Relativity: Explaining Length Contraction from γL to L

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SUMMARY

The discussion centers on the concept of length contraction in the theory of relativity, specifically how the distance between two balls moving at speed v changes from γL to L. Here, γ (gamma) represents the Lorentz factor, which accounts for relativistic effects. When observed from the frame of reference of stationary observers, the distance between the balls is perceived as L due to length contraction, despite being γL in the balls' rest frame. This illustrates the principle that simultaneity is relative, as events that are simultaneous in one frame may not be in another.

PREREQUISITES
  • Understanding of the Lorentz factor (γ) in special relativity
  • Basic knowledge of reference frames in physics
  • Familiarity with the concept of simultaneity in different frames
  • Comprehension of length contraction principles in relativity
NEXT STEPS
  • Study the derivation of the Lorentz transformation equations
  • Explore the implications of simultaneity in different inertial frames
  • Investigate the mathematical formulation of length contraction
  • Examine practical applications of relativity in modern physics
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Physics students, educators, and anyone interested in understanding the principles of special relativity and their implications on space and time measurements.

Tonyt88
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Relativity

Two balls move with speed v along a line toward two people standing along the same line. The proper distance b/w the people is L, and the proper distance b/w the ball is γL [Note: γ is gamma]. Due to length contraction, the people measure the distance b/w the ball to be L, so the balls pass the people simultaneously (as measured by the people). Assume tha the people's watches both read T at this time. If the people catch the balls, then the resulting proper distance b/w the balls becomes L, which is shorter than the inital proper length of γL [Note: γ is gamma].

By working in the frame in which the balls are initially at rest, explain how the distance b/w the balls decreases from γL to L.
 
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Hint: Spatially separated events that are simultaneous in one reference frame may not be simultatneous in a reference frame in motion relative to the first frame.
 

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