Mr. Bouyer

Day 1 - 2 | Day 3 - 4 | Lab | Vocabulary Test

This Week's	3D, 3E, 4B

Time Dilation Space Time Continuum Albert Einstein Relativity Speed of Light Michelson-Morley 1st Postulate of Relativity	Postulate Special Theory of Relativity Background Radiation String Theory Second Postulate of Relativity

Albert Einstein was not the first person to deal with the subject of relativity. Relativity actually has its roots in problems that were dealt with by Galileo. These problems were brought to the forefront of modern Science in 1887 when the Michelson-Morley experiment showed that the speed of light was a constant of approximately 186,282 miles per second.

The problem is that a staple of Classical Physics is the idea of addition of vectors. Example, if a an airplane is flying at a speed of 600 miles per hour and a passenger gets up and walks to the front of the plane at a speed of 3 miles per hour then the person is actually traveling at 603 miles per hour relative to the ground.

The problem is that according to the Michelson-Morley experiment that if a person were to shine a flashlight from the front of the same airplane, they would find the speed of the light beam would be 186,283 miles/second not 186,282 miles/second + 600 miles/hour. This may seem like a trivial problem to you but to scientists and mathematicians whose lives involve mathematics its about the equivalent of learning that 2+2=4.01 instead of 4.

In 1920, Einstein's book "Relativity: The special and general theory" was published. In the book, Einstein explained a way that this difference could be understood and he introduced the world to a slightly different way of looking at the universe then what they had done in the past.

Due to some pretty complex mathematics and abstract ideas, a full review of the book is beyond the scope of this lesson. Perhaps, I can explain a few of its concepts to you.

The interesting thing about the book is that it deals with things that occur at very high rates of speed. In Einstein's time is was very difficult to accurately measure light speed and impossible to accelerate objects to velocities close to it, so Einsteins book was a little different than most classical Science treaties. Einstein relied mostly on analogies to prove his theories and the actual proof of many of his ideas took years to become experimentally verified.
Let's begin by taking a close look at a couple of everyday events.

Concepts:

• Space (distance) is a relative concept, a trajectory that appears to be 2 foot long to one person may appear to be 3 foot long to an observer in a different frame of reference.

  Example: Let's say that a man on a moving bus is pitching a ball in the air. To the man, the ball only appears to be going up two feet and down two feet. A total trip of four feet. If the ball takes one second to complete the trip then the ball has a speed of 4 ft/sec.
  Now let's observe the same thing from the perspective of someone watching the same event from outside the bus. The bus provides a horizontal motion that is also affecting the ball. If we were to point at the ball as it went up and down we would actually have to trace out a line that was much longer than just four feet. If the ball still made this journey in 1 second then its speed would appear to be much faster to us.

• Time works in a similar way. Time may pass more quickly to one person than another in a different frame of reference. This idea is known as time dilation.

  Example: Einstein said that there is no such thing as an absolute time. That time itself was relative to the observer.
  He stated that if two events occured at exactly the same time they may be perceived differently by different observers.

  Einstein said to take a section of railroad track and measure off a distance of say 100 feet. Then find the midpoint between the two ends. Stand at the midpoint with a mirror that is shaped so that you can see both ends. Now let's say that lightning strikes both ends at exactly the same time. An observer at the midpoint would say the two lightning bolts struck at the same time.

  Now let's take our mirror and board the moving train and have the event happen again. As we hit the midpoint lightning strikes both poles again at the same time but we would not see the events at the same time. We would see the lightning strike the pole we are moving toward first and then a split second later we would see it strike the pole we are moving away from (the light would have to catch up to us as we moved away from the pole.)
  So therefore time is just as relative as distance.

  Now that Einstein proved that time could change just as much as distance it b Einstein actually applied a little algebra and geometry in the form of the Lorentz Equation to his time theory and came up with a mathematical equation that would allow someone to calculate the amount of time that time would seem to change with varying speeds.

  a² + b² = c²

  The math is not all that hard to understand.
  Speed X Time = Distance
  So;
  a=ct_{Frame1
  b=vt
  c=clight speedtimeFrame 2}

  Therefore:
  (ct)² = (vt)² + (c_{light speed}time_{Frame 2})²

  This equation can be changed to this form.
  
  This has some amazing results. Solving for each component, at the speed of light time stops and length shrinks to zero.

  The implications of relativity also greatly affect our present understanding of gravity

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