Science Weblecture for Unit 56

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**Topic area**: Relativity**Terms and concepts to know**: ether, contraction and dilation, absolute speed, simultaneity**See historical period(s)**: 1890-1920

**Lecture**:

Relativity asks the question: "What does it mean for two events to be simultaneous?" It recognizes that different observers use different ways of measuring time and location from some point of reference. Einstein's thought experiments involved observers who where stationary (not moving) relative to one another but at different distances from an event. He realized that because light travels at a finite speed, the two observers would see the event at different times. In normal life, where people are relatively close to one another, the small differences in observations does not affect our calculations or general conclusions, but when we start looking at objects on very large or very small scales, or try to reconcile the experiences of observers moving at very different speeds, classical mechanics can no longer explain what we *actually* observe.

Any time we discuss velocity or acceleration, we use a *frame of reference* to measure distance traveled and time elapsed. The frame of reference can be any convenient set of coordinates. For example, when considering a car with an open sunroof moving down the road, we can use a frame of reference that is fixed to the road. We also pick directions -- for example, we might start counting from Main Street, positively in the north direction and negatively in the south direction.

We could also use a frame of reference fixed to the car, with a point of origin in the middle of the sunroof.

Consider now a person standing on the seat of the car with his head and arms through the sun roof as the car rolls down a deserted street at 20 mph, facing south as the car moves north. Our aspiring baseball player tosses a ball at 95mph away from the car. From his point of view, in the frame of reference of the car, the ball is moving at 95mph with respect to the car. However, from the frame of reference of a person on the street, who has to take into account both the motion of the car forward at 20mph and the motion of the ball rearward from the car at 95mph, the ball only appears to be going 75mph.

In classical mechanics, frames of reference for non-accelerating systems are equivalent. If we analyze the forces involved using either frame of reference, we will get equivalent answers once we take into account the difference in velocities of the frames of reference relative to each other.

To see how this works, study the basic concepts on Frames of Reference.

- What is a frame of reference? How do we determine a "convenient" frame of reference?
- Why can two different frames of reference be used to analyze a situation?
- How does acceleration affect phenomena perceived in the accelerating frame of reference?

Now that you've got that down, it is time to enter the weird and wonderful world of relativity.

Read about the theory of special relativity at the Nobel Prize site. There are seven sections, one each on

- The Michelson-Morley Experiment .
- The Postulates of Relativity
- The Twin Paradox
- Lorentz Transformations
- Mass-Energy Equivalency
- Relativity as a Tool
- The History of Relativity

- How did the Michelson-Morley Experiment show there was no ether?
- What are the two main postulates of special relativity? What do we mean by "inertial frame of reference"?
- What is a
*gedanken*experiment? Why does one use these in analyzing relativity situations? - What is simultaneity?
- What are Lorentz transformations?
- What does it mean to say that "time is relative"?
- What is the Lorentz contraction?
- What is the physical evidence for time dilation?
- What is Minkowski space?
- What is the "twin paradox"?
- What do we mean by "mass energy equivalence"?

As formulated, special relativity applies only to inertial reference frames. In point of fact, most systems are accelerating, so Einstein proposed a general theory of relativity to cover those situations as well.

Read about general relativity at the USC astronomy course site. [1 long page.]

- What is covariance?
- What is "curved spacetime"?
- What do we mean by linear and non-linear geometry?
- What three classical situations can relativity explain that cannot be explained by classical or Newtonian mechanics?

- How does the theory of relativity affect people in their daily lives?
- Why is it important to recognize the differences between a relativistic and classical universe?

- No extra links for this unit.

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