Can Two People in Relative Motion See the Other’s Point of View?


By Don Lincoln, Ph.D., Fermi National Accelerator Laboratory (Fermilab)

There are some very serious misconceptions about what relativity really is. It’s very easy to think that it is some complex and mysterious thing. However, relativity is something really very simple; it is about how two people in relative motion see the world differently. Read on to learn more.

Image representing the warping of spacetime.
Relativity is seen as a complex and complicated theory, but it has a few simple concepts underlying it. (Image: Rost9/Shutterstock)

Two Raging Egomaniacs at the Center of the Universe

When thinking about relativity, all that business about clocks and objects shrinking and velocities adding up in funny ways are actually true, but, at its core, that’s not what relativity is all about. Let’s start with a much more familiar example and illustrate what relativity does.

We’ll begin with two raging egomaniacs who are both moving with respect to one another. Both insist that they are at the center of the universe and that they’re not moving. Instead, the rest of the world is moving around them.

So, let’s call these two people A and B, and start with A’s perspective. From his perspective, he’s not moving and B is moving, for example, to the left. But, of course, from B’s perspective, he’s not moving, and A is moving to the right. They’re both adamant that their point of view is the right one, but they’re willing to try and see the world from the point of view of the other person.

This is a transcript from the video series Understanding the Misconceptions of Science. Watch it now, on The Great Courses Plus.

The Location of the Unmoving Observer

So, let’s start by asking what A thinks his location is. Well, since he claims that he’s not moving, then his location is unchanging.

Let’s start by naming the left-right direction as x and say that to the right of A is positive and to the left of A is negative. We could assign the number of his location as x0.

Now, let us look at locations around A. A location a mile to the right of A is x1 = +1 mile, and a location a mile to the left is x1 = –1 mile.

In fact, we can pick any location on the x axis and call it x1 and give it a value.

The Location in Relative Motion

Now, what does B see? Let’s say that when A passes B’s location, they both call that location 0, meaning that xA = 0, and xB = 0.

GPS location indicators representing multiple locations.
In relativity, locations of different places can seem to vary, based on who is observing the locations. (Image: LightAndShare//Shutterstock)

Let’s assume that B sees A moving to the right. Let’s use the symbol v to denote A’s velocity as far as B is concerned. Say A is moving 30 miles per hour to the right according to B. Then B would see A’s location as x2 = +30 miles after an hour, and x2 = +60 miles after 2 hours. We can generalize this to any location.

Additionally, the location that A sees to be stationary a mile ahead of him is also moving according to B. After an hour, it seems to be at a location of +31 miles, and after 2 hours, it seems to be at a location of +61 miles.

We can now generalize even more and figure out a formula for any location that A sees as stationary, which we will name x1, and what B would call its location, which we will name x2. The equation is simply this: x2 = x1 + (v*t) (t stands for time). That’s it.

Learn more about Einstein’s problems with time travel.

Primed and Unprimed Observers

Now, the two observers, A and B, would be generally called the unprimed observer and the primed observer. That means that the above equation can be written as xprime = x + (v*t).

So what does this equation show? It shows that if you take a location not moving with respect to the unprimed observer (A, in our example), you know its position according to the primed observer.

But there is something that is just stupefyingly obvious. Both the primed and unprimed observers experience time the same way.

If we call the primed observer’s time ‘tprime’ and the unprimed observer’s time just ‘t’, we can say that tprime = t.

These are very simple ideas. They just tell the two people who both claim to be the unmoving center of the universe how to convert a location that one of them says is stationary to the worldview of the person who claims that the other person is moving.

Galilean Transformations in Relative Motion

Close-up of a person's left eye.
The relativity transformations allow one observer to understand the other’s perspective in terms of motion and location. (Image: demarcocaio/Shutterstock)

Now, these two equations are not new. They are called the Galilean transformations, after Galileo Galilei. It turns out that Einstein’s transformations are different, but still similar to the Galilean ones. And they are identical in what they mean.

Relativity is nothing more and nothing less than a way to transform between the two viewpoints of two egomaniacs. Everything else is a consequence of that one thing. At its center, relativity is a very simple idea.

Learn more about how Einstein unifies space, time, and light.

Common Questions about Two People in Relative Motion

Q. In relativity, how is location of a place defined?

In relativity, any location can be defined with respect to its relative position to an observer. This observer is assumed to be static, and the other location may be visualized as either moving or unmoving with respect to the observer.

Q. What is an unprimed observer?

An unprimed observer is an observer who observes his own location, and for whom it is unmoving.

Q. Who is a primed observer?

A primed observer is an observer of a location which is in motion with respect to his own location.

Q. According to relativity, how do primed and unprimed observers experience time?

According to relativity, time is the same for both primed and unprimed observers.

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