Time Travel is Complex

If we look again at the conservation of energy equation,

${ v }_{ t }^{ 2 }+{ v }_{ s }^{ 2 }={ c }^{ 2 }$

what happens when ${ v }_{ s }>{ c }$,

${ v }_{ t }^{ 2 }= -{ V }^{ 2 }$ where ${ V }^{ 2 }={ v }_{ s }^{ 2 }-{ c }^{ 2 }$

${ v }_{ t }^{ ' }=iV$

$\nwarrow \quad +\quad \nearrow \quad +\quad \swarrow \quad=\quad \upuparrows$
${ v }_{ t }$             ${ v }_{ s }$             $i{ v }_{ t }^{ ' }$             ${c }$

A complex component develops in ${ v }_{ t }$ that cancels that part of ${ v }_{ s }$ that is greater that ${ c }$.  The use of $i{ v }_{ t }^{ ' }$ is to illustrate that ${ v }_{ t }$ and $i{ v }_{ t }^{ ' }$ are not of the same magnitude.

Similarly, if we develop a complex component in ${ v }_{ s }$ we will then be able to cancel part of ${ v }_{ t }$ and given a great enough complex component in  ${ v }_{ s }$, we will be able to make  ${ v }_{ t }$ negative.  ${ v }_{ t }$, ${ v }_{ s }$ are dummy variables we can swap them and we have

$\nwarrow \quad +\quad \nearrow \quad +\quad \swarrow \quad=\quad \upuparrows$
${ v }_{ s }$             ${ v }_{ t }$             $i{ v }_{ s }^{ ' }$             ${c }$

Remember that  ${c }$ is a constant.  If we are able to generate $i{ v }_{ s }^{ ' }$ we can then slow ${ v }_{ t }$ and even reverse ${ v }_{ t }$.