Lets say that I am at the origin of an inertial reference frame traveling at +.9c with respect to you. At the moment that our positions coincide (t’=t=0), you shoot a tachyon from a tachyon gun in the direction of my motion. The tachyon travels at 10c as observed by you. After 10 seconds, the tachyon is meters from you, and there it hits a collector that happens to be at rest in my reference frame manned by my observer. My observer dutifully records the collection.
The values my observer records must satisfy the Lorentz Transformations:
In your reference frame, collection happens at t = 10 seconds, x = meters.
In my reference frame, collection happens at t = -408.seconds, x = meters.
Chronologically, this is what I have. I am in a reference frame traveling at .9c with respect to you.
1. At t’= -408 sec, a tachyon hits a collector in a distant part of my reference frame. I don’t know about it yet, but it is now recorded history.
2. At t’ = 0, I cross paths with you just as you are about to shoot the tachyon. I knock the tachyon gun out of your hand before you have a chance to shoot.
3. I declare that I have changed history because my observer could not now have collected a tachyon.