" This planet is far, far from Earth, and orbits VERY close to a black hole. As such, their perception of time and energy is very different from the rest of the universe."
OK, the black hole causes a blue-shift - so effectively, the black hole's gravity is the source of the energy - right?
But - can you do something like this on planet earth?
What fun synchronicity PhysicsProf, I was writing a follow-up just as you posted
Yes, in this case the blue-shift is the source of the increased energy, and the black-hole's gravity is the source of the blue-shift. The satellite is the 'modulation' between a low and high energy state.
What we are doing is cycling between a high and low density environment and synchronously adding/removing energy at certain points of this cycle.
* Energy is added to the satellite at a low-point in the cycle (without changing its mass)
* Satellite proceeds to a higher-orbit
* Satellite beams the same energy back
* Blue-shift refraction causes the frequency (and thus energy) to increase.
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Dimensionally, we would do the same thing on earth by cyclically varying inductance/capacitance of a system while adding/removing at certain points of the cycle.Imagine a lossless LC tank circuit consisting of an inductor and variable air capacitor. We add 1 unit of energy and it shuttles between dielectric and magnetic domains at a certain frequency (standard LC resonance).
Now if we decrease the capacitance of this circuit, the same energy is now resonating at a higher frequency (
as if it had been blue-shifted ). This change in C does not necessarily take any energy, as this parameter can be changed at the point in the cycle when the capacitor is nearly empty (or physically switching between series+parallel).
To gauge the amount of change in total energy, we would use:
* E=HF to compare the min+max frequencies of the system
* the initial amount of energy that was added to the circuit
* and the phase-angle of modulation to the charge/discharge cycle.
Now if such a system were ran in reverse (starting with a high-frequency oscillation and increasing capacitance), one would instead red-shift the resulting EM wave and decrease the total energy contained in the system.
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Hopefully some of this makes sense?