Changes

A common interpetation using time dilation is that a tachyon would travel backwards in time. The basis for this logic is in the kinematic equations called the Lorentz transformations. There are several; the relevant one is

A common interpetation using time dilation is that a tachyon would travel backwards in time. The basis for this logic is in the kinematic equations called the Lorentz transformations. There are several; the relevant one is

::<math>t = \gamma (t' - x \frac{v}{c^2}) = \gamma t'(1 - \frac{x}{t'} \frac{v}{c^2})</math> where x is the change in position.

::<math>t = \gamma (t' - x \frac{v}{c^2}) = \gamma t'(1 - \frac{x}{t'} \frac{v}{c^2})</math> where <math>x</math> is the change in position.

 

Consider an observer moving at <math>86.6%</math> the speed of light again, observing the movement tachyons.

Plugging in values of <math>\gamma = 2</math>, <math> \frac{v}{c} = .866</math>, <math>t' = 1</math>, and <math>\frac{x}{t'} = 2c</math> (or twice the speed of light) gives

Plugging in values of <math>\gamma = 2</math>, <math> \frac{v}{c} = .866</math>, <math>t' = 1</math>, and <math>\frac{x}{t'} = 2c</math> (or twice the speed of light) gives

::<math>t = 2(1 - \frac{2c}{1} \frac{.866}{c}) = 2 - 4(.866) = -1.464</math>

::<math>t = 2(1 - \frac{2c}{1} \frac{.866}{c}) = 2 - 4(.866) = -1.464</math>

so <i>negative</i> time has passed for the external observer; the tachyon has moved back in time according to the rest of the universe. This creates obvious potential for paradox.  

so <i>negative</i> time has passed for the external observer; the tachyon seems to have arrived before it left, and so has moved back in time according to the rest of the universe. This creates obvious potential for paradox.  

This possibile paradox of effect precluding cause indicates that, if tachyons truly existed, then there may be no free will, and actions would always be pre-determined. Dr. Richard Muller vividly illustrates this in his "tachyon murder paradox," commenting that it gives him personal reason to wish faster than light travel impossible.<ref>Dr. Richard Muller "Tachyon Murder Paradox" - https://www.quora.com/Will-humans-ever-develop-faster-than-light-travel</ref>

This possibile paradox of effect precluding cause indicates that, if tachyons truly existed, then there may be no free will, and actions would always be pre-determined. Dr. Richard Muller vividly illustrates this in his "tachyon murder paradox," commenting that it gives him personal reason to wish faster than light travel impossible.<ref>Dr. Richard Muller "Tachyon Murder Paradox" - https://www.quora.com/Will-humans-ever-develop-faster-than-light-travel</ref>

[[Category:Relativity]]

[[Category:Relativity]]