As long-time readers may have noticed, when it comes to complicated issues, as in the case of the current series on radiation paradoxes, I tend to post about it in installments. I have had many, many ten-to-twenty-or-more part series dealing with important questions, such as the Higgs, evolution, and the Big Bang. This doling out in small portions may be irksome to some, especially those who already know quite a bit about the subject, who may be impatient at my slow pace. They may wonder why I do not write out the entire thing first and post it in one long entry so that everything is settled once and for all.

There are several reasons for this. One is purely pedagogical. I think that it is hard to digest a lot of new and difficult material in one gulp. With small doses, where each post focuses on just one or more important issue, people can think and reflect on it, ask questions, and get things clarified in their own minds as best as possible and are thus more ready to move on to the next installment.
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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)

We saw in the previous post how Einstein’s Principle of Equivalence explained why two masses dropped from the same height in a gravitational field will fall at the same rate and hit the ground at the same time. It also seemed to resolve the paradox about whether an electric charge will fall more slowly than a neutral particle in a gravitational field. The answer arrived at was ‘no’ because since according to the PoE, the situation with the falling accelerating charge in the frame of the Earth E was equivalent to the charge being stationary in the inertial frame of space S, the charge would not radiate energy, contrary to naive expectations that any accelerating charge would radiate. On the surface, that seems to resolve the paradox that started this series of posts. The price we have paid is that we must abandon Postulate #2 and conclude that accelerating charges do not radiate when falling freely in a gravitational field.
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The Webb telescope team reported that a major step had been successfully completed on schedule. The telescope was launched on December 24th and all its components had to be folded into a small space to fit into the rocket nose cone and then opened up once it was in space, After seven days, the schedule called for the five-layered tennis court-sized silvery heat shield to be opened up and it did so.

The shiny silver shield measures 69.5 feet long by 46.5 feet wide (21.2 by 14.2 meters) when fully deployed — far too large to fit inside the protective payload fairing of any currently operational rocket. So it was designed to launch in a highly compact configuration and then unfold once Webb got to space.

That deployment is an elaborate, multistep process with many different potential failure points that could sink the entire mission.

“Webb’s sunshield assembly includes 140 release mechanisms, approximately 70 hinge assemblies, eight deployment motors, bearings, springs, gears, about 400 pulleys and 90 cables totaling 1,312 feet [400 m],” Webb spacecraft systems engineer Krystal Puga, who works at Northrop Grumman, the prime contractor for the mission, said in a video about Webb’s deployments that NASA posted in October.

Over the next six days, the rest of the telescope will get unfolded, starting in three days with the deployment of the secondary mirror support structure. And then it heads to its destination, the second Lagrange point which it should reach after 29 days.

You can see the sequence of steps in this short video.

It is a truly remarkable piece of engineering.

The pandemic has given us a crash course on evolution. Evolution deniers must be having a hard time explaining away the evolution-suffused news dealing with mutations, growth rates, and the like. But it also provides an opportunity to explain some of the mathematics of the phenomenon.

You would think that if a mutation had a slight advantage over its predecessor, then it would over time grow in size relative to the other but the older one would still be around. But that is not what happens. We see how some new variant, if it has some advantage over its competitors such as greater transmissibility, rapidly becomes dominant in the population, pushing the previously dominant ones into the background.

This graph shows the different peaks due to the different variants at the current time.

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(Previous posts in this series: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7)

We have now acquired most of the background knowledge needed to start directly addressing the question that this series of posts started with, as to whether an electric charge and a neutral particle dropped from the ceiling will hit the ground at the same time. The first stage of that is what is known as the Principle of Equivalence.

Recall the Postulate #1 we started with that said that all objects falling freely in a gravitational field will fall at the same rate and hit the ground at the same time. We were able to explain this by saying that it followed from the fact that gravitational and inertial masses were equal. But we did not explain why they should be equal. The two masses were arrived at, after all, by distinct methods using different operational definitions. But by considering accelerating frames and the Principle of Equivalence, we have a simple explanation for it.

