Resource: Motion and Relativity

Galileo Galilei was the first person to describe the principle of relativity, which states that the basic laws of physics are the same in all inertial reference frames. (An inertial reference frame is a frame of reference that moves at a constant speed and does not change in direction.) The laws of motion, as formulated by Isaac Newton, describe the basic laws of physics for the motion of objects under ordinary conditions. Thus, Galilean relativity is sometimes called Newtonian relativity.

As seen in the first half of the video, according to Galilean relativity, speeds in different inertial frames of reference can be added to determine the relative speed of a moving object. For example, imagine you throw a ball forward at 10 mph while standing on a boat that is floating down a river at 5 mph (in the same direction that you throw the ball). In your frame of reference, the ball moves forward at 10 mph. However, from the point of view of an observer standing on the riverbank, the motion of the ball is described differently; to the observer, the ball moves forward at the speed of the throw plus the speed of the boat. Measured in the reference frame of the observer on the riverbank, the ball moves forward at 15 mph.

Now imagine an experiment in which, instead of measuring the speed of a ball from different reference frames, you measure the speed of light. The speed of light is represented as c, approximately 186,000 miles/second (300,000 km/s) in a vacuum. According to Galilean relativity, you (on the boat) would measure the speed of light to be c and the observer on the riverbank would measure it to be c plus the speed of the boat. But it is known that the speed of light is invariable—in other words, the speed of light is constant in all reference frames. Even if your boat were moving at 50,000 miles per second, the observer on the riverbank will always measure the speed of light to be c, not the sum of the speed of the boat and c.

This example illustrates that Galilean relativity fails to adequately describe the speed of light in a moving reference frame. Albert Einstein's special theory of relativity takes the basic principle of Galilean relativity and combines it with the postulate that the speed of light is invariant. While Galilean relativity can adequately describe motion at low speeds, only Einstein's special theory of relativity can describe motion at or close to the speed of light. Einstein developed a new understanding of space and time, described their relationship mathematically, and dramatically changed our understanding of physics.

To learn more about time dilation, check out Speed of Light: Time Traveler.

To learn more about special relativity, check out Einstein's Special Theory of Relativity and Time and Relativity.

To learn more about Einstein’s general theory of relativity, check out String Theory: Newton's Embarrassing Secret and String Theory: A New Picture of Gravity.

• Why in Newton's world can you add the velocity of two moving objects?
• What do you think the velocity of the orange would be if the girl in the train threw it in the opposite direction from that in which the train is moving?
• You are on a train traveling east at 20 m/sec and toss a ball at 8 m/sec. How fast is the ball traveling? Does that question make sense? How can you turn it into a sensible question?
• Light travels at 300,000 km/sec. If you are on a very fast train going east at 100,000 km/sec and you shine the light forward, how fast is the light traveling to the east?