I just started the Kingkiller Chronicle, and I have gotten to the general explanation of how Sympathy works. I'm wondering if there's an explanation for what happens to the extra energy when you sympathetically bind dissimilar objects and energy "leaks".

Specifically, the concern I noticed is this:

Energy is supposed to be conserved. In a theoretical perfect sympathetic binding, lifting one object requires as much force as lifting both objects, but usually the binding "leaks", and lifting one object requires more energy than lifting both, and this leakage becomes even worse with dissimilar objects. Kvothe gives an example: he attempted to bind a piece of chalk with a bottle of water. The bottle only weighed about two pounds, but lifting it sypmathetically through the chalk was like lifting 60 pounds.

So now some math:

(at 9.81 m/s^2 of gravitational acceleration):

  • A piece of chalk weighs about 0.02N
  • A 2lb bottle of water weights about 9N
  • 60lbs is about 250N
  • Lifting the chalk and water bottle 1m would require 9.02J of energy
  • Lifting 60lbs 1m would require 250J of energy.

So if you lift the the two objects using sympathy, you expend 250J, but if you break the sympathetic link while the objects are elevated, the two resulting objects have only a combined 9.02J of gravitational potential energy. What happens to the other 240.98J of energy you expended to get them there?

Side note

This also applies in reverse, if you lift the objects normally, then sympathetically link them, and drop one. If dropping one object while they are sympathetically linked exerts significantly more force on the other object, then creating the sympathetic link creates 240.98 extra joules of energy instead of removing it. You could theoretically build a a perpetual motion machine this way.

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    I'm strongly tempted to close this as real-world science but I think it can be explained in-universe. – KutuluMike Nov 28 '16 at 17:04
  • It's entirely possible it can't be explained in-universe. It's really hard to construct a magic system that doesn't inadvertently allow you to break conservation of energy, no matter how hard you try to avoid it. (I'm not convinced it would actually fully conserve energy even if these links didn't leak). – zstewart Nov 28 '16 at 17:07
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    I don't think your side note is correct. The link is weak both ways, energy is never created, only dispersed. – DaaaahWhoosh Nov 28 '16 at 17:14
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    @zstewart I mean that dropping either object would impart a lesser force on the non-dropped object. It's not that one object is heavy and the other is light, it's that the effort required to move an object over a sympathetic link is greater in inverse proportion to the quality of the link. – DaaaahWhoosh Nov 28 '16 at 17:57
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    @DaaaahWhoosh the force from one object also has to impart a greater force on the other object -- otherwise it would be easier to lift an object over a sympathetic link. This gets interesting if you have two people pull in opposite directions on objects that are sympathetically linked. Each person is pulling only against the force applied to the other object by the other person -- their own object is free to move otherwise. Each person exerts a force of exactly one newton away from their opponent; what happens? – zstewart Nov 28 '16 at 18:20

This is actually explained in-universe in The Wise Man's Fear, where Denna is speaking with Kvothe and a few other arcanists at the Eolian. Denna asks where the energy goes, and the answer is that some of it is lost into the air and some of it goes into the body of the arcanist, which can cause serious problems for them, up to and including cooking them from the inside out.

From Chapter 18, Wine and Blood:

"But you said that energy couldn't be created or destroyed," Denna said. "If I have to struggle to lift this tiny piece of chalk, where does the extra energy go?"

"Clever," Willem chuckled. "So clever. I spent a year before I thought to ask that." He eyed her in admiration. "Some energy is lost into the air." He waved one hand. "Some goes into the objects themselves, and some goes into the body of the sympathist who is controlling the link." He frowned. "That can get dangerful."

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