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by reaperman
598 days ago
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Your [0] provides the "classical" equation for momentum transfer (p=mv), which is only reasonably accurate up to speeds 40-50% of the speed of light. But TFA talks about accelerating electrons to 80% of the speed of light. Then it's p=γmv where γ=1/sqrt(1-v^2/c^2) Basically, it's taken as a "fact" that the relative speed of light is the same for two observers regardless of one observer's velocity vs. the other observer's. So if something is going 0.8x the speed of light, but light is still somehow observed to be traveling at the same speed for both (speed of light relative to both the fast-moving observer and the slow-moving observer), this apparent inconsistency is solved by realizing that ("magically") lengths are contracted for the faster observer. So the light appears to go the same distance to both observers, because distance itself is different to the two observers. The net effect is that from 0.5x to 0.99999x the speed of light, momentum increases asymptotically as an object approaches the speed of light. Theoretically, if your spaceship could (truly magically) capture the momentum from ejecting one single electron to 0.9999....(58 nines in total)... a 1,000kg spaceship could achieve escape velocity to leave the entire solar system just from that one electron! 0: https://library.fiveable.me/principles-of-physics-iv/unit-9/... 1: https://en.wikipedia.org/wiki/Lorentz_factor |
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