(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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