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Figure 1. People might describe distances differently, but at relativistic speeds, the distances really are different. Have you ever driven on a road that seems like it goes on forever? If you look ahead, you might say you have about 10 km left to go. If you both measured the road, however, you would agree. Traveling at everyday speeds, the distance you both measure would be the same. You will read in this section, however, that this is not true at relativistic speeds. Close to the speed of light, distances measured are not the same when measured by different observers.
One thing all observers agree upon is relative speed. Even though clocks measure different elapsed times for the same process, they still agree that relative speed, which is distance divided by elapsed time, is the same. If two observers see different times, then they must also see different distances for relative speed Want u ton tkm or for foever be the same to each of them. To an observer on the Earth, the muon travels at 0. Thus it travels a distance. It has enough time to travel only. The distance between the same two events production and decay of a muon depends on who measures it and how they are moving relative to it.
Proper length L 0 is the distance between two points measured by an observer who is at rest relative to both of the points. The Earth-bound observer measures the proper length L 0because the points at which the muon is produced and decays are stationary relative to the Earth.
To the muon, the Earth, air, and clouds are moving, and so the distance L it sees is not the proper length. Figure 2. The Earth, air, and clouds are moving relative to the muon in its frame, and all appear to have smaller lengths along the direction of travel. To develop an equation relating distances measured by different observers, we note that the velocity relative to the Earth-bound observer in our muon example is given by.
The velocity relative to the moving observer is given by. The two velocities are identical; thus. Substituting this equation into the relationship above gives. If we measure the length of anything moving relative to our frame, we find its length L to be smaller than the proper length L 0 that would be measured if the object were stationary. Those points are fixed relative to the Earth but moving relative to the muon. Figure 3. She can travel this shorter distance in a smaller time her proper Want u ton tkm or for foever without exceeding the speed of light.
First note that a light year ly is a convenient unit of distance on an astronomical scale—it is the distance light travels in a year. For Part 1, note that the 4. To the astronaut, the Earth and the Alpha Centauri are moving by at the same velocity, and so the distance between them is the contracted length L. First, remember that you should not round off calculations until the final result is obtained, or you could get erroneous. This is especially true for special relativity calculations, where the differences might only be revealed after several decimal places. Since the distance as measured by the astronaut is so much smaller, the astronaut can travel it in much less time in her frame.
People could be sent very large distances thousands or even millions of light years and age only a few years on the way if they traveled at extremely high velocities. But, like emigrants of centuries past, they would leave the Earth they know forever. Even if they returned, thousands to millions of years would have passed on the Earth, obliterating most of what now exists.
There is also a more serious practical obstacle to traveling at such velocities; immensely greater energies than classical physics predicts would be needed to achieve such high velocities. This will be discussed in Relatavistic Energy. Figure 4. The electric field lines of a high-velocity charged particle are compressed along the direction of motion by length contraction.
This produces a different al when the particle goes through a coil, an experimentally verified effect of length contraction. The distance to the grocery shop does not seem to depend on whether we are moving or not.
But length contraction is real, if not commonly experienced. For example, a charged particle, like an electron, traveling at relativistic velocity has electric field lines that are compressed along the direction of motion as seen by a stationary observer.
See Figure 4. As the electron passes a detector, such as a coil of wire, its field interacts much more briefly, an effect observed at particle accelerators such as the 3 km long Stanford Linear Accelerator SLAC. In fact, to an electron traveling down the beam pipe at SLAC, the accelerator and the Earth are all moving by and are length contracted. The relativistic effect is so great than the accelerator is only 0. It is actually easier to get the electron beam down the pipe, since the beam does not have to be as precisely aimed to get down a short pipe as it would down one 3 km long.
This, again, is an experimental verification of the Special Theory of Relativity.
To an Earth-bound observer, the distance it travels is 2. Special Relativity. Search for:. Length Contraction Learning Objectives By the end of this section, you will be able to: Describe proper length. Calculate length contraction. Proper Length Proper length L 0 is the distance between two points measured by an observer who is at rest relative to both of the points. Example 1. She travels from the Earth to the nearest star system, Alpha Centauri, 4. How far apart are the Earth and Alpha Centauri as measured by the astronaut?
In terms of cwhat is her velocity relative to the Earth? You may neglect the motion of the Earth relative to the Sun. See Figure 3. Conceptual Questions To whom does an object seem greater in length, an observer moving with the object or an observer moving relative to the object? Relativistic effects such as time dilation and length contraction are present for cars and airplanes.
Why do these effects seem strange to us? Suppose an astronaut is moving relative to the Earth at a ificant fraction of the speed of light. What is its length as measured by an Earth-bound observer? How fast would a 6. Base your calculation on its velocity relative to the Earth and the time it lives proper time.
Unreasonable. An astronaut measures the length of her spaceship to be A spaceship is heading directly toward the Earth at a velocity of 0. The astronaut on board claims that he can send a canister toward the Earth at 1. s and Attributions. CC d content, Shared ly.Want u ton tkm or for foever
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