Ciro Santilli
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Lorentz transform consequence: everyone sees the same speed of light | 🗖 nosplit | ↑ parent "Lorentz transformation" | 311

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OK, so let's verify the main desired consequence of the Lorentz transformation: that everyone observes the same speed of light.
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Observers will measure the speed of light by calculating how long it takes the light going towards cross a rod of length laid in the x axis at position .
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TODO image.
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Each observer will observe two events:
  • : the light touches the left side of the rod
  • : the light touches the right side of the rod
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Supposing that the standing observer measures the speed of light as and that light hits the left side of the rod at time , then he observes the coordinates:
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Now, if we transform for the moving observer:
and so the moving observer measures the speed of light as:
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