# Chapter 6: Relativity

## What is Relativity?

Some physical quantities depend on the perspective of an observer. Consider, for instance, the quantity we call speed. In order to determine the speed at which something is moving, we must first decide what isn’t moving. Here’s an illustration inspired by my morning commute to campus.

I hand my ticket to the train conductor, who is trudging down the aisle to collect fares from drowsy passengers. It’s still dark outside, and I forget for a moment that the train is in motion. From my present perspective, the conductor is moving slowly, perhaps half a meter per second, relative to the aisle of the train.

The train car rattles a little, and suddenly I remember that this vehicle is screeching along the rails at approximately 30 m/s. Now I regard the earth as being at rest, and from this new perspective, the conductor is moving rather quickly. As he walks at a pace of 0.5 m/s toward the front of the moving train, his speed relative to the ground is 30.5 m/s.

Then it occurs to me that the earth is also in motion, and my perspective changes again. The earth and its inhabitants are whizzing around the sun at nearly 30 kilometers per second, or approximately 66,000 miles per hour—about 40 times faster than a bullet, and almost 90 times the speed of sound. When I regard the center of our solar system as being at rest, the train conductor’s speed seems very fast indeed!

But why stop there? The sun is also in motion, relative to other stars in our galaxy. And our galaxy itself is moving relative to other galaxies. In fact, our Milky Way Galaxy and its nearest neighbor, the Andromeda Galaxy, are hurtling toward each other at an alarming speed of about 110 km/s, or 250,000 miles per hour.See here for more information about the impending collision.

Should I regard the Milky Way Galaxy as being at rest while other galaxies move, or should I instead consider some other galaxy at rest, and regard the Milky Way as being in motion? The choice seems arbitrary. Perhaps there is simply no fact of the matter which star or galaxy is truly at rest. In that case, I might as well consider the train to be at rest after all.

Oh, look! I’ve arrived at the station already. Or, rather, it has arrived at me?

The point of the above story is not to make you dizzy (though if you’re feeling dizzy already, brace yourself: the dizziness is going to get a lot worse later in this chapter). The point, rather, is that it is far from obvious whether the train conductor is objectively at rest or really in motion, in a way that doesn’t depend on anyone’s perspective. Some physical quantities—like speed and velocity—seem to depend on the perspective of an observer. Does this mean that everything is relative, or that it’s all just a matter of perspective? Definitely not, as I will explain.

When we choose to regard some object (or set of objects) as being at rest, we are choosing what physicists call a frame of reference (or a reference frame, or just a frame). A more precise definition will be given later in this chapter; for now, we can think of reference frames simply as perspectives concerning which objects are at rest. For example, one frame of reference considers the train to be at rest; another frame considers the earth to be at rest. In the train’s reference frame, the conductor is moving 0.5 m/s; in the earth’s frame, he’s going 30.5 m/s. And so on.

The train conductor’s speed depends on which reference frame we use to describe his motion. Numerous other physical quantities, besides speed, also differ from one reference frame to another. The conductor’s momentum and kinetic energy likewise vary between frames, for example. Quantities like these—quantities that vary from one reference frame to another—are called relative quantities.

Not all quantities in physics are relative, however. Many quantities are absolute in the sense that they do not depend on which frame of reference is chosen. For instance, electric charge is an absolute quantity: a proton has an electric charge of +1 e (approximately 1.6 × 10−19 coulombs)See chapter 2. regardless of how fast it is moving relative to other objects, and regardless of which objects are considered to be at rest.

All theories of physics agree that some quantities are relative and that others are absolute. However, it isn’t always obvious which quantities are absolute and which are relative. Common sense tells us that speed is always relative; but as we’ll see in this chapter, Albert Einstein theorized that common sense is wrong: the speed of light—unlike the speed of any other object—is not relative, it’s absolute! Moreover, the ways in which physical quantities depend on reference frames (and vice versa) turn out to be subtler than anyone expected.

A theory of relativity is a theory that tries to identify which quantities are absolute, and to describe exactly how the relative quantities vary depending on which frame of reference is chosen. In this chapter, we’ll examine Einstein’s theories: the Special Theory of Relativity and the General Theory of Relativity. Einstein was not the first physicist to propose a theory of relativity, however. To better understand his theories, it will be helpful to examine the historical context in which Einstein developed his ideas.

Relativity is not relativism! Theories of relativity in physics have nothing whatever to do with silly claims like “there are no absolutes” or “everything is relative.” All scientific theories of relativity, including Einstein’s, say that there are absolutes. Nor should relativity be confused with any of the numerous philosophical views that go by the name “relativism”—e.g. moral relativism, which claims that there are no moral absolutes, or alethic relativism, which claims that truth is all a matter of perspective. Views such as these are definitely not supported by scientific theories of relativity.