# This Is Why Understanding Space Is So Hard

If all the matter in the universe suddenly disappeared, would space still exist? Isaac Newton thought so. Space, he imagined, was something like Star Trek’s holodeck, a 3-dimensional virtual-reality grid onto which simulated people and places and things are projected. As Newton put it in the early pages of his Principia: “Absolute space, of its own nature, without reference to anything external, always remains homogeneous and immovable.” 1

This seems persuasive in everyday life. I’m walking east, you’re walking west, and the post office stays put: The frame of reference remains static. But Newton’s contemporary, the German mathematician and philosopher Gottfried Leibniz, balked at this idea of absolute space. Take away the various objects that make up the universe, he argued, and “space” no longer holds any meaning. Indeed, Leibniz’s case starts to look a lot stronger once you head out into space, where you can only note your distance from the sun and the various planets, objects that are all moving relative to one another. The only reasonable conclusion, Leibniz argued, is that space is “relational”: space simply is the set of ever-changing distances between you and those various objects (and their distances from one another), not an “absolute reality.” 2

Au contraire, responded Newton. The effects of absolute space are quite observable. And Sir Isaac had just the experiment to prove it: a spinning bucket of water. Simple as the experiment may sound, it set off a debate about the nature of space, time, motion, acceleration, and force that continues to this day.

Ever since the formation of the solar system, billions of years ago, Earth’s been spinning around with its equator “bulging out,” just like the water in the spinning bucket.

In the Principia, Newton asks us to imagine a bucket of water, suspended by its handle from a rope. Turning the bucket clockwise, the rope winds up. What happens when you let go? The bucket begins to spin counter-clockwise, slowly at first, then faster. But something else happens, too: As Newton writes, the surface of the water “will gradually recede from the middle and rise up the side of the vessel, assuming a concave shape.” For a while, the bucket and the water spin together. Eventually, the bucket slows and its spin reverses; the water slows too, gradually flattening again.

High school students learn about “centrifugal force”—it’s nice to have a name for it—but what’s actually causing the water to rise up against the rim of the bucket? It can’t be the motion of the water relative to the bucket, Newton observed, because the water’s surface is most distorted when the water is spinning most rapidly, “in synch” with the bucket. Of course, the bucket and the water are spinning relative to Earth, but that can’t be the explanation, either, because a similar experiment performed in space, Newton believed, would produce the same results.

For Newton, the only way to explain the bucket experiment was to say that the water was spinning with respect to absolute space. This meant invoking inertia—another key idea in the Principia—the resistance of a body to any change in its speed or direction of motion. Once the bucket and the water are spinning, the sides of the bucket prevent the water from moving in a straight line; it pushes up against the rim instead.

But why do objects have inertia in the first place? In the 19th century, Austrian physicist Ernst Mach came to believe that any explanation of motion and inertia—including the motion of water in a spinning bucket—could only be understood in relation to the rest of the matter in the universe. For Mach, a scaled-up version of the bucket could be seen in the Earth itself: Ever since the formation of the solar system, billions of years ago, Earth’s been spinning around with its equator “bulging out,” just like the water in the spinning bucket. Mach wondered: If Earth’s rotation could be stopped, and instead the rest of the planets and stars spun around it, would Earth’s equator still bulge?

Newton would have said no: No spin, no bulge. But Mach realized that the answer depended on where an object’s inertia comes from. If it were somehow the result of the bulk of the matter in the universe, then indeed the planet would still bulge as the rest of the planets and stars turned around it.3 This is Leibniz’s relational picture on steroids: Not only is motion relative, but inertia, Mach decided, is a measure of the relationship between the object and the rest of the matter in the universe. If Mach’s view is right, the stars and galaxies, near and far, are, in some sense, responsible for Earth’s shape and the concave shape of the water in Newton’s spinning bucket. But Mach didn’t say how those distant stars and galaxies exerted their influence—and even today, the answer is far from clear.

Perhaps Mach’s keenest reader was the young Albert Einstein, who would later struggle to incorporate what he referred to as “Mach’s Principle”—that the inertia of a body is dependent on the aggregate of matter throughout the universe—into his theory of gravity, General Relativity.

The overwhelming success of Einstein’s theory was the final blow for Newton’s absolute space—but without absolute space, we continue to struggle to make sense of Newton’s bucket. In his popular book The Fabric of the Cosmos, physicist Brian Greene explains that although Einstein’s theory demolished Newton’s absolute space, it gave us something else in its place—a four-dimensional structure known as spacetime—and this, Greene argues, is absolute. You and I might disagree about the duration of a parade, or the distance that the marchers covered—but we’d agree on the total distance through spacetime between the start and end of the parade. This is hard to picture, since we can’t see in four dimensions, but it’s guaranteed by the equations in Einstein’s theory.

And yet, this is not Greene’s final word on the matter. Physicists now suspect the “Higgs field,” believed to endow particles with mass, permeates the universe. Although Einstein’s spacetime might serve as a reference frame against which accelerations can be measured, the Higgs field goes one better: By offering resistance to anything that passes through it, it may explain why objects have inertia in the first place.

Still another idea comes from Arizona State University physicist Paul Davies, who points out that “empty” space is actually a seething foam made up of short-lived subatomic particles popping in and out of existence. This quantum “vacuum frolic,” he says, could serve as a substitute for absolute space.

After more than three centuries, the questions sparked by Newton’s spinning bucket—about space and motion, about mass and inertia—continue to trouble both physicists and philosophers. Something makes the water rise up against the side of the bucket—but whether it’s ultimately the structure of spacetime, or the Higgs field, or some kind of quantum foam, remains to be seen.

Dan Falk is a science journalist based in Toronto. His books include The Science of Shakespeare and In Search of Time. Follow him on Twitter @danfalk.

References

1. Cohen, I.B. & Whitman, A. Isaac Newton / The Principia: Mathematical Principles of Natural Philosophy: A New Translation University of California Press, Berkeley CA (1999). All quotations from The Principia are from this edition.

2. Alexander, H.G. The Leibniz-Clarke Correspondence, Together With Extracts from Newton’s Principia and Opticks Manchester University Press, Manchester (1956).

3. Barbour, J. & Pfister, H. (Eds.) Mach’s Principle: From Newton’s Bucket to Quantum Gravity (Einstein Studies, Volume 6) Birkhäuser, Boston, MA (1995).

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This classic Facts So Romantic post was originally published in January 2016.