Now I am aware that it is commonly stated that a tachyons moves backwards in time, why is this? Because by my calculations (see below) the movement through the temporal dimension should be imaginary rather than negative. If anyone could help me check this over, it would be much appreciated.

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In a spacetime 3d volume with 2 dimensions of space and 1 time, relativity tells us that the total magnitude of an objects motion is C (the speed of light). (I believe, hence the fact that movement through time slows down as you accelerate, verification of this would also be appreciated)

Using Pythagoras' theorem wear “a” is the distance travelled through space, “b” the distance travelled through time and “c” the overall magnitude in the spacetime volume we get the following:

a

^{2}+b

^{2}=c

^{2}

substituting in “a” as C+x (x positive real) and “c” as C we get the following:

(C+x)

^{2}+b

^{2}=C

^{2}

C

^{2}+2cx+x

^{2}+b

^{2}=C

^{2}

2Cx+x

^{2}+b

^{2}=0

as x and C are both positive then so must x

^{2}and 2Cx be.

This implies that b

^{2}<0

This implies that b is imaginary not merely negative.

I cannot see any mistakes but then I cannot proof read my essays, html, maths or circuits well so if someone else could check this over that would be good.

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Of course, if the movement through time is imaginary then wouldn't that make the line impossible to plot without introducing another fourth imaginary axis to our spacetime volume to create a 4d complex spacetime volume.