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In special relativity the space-time can be seen as a static four-dimensional picture that contains the entire past and the future of a flat universe. And the patterns in it are subject to several constraints to make it physically feasible. Observers within it observe it by sweeping their plane of simultaneity through it. In this case anything that moved faster than the speed of light would draw a space-like line through spacetime.

And one doesn't even need to have tachyons to have a space-like line of events. For example it's possible to flash a ribbon of lights simultaneously, which can draw a similar space-like line of events. And observers wouldn't notice anything special other than just a regular line of space-like events.

Would tachyons be any different than just a ribbon light flashed simultaneously in a frame of reference?

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The problem is, that the word simultaneously means that the events are light-like connected. So, the flashing of two lights on your ribbon is not a space-like event.

Tachyons behave very peculiar, i.e. in such a way that they lose energy while accelerating. It takes more and more energy to asymptotically slow them down towards the speed of light. It can never be stopped and thus has no connection to (no interaction with) our side of the barrier that is the speed of light. Therefore the answer is no, we can never notice them, even though they might be there (some string theories have something to say about Tachyons).

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  • $\begingroup$ You can create space-like separated events by putting the trigger in the past light cone of them. The simplest case is flashing a light in the room. The event where the two light rays reach two opposite walls and scatter from them is spacelike separated. $\endgroup$ – Calmarius Feb 11 '15 at 14:40
  • $\begingroup$ Ok, now you have generated two space-like events that are not causally linked (since one telling the other that he/she saw the flash of light as well, is a light-like event at best). In such a way, you can always claim, that two events, that are not causally linked, were triggered by one and the same Tachyon. Proving this, however, would be impossible. $\endgroup$ – Clever Feb 11 '15 at 14:43
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    $\begingroup$ No, the word "simultaneous" means that they are observed to occur at the same time by some observer. This is always the case for space-like separations and it is mutually exclusive to the two events being light-like connected. The answer is incorrect from the outset. $\endgroup$ – Emilio Pisanty Feb 11 '15 at 14:45
  • $\begingroup$ I still think that observed simultaneously is something else than to flash a ribbon of lights simultaneously (which IMO suggests simultaneity of the emitting). $\endgroup$ – Clever Feb 11 '15 at 15:52
  • $\begingroup$ I've read that tachyons would produce Cherenkov radiation in empty space. Is this not true? $\endgroup$ – zeta-band Sep 11 '17 at 23:53

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