Length Contraction: Why Must dx be Measured in the Prime Frame?

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SUMMARY

The discussion centers on the derivation of the length contraction formula using the Lorentz transformation, specifically addressing the necessity of measuring dx in the prime frame. The transformation indicates that when converting from dx to dx', the time component must be zero, resulting in the equation dx' = gamma(dx). The key point is that dx must represent the length measured in the prime frame to accurately reflect the effects of relative motion, as measurements taken in the unprimed frame yield incorrect results. This highlights the importance of frame selection in relativistic measurements.

PREREQUISITES
  • Understanding of Lorentz transformations
  • Familiarity with the concept of gamma (γ) in special relativity
  • Knowledge of reference frames in physics
  • Basic grasp of length contraction in special relativity
NEXT STEPS
  • Study the derivation of the Lorentz transformation equations
  • Explore the implications of gamma (γ) in relativistic physics
  • Investigate the concept of simultaneity in different reference frames
  • Learn about the experimental evidence supporting length contraction
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Students and professionals in physics, particularly those focusing on special relativity, as well as educators seeking to clarify concepts related to length contraction and reference frames.

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The Lorentz transformation for motion in the same direction along the x-axis of two frames can be used to derive the length contraction formula. Say we are converting from dx to dx'. The t would obviously have to be 0. That would leave us with dx'=gamma(dx). My question is why dx here has to be the length measured in the prime frame? If we do pick an object in the prime frame we get a longer length that the prime observer measures. However what happens if we pick dx to be an object length in the unprimed frame? Then again it turns out that the primed observer would get a longer measurement but I know this isn't correct. I'm just trying to find the reason as to why dx has to be the length of an object measured in the PRIME frame with a relative velocity and why it cannot be a stationary object.
 
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I mean why can I not measure the object instantaneously in my own frame and enter it as dx.
 

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