Speculation of Special Relativity and Information

  Consider a mass at rest mo at x=0 at t=to. To an observer moving at a constant speed v, the values x and t are such that their ratio is v=x/t, but the mass now has momentum and a new energy. Yet the two scenarios represent the same information. In fact one may consider all constant v values as creating new representations of the same information state. This is like a rotation with a constant magnitude in linear algebra. x,t and v are chosen instead of g1(x), g2(t) and g3(v) for linearity. As noted, motion is directly linked to momentum and energy so one may postulate that not only does x,t  behave like a rotation with fixed magnitude (dot product), but momentum and energy should be proportional to x and t with only constants and Lorentz invariants (i.e. a function of the dot product of x and t) as the proportionality factor. 

  X and t have different dimensions and in addition one still needs to define the dot product in terms of a metric. To do so we suggest comparing with light. This introduces c and the dot product form xx-cctt. 

   The above ideas may be used to obtain the form of  special relativity namely E= mo/sqrt(1-vv) (c=1) and p=Ev. They are also linked to the inner product -Et + px which is the classical Action for a free particle (relativistic or nonrelativistic) with t and x being treated as independent. By keeping this dot product constant one may also derive the form of special relativity i.e. E= mo/sqrt(1-vv)  (c=1).