[Wobble73]

And thus parallel universes are born.

[General Battuta]

Aardwolf, if you still don't get it, examine this diagram.



Take the origin as event 1.

Now, event 2 is going to occur somewhere on this diagram. If event 2 is on a slower-than-light, timelike worldline, it WILL fall somewhere in the absolute future: the white delta at the top of the graph. All spacetime events in this area will, one hundred percent guaranteed, occur after (or simultaneous with) event 1. However, the exact interval between event 1 and 2 is up for debate.

If event 2 falls in the spacelike grey zones, however - which any FTL worldline will - then the event does not have to occur in the future (above the X axis). It could fall into the past.

This is why FTL = time travel. In some IRFs, the object will not appear as traveling faster than light; instead, it will appear as if it is moving back in time.

From here causality violations are inevitable. And:

In the theory of general relativity, the concept of causality is generalized in the most straightforward way: the effect must belong to the future light cone of its cause, even if the spacetime is curved

[The E]

Hmm......The problem is, there is no easy way to simplify it down more than the wikipedia summary without losing important details.

The "light cone" analogy is slightly misleading. In special relativity, everything in an event's forward light cone will happen in the future. That is, it will be affected by the event. Everything outside that light cone is indeterminate, there is no way to tell if something happened before the event, after it, or at the same time. If you send an FTL transmission, you are sending something outside your light cone. That means that it is absolutely possible to send a message to a point that has already happened, thereby altering that point and the light cone it generates, affecting your own light cone.

EDIT: Here's some math explaining the tricky bits (for very mathematical values of "explaining"):  http://en.wikipedia.org/wiki/Tachyonic_antitelephone

[Aardwolf]

you made the mistake of assuming that there existed a 'visibility cone', rather than understanding [...]¹ that the light cone represents a fundamental causal horizon.

Wat. I know it's not just light, it's the normal propagation of all information, including gravity.

But... at any point in space-time (the observer), there should be some region of space-time which is 'visible' to that point. That is, photons emitted from within this region of space-time are arriving at the observer. The force of gravity from masses within this region should be affecting the observer. Charge and magnetism from objects in this region should be affecting the observer. In effect, I'm talking about the region of space-time characterized by the fact that the propagation of its information is immediately affecting the observer. And I'm pretty sure that under normal circumstances, this region is the same as the surface of the past light cone.

Hm... according to this diagram, I should possibly be using the word 'hypersurface' instead of saying "region of space-time".


That said, if somehow you had an object moving with constant speed, and it's faster than the speed of light, then the curve through space-time traced by that object is a line. And that line is shallower than the slope of the cone, so as the cone moves through time, the intersection of the cone and the line goes from being the null set, to a single point, to two points which move hyperbolically farther apart in space, i.e. the distance between them would be something like c₁ * (c₂ + t²)^-0.5

Update after seeing people have replied before I finished typing:

@Battuta: Old news. I still don't get what's bad about violating causality, other than that you've violated causality --- which is apparently bad, but I still don't get what's bad about it.

This is why FTL = time travel. In some IRFs, the object will not appear as traveling faster than light; instead, it will appear as if it is moving back in time.

An object moving back in time appears identical to, and for all intents and purposes is equivalent to an object moving forward in time in the opposite direction.

You've got to prove there would be paradoxes. Unless you can do that, the only bad thing about violating causality is that it looks really weird².




¹ I've taken the liberty of omitting that remark. It seemed like attribution error, if you ask me.
² Also it confuses the **** out of people who were taught that it's impossible to do it

Note: personally I don't believe it's possible to go faster than light. But all of the arguments in favor of this seem to hinge on the fact that if causality could be violated,  it would have XYZ paradoxical outcomes. Which doesn't make sense to me.

[The E]

Okay, back to the light cone analogy.

From your point of view, there are two light cones. One moving outward from you, representing things that are, with absolute certainty, in your future. Another one pointing toward you, containing everything that is definitely in your past.
Everything outside those two cones will either happen in your future, happen concurrently with you, or has happened in your past (although those will only affect you if the light cones of those events intersects with yours).
Now, if you are sending an FTL message from your current point of view ("message" including anything moving at FTL speeds), you are sending it effectively into that realm of undefinedness. Meaning that there is a very real possibility that your message will be received at a point that lies in your relative past. The reception of that message would alter the outcome of that event, thereby altering what will happen when the light cone of the event intersects with yours.

