The Big Picture

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The Big Picture Page 5

by Carroll, Sean M.


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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

 

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