About site: Physics/Relativity/Time Travel - Tachyon Pistols

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Title: Physics/Relativity/Time Travel - Tachyon Pistols Simile and diagram explaining faster than light travel.

Tachyons,_Time_Travel,_and_Divine_Omniscience Philosophy of science and religion, theological fatalism, equations and footnotes.

Taking_the_Cosmic_Shortcut The future, Einstein's special theory of relativity, the past, theory of gravitation, black holes, wormholes, negative energy and links.

TIME_LOOPS An interview with Paul Davies, paradox, wormhole, black hole, Newtonian mechanics and quantum computations.

The_Time_Machine Einstein's theory, special relativity, communication faster than light, quantum cosmology, interview with Carl Sagan and links.

Time,_Time_Travel_&_Traversable_Wormholes Links to articles and sites about the possibility and impossibility of time travel.

Time_Travel Simple explanation, black hole containment device, mathematics, energy equation, chaos and super string theories, power of the crystal, FAQ and links.

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Why FTL implies time travel (tachyon pistols)

The entire "FTL implies time travel" meme has to do with what'ssometimes called "failure of simultaneity at a distance". In additionto the effects that pop treatments of relativity mention (that is, timedilation and length contraction), relativity proposes that thedefinition of "right now" is also different, depending on whichobserver's coordinate system you use. This is an effect much like therevolution of deciding that the direction "up" wasn't the sameeverywhere, but varied from place to place on earth. With relativity,the revolutionary notion is that the direction "futureward" (or"now-ward") isn't the same everywhere, and varies with velocity. We can describe this effect by idealizing FTL to be "instantaneous", anddescribing how the more familar time dilation implies this effect. Butremember, the same points apply to any FTL speed, you just have moremessy arithmetic to grind through. Consider a duel with tachyon pistols. Two duelists, A and B, are tostand back to back, then start out at 0.866 lightspeed for 8 seconds,turn, and fire. Tachyon pistol rounds move so fast, they areinstantaneous for all practical purposes. So, the duelists both set out --- at 0.866 lightspeed each relative tothe other, so that the time dilation factor is 2 between them. DuelistA counts off 8 lightseconds, turns, and fires. Now, according to A(since in relativity all inertial frames are equally valid) B's the onewho's moving, so B's clock is ticking at half-speed. Thus, the tachyonround hits B in the back as B's clock ticks 4 seconds. Now B (according to relativity) has every right to consider A as moving,and thus, A is the one with the slowed clock. So, as B is hit in theback at tick 4, in outrage at A's firing before 8 seconds are up, Bmanages to turn and fire before being overcome by his fatal wound. Andsince in B's frame of reference it's A's clock that ticks slow, B'sround hits A, striking A dead instantly, at A's second tick; a full sixseconds before A fired the original round. A classic grandfather paradox. Note, this is NOT a matter of when light gets to an observer, it is NOTan optical illusion. It is due to the fact that, in SR, the question ofwhat occurs at the "same time as" something else is observer dependent. As A fired that first show at tick 8, the bullet effectively teleportedfrom A's gun to B's back instantly --- instantly according to A. Butfor B, who was moving at 0.866 lightspeed WRT A, B was hit in the backby the bullet 4 seconds BEFORE the bullet was fired. And again note,this is NOT due to the optical illusion of lightspeed delay in viewingA's turn-and-shoot; the light form that event wouldn't reach B untilMUCH later, not tick 4. Here's a spacetime diagram of a referee (O3) and two duelists(O1 and O2). Space is up/down, time is left/right, in the diagram.

The paths O1 and O2 take through spacetime are the colorcoded arrowedlines. The events in spacetime that each considers "simultaneous" and"8 seconds after the start" are along the thinner, non-arrowedcolorcoded lines. So we see that, each of the three observers thinksthe other two have slow clocks, and that if we are allowed to movefaster than a lightcone, we'll end up going "pastward" in somebody'sreckoning. We can trace out the shots on this diagram, also. Step through it one more time: if green shootsat 8 seconds out, the shot will go along the green "line of simultaneity",and hit blue at 4 seconds elapsed. If blue returns fire from there,it will return along a line paralel to the blue "line of simultaneity",and catch green napping at 2 seconds elapsed.You can see more about spacetime diagrams, and more about thenotion of "lines of simultaneity" atsr-ticks-n-bricks.htmlsr-twin-01.htmlFinally, FTL still can can bite you in non-instantaneous cases;where we're only going a "little bit" faster than light. If you warp out, go to Tau Ceti, then with normal reaction enginesaccelerate away from earth, warp out again to go back to earth,you will indeed get back before you left. (Presuming that thereal-space delta-v before the warp/hyperdrive/tachyon-watziztrips was "large enough"... there are formulas for such thingsin the textbooks). [home]

Last edited Tue Oct 15 19:24:00 1996 - Last generated Tue Oct 15 19:24:02 1996geovisit();

Simile	and	diagram	explaining
faster	than	light	travel.

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