Consider two objects floating freely in space that are at rest with respect to each other and to an observer S, to signify space. No suppose we enclose the two objects in a closed room and accelerate the room ‘upwards’ (i.e., in the direction from the ‘floor’ to the ‘ceiling’) with a value g. We will call this frame E to signify an elevator or Earth. Then in the frame E, both objects will seem to be accelerated ‘downwards’ (i.e., towards the floor of the room) with a value g, just as if they were falling freely on Earth, and will both hit the floor at the same time. They will behave just as if they were falling down near the surface of the Earth and since they hit the floor at the same time, we can infer that their gravitational and inertial masses are equal, rather than tacitly assuming it to be the case as we did before.
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The virus that causes covid-19 is officially called SARS-CoV-2. This website gives the definition of the various elements of this virus.

Viruses like SARS-CoV-2 continuously evolve as changes in the genetic code (genetic mutations) occur during replication of the genome. A lineage is a genetically closely related group of virus variants derived from a common ancestor. A variant has one or more mutations that differentiate it from other  variants of the SARS-CoV-2 viruses. As expected, multiple variants of SARS-CoV-2 have been documented in the United States and globally throughout this pandemic. To inform local outbreak investigations and understand national trends, scientists compare genetic differences between viruses to identify variants and how they are related to each other.

Key Definitions:

• Mutation: A mutation refers to a single change in a virus’s genome (genetic code). Mutations happen frequently, but only sometimes change the characteristics of the virus.
• Lineage: A lineage is a group of closely related viruses with a common ancestor. SARS-CoV-2 has many lineages; all cause COVID-19.
• Variant: A variant is a viral genome (genetic code) that may contain one or more mutations. In some cases, a group of variants with similar genetic changes, such as a lineage or group of lineages, may be designated by public health organizations as a Variant of Concern (VOC) or a Variant of Interest (VOI) due to shared attributes and characteristics that may require public health action.

When the Omicron was labeled as a ‘variant of concern’, that label is one of four that is used to classify the nature of the danger the variant poses, which are in increasing order: Variant Being Monitored (VBM), Variant of Interest (VOI), Variant of Concern (VOC), and Variant of High Consequence (VOHC), the last being the most alarming. Delta and Omicron are the only two in the VOC category, while there are ten in the VBM category, including the Alpha and other variants with Greek letter labels that did not get much publicity.

There are none as yet that fall into the VOI nor (thankfully) the VOHC categories. One shudders to think what a VOHC variant would do.

I wrote earlier about the amazing migration of the monarch butterfly. This tiny creature does the same trek of thousands of miles each year even though their lifetimes are so short that any given butterfly will do it only once.

This website gives more information.

Some monarch butterflies are able to fly for a migration of 2500 miles. Most of them can find their ways to their ancestors’ winter homes when they go there, and then find their ways back to the places they left in spring. This ability made them seem like the strongest, smartest, and toughest of all butterflies. In much of their range they are also the biggest butterflies, with wingspans up to four inches (10cm).

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(Previous posts in this series: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6)

At this point, we need to take a slight detour and examine more closely the role of accelerating frames because that is central to resolving the paradox that started this series if posts, of whether an electric charge falling freely under gravity radiates or not. The discussion up to this point has seemed to privilege inertial frames when it came to discussing the laws of physics. This was because we knew how to transform physical quantities between any two inertial frames, using Galilean transformations for Newtonian motion at low speeds and Lorentz transformations when we needed more accurate results or were dealing with speeds comparable to that of light in the regime of special relativity. But transforming between inertial frames and accelerating ones was another story.

Einstein used the insight that any two masses will fall at the same rate in a gravitational field to argue that the distinction between inertial frames (where the laws of physics such as Maxwell’s equations are supposedly valid) and non-inertial frames (where they are not) should not matter and that we should be able to find transformational relations between them.
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