# FTL implies Backward Time Effect

## Main Question or Discussion Point

Any faster than light signal can create backward time effect by means of some frames seeing the signal go to the past of the origin.

Is there any illustration or web site that illustrates this clearly?

I'd like to know if the return path carrying the signal needs to travel faster than light or mere superluminal signalling is enough.

For example. Supposed we sent a faster than light signal to pluto. Then it was sent back at similarly superluminal velocity. Would it reach the origin before it was sent out.. or do you have to carry the signal in a superluminal carrier like spaceship for this backward time effect to manifest at the origin?

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For example. Supposed we sent a faster than light signal to pluto. Then it was sent back at similarly superluminal velocity. Would it reach the origin before it was sent out.. or do you have to carry the signal in a superluminal carrier like spaceship for this backward time effect to manifest at the origin?
You need a subluminal spaceship submitting the signal in its own rest frame with superluminal velocity.

You need a subluminal spaceship submitting the signal in its own rest frame with superluminal velocity.
For example. Earth sent a superluminal signal to a station in Pluto. If the station there sent another superluminal signal back to earth. Would it arrive in earth past? Is a spaceship back to earth really necessary? Please elaborate the pathways. Thanks.

For example. Earth sent a superluminal signal to a station in Pluto. If the station there sent another superluminal signal back to earth. Would it arrive in earth past?
Of course not.

Is a spaceship back to earth really necessary?
In fact you need two spaceships: One that transmits the signal from Earth and another that receives it at Pluto and vice versa for the way back. If the signal velocity is superluminal in the rest system of the ships it can be negative in the rest system of Earth or Pluto and a negative velocity leads to a negative time of flight.

Fredrik
Staff Emeritus
Gold Member
Is a spaceship back to earth really necessary? Please elaborate the pathways. Thanks.
The spaceship needs to be moving away from Earth. This is very easy to see in a spacetime diagram. I'm too lazy to draw one, so I'll just use this one from Wikipedia to explain my point.

Think of the black axes as describing the coordinates assigned by an observer on Earth. Think of the blue line marked ct' as the world line of the spaceship. The other blue line represents a set of events that the observer on the spaceship would assign the same time coordinate. In other words, those are events that he considers simultaneous. Yet another way of saying it: That's a slice of spacetime that he thinks of as "space". I call such a line a "line of simultaneity".

The kind of FTL message that's the easiest to draw is one that moves at infinite speed in the inertial coordinate system in which the emitter is at rest. When someone on Earth sends such a message, you draw it as a horizontal line. When someone on the spaceship sends it, you draw it as a line parallel to the blue simultaneity line (the one marked x'). (If the idea of infinite speed bothers you, just tilt the line a little bit, so that it now represents ludicrous speed instead of infinite speed).

Now, a horizontal line representing a message sent from a small x coordinate (Earth) to a large one (spaceship) will cross one of the spaceship's simultaneity lines (a line parallel to the blue line marked x'). So the sending event and the receiving event are not simultaneous. In the diagram, the sending event is above the simultaneity line, and the receiving event is below it. So the sending event has the larger time coordinate in the inertial coordinate system in which the spaceship is at rest. From their point of view, they got a message from the future.

If they reply to it immediately, the reply message will be a line parallel to (or almost parallel to) the blue simultaneity line, and will therefore arrive at Earth before the message they replied to was sent.

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The spaceship needs to be moving away from Earth. This is very easy to see in a spacetime diagram. I'm too lazy to draw one, so I'll just use this one from Wikipedia to explain my point.

Think of the black axes as describing the coordinates assigned by an observer on Earth. Think of the blue line marked ct' as the world line of the spaceship. The other blue line represents a set of events that the observer on the spaceship would assign the same time coordinate. In other words, those are events that he considers simultaneous. Yet another way of saying it: That's a slice of spacetime that he thinks of as "space". I call such a line a "line of simultaneity".

