
#1
Jan2013, 01:42 AM

P: 26

Okay first of all, I know it's impossible to travel faster than light. But they say that IF.... IF you could, then you would arrive at your destination before you left.
That's what I don't understand. Like for example, it takes light 8 minutes to get to us from the Sun. So if a person left Earth at 6:00 and arrived at the Sun at 6:07, he traveled faster than light. But that doesn't sound like he arrived there before leaving. It just sounds like he arrived 7 minutes LATER. Faster than expected of light, but still LATER. Can someone explain this? 



#2
Jan2013, 01:45 AM

P: 2,043

In some valid reference frame which is in motion with respect to the EarthSun system, it will be that you arrived before you left because any two events which are spacelike separated (you leaving and you arriving would be 2 events which are spacelike separated) can be found to change order by making a lorentz boost. I will let someone else show the math because I'm lazy.




#3
Jan2013, 08:10 AM

P: 1,657

[itex]x_1' = 0[/itex] [itex]t_1' = 0[/itex] [itex]x_2' = \gamma (x_2  v t_2) = \gamma (Uv)T[/itex] [itex]t_2' = \gamma (t_2  \dfrac{v}{c^2} x_2) = \gamma (1\dfrac{Uv}{c^2})T[/itex] Note: if [itex]U = \dfrac{c^2}{v}[/itex], then [itex]t_2' = 0[/itex]. So if [itex]U > c[/itex] in one frame, then travel time can be instantaneous in another frame. But it gets weirder than that. If [itex]U > \dfrac{c^2}{v}[/itex], then [itex]t_2' < 0[/itex]. So in frame F', the fasterthanlight ship arrives Before it leaves. So if fasterthanlight travel is possible in one frame, then there are frames in which backintime travel is possible. 



#4
Jan2013, 12:47 PM

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Something I don't understand about FTL travelThe t and x axes are the ones used by the observer on Earth. The points on a line that's parallel to the x axis all have the same t coordinate. The t' and x' axes are the ones used by an observer whose motion is described by the t' axis. The points on a line that's parallel to the x' axis all have the same t' coordinate. Note that it's possible to draw a horizontal line in the diagram below the Sun 6:01 event and above the Earth 6:00 event. This means that the Sun 6:01 event has a later t coordinate than the Earth 6:00 event. But the Earth 6:00 event is above the x' axis, while the Sun 6:01 event is below the x' axis. This means that the former has a later t' coordinate than the latter. So in the "primed" coordinate system, the thing you think of as going from the Earth to the sun is described as going from the Sun to the Earth. Alternatively, it can be considered going from the Earth to the sun, but arriving before departing (i.e. going back in time). Edit: I have to add that it doesn't make sense to use a person in the example, because a person moving FTL contradicts SR. So SR plus your assumption is logically inconsistent, and in an inconsistent system, every statement is true (including things like 7=3). It never makes sense to ask what would happen if something that contradicts the theory we're supposed to use to answer the question is true. But it's fine to ask what happens if some weird*** particle makes this trip, because that doesn't immediately contradict SR. (Apparently we can't say "***". I didn't know that). 



#5
Jan2213, 11:03 AM

P: 26

Thanks everyone for answering. I've read all your posts.
I'm not that great in understanding mathematics, however. So in other words, not all observers will see the ships arrival before it's departure? Only the one moving towards the Sun? Is the way I described it in my first post assumes that time and simultaneity are absolute and not relative? Or is there at least one observer who would see it that way? 



#6
Jan2213, 12:06 PM

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#7
Jan2213, 01:10 PM

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Someone in a certain reference frame will see you arrive before you left, but they'll see you arrive as a flying purple telephone made of strawberry sausage since the journey took you 5i years.




#8
Jan2413, 04:35 AM

P: 128





#9
Jan2413, 05:32 AM

P: 128

I think the distinction between spacelikeseparated, timelikeseparated and nullseparated events is good to point out here.
If a velocity under the speed of light is required to visit both of a pair of events in one reference frame, then that is also true for all other inertial reference frames. The order of the events is also always the same in all reference frames. Such events are called "timelike separated", and because of the invariance of their relative order, causal relation between them is possible. If a velocity above the speed of light is required to visit both of a pair of events in one reference frame, then that is also true for all other inertial reference frames. The order of the events is not the same in all reference frames. In some frames they are simultaneous, in others one preceeds the other, and in others yet their order is reversed. Such events are called "spacelike separated" and because of the undefiniteness of their relative order, causal relation between them is considered impossible. In other words, they can not belong on a single "worldline", or be events concerning a single object. If a velocity exactly equal the speed of light is required to visit both of a pair of events in one reference frame, then that is also true for all other inertial reference frames. The order of the events is also always the same in all reference frames. Such events are called "null separated", causal relation between them is possible, but only as electromagnetic or gravity field changes, not massive particle travel. 



#10
Jan2913, 06:54 PM

P: 23

Do I read Fredrik's diagram correctly if I conclude that the fastmoving observer will see the "FTL" ship moving backwards, but due to the distances between Earth and sun and the observer moving slower than light it could never interfere, fr. ex by first seeing the ship leaving (backwards) the sun and then sending a message to tell the ship not to start the journey in the first place.
Oh, this is hard to put to words, but my point is, is there some kind of difference between a scenario leading to a paradox where an observer would observe an effect leading to a cause (=time going backwards) but not being able to interfere due to the limits of lightspeed, and an observer being able to either contact his own past, or convey a message from the sun to Earth backwards in time? Are both scenarios "equally impossible?" 



#11
Jan3013, 03:43 AM

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#12
Jan3013, 07:26 AM

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But if FTL is possible, and all frames are equivalent (the relativity principle), then it is possible to send a message to your own younger self. Send a backintime message from yourself to a colleague, and have the colleague send a backintime message back to you. 



#13
Jan3013, 07:58 AM

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#14
Jan3013, 08:34 AM

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What am I missing here? Andromeda RXJ seems to be asking .........What would the outcome be if you did something that's impossible to do?




#15
Jan3013, 08:59 AM

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#16
Jan3013, 08:59 AM

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#17
Jan3013, 09:04 AM

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