The pandemic with its virus mutations has rekindled my interest in the mathematics of evolution. Way back in 2007, I wrote a 20-part series of blog posts on evolution. This was way ‘out of my lane’, as the kids say these days, since I am a physicist and have zero formal training in biology, having taken my one and only course in that subject when I was in eighth grade. But I did this for the same reason I write about a lot of things, in order to force myself to learn about a topic that interests me and to sort out my ideas.

One of the things that had intrigued me is how a mutation that occurs in just one organism could become not just dominant in the population but end up being the only one. In some posts in the series, I discussed the mathematics of how this happens, which I have edited and reproduce here.
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When it comes to wearing masks during the pandemic, not all masks are equal in the protection they provide. From what I have read, cloth masks seem to provide the least protection, though they allow the wearer colorful options and the ability to make some kind of statement, though why some people feel the need to make statements through their attire is something that I find puzzling. The blue surgical masks appear to be better than cloth and the N95 masks are the best. But while the surgical masks are relatively cheap, the N95 masks are pricey (ranging from $1 to $3 each) and that raises the question of how long one can use them and whether they can be reused.

The good news is that the answer is yes, based on the fact that the coronavirus has a survival time of about 72 hours when outside a host.
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The space telescope has reached its destination of the second Lagrange point.

The mirrors on the space observatory must still be meticulously aligned and the infrared detectors sufficiently chilled before science observations can begin in June. But flight controllers in Baltimore were euphoric after chalking up another success.

“We’re one step closer to uncovering the mysteries of the universe. And I can’t wait to see Webb’s first new views of the universe this summer!” the Nasa administrator, Bill Nelson, said in a statement.

“Wow, what a ride this last month it’s been,” said Amber Straughn, a deputy project scientist for Nasa.

The telescope has been described as a “time machine” by scientists and will enable astronomers to peer back further in time than ever before, all the way back to when the first stars and galaxies were forming 13.7bn years ago. That’s a mere 100m years from the Big Bang, when the universe was created.

The Webb will also hunt for signs of extraterrestrial life.

Considered the successor to the Hubble, which orbits 330 miles (530km) up, the Webb is too far away for emergency repairs. That makes the milestones over the past month – and the ones ahead – all the more critical.
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Whether chasing optical and ultraviolet light like the Hubble or infrared light like the Webb, telescopes can see farther and more clearly when operating above Earth’s distorting atmosphere. That’s why Nasa teamed up with the European and Canadian space agencies to get Webb and its massive mirror – the largest ever launched – out into the cosmos.

So far, things have gone really smoothly for this highly complicated mission but there are still challenges ahead. One can only hope that now that the major hurdles have been overcome, especially the whole business of unfolding of a tennis court size structure from the small confines of a rocket nose cone, that some small glitch does not ruin things.

The whole operation reflects great credit on all the engineers and scientists who were involved in designing, building, and launching it.

(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, Part 14)

This series started by asking a simple question, whether a charged particle and a neutral particle would fall at the same rate when dropped from the same height and reach the ground at the same time. You would think that it would have a simple answer. But no. After a fairly long journey, we arrived at the conclusion that they would. But in the process, the series had to address a whole host of related issues along the way. While many of those were seemingly resolved, there are some fundamental questions that remain murky.

We saw in part #13 that the mass of a point charge like an electron is not a simple thing, because an electric charge has an associated electric field that itself has energy and thus should be thought of as contributing to the mass, except that the field energy density goes to infinity at zero distances, which is of course awkward for point-like charges. By looking at the radiation reaction force created by an accelerating charge, we learned about something called the acceleration energy Q that increases with the speed of a charge, and the energy radiated by a linearly accelerating charge comes from this source.
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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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