The kind of FTL message that's the easiest to draw is one that moves at infinite speed in the inertial coordinate system in which the emitter is at rest. When someone on Earth sends such a message, you draw it as a horizontal line. When someone on the spaceship sends it, you draw it as a line parallel to the blue simultaneity line (the one marked x'). (If the idea of infinite speed bothers you, just tilt the line a little bit, so that it now represents ludicrous speed instead of infinite speed).

Now, a horizontal line representing a message sent from a small x coordinate (Earth) to a large one (spaceship) will cross one of the spaceship's simultaneity lines (a line parallel to the blue line marked x'). So the sending event and the receiving event are not simultaneous. In the diagram, the sending event is above the simultaneity line, and the receiving event is below it. So the sending event has the larger time coordinate in the inertial coordinate system in which the spaceship is at rest. From their point of view, they got a message from the future.

If they reply to it immediately, the reply message will be a line parallel to (or almost parallel to) the blue simultaneity line, and will therefore arrive at Earth before the message they replied to was sent.
How come there are particles that can travel faster than light?

Thanks Fredrik and others for the tips. I found a web site:

http://sheol.org/throopw/tachyon-pistols.html [Broken]

Consider a duel with tachyon pistols. Two duelists, A and B, are to stand back to back, then start out at 0.866 lightspeed for 8 seconds, turn, and fire. Tachyon pistol rounds move so fast, they are instantaneous for all practical purposes.

So, the duelists both set out --- at 0.866 lightspeed each relative to the other, so that the time dilation factor is 2 between them. Duelist A counts off 8 lightseconds, turns, and fires. Now, according to A (since in relativity all inertial frames are equally valid) B's the one who's moving, so B's clock is ticking at half-speed. Thus, the tachyon round 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 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.
So the requirements to get a signal back in time is if the sender and emitter should be moving near light speed to take advantage of time dilation?

Fredrik. What is the speed of the spacetime in your example with respect to light? Is it in the speed comparible to our space shuttle now or more impractical like 1/3 the speed of light?

So you mean to say we can't do any backward in time superluminal experiment even if the neutrino were proven to be superluminal... like we need a signal faster like twice the speed of light?

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So the requirements to get a signal back in time is if the sender and emitter should be moving near light speed to take advantage of time dilation?
The minimum speed u of sender and emitter depends on the signal velocity v in their rest frame: u·v > c²

The spaceship needs to be moving away from Earth. This is very easy to see in a spacetime diagram. I'm too lazy to draw one, so I'll just use this one from Wikipedia to explain my point.

Think of the black axes as describing the coordinates assigned by an observer on Earth. Think of the blue line marked ct' as the world line of the spaceship. The other blue line represents a set of events that the observer on the spaceship would assign the same time coordinate. In other words, those are events that he considers simultaneous. Yet another way of saying it: That's a slice of spacetime that he thinks of as "space". I call such a line a "line of simultaneity".

The kind of FTL message that's the easiest to draw is one that moves at infinite speed in the inertial coordinate system in which the emitter is at rest. When someone on Earth sends such a message, you draw it as a horizontal line. When someone on the spaceship sends it, you draw it as a line parallel to the blue simultaneity line (the one marked x'). (If the idea of infinite speed bothers you, just tilt the line a little bit, so that it now represents ludicrous speed instead of infinite speed).

Now, a horizontal line representing a message sent from a small x coordinate (Earth) to a large one (spaceship) will cross one of the spaceship's simultaneity lines (a line parallel to the blue line marked x'). So the sending event and the receiving event are not simultaneous. In the diagram, the sending event is above the simultaneity line, and the receiving event is below it. So the sending event has the larger time coordinate in the inertial coordinate system in which the spaceship is at rest. From their point of view, they got a message from the future.

If they reply to it immediately, the reply message will be a line parallel to (or almost parallel to) the blue simultaneity line, and will therefore arrive at Earth before the message they replied to was sent.
Why are the spaceships necessary in the first place? Is it to experience time dilation. I can't totally understand the above. My background of backtime time signalling is based on the following:

http://sheol.org/throopw/tachyon-pistols.html [Broken]

Consider a duel with tachyon pistols. Two duelists, A and B, are to stand back to back, then start out at 0.866 lightspeed for 8 seconds, turn, and fire. Tachyon pistol rounds move so fast, they are instantaneous for all practical purposes.

