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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Yesterday NASA’s James Webb Space Telescope was successfully launched into space from French Guiana, using the European Space Agency’s Ariane 5 rocket. If all goes well, within the next year we will be seeing images of when the universe was in its infancy.

Here is a quick overview of the telescope.

The launch is just the first stage of a very complex journey in which engineers have said that there are many delicate steps that need to go right and the failure of any one could ruin the mission.The telescope is a truly extraordinary piece of engineering design.

The James Webb – named after a former Nasa administrator – will spend a month on its journey and will then need a further five months to get ready. First, its enormous gold-plated 6.5 metre mirror and its huge, tennis-court-sized sunshield need to unfurl; they were folded origami-style to fit into the nose cone of the Ariane 5. Then its instruments will have to be carefully calibrated. In all, hundreds of release mechanisms need to work perfectly in order for the telescope to succeed.

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

The fact that all masses accelerate at the same rate when subjected to purely gravitational forces but do not do so for any other type of force indicates the singular nature of gravity. Another peculiarity of gravity is that although we can shield bodies from the effects of other forces, we cannot shield them from gravitational forces. Although the concept of gravity has been around for a long time and we have used it to explain so much, from the motion of planets to terrestrial events, gravity remains a somewhat mysterious force, difficult to incorporate into more general schemes. Attempts to create unified theories of all the forces have been foiled by gravity. Trying to unify quantum mechanics with gravity has also proven to be extremely difficult, resisting the most determined efforts from some the best minds in physics, including Einstein. This is partly because gravity, unlike electric and magnetic forces, is a non-linear force and non-linear forces are notoriously difficult to handle mathematically.
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Recall how in one of my recent posts on the radiation paradoxes, I spoke about how you can measure the spinning rate of the Earth by looking at the stars and also by measurements taken purely on the Earth and that these two methods produce results that are remarkably close. This was used in support of the claim by Bishop Berkeley that it was the stars that exerted a dynamical influence on the Earth and that our motion was relative to, not space itself as Newton thought, which he felt was an unobservable entity and thus had no relevance.

The rate at which the Earth is spinning on its axis is not fixed though. Over time it has been slowing down, meaning that the days have been getting longer. Around 600 million years ago, the day was about 21 of our present hours. But a new wrinkle appeared in the last half century in that the rate of rotation was increasing slightly and this caused problems. As our ability to measure time became more accurate with the adoption of atomic clocks, this required the regular adoption of the so-called ‘leap second’, which was a second added to clocks to bring them back into sync with the time as measured with respect to the stars.
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