Length Contraction and Time Dilation in Relativity: An Electron's Perspective

In summary, an electron traveling in an accelerator tube at a speed of 0.997 c relative to Earth has a length of 1.20 m in its own frame of reference. To determine the length of the tube relative to Earth, the equation l = lo √1-v^2/c^2 was used, resulting in a length of 15.5 m. The time it takes for the electron to travel the full length of the tube in Earth's frame of reference was calculated using t = d/v, giving a value of 5.18 x 10^-8 seconds. In the frame of reference of the electron, the speed of the tube is 0.997 c, and it takes 4.012
  • #1
RichardT
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Homework Statement


An electron travels in an accelerator tube at a speed of 0.997 c relative to the Earth. In the frame of the electron, the length of the tube is 1.20 m.
A. What is the length of the tube relative to Earth?

B. Relative to Earth, how long does it take for the electron to travel the full length of the tube?

C. In the frame of reference of the electron, What is the speed of the tube?

D. In the frame of reference of the electron, how long does it take for the full length of the tube to pass the electron?


Homework Equations


l = lo √1-v^2/c^2
t = d/v
c = speed of light = 3.0 x10^8m/s

The Attempt at a Solution


For Part A. I did l = lo √1-v^2/c^2 and plugged it in so 1.2 = lo√1-(0.997)^2 and solved for lo which became to be 15.5m

For Part B. i used t = d/v and plugged in t = 15.50m/0.997c = 5.18 x 10 ^-8 seconds

For Part C. I said that the speed is the same and is constant so speed of the tube in frame of reference of the electron = 0.997c

For Part D. t= d/v = 1.20m/0.997c = 4.012 x 10^-9 seconds.

Something just doesn't feel right about this, Please check if i did it properly.
 
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  • #2
Looks okay to me. :)
 

1. What is length contraction in the context of special relativity?

Length contraction is a phenomenon predicted by special relativity, which states that the length of an object in motion will appear shorter to an observer than its actual length when at rest.

2. How does length contraction occur?

Length contraction occurs because of the dilation of time and space as objects move at high speeds. As an object's velocity increases, its length in the direction of motion appears shorter to an outside observer.

3. Is length contraction a real physical phenomenon?

Yes, length contraction has been observed and confirmed through various experiments and observations, such as the famous Muon experiment. It is a fundamental principle of special relativity and is used in many technologies, such as GPS systems.

4. What is the formula for calculating length contraction?

The formula for calculating length contraction is L' = L * √(1 - v^2/c^2), where L' is the contracted length, L is the rest length, v is the velocity of the object, and c is the speed of light.

5. Can length contraction be reversed?

No, length contraction is a fundamental property of special relativity and cannot be reversed. However, as an object's velocity decreases, its length will appear longer to an outside observer, but it will never return to its original rest length.

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