Ciro Santilli
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# Lorentz transformation | 🗖 nosplit | ↑ parent "Special relativity" | 224, 7, 1k

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The equation that allows us to calculate stuff in special relativity!
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Take two observers with identical rules and stopwatch, and aligned axes, but one is on a car moving at towards the direction at speed .
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TODO image.
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When both observe an event, if we denote:
• the observation of the standing observer
• the observation of the ending observer on a car
It is of course arbitrary who is standing and who is moving, we will just use the term "standing" for the one without primes.
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Then the coordinates of the event observed by the observer on the car are: $$t′x′y′z′​=γ(t−c2vx​)=γ(x−vt)=y=z​ (8)$$ where: $$γ=1−c2v2​​1​ (9)$$
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Note that if tends towards zero, then this reduces to the usual Gallilean transforms which our intuition expects: $$t′y′z′​=tx′=y=z​=x−vt (10)$$
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This explains why we don't observe special relativity in our daily lives: macroscopic objects move too slowly compared to light, and is almost zero.
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