Theory of Special Relativity: Definition & Equation

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  • 0:03 Einstein's Theory
  • 0:34 Theory of Special Relativity
  • 1:29 Trains and Tribulations
  • 2:49 Consequences
  • 5:29 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

This lesson will go through the main postulates of the special theory of relativity and look at a few of the consequences. The principle equations will also be introduced. A short quiz will follow.

Einstein's Theory

Einstein was a genius and his work extremely complicated. It would be impossible to fully explain special relativity in a short lesson. But contrary to popular belief, it is possible to understand the basic ideas behind it without having a degree in physics. By the end of this lesson, you will be able to show off to your friends by saying that you actually understand the basics of Einstein's famous theory: a theory that changed physics forever.

Albert Einstein
Albert Einstein

What is the Theory of Special Relativity

Special relativity is a theory in physics that concerns the relationship between space and time and says that they're two sides of the same coin: spacetime. Like all scientific theories, it is backed by a large body of evidence and is widely accepted as being accurate.

The two main postulates of special relativity are:

  1. The laws of physics are the same in all reference frames that are moving at a constant velocity (not accelerating).
  2. Two: The speed of light is the same in all of these reference frames, even if the source of the light is moving.

A reference frame is just a particular point of view. An observer on a moving train is in a different reference frame to an observer beside the tracks. These two postulates might seem obvious, but they have some baffling and hard to understand consequences.

Trains and Tribulations

Einstein liked to explain his theories using thought experiments, so let's try one. Imagine for a moment that a person is sitting in the exact middle of a moving train car. This person releases a pulse of light in two directions: one towards the front of the train car, and the other towards the back. Which pulse of light reaches the edge of the train car first?

German ICE High Speed Train
German ICE High Speed Train

It turns out that the answer is relative. The answer depends on your point of view. To the person on the train, the light reaches both ends of the train car at the same time. This seems obvious to them - they're in the exact middle of the train car, and so, each pulse of light travels the same distance in the same time.

But someone watching the train from alongside the tracks would see something quite different. To them, because the train is moving, it catches up with the light pulse moving towards the back of the train car. So the backward-facing pulse gets to the back of the train first. For this to be noticeable, the train would have to be going a significant percentage of the speed of light, but it is still the case even if you can't see it at normal speeds. These might seem like contradictory answers, but according to special relativity, both observers are absolutely correct.

What Are the Consequences?

The train thought experiment shows how strange the consequences of special relativity can be, and there are many such consequences. The ones we will discuss in this lesson are length contraction, time dilation and mass-energy equivalence. Most of these consequences only apply when objects are moving at a significant percentage of the speed of light, otherwise they are unnoticeable.

Length contraction says that a moving object will appear shorter than an object that is stationary relative to the observer. This effect can be summarized by this equation:

Length Contraction Equation

Time dilation says that time passes at different rates depending on whether objects are moving relative to each other. As humans, we are used to time being a constant, but special relativity tells us that the passage of time actually varies depending on your point of view. This equation describes this difference in the amount of time that will have passed:

Time Dilation Equation

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