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## Main Question or Discussion Point

Hi, folks!

I am interested for the following question:

The original Einstein's formulation of the special theory of relativity does not permit consideration of the accelerated observers, but this limitation is not essential because we can consider the special relativity as limit case of the general relativity by substituing gravitational constant by 0. Is it possible to consider accelerated observers in the special relativity without mathematical language of the general relativity (manifolds, tensors etc.)?

My idea is introducing following additional axiom:

Acceleration is relativistic irrelevant.

Let we consider two birds A and B, flying nonlinearly and nonuniformly with the motion laws A(t) and B(t) in inertial system S (of the ground), where A(t) and B(t) are indefinitely differentiable vector functions of the time. How the bird A see the bird B.

We will fix a moment [tex]t_0'[/tex] of the bird's A clock and compute [tex]t_0[/tex] such that [tex]t_0'=\int_0^{t_0}\sqrt{1-(A'(t)/c)^2}\,dt[/tex]. Then we compute the vector [tex]v=A'(t_0)[/tex] and fix the Innertial system S' such that S' has constant velocity [tex]v[/tex] relative to system S. Then we transform coordinates [tex](A(t_0),t_0)[/tex] of bird A to coordinates [tex](a',t_0')[/tex] in system S' and coordinates [tex](B(t_1),t_1)[/tex] of bird B to coordinates [tex](b',t_1')[/tex]. We compute moment [tex]t_1[/tex] using condition [tex]t_1'=t_0'[/tex], and position [tex]b'[/tex] using computed moment [tex]t_1[/tex]. Then, intensity of vector [tex]b'-a'[/tex] is distance bitween two birds measured by bird A when it scan the time [tex]t'[/tex] from it's clock.

Is it correct?

I am interested for the following question:

The original Einstein's formulation of the special theory of relativity does not permit consideration of the accelerated observers, but this limitation is not essential because we can consider the special relativity as limit case of the general relativity by substituing gravitational constant by 0. Is it possible to consider accelerated observers in the special relativity without mathematical language of the general relativity (manifolds, tensors etc.)?

My idea is introducing following additional axiom:

Acceleration is relativistic irrelevant.

Let we consider two birds A and B, flying nonlinearly and nonuniformly with the motion laws A(t) and B(t) in inertial system S (of the ground), where A(t) and B(t) are indefinitely differentiable vector functions of the time. How the bird A see the bird B.

We will fix a moment [tex]t_0'[/tex] of the bird's A clock and compute [tex]t_0[/tex] such that [tex]t_0'=\int_0^{t_0}\sqrt{1-(A'(t)/c)^2}\,dt[/tex]. Then we compute the vector [tex]v=A'(t_0)[/tex] and fix the Innertial system S' such that S' has constant velocity [tex]v[/tex] relative to system S. Then we transform coordinates [tex](A(t_0),t_0)[/tex] of bird A to coordinates [tex](a',t_0')[/tex] in system S' and coordinates [tex](B(t_1),t_1)[/tex] of bird B to coordinates [tex](b',t_1')[/tex]. We compute moment [tex]t_1[/tex] using condition [tex]t_1'=t_0'[/tex], and position [tex]b'[/tex] using computed moment [tex]t_1[/tex]. Then, intensity of vector [tex]b'-a'[/tex] is distance bitween two birds measured by bird A when it scan the time [tex]t'[/tex] from it's clock.

Is it correct?