Einstein’s Special Theory of Relativity only considered frames moving with constant velocity (where observers can legitimately regard themselves as being at rest) to each other. What happens when we want to generalise to all frames, including those where there is relative motion of a different kind (e.g. rotation/acceleration; where observers can ‘feel’ a force being applied – hence can’t consider themselves to be at rest)? Well, the book isn’t anywhere as good with this – the General Theory of Relativity – possibly because the maths is vastly more complicated. But, here are a few bits and pieces.

Mass produces a gravitational field in its surroundings which acts on their masses. Gravitational mass is equivalent to inertial mass. Acceleration is equivalent to the intensity of the gravitational field. Acceleration feels the same to an observer as being subjected to a gravitational field whilst being at rest; the observer can’t distinguish between them, and, hence, they are equivalent. The Special Theory is a limiting case of the General Theory.

The one substantive example given in the book is of an accelerating frame consisting of a rotating flat disc where the velocity (which is speed and direction) changes constantly and differentially across the disc. Consideration of this situation leads to the conclusion that distance and time are different at different points on the disc, such that it is not possible to say anything about how the laws of physics apply in the frame. Basically, Euclidean (flat surface) geometry doesn’t apply. Instead, it is necessary to implement a non-rigid reference body (a reference-mollusk) moving in any way whatsoever, and irregularly (Riemann is mentioned). Sounds like mathematical chaos, but of course it isn’t. What it also isn’t, is easy to explain in a non-mathematical book. More’s the pity.

Three practical (testable) predictions are mentioned in the book, which arise from the General Theory.

Firstly, it has been known for a long time that the orbit of Mercury about the Sun rotates slowly in the plane of the orbit (43 seconds of arc per century), which cannot be explained by Newtonian physics. But can be explained by the General Theory.

Second, the General Theory predicts a larger bending away from straight lines of travel for light passing close to the Sun than Newtonian physics does. This was measured during eclipses of the Sun after the prediction was made, and found to be according to the General Theory.

Thirdly, the General Theory predicts that the wavelength of light arising from transitions in molecules will be red shifted when observed from Earth, when the molecule is in the atmosphere of a rotating heavy body. This prediction had not been proved when the book was published, but my guess is that it has now.

It is clear that the Special Theory of Relativity is a spectacular game changer of a theory. For me, the whole idea of frames of reference is an ‘of course!’ event. The simultaneity thought experiment is brilliant. It is so difficult to imagine observing anything from any frame of reference than the one you happen to be standing in, but to do so (Einstein’s genius, in my opinion) leads to interesting places.

I’m sure that the General Theory leads to even more interesting places, but I’m not sure if I will get there. I need to find another book, but conceptual understanding, which I think is just possible with the Special Theory, might be beyond me for the General Theory. Not time to give up yet, though.

# Gravitation (notes 5)

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