[FOM] Re: 206:On foundations of special relativistic kinematics 1

[Vladik Kreinovich]

Dear Friends, In view of Professor Chow's comment, you may want to look into 
our 1980 paper where we explain how the use of real numbers as coordinates with 
their algebraic structure etc come from physical postulates. 

Piet G. Vroegindeweij, Vladik Kreinovich, and Olga Kosheleva.
  "From a connected, partially ordered set of events to a field of
  time intervals,"  Foundations of Physics, 1980, Vol. 10, No.
  5/6, pp. 469-484 

> I think a foundational treatment of special relativity would be
> interesting, because as Harvey Friedman says it is supposedly all
> worked out and clear as glass, yet there remain some puzzling features.
> 
> By puzzling features I don't mean Lorentz contraction and time dilation
> and all those glamorous phenomena that confuse students and wow the
> general public.  I mean, for example, the commonly-heard claim that
> special relativity can be derived from just two postulates (the constancy
> of the speed of light and the relativity principle), when in fact it is
> clear that tons of other, unstated assumptions are needed as well.  These
> include obvious assumptions such as the assumption that there are three
> spatial dimensions, and subtler ones such as the assumption that space
> satisfies certain basic geometric axioms (two points determine a line
> and so forth).