Unless you have some kind of medical condition that makes the risk of vaccination greater than the risk of getting covid-19, you should get vaccinated. But there are people who decide, against the best scientific advice, that they know better alternatives. Not all of them are rabid anti-vaxxers or are opposing it because of some ideological fixation or because they believe in some bizarre conspiracy theory that it is a device for the government to gain control over one’s body. There are those who do not get it because they have folkloric beliefs, such as that healthy people have natural immunity or that the symptoms will not be serious or that certain practices such as wellness or Ayurveda or other folk remedies will stave off the infection.
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(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, Part 12, Part 13)

The history of analyses of the question “Does a charge falling freely in a gravitational field radiate energy?” is quite fascinating with experts being all over the place, even to this date. The biggest disagreement is over whether the answer to the above question is yes or no. But even among those who agree on the answer, there are disagreements as to the reasons. For example, among those who say that it radiates, some argue that it leads to a loss in kinetic energy and that the Principle of Equivalence may not even hold in the case of a charge falling freely in a uniform gravitational field. Others disagree on what the source of the radiation is.
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(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, Part 12)

We seem to have arrived at a resolution to the paradox that this series started with that maintains our traditional expectations. Recall that it seemed like two postulates that were thought to be incontrovertible were incompatible when applied to a situation in which an electric charge and a neutral particle were dropped from the same height. It seemed like one or both had to be wrong. Those two postulates were:

Postulate #1: If we eliminate all other forces such as friction, all objects that are dropped from the same height in a gravitational field will fall at the same rate and hit the ground at the same time.

Postulate #2: An accelerating charge will radiate energy.

In the previous post, we arrived at a resolution in which the falling charge will radiate, in agreement with Postulate #2, but that this radiated energy does not result in a loss in the kinetic energy of the charge and thus it will fall at the same rate as the neutral particle, in agreement with Postulate #1.

The way this resolution was arrived at may not satisfy everyone. It involved invoking an aspect of the mass of a charged particle that we may not be familiar with. We looked at some aspects of the subtlety of mass back in Part 5. But there’s more, and this was the introduction of a mysterious source Q that provided the energy radiated by an electron that was accelerating under the influence of a uniform gravitational force. Recall that the rate of energy radiated by the charge was given by the familiar Larmor expression ℛ = 2e²g²/3c³ for a charge e having an acceleration g. Q = 2e²a^o/3c² where a^o is the zeroth component of the covariant four-acceleration of the charge given by a^μ = dv^μ/d𝜏, such that a^o = γv.a.
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