Stephen Hawking on the Relativity of Space and Motion

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Is space relative or absolute? What about motion? How are space and motion related to each other?

In A Brief History of Time, physicist Stephen Hawking shares his insights on some of the major scientific discoveries of the twentieth century that deepened our knowledge of the universe. These insights include Hawking’s explanation of the relative nature of space and motion. He provides his analysis of ancient and modern theories.

Continue reading to learn about Hawking’s insights on the relativity of space and motion.

The Relative Nature of Space and Motion

Hawking explains the relative nature of space and motion in his book A Brief History of Time. First, let’s consider the concept of relativity in general.

Relativity in the Big Picture

Philosophers have long argued about whether reality is objective or subjective: If something is true for me, does that make it true for you? Or could your truth be different and yet equally valid? Science is founded on the assumption that reality works the same for everyone: If two scientists conduct exactly the same experiment, they should get the same results. 

Ironically, this principle has driven scientists to the conclusion that many things, including motion, position, time, and weight are relative to the observer (or rather to the observer’s frame of reference, which is what you are taking measurements relative to). 

Space Is Relative 

To illustrate the relativity of space, Hawking begins by discussing how ancient theories of absolute space were disproven and then presents the more modern theories that replaced them.

Specifically, he explains that the ancient Greek philosopher Aristotle believed that space and motion were absolute. In other words, there was some frame of reference that all observers could agree was stationary, from which you could measure absolute position or velocity. 

Furthermore, as Hawking points out, Aristotle believed that objects would only move when force was applied to them. If the force was removed, they would stop moving. Thus, you could use anything that wasn’t moving as a reference for determining the absolute motion of anything that was moving. Of course, in Aristotle’s day, most people assumed the earth was stationary, so they believed it was an appropriate reference point from which to measure absolute motion (we know now that this isn’t true because the earth isn’t actually stationary—it’s moving through space).

However, Hawking recounts that Italian scientist Galileo Galilei observed objects in motion and found that Aristotle’s theory didn’t agree with observations. To explain Galileo’s observations, English scientist Isaac Newton developed a theory of motion that would come to be known as “Newtonian mechanics.” 

Unlike Aristotle’s theory, Newton’s theory predicted that an object in motion would stay in motion unless a force was applied to it to change its course. This challenged the concept of absolute motion, because it implied that objects didn’t naturally come to rest with respect to the absolute reference frame. And since objects didn’t naturally come to rest, there wasn’t any obvious way to establish an absolute reference frame (because everything is always moving).

Overview Newtonian Mechanics

Hawking’s stated purpose in writing A Brief History of Time is to make modern physics (mostly general relativity and quantum mechanics) accessible to a general audience. As such, he brings up some of Newton’s laws in passing and assumes that the average reader already has some understanding of traditional Newtonian mechanics, which may not be the case for all readers. Thus, to provide additional context, let’s consider an overview of Newtonian Mechanics. 

Newtonian Mechanics consists of four principles, known as Newton’s three laws of motion and Newton’s law of universal gravitation. (Some basic definitions: Your “velocity” is your change in position over time, and your “acceleration” is your change in velocity over time.)

Newton’s First Law of Motion states that an object’s velocity will not change unless a force is applied to the object.

Newton’s Second Law of Motion quantifies how much an object’s velocity will change when a force is applied to it. Specifically, it states that the force (F) required to make an object of a certain mass (m) accelerate at a certain rate (a) is given by the equation: F = m x a

Newton’s Third Law of Motion states that whenever objects apply forces to each other, the force on both objects at their point of contact is the same. For example, if you’re pushing your son on a swing, he feels the same amount of force applied to his back as you feel your hands applying to him.

Newton’s Law of Universal Gravitation states that the gravitational force of attraction between two objects is equal to the mass of the two objects multiplied together, divided by the square of the distance between them, and scaled by the gravitational constant. 

Newtonian Mechanics Implies Motion Is Relative

As Hawking points out, Newtonian mechanics implies that motion is relative to the observer because there is no absolute reference frame

To illustrate this concept, imagine you’re sitting in a boat on a body of water. Looking into the water, you see a fish swim by. Relative to your frame of reference, the fish is moving at a certain speed. But an observer on land might disagree. Let’s say the body of water is a river, and the fish is holding a constant position, relative to the river bottom, while your boat drifts by. So is the fish moving or staying in the same place? In an absolute sense, we can’t tell. Relative to your boat, the fish is moving. Relative to the earth, the fish is stationary. But of course the earth is also moving, relative to the sun, so the fish is moving relative to the sun. And the sun is moving, relative to the galaxy, and so on.

Applying Relative Motion to Driving

One familiar scenario where the relativity of speed becomes important is driving a car. To avoid collisions, you have to keep track of the motion of other cars relative to your own. You also have to keep track of your speed relative to the road, since posted speed limits are implicitly specified relative to the road. 

To maintain a constant following distance behind another car, you have to adjust your speed to be zero relative to the other car (meaning you’re traveling the exact same speed as the other car). Studies of traffic jams show that traffic jams form because of a chain reaction in how drivers respond to changes in the relative speed of other vehicles. Specifically, if you see the car in front of you slowing down, such that you have to apply the brakes to maintain a relative speed of zero, you’ll instinctively tend to over-compensate. The driver behind you will do the same, and so on, ultimately causing a traffic jam if there’s enough traffic on the road. 

Space Is Relative Because Motion Is Relative

Furthermore, as Hawking points out, if motion is relative, then location (or space) is also relative. In other words, we cannot tell, in any absolute sense, whether two events that happened at different times happened at the same location in space. 

To illustrate this, imagine you’re driving a car with a leaky sunroof. You just drove through a rain shower, and now water is dripping through the roof onto your head. From your perspective, each droplet of water lands in the same place. However, a pedestrian who watches you drive by sees one water drop hit your head as you pass her, and by the time the next drop hits you, you’re half a block further down the road from her. Relative to the pedestrian, each drip lands at a different location.

(Shortform note: You may not realize it, but you probably think in terms of relative space all the time. Since space is relative, you can only specify the location of something relative to a certain “frame of reference,” such as a landmark. According to professor Barbara Oakley, the human brain is wired to record “visuo-spatial information,”—that is, images of objects or scenes and where they’re located relative to each other. Oakley explains that these mental chains of interconnected reference points helped our ancestors to survive as hunter-gatherers. In other words, we’re wired to recognize the relativity of space.)

Stephen Hawking on the Relativity of Space and Motion

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Elizabeth Whitworth

Elizabeth has a lifelong love of books. She devours nonfiction, especially in the areas of history, theology, and philosophy. A switch to audiobooks has kindled her enjoyment of well-narrated fiction, particularly Victorian and early 20th-century works. She appreciates idea-driven books—and a classic murder mystery now and then. Elizabeth has a blog and is writing a book about the beginning and the end of suffering.

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