*John Simmons*Show bio

John has taught college science courses face-to-face and online since 1994 and has a doctorate in physiology.

Lesson Transcript

Instructor:
*John Simmons*
Show bio

John has taught college science courses face-to-face and online since 1994 and has a doctorate in physiology.

The relativity of distance and time accounts for the constant speed of light. Explore the theory of relativity, classical relativity and an example, discover if motion and speed are relative, and learn about relativity at high speeds and how light speed can be constant.
Updated: 08/24/2021

The **theory of relativity** provides a way for observers to agree on what they see from different perspectives. The perception of an object can vary from situation to situation or from person to person. For example, objects up close appear to be larger than when farther away. Furthermore, objects traveling in a moving car appear to be at rest relative to the observer in the car. An observer on the side of the road, however, perceives the objects moving at the same speed as the car itself. In other words, while the objects in the car are not moving relative to the car, they are moving relative to the road. **Classical relativity** tells us that motion is relative to the observer's state of motion.

Here's a question: is all motion relative to the observer's state of motion as classical relativity would suggest? It appears the answer is no. Classical relativity breaks down at really high speeds - for example, the speed of light. Several observations and numerous experiments have shown that light travels at the same velocity regardless of the observer's perspective. Whether the observer is standing still or moving, the speed of light appears to be the same. **The speed of light** is 186,283 miles per second or 299,792 kilometers per second, and we abbreviate the speed of light with the letter *c*. To make our math easier, we're going to consider the speed of light to be 300,000 km/sec.

The speed of light is *c*, and it's *c* regardless of the source of the light or the perspective of the observer. Let's look at an example. Imagine you're traveling away from the sun at a velocity that is really close to the speed of light - let's say 250,000 km/sec (that's pretty fast). Let's have fun with this and say you can see a photon of light moving away from the sun and passing you up through some window on your spaceship. Now get out your trusty radar gun and measure the speed of light as it passes by the window. What would the speed of light measure relative to your ship?

Based on classical relativity, you might predict the velocity of the light relative to your ship to measure 50,000 km/sec, as your ship is already traveling 250,000 km/sec and 300,000 km/sec - 250,000 km/sec = 50,000 km/sec. However, you would measure the speed of light to be 300,000 km/sec. Don't buy a new radar gun just yet. As it turns out, your radar gun is correct. The speed of light is the same relative to your fast-moving ship or even an external stationary point.

Now let's say you shoot a laser of light away from your spaceship. Using your trusty radar gun, you would measure the speed of the laser to be 300,000 km/sec. Let's say your buddy has the same radar gun on Earth. How fast would she record the laser of light to be moving? You guessed it - your buddy would measure the velocity of 300,000 km/sec. As you see, the speed of light is the same relative to your fast-moving spaceship as it is relative to your buddy standing still on Earth. The speed of light is not relative.

We need to reconcile this apparent inconsistency of light speed with the theory of relativity - at least classical relativity. Is it possible for speed to be both relative to the perspective of the observer and constant when it comes to really fast-moving speeds such as light? Albert Einstein, perhaps the greatest physicist of the 20th century, proposed that both indeed are true. He proposed that a person traveling at a constant velocity will observe the same laws of physics as a person at rest.

Speed is a measure of distance traveled over time. This is true for light as well as it is for any other object in motion. Since light follows the laws of physics, Einstein postulated that all observers will measure the same speed of light regardless of their state of motion. In other words, light will travel at the same distance in the same amount of time.

We can understand Einstein's proposal by breaking down speed. **Speed** is simply a measure of distance traveled over time. In fact, we use the term **light year** to express the distance traveled by light in one year. The formula for speed is ** s = d / t** where

For example, one car traveling 10 miles in 1 hour and another car traveling 100 miles in 10 hours will both travel at a speed of 10 miles per hour - their speed is the same. Likewise, different observers can agree on the same speed of light if they disagree on distance and time. As it turns out, both distance and time are relative to speed. At very fast speeds, say the speed of light, time slows down and distance shortens. This allows both stationary and moving observers to record the same speed of light. But how does time slow down and how does distance contract at high speeds? These phenomena will be explained in subsequent lessons.

In summary, the **theory of relativity** provides a way for observers to agree on what they see from different perspectives. **Classical relativity** tells us that motion is relative to the observer's state of motion. However, classical relativity breaks down at the speed of light. The speed of light is not relative but rather is always measured at 300,000 km/sec. And that's regardless of the source of the light or the perspective of the observer. Einstein proposed that observers may have to disagree on distance and time in order to agree on the speed of light. As **speed** is a measure of distance over time, speed can remain constant if distance and time change by the same magnitude. Science has demonstrated that both distance and time shorten at really fast speeds. This allows the speed of light to be the same regardless of its source or the perspective of the observer. Therefore, distance and time are relative to speed.

After watching this lesson, you should be able to:

- Define the theory of relativity, classical relativity and speed
- Explain how the speed of light is always constant

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