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28.3 Length Contraction

- The distances are different at high speeds.

- You could say you have about 10 km left to go.
- A traveler might say the road is about 15 km long.
- You would agree if you measured the road together.
- The distance you both measure would be the same.
- This is not true at high speeds.
- When measured by different observers, distances are not the same.

- Relative speed is one thing all observers agree on.
- Relative speed, which is distance divided by elapsed time, is the same, even though clocks measure different elapsed times for the same process.
- The observer's relative motion affects the distance.
- If two observers see different times, they must also see different distances for relative speed to be the same to each of them.

- The muon travels from the time it is produced until it decays.

- The lifetime of the muon is in the frame of reference.

- The distance between the production and decay of a muon depends on a number of factors.

- The points at which the muon is produced and decays are stationary relative to the Earth, so the Earth-bound observer measures the proper length.
- The distance that the muon sees is not the proper length because the Earth, air, and clouds are moving.

- The Earth, air, and clouds seem to be moving in a different direction than the muon.

- The object being timed is moving relative to the observer.

- The observer travels with the muon and observes the time.

- An equation relating the distances measured by different observers is given by substituting for.

- If we measure the length of anything moving relative to our frame, we find it to be smaller than the proper length that would be measured if the object were stationary.
- The muon's reference frame shows the distance between the points where it was produced and where it decayed.
- The points are moving relative to the muon.
- Clouds and other objects are contracted by the muon's reference frame.

- An astronauts such as the twin discussed in Simultaneity and Time Dilation would travel so fast.
- The Earth is relative to the Sun.

- She can travel in a shorter time without exceeding the speed of light.

- It is the distance light travels in a year that is a light year.

- The 4.300 ly distance between the Alpha Centauri and the Earth is the proper distance because it is measured by an Earth-bound observer.
- The contracted length is the distance between the Earth and Alpha Centauri.
- We can find this by rearranging the definition of to express in terms of.

- The knowns should be identified.

- The appropriate equation can be chosen.

- To solve for the unknown, Rearrange the equation.

- The known can be identified.

- The appropriate equation can be chosen.

- To solve for the unknown, Rearrange the equation.

- You should not round off calculations until the final result is obtained.

- For special relativity calculations, the differences might only be revealed after several decimal places.

- The effect is large and approaching the speed of light.
- The astronauts distance is so small that she can travel it in less time.

- If they traveled at a high rate of speed, people could be sent thousands or millions of light years away and they would only have a few years to live.
- They would leave the Earth the same way they left centuries past.
- If they came back, thousands to millions of years would have passed on the Earth, obliterating most of what now exists.
- It is more practical to travel at such high speeds than it is to classical physics predicts.
- In Relatavistic Energy, this will be discussed.

- We don't seem to know the distance to the grocery shop if we are moving or not.
- The classical expectation is that the lengths are nearly equal.
- If not commonly experienced, length contraction is real.
- A charged particle, like an electron, has electric field lines that are compressed along the direction of motion as seen by a stationary observer.
- The effect of the electron passing a coil of wire on its field is observed at particle accelerators.
- The Earth is moving by and the beam pipe is being traveled down by an electron.
- The effect is so strong that the electron is only half the size.
- It is easier to get the electron beam down the pipe than it is to go down one 3 km long.

- This is an experimental verification of the theory.

- The electric field lines of a high-velocity charged particle are compressed.

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