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Searching for clear explanations of why FTL equals time travel I found this http://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-time-travel Go at the bottom, when he draws the blue lines. He says that those are the lines of costant time and they are parallel to the space line of the relativistic ship. This imply that the time line is perpendicular to the space line. But before he had said that the time line of the ship was the one named "space ship time" that is skewed towards the space line. So it seems to me that there are two time lines for the ship: the "space ship time" line and the one perpendicular to the space line that isn't drawn.

To say it in other words: if we have a relativistic ship its space and time lines should both be skewed towards the light line, right ? Because light speed is costant for any observer. This means that the light line should always be at the same distance from both the time and the space line. But when the blue lines are drawn the time line is said to be perpendicular to the space line. This means that the light line would be closer to the space line that the time line. Thus meaning that light would be faster for that observer.

The problem is that if we consider the "space ship time" line as the correct time line there is no time travel.

EDIT: I think I'm starting to understand. In other examples I found online they suggest to rotate the graph, so that the time line of the space ship is pointing towards high. That makes evident the FTL communications between Earth and AC are distorted from the point of view of the ship, with the ones sent from AC to Earth arriving before they are sent. If the ship can sent messages at near istantaneous speed those messages would be a line perpendicular to their time line, but these lines woldn't be perpendicular to the time lines of Earth and AC, arriving after or even before they are sent. So to avoid time paradoxes you have time lines of different reference frames to always make an acute angle. If they were to make a dull angle (by going FTL) that would mean they are going in the past of each other. In fact you could rotate the graph to make on of them your y axis and see that the other is going down (towards the past). Is this correct ?

EDIT 2: Graph I made enter image description here In the horrbible graph above we have Earth and AC time lines (black), the realtivistic ship time line (blue) and near istantaneous FTL communications (purple). The first message is sent from AC to Earth, from their point of view is istantaneous, but from the point of view of the ship is going back in the past. When they receive it they sent a message back to AC (purple line perpendicular to blue line). Again this message is istantaneous from their POV, but from AC POV it arrives before it is sent. So AC receive an answer to a message that they haven't sent yet. What did I do wrong ?

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marked as duplicate by Kyle Kanos, Jon Custer, ZeroTheHero, Yashas, Hritik Narayan May 27 '17 at 14:21

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    $\begingroup$ The space and time axes in a Minkowski diagram are not perpendicular en.wikipedia.org/wiki/Minkowski_diagram $\endgroup$ – user126422 May 24 '17 at 14:32
  • $\begingroup$ "Perpendicular" means orthogonal with respect to the Lorentz metric, not the euclidean metric. So in two dimensions, this means that the vectors $(x,y)$ and $(z,w)$ are perpendicular iff $xz-yw=0$. Note the minus sign. $\endgroup$ – WillO May 26 '17 at 12:45
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I guess the source of your confusion is that you suppose that "time lines" (dots on diagram having same coordinate in ship's frame of reference) and "space lines" (dots on diagram having same time in ship's frame of reference) must be perpendicular on diagram. This is not true. Actually both sets of lines are skewed towards the direction of "light line". Here are several examples: https://en.wikipedia.org/wiki/Minkowski_diagram

It was quite difficult for me to follow the article. It seems that actually author did NOT show that FTL travel must mean time machine is possible.

What author showed is that if FTL message transmission is possible than in some frame of reference the message would be received before the message was sent. It seems impossible (all the results of Relativity Theory seem impossible at first), but this is not a time machine yet.

Time-travel paradoxes would happen if someone would be able to receive the message before he sends it out (this someone send a message to himself in the past). If arbitrary fast message transmission is possible than it is quite easy to send messages to the past. In the example described in the article observer sees:

1) message from Earth received on Alpha Centauri

2) later on this message is sent from Earth

and the observer has some time to get the contents of message received on Alpha Centauri and transmit it to Earth so that it would be received before it is sent. But to do it would be necessary to transmit information between AC, observer and Earth quite fast: faster than light and faster than the original message from Earth to AC was sent.

So, if Relativity Theory is correct and you can send messages arbitrary fast, than you have time-travel paradoxes.

Actually if one can send signals just a little bit faster than light you would be able to send messages to yourself in the past. But the article does not explain why and how.

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  • $\begingroup$ I think I'm starting to understand. In other examples I found online they suggest to rotate the graph, so that the time line of the space ship is pointing towards high. That makes evident the FTL communications between Earth and AC are distorted from the point of view of the ship, with the ones sent from AC to Earth arriving before they are sent. If the ship can sent messages at near istantaneous speed those messages would be a line perpendicular to their time line, but these lines woldn't be perpendicular to the time lines of Earth and AC, arriving after or even before they are sent. $\endgroup$ – Zeta May 28 '17 at 17:05
  • $\begingroup$ @Zeta Not sure, but I am afraid you are still confused. Ship's time-lines and space-lines are not perpendicular on the presented graphs! The series of blue lines on the graphs at the end of article are set's of events happened at the same moment (according to ship). If some message was transmitted instantly ("message sent" and "message received" events happened simultaneously according to ship's frame of reference) both these event's must be located on the same blue line. $\endgroup$ – lesnik May 28 '17 at 17:31
  • $\begingroup$ Message above was limited by number of words. I edited my question with the complete message. I understand that the ship time and space lines aren't perpendicular, but my question is about the time line and the lines of costant time. Events that happen at the same time (from the point of view of the ship) should be on a line perpendicular to the time line of the ship, right ? If this is not the case, how should the time be viewed from the frame of reference of the ship ? Rotating the graph so that the time line of the ship is going upwards is a correct way to visualize this ? $\endgroup$ – Zeta May 29 '17 at 18:12
  • $\begingroup$ I edited the question. Check EDIT 2. Thanks. $\endgroup$ – Zeta May 29 '17 at 18:34
  • $\begingroup$ Instant message between AC and Earth is correct. But instant message from ship is not. You draw it perpendicular to blue line, and that's wrong. You should draw another line pointing approximately to the same direction as blue line, but a little lower, so that it goes below the yellow line. All the points on this new line happened simultaneously from the ship's point of view. And all the instant messages the ship sends are parallel to this new line. Earth sends instant message to ship (horizontal line), ship sends message to Earth (line parallel to a new one) it is on Earth before it was sent. $\endgroup$ – lesnik May 29 '17 at 19:33

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