Is the Universe a Fractal According to Einstein's Local Time Theory?

[kleinwolf]

Fractal or ??

Let consider the well known Einstein Idea of local time disposed on Earth (attached to material points). Nobody can forbid me to consider this whole Earth (global realtive to earth) as a point again, with only one space-time coordinate (this way is easy of course, but the other seems less ?). Questions :

1) How do you make this transformation and it's inverse ?
2) Can this be seen as a kind of fractal universe ?

 

[Integral]

Let consider the well known Einstein Idea of local time disposed on Earth (attached to material points). Nobody can forbid me to consider this whole Earth (global realtive to earth) as a point again, with only one space-time coordinate (this way is easy of course, but the other seems less ?). Questions :

1) How do you make this transformation and it's inverse ?

What transform? Inverse of what?

2) Can this be seen as a kind of fractal universe ?

Unfortunatly I simply do not understand what you are asking. Perhaps you need to rephrase your question.

 

[kleinwolf]

Precision of the former post

Well i just try to say the following :

let consider the Earth in a let say theoretical atomistic approach : the Earth in this academic view is a (idealized for calculation) sphere composed of a continuum of point particles (density of matter). Following Einstein's relativity point of view, every point of this density has it's own space-time coordinate. In Galilean/Newtonian approach, the time is the same for every "point particle" there. Hence in the classical (Galilean) approach, when one simplifies the problems toward classical dynamics, it just considers the coordinate of the center of mass and the time is of course the time of any of the given set of point particle, since they all have the same local time.

However, with the venue of relativity, one is not allowed to take this simple way. Now, if there exist an oberver for which the clocks attached to every point particle has the same flow, then can we consider this special point for the "pointification" of the above Earth ?

For example, let consider 2 uniformly moving particles, then I think it is almost obvious that there exist a uniformly moving one, such that both clocks tick the same way...What is the condition of existence of such (a) point(S).

For 2 particles, the speed of the middle equivalent time point is given by :

v_c=c^2/v_2 pm c sqrt(c^2/v_2^2-1)

From this point, the two clocks are clicking at the same rate
(example for two...what about 3 ?)