Going back to this Gedankenexperiment, it can be shown mathematically that there are situations where it is possible to receive an answer to a message before the message that incited the answer was sent. Something like that would alter the sending of the message, thereby altering the response, ad nauseam et infinitum. There you have your paradox, because there is no way for an outside observer to tell what message was actually sent.

[General Battuta]

@Battuta: Old news. I still don't get what's bad about violating causality, other than that you've violated causality --- which is apparently bad, but I still don't get what's bad about it.

This is why FTL = time travel. In some IRFs, the object will not appear as traveling faster than light; instead, it will appear as if it is moving back in time.

An object moving back in time appears identical to, and for all intents and purposes is equivalent to an object moving forward in time in the opposite direction.

You've got to prove there would be paradoxes. Unless you can do that, the only bad thing about violating causality is that it looks really weird².

Wow, you're pulling a Marcov. It takes a special kind of stupid to ignore a huge post not just once but twice, the second time after it was pointed out to you.

I'll repost it for you:

To summarize: for a FTL (spacelike) worldline, there will always exist some IRFs which interpret the worldline as an object moving back in time. This leads to paradoxes which cannot occur, like signals being received before they are sent.

For an illustration of why this is bad, imagine that you have a radio signal you will send to detonate a bomb under your chair. You send the signal down a spacelike geometry, and it is received before it is sent, detonating the bomb and killing you. Yet this means you never sent the signal, because you are dead, so the bomb never detonates, allowing you to send the signal, detonating the bomb, killing you before you can send the signal, so the bomb never detonates, allowing you to send the signal, detonating the bomb, killing you before you can send the signal, so the bomb never detonates, allowing you to send the signal, detonating the bomb, killing you before you can send the signal, so the bomb never detonates, allowing you to send the signal, detonating the bomb, killing you before you can send the signal, so the bomb never detonates, allowing you to send the signal, detonating the bomb, killing you before you can send the signal, so the bomb never detonates, allowing you to send the signal, detonating the bomb, killing you before you can send the signal, so the bomb never detonates, allowing you to send the signal, detonating the bomb, killing you before you can send the signal, so the bomb never detonates, allowing you to 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hurk

Now let me address a specific and particularly asinine misconception you have:

An object moving back in time appears identical to, and for all intents and purposes is equivalent to an object moving forward in time in the opposite direction.

Really. Is that so.

Why are you talking about objects instead of worldlines? Why are you ignoring the relative position of the ends of the object's worldline?

First off, in whose reference frame? The telltale sign of a relativity novice is their failure to identify reference frames. You keep assuming that there is a 'correct' IRF where things 'actually' happen.

In the above example, describe to me what you see from the standpoint of the hapless victim.

Before you ever touch the detonator, the explosives spontaneously detonate. You die. Just after that moment, a signal appears from the explosives, moves along the wire to your detonator, and enters the detonator, which is no longer there because it has exploded.

Yet the detonator

is the cause and the signal is the effect.

In the effect's worldline, the cause must precede the effect (otherwise the signal will never occur), yet here the signal's worldline crosses its own origin and prevents the origin event from ever occuring!

So from the standpoint of the (subluminal) signal, it should go like this:

The signal leaves the detonator (event 1), moves down a spacelike geometry, and arrives at the explosives (event 2), all in correct linear order. This is logically equivalent to the FTL ship blowing itself up while it's under construction: event 2 prevents event 1 from occurring.

And, again, to the hapless victim, event 2 precedes event 1, making event 1 impossible.

You're calling that for all intents and purposes identical?

If you accept that superluminal signals travel back in time, how do you avoid this paradox?

[Wobble73]

In one universe you explode, in another nothing happens cos the signal transferred to another universe?

[The E]

In one universe you explode, in another nothing happens cos the signal transferred to another universe?

Well.....no. Your status is impossible to determine. Meaning that the Universe you occupy is inconsistent. Which could be bad.

