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

AI Thread Summary
The discussion centers on the derivation of the length contraction formula using the Lorentz transformation, specifically addressing why dx must be measured in the prime frame. It highlights that when converting from dx to dx', the time component must be zero, leading to the equation dx' = gamma(dx). The confusion arises when considering whether dx can represent an object's length in the unprimed frame, as this would yield an incorrect longer measurement by the primed observer. The key point is that dx must reflect the length measured in the prime frame to maintain consistency with the principles of relativity. Understanding this distinction is crucial for correctly applying the concept of length contraction in relativistic contexts.
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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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