So, the duelists both set out --- at 0.866 lightspeed each relative to the other, so that the time dilation factor is 2 between them. Duelist A counts off 8 lightseconds, turns, and fires. Now, according to A (since in relativity all inertial frames are equally valid) B's the one who's moving, so B's clock is ticking at half-speed. Thus, the tachyon round 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 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.
Now what is its analogy to your example? In the case of the dualists. They don't need a third party spaceship. Maybe we need it in the Earth-Pluto example because the two planets are not moving significantly with respect to each other so you need spaceships that are at least half the speed of light in addition to the earth and pluto?

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Fredrik
Staff Emeritus
Gold Member
How come there are particles that can travel faster than light?
There aren't. At least none that we know of.

So the requirements to get a signal back in time is if the sender and emitter should be moving near light speed to take advantage of time dilation?
What they're taking advantage of is the tilting of the simultaneity lines, which is of course related to time dilation, but not quite the same thing.

Fredrik. What is the speed of the spacetime in your example with respect to light? Is it in the speed comparible to our space shuttle now or more impractical like 1/3 the speed of light?
The speed we need depends on how far away the shuttle is. If it's really far away, then it doesn't need to move really fast.

So you mean to say we can't do any backward in time superluminal experiment even if the neutrino were proven to be superluminal... like we need a signal faster like twice the speed of light?
No, we could get the same effect with messages moving at any speed >c. I chose almost infinite speed only because it makes it easier to draw the diagram.

Why are the spaceships necessary in the first place?
To tilt the simultaneity lines so that an event on the spaceship is simultaneous with an earlier event on Earth.

In the case of the dualists. They don't need a third party spaceship.
That's because they're assumed to be walking at speed 0.866c.

There aren't. At least none that we know of.

What they're taking advantage of is the tilting of the simultaneity lines, which is of course related to time dilation, but not quite the same thing.

The speed we need depends on how far away the shuttle is. If it's really far away, then it doesn't need to move really fast.

No, we could get the same effect with messages moving at any speed >c. I chose almost infinite speed only because it makes it easier to draw the diagram.
You said "we could get the same effect with messages moving at any speed >c". Now if the neutrinos as reported current were really superluminal. How can you design an experiment setup where the neutrinos can be sent backward in time?

Fredrik
Staff Emeritus
Gold Member
You said "we could get the same effect with messages moving at any speed >c". Now if the neutrinos as reported current were really superluminal. How can you design an experiment setup where the neutrinos can be sent backward in time?
If you send them to someone who's already moving away from us at a speed that's extremely close to c, then the guy on the receiving end will assign an earlier time coordinate to the event where he receives the message than to the event where it was sent from Earth. So in this sense, he would consider it a "message from the future".

If you want to send a message to yourself in the past, you need a more complicated setup, and...uh, it looks like you also need the reply messages to travel with a much higher speed than the original message. Looks like I was wrong to suggest that you can get all of the same effects with a speed only slightly higher than c.

If you send them to someone who's already moving away from us at a speed that's extremely close to c, then the guy on the receiving end will assign an earlier time coordinate to the event where he receives the message than to the event where it was sent from Earth. So in this sense, he would consider it a "message from the future".

If you want to send a message to yourself in the past, you need a more complicated setup, and...uh, it looks like you also need the reply messages to travel with a much higher speed than the original message. Looks like I was wrong to suggest that you can get all of the same effects with a speed only slightly higher than c.
But practically. Can we even design spaceships that can move even half the speed of light? What is the most practical maximum speed that our spaceships can attain in the next hundreds or thousands of years based on physics as we know now. If we can never attend even half the speed of light. Then there may be things in the world like superluminal neutrinos yet causality never violated because we can never design the experiments to practical usage even in principle. Right?

Fredrik
Staff Emeritus