(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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On the surface mass, like space, seems like a simple and straightforward concept but there are deep subtleties involved here too. In order to bring out the subtleties about mass, I had a practice of asking students in my introductory physics classes to explain what they understood when they spoke of the mass of some object. The would usually give some vague formulation along the lines ‘the amount of stuff’ it has. When I pressed them by asking how that differs from their concept of volume, they would sharpen their answer, usually saying that volume was a measure of the amount of space that was occupied by the object but mass was a measure of how heavy it was. There are teachers who insist that we must emphasize that mass and weight are different but I am not one of them. After all, we all know from experience that objects with greater mass are heavier to lift. The intuitive idea that mass has a relationship to weight is a good enough starting point for learning about the subtleties of mass.
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Take a look at this graph that disaggregates the rates of covid-19 deaths according to vaccination status.

Note that if you are unvaccinated you have at least a five-fold greater risk of dying. This is a massive difference. And yet, many people choose to ignore information that is effectively smacking them upside the head and telling them to get vaccinated.

Compare this with how people are willing to adopt all manner of practices that promise even small benefits. People start taking things like turmeric, acai berries, pomegranate, and adopt all manner of diets, exercise routines, and things like detoxing even though the promised benefits may be just a few percent reduction in cancer or a slight increase in longevity, and the like. And even those benefits have been shown to not be that robust or are even spurious. This behavior reminds me of something that Jesus said in Matthew 23:24 about people straining at a gnat while swallowing a camel.
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How do you tell if you are in an inertial frame or not? According to Newton’s model of a fixed space, an inertial frame is one which is at rest or moving with constant velocity through that fixed space. We saw that determining this required us to observe the state of motion through that space of an object Q that was known to be not under the influence of any forces. If you observe Q to be at rest or moving with constant velocity, then you are in an inertial frame. If however, even in the absence of forces, the freely floating object Q appears to be accelerating in some direction with respect to you, you could conclude that this must be because you are in a frame that is an accelerating in a straight line in the opposite direction and hence you are not in an inertial frame.
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