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"when it comes to "it requires more energy to create pair particles in a high gravitational potential." I'm not sure. If you assume that the particles are in a 'free fall' then the gravity as such will be the same everywhere, and the 'gravitational field' will be negligible.
MikeS, I'm not clear where the perpetual motion paradox comes in.Any gain in power for a motor on the ground as compared to a motor in orbit is due to the energy gained by the electrons when they fall from orbit to the ground. This energy has to come from somewhere, and it comes from transporting the electrons (or their parent particles) up into orbit to begin with, which takes energy.Back to your original question, yes, it does take more energy to create particles in orbit than it does on the earth's surface because you have to get those particles into orbit and then collide them, and moving them up into orbit takes energy. Also, general relativity is a red herring here. You don't need it to work this out--Newtonian gravity works just fine since this effect doesn't require the precision of GR.
You send current up the wire. It takes more energy to do so because it's rising against gravity. Where's the problem with that?
Why is that a problem? The energy can, and should, exactly cancel out. If you throw a ball up in the air, the energy needed to toss it up to a given height is exactly the same as the energy it gains falling from that height, so it reaches the ground with the same speed and kinetic energy it left with (minus losses due to air resistance.) The exact same thing happens in a wire. The electrons returning to the ground do so with exactly the energy they left with (minus losses due to resistivity in the wire), so there's no gain of energy and no perpetual motion.
JPThanks for your honest answer.yor_onLet me re-phrase the question.Would it take more energy to create pair particles high above the Earth than at ground level?From a previous post“Consider the following experiment.We use a given amount of energy to create pair particles at a high gravitational potential at the top of a tower and let them fall. In falling they gain kinetic energy which we use to operate an electric generator at the bottom of the tower. The electricity generated is used to produce more photons at the top of the tower which are then used to create pair particles which fall gaining kinetic energy and so on.In your little experiment in last two posts you can even remove the need to generate paricles - just have a laser light in high orbit connected with a wire to a photovoltaic cell in low orbit. We can assume very low inefficiency and superconductivity etc - and a huge drop in potential. I do not know the mechanism - but clearly the transfer of electrical energy thru a wire from low to high grav pot cannot be lossless as this would entail a net energy gain.[/quote imatfaal]Both of the above examples, if they worked would be perpetual motion. Clearly this cannot be. Assuming super conductors etc. Its a two wire circuit, electrons go up one wire presumably slowed by gravity accelerated down the other. The gravitational effect being cancelled. So where is the energy going? The electricity is being produced in a low gravitational potential where time is dilated relative the high GP where electric is being used. Due to time dilation at source and contraction at sink the current generated at source is more than at sink. There is a loss of energy due to gravitational time dilation.”Clearly, to me at least, it requires more energy to create pair particles in a high gravitational potential. The mass energy equivalence principle holds but extra energy is required if particles are to be created in a higher gravitational potential.It costs energy, lots of energy to raise an object to a higher gravitational potential, take the space shuttle for instance. I don't see why pair particle production would be any different?
It could be argued that photon blue-shift which is usually interpreted as a gain of energy is nothing more than an effect of observing the photons from a dilated time frame.
Photons do not gain energy falling within a gravitational field, they only appear to.
“Consider the following experiment.We use a given amount of energy to create pair particles at a high gravitational potential at the top of a tower and let them fall. In falling they gain kinetic energy which we use to operate an electric generator at the bottom of the tower. The electricity generated is used to produce more photons at the top of the tower which are then used to create pair particles which fall gaining kinetic energy and so on.