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Alsadius comments on Harry Potter and the Methods of Rationality discussion thread, part 17, chapter 86 - Less Wrong
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So what would it do with a wizard who had truly internalized the principle of relativity, and who understood that there was no privileged reference frame? Could he use it to de facto impart an arbitrary velocity to an arbitrary object?
You can equalize velocity of a given small object with that of the caster's reference frame. The excess momentum is transferred to the Earth (or potentially another massive body, though there is no proof that magic works outside the Earth's atmosphere, which incidentally means that the Pioneercrux may have decayed). This way there is no preferred reference frame.
Of course there's no proof, but I don't think it's really possible, if only for literary reasons, that the Sphere of Stars spell is just a fancy hologram. I think we can take that as fairly strong evidence it's working as intended.
So "arbitrary" might be a bit strong, but what's to prevent him from using the Moon or the Sun as a reference frame? Or even the Earth as a whole, instead of the local part? Even imparting a relative 1000 mph to an object near the equator would be pretty powerful.
"the caster's rest frame" is relativistically invariant.
But he didn't say "the caster's reference frame", he said "some much larger mass that the wizard thinks is a reference frame".
Just saying that if the spell is designed to work relative to the rest frame, then no amount of relativistic internalizing will change how it works. Of course it is possible in the HPMOR universe to design new spells, and a competent Wizard with a good grasp of invariance in physics might be able to create a new spell, Attache Momentum.
And I'm just saying, the way Eliezer phrased it above, there's no singular reference frame - any suitable mass will do.
You are right, he did phrase it this way, which makes this spell unreasonably easy to munchkin. He would have probably thought harder about it were he a DM of an actual DD game.
It seems like a hack of the rules on the level of partial transfiguration. Also, if you house-rule that it requires "magical energy" in proportion to the delta-momentum, it shouldn't be too overpowered.