First, there was the Higgs, then LIGO. Physics is big, and brash…..all ‘in yer face’, but, also, fascinating. So, I bought and read Jon Butterworth’s book on particle physics and the search for the Higgs (Smashing Physics…@jonmbutterworth), and read it in a few days. Very good. But one of the things that particularly struck me was that the Higgs is a sort of byproduct of the existence of gravitational fields; it was predicted to exist from the mathematical description of the field. Then, LIGO; confirming the existence of gravitational waves…and hence, the existence of both gravitational fields and another proof of the appropriateness of Einstein’s General Relativity.

I remember the Special Theory of Relativity from University (over 30 years ago). But, I had never studied the General Theory. I had purchased a big book on gravity (Gravitation) even though by that time I was no longer studying Physics, but the maths in it made the whole book incomprehensible. After LIGO, I dug the book out again, and also looked for Einstein’s books on Special and General Relativity that I know I owned at one point. Couldn’t find them, so bought them again (as one volume). Special Relativity was covered well, but General was very vaguely presented. So, I looked for another, stepping stone book, that could bridge my current state of knowledge and put me in a position to attempt Gravitation. A Most Incomprehensible Thing by Peter Collier is that book.

Not lightweight. Lots of maths; of a sort I’m not very familiar with. But, so well written that I could follow it. Three hundred and nineteen pages later, and I’m now ready for Gravitation. So what did Incomprehensible teach me about General Relativity? Well, for a start, it is indeed a spectacular theory (this much I already suspected). Einstein’s conceptual leaps came first, then the maths to explore them. He recognised that acceleration is equivalent to being subject to a gravity field (their effects are equivalent, and therefore so are they). That the motion and pathway travelled by mass is determined by the geometry of spacetime, and the geometry of spacetime is determined by the proximity of mass. The maths seeks to capture this relationship, and hence allow the calculation of the behaviour of mass (and time, and energy) given the ‘mass proximity’ circumstances. The framework for that mathematical framework is the Einstein Field Equations: specific solutions to these equations yield the actual mathematical expressions that allow the actual calculations to be done (e.g. The Schwarzschild metric is one solution to the Einstein Field Equations).

So, spacetime (which is not the 3D space we see around us) is curved, and the metric describes both the curvature and the manner in which a mass will move at that point in spacetime. It is very elegant, as is that the mathematical description of spacetime must be able to collapse into the Newtonian description of gravity, and into Special Relativity (which is essentially flat spacetime – i.e. the absence of gravity or acceleration). My understanding is that: all objects are in free fall unless something acts on the object to prevent the free fall from continuing – the path taken in the free fall depends on the curvature of spacetime (the geometry) which depends on the proximity of mass (which curves spacetime from ‘flat’). The free fall motion is a function of the mathematical metric at that point in spacetime, which describes both the curvature and the manner in which the object moves (acceleration is a function of the geometry). The object always takes the shortest line (geodesic) through the curved spacetime. The mathematical metric is a solution to the Einstein Field Equations.

The cool thing about all this is that it predicts things about the physical universe (often demonstrated by the behaviour of light) that isn’t predicted by Newtonian physics or Special Relativity (e.g. red shifting of light as it moves away from a star, magnitude of the bending of light as it grazes the sun, black holes, in free fall no ‘force’ is experienced). Also, I had thought of maths as giving precise solutions. That’s not what it really does in General Relativity – it gives a language that can be used conceptually to describe the physics of the Universe, a framework in which to think and explore and explain. The precise solutions come later, but it is being able to construct the framework which is the real breakthrough, I think.

Next, to tackle Gravitation, having been given the mathematical language to understand the framework.

# Gravitation (notes 6)

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