Hi Whitestar,
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1) How would the energy bank look like?
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This can be anything that can generate a huge amount of power. For example, turning an apple into pure energy would release enough energy to put the Nimbus (largest aircraft carrier into orbit). So I guess the energy source must be an atomic power station that converts matter into 100% energy.
Use the formula E=mc^2 to get the energy in Joules.
Divide this by the time (t seconds) of the "energize" process and that gives the power in watts. Typically modern atomic power stations give about 10MegWatts. So it's not up to the job - it would be like an ant trying to push a lorry up a hill.
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2) Why wouldn't it be practical to send the energy long distances?
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The energy is just too great to control when sending long distances. If it were beamed as a ray, it would act like a death ray, destroying everything in its path.
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The thing that always bothered me about the transporter in Star Trek was that it had no receiving end. The more I think about it, the more implausible it sounds.
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I think you should keep an open mind on technology advances. Many times I thought I had reached a limit on something and then someone finds something that suprises me. Podkletnov's impulse gravity beam is one example that has the potential of transmitting energy through space without wires.
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4) Do you consider the conversion of matter into energy a form of capital punishment?
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Yes, if the conversion process goes wrong.
No, if it doesn't. It doesn't matter if we rematerialize in a body made from different atoms, so long as our physical structure, memories and thoughts are retained.