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> I've always wanted to know why a ball doesn't follow a beam of light if they are both following straight lines in spacetime.

Because light is much faster. Throw a ball at the speed of light and you will see exactly the same path.

Lets say you shoot rifles with different calibers. Each time the bullet takes one second to hit the ground but the faster bullets travel longer distances. Light is so fast it escapes from the planet but if the planet were big enough even light would hit the ground like a bullet.



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