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Lesson 2: Time Dilation

Lesson 1: Relativity - What is it?

  1. Fermilab's Time Dilation Challenge.
  2. The Basics of Relativity (6 seconds)
  3. The Relativity Game - Challenge what you know!

Note: For Fermilab's Time Dilation Challenge and The Relativity Game, you need Shockwave. You may painlessly Download Shockwave here if you do not have it.

Lesson 2: Time Dilation

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the basketball analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

Lesson 3 : Relativistic Mass

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the space pool analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

Lesson 4 : Length Contraction

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the pole and the barn analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

Some muon facts!

Muons are famous cousins of electrons. In the 1950's scientists observed muons to have an average lifetime of 2.2 x 10-6 seconds. Knowing this, scientists knew that if they went to the top of a mountain to count the number of muons present, the number should drop considerably if the same measurements were taken at the bottom of the mountain. However, because of relativistic effects, many more muons make it to sea level than predicted without relativity. This is one of much data that supports relativity.

If you put all the problems you have an opportunity to work together with the muon, you can see how the different areas of relativity complement each other.

Time Dilation:

Without time dilation and with its 2.2 x 10-6 seconds lifetime, the muon should only travel 660 meters traveling at 0.998 c . With time dilation, the muon's lifetime is 34.8 x 10-6 seconds allowing it to travel 10,400 meters. This carries it down into the earth's atmosphere.

Length Contraction:

The muon travels 10,400 meters in the earth's reference frame as it travels 0.998 c. At this speed, the muon measures the earth's 10,400 meters of atmosphere to be 660 meters. Therefore, its lifetime of 2.2 x 10-6 seconds is enough to carry it through the atmosphere!

Relativistic Mass:

The muon is also observed to be more massive at 0.998 c. Given a push from the earth's frame, the muon would not cover as much distance in a small time as we would predict at relativistic speeds. Combining this with its time dilation makes it appear more massive.

Check out Fermilab's Time Dilation Challenge to see a recent example of lifetime dilation!

Lesson 2: Time Dilation

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the basketball analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

 


© Brian Wegley, 1998
Comments and suggestions can be sent by e-mail to
Brian Wegley of Glenbrook South High School..
This page last updated on 7/23/98.