I don't mean to be condescending, carbonlife, but that's a particularly incoherent explanation of the "tachyon pistol" paradox. A much clearer one can be found by typing the words "tachyon pistol paradox" into Google, and hitting "I'm feeling lucky"
That link is http://sheol.org/throopw/tachyon-pistols.html
and it's got a mistake in it. The author ( Wayne Throop ) does a nice job of explaining why there's no "simultaneous now" valid everywhere in all frames of reference.
However at the end Throop states incorrectly:
"FTL still can can bite you in non-instantaneous cases; where we're only going a "little bit" faster than light..." [true].
"If you warp out, go to Tau Ceti, then with normal reaction engines accelerate away from earth, warp out again to go back to earth, you will indeed get back before you left. (Presuming that the real-space delta-v before the warp/hyperdrive/tachyon-watziz trips was "large enough"... there are formulas for such things in the textbooks)." [fa;se].
The textbook formulas break if you try to calculate elapsed time while warping "a little bit faster" than light. The elapsed time for the warp jump doesn't come out negative -- it comes out square root of a negative number -- so the textbook formulas don't say you get back from Tau Ceti before you left.
Implicit in the textbook formulas is that velocity is equal-to-or-less-than c, usually stated somewhere in the derivation. This is called the "domain of applicability" of the formula.
The easiest handle on paradoxes like that is to use the invariant interval, which is explained nicely in _Feynmann's Lectures on Physics_. Say you've got 2 firecrackers well-separated in space, with fuses lit. The fuses can be of the same length or different lengths, doesn't matter. The firecrackers can be moving relative to each other or not; doesn't matter. Sensors aboard the nearst space station record 2 events -- call them flash A and flash B. In the space station's frame of reference, the flashes are separated by distance x and time t. The neat part is that for any other observer in any other inertial frame of reference, the invariant interval between those 2 events always comes out the same, namely square_root ( delta_x_squared minus delta_t_squared ).
The neat part is, it's like the Pythagorean theorem -- if ANY observer in ANY inertial reference frame reported the invariant interval, you can solve for t_prime if you've got x_prime or vice versa in any other frame of reference. In verbal shorthand, the flashes might be 5 light-seconds apart in space in frame A, and 4 seconds apart, so the invariant interval would then be sqrt ( 5^2 - 4^2 = sqrt ( 25 - 16 ) = 3 light-second interval. That's a bit confusing though, because it's easy to confuse seconds ( of time ) and light-seconds ( of distance ). The idea is that if you're computing sqrt ( distance_squaed minus time squared ), you need both in the same units. So rather than mess around with seconds and light-seconds, the common practice in physics is to choose the unit of time so that one time tick is the time light takes to travel one meter ( roughly 3.3 nanoseconds ). That way invariant intervals have units of meters, which simplifies the notation and helps keep the units straight.
It's perfectly legit for the invariant interval to come out imaginary, because one firecracker flash didn't cause the other -- e.g. if the flashes are 5 seconds apart and 4 light-seconds apart, then sqrt ( 16 - 25 ) = sqrt ( - 9 ) which is written 3i, called an "imaginary number".
In practice you use th vector form, so that flash1 is at coordinates ( x1. y1, z1, t1 ), and flash2 is at coords ( x2, y2, z2, t2 ), and the invariant interval is sqrt ( delta-x-squared + delta-y-squared + delta-z-swuared MINUS delta-t squared ).
Measuring time in meters also simplifies thought experiments. For example, an easy way to calculate slowdown of clocks aboard Einstein's train is to simply glue a mirror to each end of a meter stick and set a light pulse bouncing between the mirrors. Each bounce is on tick of light-travel time. However for a stationary observer beside the tracks, the light seems to be following a slant-wise path between the mirrors, yet still travels at c along the slantwise path, so long story short you apply the Pythagorean theorem and end up with the invariant interval equation ( look it up in _Feinmann_; I ain't gonna draw it ).
OK, suppose you're back aboard the space station, Automatic sensors record an alien ship going into warp with a bright flash at location ( x1, y1, z1, t1 ), and drop out of warp with a bright flash at location x2, y2, z2 and t2 ). Excited at having seen the first warp jump ever observed by humans, you contact the other deep-space stations, which recorded it too. Each station is moving with a different relativistic velocity and direction, so they each get different separations and timings on the pair-of-flashes, but they all (a) calculate the same invariant spacetime interval BETWEEN the flashes. All stations agree on one other point -- each flash occurred at a definite point in realtime in their frame, not in imaginary time. If the alien shop entered warp at time t1, it didn't exit warp at time t1 + sqrt ( -25 ) seconds. The alien ship exited warp at some definite time on the station clocks.
