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Luke_A_Somers comments on Why is the A-Theory of Time Attractive? - Less Wrong
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... from what do you get this impression, and in what way is it relevant? Yes, there are many parts of modern mathematics I am not familiar with. However, nothing that had come up up to this point was defined in the last 100 years, let alone the last 50.
I have a PhD in physics. I know what an affine space is. If you were thrown off by my uses of basis changes to effect translations, which would signal ignorance since vector addition is not equivalent to change of basis... I did clarify that I was in a function space defined over time, and in the case of function spaces defined over vector fields, translations of the argument of the function are indeed changes of basis.
In physics, we set the origin to be whatever. All the time. This is because we need to do actual arithmetic with actual numbers, and number systems with no 0 are needlessly cumbersome to use. Moving 0 around all the time in context-dependent and arbitrary ways completely defuses the 'harm' of A-theory, as far as I can tell.
I apologize for the snipy remark, which was a product of my general frustrations with life at the moment.
I was trying to strongly stress the difference between (1) an abstract R-torsor (B-theory), and (2) R viewed as an R-torsor (your patch on A-theory).
Any R-torsor is isomorphic to R viewed as an R-torsor, but that isomorphism is not unique. My understanding is that physicists view such distinctions as useless pendantry, but mathematicians are for better or worse trained to respect them. I do not view an abstract R-torsor as having a basis that can be changed.
Indeed it wouldn't. A function space defined on an R-torsor would have a basis which you could change.