/sci/ - Science & Math

You seem to have a misconception of the sense in which "absolute this and that" resp. "no absolute this and that" is understood. The universe in these mechanical theories is a pseudo-riemannian manifold which as itself is rigid (four-dimensional and hence unchanging) and all it's worldlies are too, as well as all fields. If you know position and tangent vector (velocity), i.e. two times four components, and if you know the acceleration vector F/m at all relevant points, then you can indeed compute the whole worldline.
Non-absolute velocity merely refers to relativity with respect to the coordinates of any (local) observer.
And regarding relativity location. You say "no absolute position" and this is potentially confusing. Any single position/event in space time is, mathematically, a point in a manifold (the set which admits a local mapping to R^4). As such it is "absolute". What is not absolute about space is not a single position, but the range (spatial spacetime slice) of spatial coordinate functions of different observers (which in special relativity should be related by a Lorentz transformation). The spatial coordinates of observers with non-vanishing relative velocity are tited in spacetime, mixind space and time.
Also, the acceleration is also just the same w.r.t. to Lorentz transformations - the local isometries of the metric. If you make an arbitrary coordinate change, then in local coordinates, the components will be fucked up.

>>5697214
>In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that "the product of a collection of non-empty sets is non-empty"

I consider this formulation polemic.
You have a bunch of other definitions in the background together with a large universe, this is why this happens.
The construction of the product is a set (per definition, so it IS a set in any case) whose elements are such and such. In your set theory without choice, "the product of non-empty sets results to be an empty set" is true, but only because the defintion requires you to collect the elements the set is supposed to contain, and then, without the axiom of choice, you can't find any. Hence the definition returns the empty set.

...fuck, I don't want to take position here, really.

As far as opionions go, I' currently in a melancholy mood, telling me to not care too much about the man made desire to have a single framework for foundation.
That is I learn towards computation and complexity considerations now.