I hereby declare Arresto Momentum to match the velocity of a small mass to the velocity of some much larger mass that the wizard thinks is a reference frame.
Does that mean Harry can’t use it (becuse there is no universal reference frame) or he can use it in all sorts of munchkiny ways (I stop the car … relative to the moon!)
Now I come to think, he would probably just conclude it uses Earth as a reference frame, just as broomsticks use Aristotelian physics and transfiguration uses form/substance duality.
You can’t use Arresto Momentum for that; you need a much more massive object as a reference, but your reference frame only contains massless objects. I guess you could say that massless objects have much larger mass than other massless objects, and use Arresto Momentum to make photons go in arbitrary directions with negligible losses.
If you can make a surface cast a long-lasting Arresto Momentum, you have a near-perfect mirror for all wavelengths from radio to gamma and all angles. That would be useful. (Of course you can also make the light slower if you wish, but the fun you can have with arbitrary refractive indices with no wavelength dependence and no absorption is redundant here.)
Also, if we figure out the necessary ratio of masses at given magical energy, we can use the spell to measure mass. Assuming your aim is precise enough to Arresto Momentum a neutrino, anyway.
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?
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.
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.
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.
I hereby declare Arresto Momentum to match the velocity of a small mass to the velocity of some much larger mass that the wizard thinks is a reference frame.
Does that mean Harry can’t use it (becuse there is no universal reference frame) or he can use it in all sorts of munchkiny ways (I stop the car … relative to the moon!)
Well, for one thing, he’s not powerful enough to cast it period, but if he were, I expect it would only work on near / nearest masses.
That requires original research, like partial transfiguration.
That’s what I had in mind, yes.
Original research is dangerous. This original research in particular seems dangerous.
Now I come to think, he would probably just conclude it uses Earth as a reference frame, just as broomsticks use Aristotelian physics and transfiguration uses form/substance duality.
http://en.wikipedia.org/wiki/The_Billiard_Ball
You can’t use Arresto Momentum for that; you need a much more massive object as a reference, but your reference frame only contains massless objects. I guess you could say that massless objects have much larger mass than other massless objects, and use Arresto Momentum to make photons go in arbitrary directions with negligible losses.
If you can make a surface cast a long-lasting Arresto Momentum, you have a near-perfect mirror for all wavelengths from radio to gamma and all angles. That would be useful. (Of course you can also make the light slower if you wish, but the fun you can have with arbitrary refractive indices with no wavelength dependence and no absorption is redundant here.)
Also, if we figure out the necessary ratio of masses at given magical energy, we can use the spell to measure mass. Assuming your aim is precise enough to Arresto Momentum a neutrino, anyway.
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.
What is it then? A signal sent from the pioneer horcrux?
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.