[quote author=richard barrett link=topic=1393.msg43985#msg43985
I think there is actually much less of a difference between Newtonian physics and Einstein's physics than there might appear to be on this issue of absolute versus relative spatial and temporal relations. IMHO the two theories, as scientific theories, are actually both neutral on the question of whether space and time (or space-time in Einstein's case) are independent of the things which inhabit them, or whether they are second order constructions out of relations between those things and events. Newton's physics qua physics is just as relational (in that sense) as is Einstein's. The difference is that he, Newton, chose to embed it in a metaphysical doctrine of absolutism (although this was not necessary for the physics still to work).
Yes, you're right there; it's a pity he didn't pay more attention to Galileo, who had done away with such things already! Actually, at least in the baby formulations (with particles and other stuch things), they both have a very definite space/time-manifold in which things live. But this is mainly a practical thing. When it comes to talking about relativity of spacial/temporal relations, there's a pretty big difference between Newtonian physics and Einsteinian Relativity I think! (not as much between Galilean and Einsteinian relativity, in that both can be viewed in the same light). I think that it was only in the Lagrangian formulation of classical mechanics that the concept of "ambient space" became much less obviously necessary.
Einstein, on the other hand, was careful not to do this but his theory could be so embedded without making any difference to his physics. The important point (er, IMHO) is not that one is absolute and one is relational per se but that Einsteinian physics could not be embedded in the same absolutist framework as the one postulated by Newton.
I agree that this is an important conceptual jump. (Also, though I have attended a course in the subject, and follow what news I can in the field with interest, I am not a physicist, and certainly not a theoretical physicist). There were similarly abstract formulations of Newtonian physics developed by Lagrange, Hamilton, Jacobi, &c., but they could all be reduced back to the simple framework, and really only found their vindication when applied to quantum physics and Einsteinian relativity.
But there's no such thing as an overall static reference grid, as there was by implication in Newton's physics.
Yes there is; one has space-time
I don't know if it's a cheat to call spacetime static or not, but that's where the equations of gr live, and it's a very well-defined geometric object; as good as any grid really.... (by grid everyone means (hyper-)plane here I hope).
The spacetime relationship between objects/events can only be given in terms of their relative positions, not in terms of map references.
This is not quite true; from a particular reference frame you get a particular view of (part of) the universe; you can map it out if you like. But to communicate the information to other people in other reference frames who have their own maps, you'll need to figure out how both your views of spacetime fit together using Einstein's equations.
(apologies for pulling what is an interesting thread slightly further off topic)
I slept on the Klavierstück VI question last night (good thing I'm not a princess or I'd be bruised all over) and I'm beginning to think that something derived from it might be worth investigating. (For those who don't know this score, it has an extra 13-line "stave" above the usual ones, on which a line indicates changes of tempo (using a "scale" of 13 tempi) and a "full stop" indicates a pause.)
That sounds like a
really charming/functional innovation. This allows one to get at what I was mumbling about earlier with no trouble at all really. Just to clear up one thing: would repeating a note on this stave correspond to changing the tempo twice, or would it just be asserting the same tempo twice?
EDT: actually I've tracked down the score; all makes sense now.
