(Previous posts in this series: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10, Part 11)
In the previous post we arrived at conclusions that will enable us to address the basic paradox that started this series of posts, and is restated as Issue 3 below. I will be introducing some mathematics here is order to make the line of reasoning clearer for those who know something of this topic but for those readers for whom this is unfamiliar, I would encourage you to not sweat the details but simply read the text between the equations and I think (hope!) you will get the gist.
Issue 3: If a detector D on Earth detects radiation from a falling charge (Scenario 3), that implies that the charge loses some energy in the form of radiation and thus one would expect that it will fall more slowly than a neutral particle, thus violating Postulate #1 and the Principle of Equivalence that says that all objects falling freely in a gravitational field will fall at the same rate. If it still falls at the same time as the neutral particle and thus does not violate Postulate #1, that must mean that its kinetic energy is unaffected by the emission of radiation. Does that not violate the law of conservation of energy? We seem to have arrived at two irreconcilable and unpalatable options.
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