body in motion until all of the impetus had dissipated. It was
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a small step forward, but one that opened up a new vista on how to think
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about the nature of motion. Rather than talking about causes, the focus
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shifted to quantities and properties of matter itself.
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Ibn Sina (Avicenna), Persian philosopher
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and polymath, d. 1037.
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Another crucial contribution was made by the Persian thinker Ibn Sina
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(sometimes Romanized as Avicenna), one of the leading lights of the Is-
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lamic Golden Age, around the year 1000. He elaborated on Philoponus’s
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idea of impetus, calling it “inclination” ( mayl). It was Ibn Sina who pro-
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posed that inclination didn’t disperse on its own, but only due to air resis-
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tance or other external influences. And in a vacuum, he points out, there is
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no such resistance: an undisturbed projectile would keep moving at a con-
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stant rate, forever.
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This brings us remarkably close to the modern idea of inertia— the con-
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cept that bodies will move uniformly unless acted upon. In the fourteenth
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century, Jean Buridan, a French cleric who was probably influenced by Ibn
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Sina, came up with a quantitative formula equating the impetus with the
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weight of an object times its velocity. At the time, however, the distinction
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between mass and weight was not understood. Galileo, influenced in turn
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by Buridan, coined the term “momentum” and said it would remain con-
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stant in a body that was not being acted on by any forces, but he didn’t
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clearly differentiate between momentum and velocity. It was René Des-
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cartes who equated momentum with mass times speed, but even he (despite
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being the inventor of analytic geometry) didn’t appreciate that momentum
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has a direction as well as a magnitude; that was left to Dutch scientist
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Christiaan Huygens in the seventeenth century. Then, it was Isaac Newton
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who put the notion to brilliant use in his systematic reinvention of the sci-
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ence of motion, which we still teach in high schools and colleges today.
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Why is conservation of momentum such a big deal? We’re not here to study
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Newtonian mechanics, as rewarding as that would be. There will be no
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exercises involving pulleys or inclined planes. We’re here to think about the
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fundamental nature of reality.
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For Aristotle, physics was a story of natures and causes. Whenever there
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was motion of any sort, there had to be a mover: an efficient cause that led
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to that motion. Aristotle had a more expansive definition of “motion” than
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we use today, one that is really closer to “transformation.” It would include,
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for example, an object changing its color, or possibilities becoming actuali-
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ties. But the same principles apply; Aristotle’s conviction was that all of
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these transformations implied the existence of a transforming cause. There’s
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nothing absurd about such an idea. In our everyday experience, things don’t
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“just happen”— something works to cause them, to bring them about. Ar-
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istotle, without any of the benefit of modern scientific knowledge, was try-
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ing to codify what he knew about the way the world works into some kind
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of systematic framework.
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So Aristotle observes a world populated by countless changing things,
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and infers a cause in each case. A is caused to move by B, which in turn is
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caused to move by C, and so on. It’s reasonable to ask: What started it all?
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To what can we trace back this chain of motions and causes? He quickly
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rejects the possibilities that any motions are self- caused, or that the chain
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of causes goes back infinitely far. It needs to terminate somewhere, in some-
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thing that causes motion but does not itself move: an unmoved mover.
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Aristotle’s theory of motion was largely set forth in his book Physics, but
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the details of the unmoved mover were left to a later one, Metaphysics.
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There, despite being nominally a pagan, he identifies the unmoved mover
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with God: not just an abstract principle but a being, immortal and benevo-
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lent. It’s not a bad argument for God’s existence, although it’s easy to poke
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holes in it by denying the underlying assumptions. Maybe some motions do
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cause themselves, or maybe infinite regresses are perfectly okay. But this
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“cosmological argument” was extremely influential, picked up and elabo-
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rated on by Thomas Aquinas and others.
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Most important for our purposes, the whole structure of Aristotle’s ar-
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gument for an unmoved mover rests on his idea that motions require causes.
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Once we know about conservation of momentum, that idea loses its steam.
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We can quibble over the details— I have no doubt Aristotle would have
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been able to come up with an ingenious way of accounting for objects on
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frictionless surfaces moving at constant velocity. What matters is that the
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new physics of Galileo and his friends implied an entirely new ontology, a
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deep shift in how we thought about the nature of reality. “Causes” didn’t
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have the central role that they once did. The universe doesn’t need a push;
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it can just keep going.
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It’s hard to overemphasize the importance of this shift. Of course, even
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today, we talk about causes and effects all the time. But if you open the
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contemporary equivalent of Aristotle’s Physics— a textbook on quantum
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field theory, for example— words like that are nowhere to be found. We
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still, with good reason, talk about causes in everyday speech, but they’re no
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longer part of our best fundamental ontology.
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What we’re seeing is a manifestation of the layered nature of our de-
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scriptions of reality. At the deepest level we currently know about, the basic
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notions are things like “spacetime,” “quantum fields,” “equations of mo-
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tion,” and “interactions.” No causes, whether material, formal, efficient, or
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final. But there are levels on top of that, where the vocabulary changes.
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Indeed, it’s possible to recover pieces of Aristotle’s physics quantitatively, as