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annagrac 's review for:
Reality Is Not What It Seems: The Journey to Quantum Gravity
by Erica Segre, Simon Carnell, Carlo Rovelli
As a mathematician, I've never really warmed to physics as a subject, it's frankly to practical for a pure mathematician. In this book, Carlo Rovelli move from physics you knew in school through to mathematics through to philosophy in a very satisfying way.
I can't pretend that I really followed some of the finer points of his thesis, but it seems to be that in the 20th century physics has realised what mathematicians have always known - that discrete objects are pretty much interchangeable as far as doing equations is concerned, as are continuous things, however the two kinds of stuff have really very different properties, so it's important to know which kind of thing you are dealing with. The insight of relativity, quantum etc.. seems to boil down to the idea that you can apply the same set of mathematical equations to space as to time as to particles as to forces which implies they are all discrete. The fact that there is an exception in gravity is not really a mathematical surprise as it could well be the case that it is governed by a continuous function which will always have different rules to discrete quanta - which may mean that the search for a unifying theory in physics is doomed to failure.
The final chapters become a little more speculative and drift off into philosophy positing that actually all these discrete fields are in some essential ways the same thing - "covariant fields" - in a similar way to how Einstein theorised that space and time are actually the same thing and we should more correctly talk about spacetime. In both cases, mathematically, I think there is some more unpacking to be done - just because the same rules can be applied to counting apples and oranges doesn't make them the same thing, or (in a rather more technical analogy), the field of rational numbers is nested within the field of real numbers which is itself nested within the field of complex numbers, the fact that there are a subset of functions (e.g. adding and subtracting) that you can apply to all of these fields and see the same type of consistent predictable algebraic behaviours doesn't make these fields interchangeable or indistinguishable from one another- they are mathematically very much different things with entirely different properties. This is actually a deeper and "truer" truth than the fact that apples and oranges are different things, even though they both happily sit around to be counted and both describe the same parabolic arcs when used as missiles.
Maybe in relativity or quantum loop theory there are valid reasons for concluding that same rules = same thing, but the logic remains somewhat hidden from me.
I can't pretend that I really followed some of the finer points of his thesis, but it seems to be that in the 20th century physics has realised what mathematicians have always known - that discrete objects are pretty much interchangeable as far as doing equations is concerned, as are continuous things, however the two kinds of stuff have really very different properties, so it's important to know which kind of thing you are dealing with. The insight of relativity, quantum etc.. seems to boil down to the idea that you can apply the same set of mathematical equations to space as to time as to particles as to forces which implies they are all discrete. The fact that there is an exception in gravity is not really a mathematical surprise as it could well be the case that it is governed by a continuous function which will always have different rules to discrete quanta - which may mean that the search for a unifying theory in physics is doomed to failure.
The final chapters become a little more speculative and drift off into philosophy positing that actually all these discrete fields are in some essential ways the same thing - "covariant fields" - in a similar way to how Einstein theorised that space and time are actually the same thing and we should more correctly talk about spacetime. In both cases, mathematically, I think there is some more unpacking to be done - just because the same rules can be applied to counting apples and oranges doesn't make them the same thing, or (in a rather more technical analogy), the field of rational numbers is nested within the field of real numbers which is itself nested within the field of complex numbers, the fact that there are a subset of functions (e.g. adding and subtracting) that you can apply to all of these fields and see the same type of consistent predictable algebraic behaviours doesn't make these fields interchangeable or indistinguishable from one another- they are mathematically very much different things with entirely different properties. This is actually a deeper and "truer" truth than the fact that apples and oranges are different things, even though they both happily sit around to be counted and both describe the same parabolic arcs when used as missiles.
Maybe in relativity or quantum loop theory there are valid reasons for concluding that same rules = same thing, but the logic remains somewhat hidden from me.