Initial Kick at Warp Speed

Notice that time dilation $\gamma$ is independent of  ${ v }_{ s }$, this means a body experiences time dilation because of a change in gravity only, irrespective of its space velocity.  However, as a body increased speed, the relative space density in the direction of its travel increases.  The situation is analogous to a body at rest counting a number of smaller bodies around it per unit volume.  If  at speed v the body counts A then at speed 2v it will count 2A.  The relative space density increases proportionally with its space velocity.

Consider the expression

${ v }_{ s }tA{ d }_{ s }$, for time t, unit area A, where ${ v }_{ s }$ is space velocity and ${ d }_{ s }$ space density.

at speed $B{ v }_{ s }$ we have  $B{ v }_{ s }tA{ d }_{ s }$ which is ${ v }_{ s }tA(B{ d }_{ s })$ which suggest a relative increase in space density

This leads us to,

$\cfrac { { v }_{ s1 } }{ { v }_{ s2 } } =\cfrac { { d }_{ s1 } }{ { d }_{ s2 } }$

but

${ v }_{ t }^{ 2 }\propto \cfrac { 1 }{ { d }_{ s } }$

as such

$\cfrac { { v }_{ t1 }^{ 2 } }{ { v }_{ t2 }^{ 2 } } =\cfrac { { d }_{ s2 } }{ { d }_{ s1 } } =\cfrac { { v }_{ s2 } }{ { v }_{ s1 } }$

which gives us

${ v }_{ t1 }={ v }_{ t2 }\sqrt { \cfrac { { v }_{ s2 } }{ { v }_{ s1 } }  }$

This result is without any experimental proof!  And is actually running away.  In reality space does not pile up indefinitely in front of the moving body.  Space like a light fluid, flows around the body as the body moves through it.  However, an initial increase in space velocity causes time velocity to decrease resulting in a further increase in space velocity (via, ${ v }_{ t }^{ 2 }+{ v }_{ s }^{ 2 }={ c }^{ 2 }$ ) .  An initial kick in the rear, nothing more.