This is a powerful way of simplifying the problem, because no matter what the alien ship may have done in subspace or whatever, the flashes of light occurred in normal spacetime, at specific measurable positions and times within any given inertial frame of reference.
Throop uses an older, weaker version of the tachyon pistol paradox because at the end of the day, both duelists are dead, and the 'official version of what happened' is only from duelist B's frame of reference.
"... as B is hit in the back at tick 4, in outrage at A's firing before 8 seconds are up, B manages to turn and fire before being overcome by his fatal wound. And since in B's frame of reference it's A's clock that ticks slow, B's round hits A, striking A dead instantly, at A's second tick; a full six seconds before A fired the original round. A classic grandfather paradox."
In stronger scenarios, duelist B is alive forevermore for some referees, and dead forevermore for other referees, depending on a particular referee's flight path. In Throop's scenario, you're lef kind of wondering if the paradox is just a mathematical illusion or if it really happened -- that's why improved versions of the tachyon duel added referees in different frames who all had to agree on whether B is dead or not -- by making the fatal shooting of A a direct result of a faster-than-light communication that WOULDN'T HAVE BEEN POSSIBLE if If B is merely outraged that A cheated, he could fire back even if both pistols were slower-than-light particle-beams. Throop's version implies that B knows for a certainty that A cheated becaus only 4 seconds had elapsed -- but there'd always be that doubt: was B's clock the one running slower, or was A's ?
Throop's version also contains an error where it says "Two duelists, A and B, are to stand back to back, then start out at 0.866 lightspeed for 8 seconds, turn, and fire." That adds the hairy element of acceleration to the problem. Yet Throop then says the result... "is due to the fact that, in SR [Special Relativity], the question of what occurs at the "same time as" something else is observer dependent." Special relativity ( by definition ) only applies when both frames of reference are coasting. If the duelits "stand got to know the acceleration curve and apply General Relativity ( GR ), not Special Relativity.
GR is a whole lot hairier and obscures the paradox .
"Standing back to back" is a common error in stating the tachyon pistol paradox, more for visual effect than for accuracy -- but then later, just when you think you understand it, you go "Wait a minute, these duelists ACCELERATED... aw crud, more math." Better versions say the duelists PASS each other in their spaceships going in opposite directions, already at speed, and synchronize their clocks at the moment of passing. If the ships almost touch when they pass, there's negligible invariant interval between the event of A clicking his stopwatch and B clicking his stopwatch. A space-suited referee pre-positioned at that point-of-passing can also synchronize HER watch with both duelists, with no pesky spacetime interval between her stopwatch-click and theirs -- and then that referee becomes a valuable point-of-symmetry for followup what-ifs where both duelists fire at the same time in their frames -- in which case the rounds should pass the referee-in-the-middle at the same time.
In fact any number of coasting referee-spaceships could coast past the same starting point at the same time going different directions and ALL synchronize their clocks, which simplifies matters because the starting time isn't history-dependent -- it's just t-zero for all of them. That's how you build simplifications into a thought experiment to make the math easier to do, and easier to cross-check.
This might seem nit-picky, but discrepancies in either relativity or quantum mechanics ALWAYS come back to bite you. The bites itch with curiosity, and it's harder to track down a misconception than to check everything first. It's kinda like defensive programming -- after awhile you find yourself resisting oversimplifications that can throw you off.Robert A. Heinlein described a Fair Witness as a person who, if you ask them "Is that house white", will answer "Well it's white on the side I can see from here", where 'here' has to be spelled out.
On the one hand people want explanations to be simple -- on the other hand, they want explanations that hold up well as they learn more.
There's a Delicate Balance between accuracy and comprehensibility -- people who know this stuff generally aren't the clearest writers, and vice versa. It's statistically unlikely that extraordinary writing talent will appear in the same person as physics talent, though it does happen as with Carl Sagan. If you set a standard that all explanations have to be easy-to-understand, you get the watered-down kind of writing you often find in places like PhysOrg. If you insist on near-perfect accuracy like that of Einstein, you end up with hard-to-find writing that only a few people on the planet may understand, Everybody just has to do the best they can in a forum like this, and be as precise as they can in framing questions / scenarios / answers. If a reader can narrow down their puzzlement to a targeted question, it's much easier to frame an answer, without having to backtrack through a bunch of misperceptions. That's not a criticism of anyone here -- frankly I LIKE to see readers agitating for more factuality on PhysOrg. Bear in mind though that even peer-reviewed physics journals sometimes get spoofed, because no editors can be omniscient, and because editors don't want to be too doctrinaire about heretical notions. Even encyclopedias typically average about 1 error per science / technology article, which frustrates the heck out of readers trying hard to get the right info.