Special relativity is not like Schrödinger's cat and the superimposed wave functions of Quantum theory.

[General Battuta]

Y'know, just so you get it, I think I'll throw in a few more thought experiments just to demonstrate how trivial it is to come up with these on your own.

Which makes it all the more mind-boggling that you didn't, Aardwolf.

1. Construct a device that fires a signal down a spacelike worldline terminating back at the device 5 minutes before the firing event. The signal prevents the device from firing for 6 minutes.

PARADOX

2. You board an FTL spaceship and take a cruise, then land thirty years before you departed. You destroy the Earth with the ship's amazing future weapons.

PARADOX

3. You have an FTL accelerator that will accept billiard-ball-sized objects. The exit is placed near the entrance. You fire a billiard ball into the accelerator in such a way that when it emerges, earlier in time, it will knock its earlier self away before it enters the accelerator.

PARADOX

4. Build a machine that asks for a numerical input every ten minutes. The machine has a number 'in mind', say, 20. If the number it receives matches the number it has in mind, it adds 10. If it does not, it adds 20. After several failed attempts, you input the number 20 and get a match, so you deduce that the machine was thinking of the number '0' ten minutes ago. You signal yourself ten minutes earlier to enter 'zero' into the machine. But the fact that you did not receive that signal ten minutes earlier is the only reason you got it wrong at that time and got '20' correct at this time; otherwise the number would have been 10 now, not 20.

PARADOX

And now, here's the killer. The coup de gras, the piece d'resistance (my French is horrid.)

The Superluminal Barn Paradox.

In this beautiful thought experiment you quite clearly get two different and mutually incompatible outcomes in two different reference frames.

In one universe you explode, in another nothing happens cos the signal transferred to another universe?

Well.....no. Your status is impossible to determine. Meaning that the Universe you occupy is inconsistent. Which could be bad.

Special relativity is not like Schrödinger's cat and the superimposed wave functions of Quantum theory.

Yep, like The_E said, this is not QM, it's special relativity. The two have yet to be fully resolved.

[Retsof]

Okay... I have read the posts and still don't understand this whole faster than light=back in time thing.  How is it any different from seeing lightning before you hear thunder?  I remember that if you accelerated something to FTL by conventional means that it would go back in time, because you need to "steal" velocity from the time dimension in order to move in the spatial ones.  But that is impossible anyway because an object reaches infinite mass at the speed of light and cannot be  further accelerated.  So any method of FTL will be disregarding the speed/mass limit, and likely the speed/time limit as well.

[General Battuta]

Okay... I have read the posts and still don't understand this whole faster than light=back in time thing.  How is it any different from seeing lightning before you hear thunder?  I remember that if you accelerated something to FTL by conventional means that it would go back in time, because you need to "steal" velocity from the time dimension in order to move in the spatial ones.  But that is impossible anyway because an object reaches infinite mass at the speed of light and cannot be  further accelerated.  So any method of FTL will be disregarding the speed/mass limit, and likely the speed/time limit as well.

Again:

Any object moving on a superluminal, spacelike world-line will be seen as moving backwards in time by some IRFs.

And because the laws of physics must be equivalent in all IRFs, then this means that if a signal can move backwards in any one frame, it has to be able to do so in every frame.

So if observer A fires an FTL signal, but observer B sees this signal as coming back from the future, but then B fires an FTL signal back and A sees it as coming back from the future, ultimately A has received a reply to his own signal before ever sending it.

And if the signal is a trigger for a bomb under A's seat...you've got a problem.

To address the thunder/lightning example: both the thunder signal and the lightning signal emanate from event A and propagate with different speeds in your IRF. But you and every other observer, no matter what the gap between the thunder and lightning, will agree that the lightning flash preceded the thunder.

Metaphorically speaking, superluminal travel creates a situation where some observers will hear the thunder before they see the lightning, and others will see the lightning before they hear the thunder. And that's a really big problem, because it means the laws of physics are working differently in different reference frames, and that causes all of physics to disintegrate. (And if you say 'but why' to that, for god's sake, re-read the above posts.)

[Retsof]

... Bah, I thought I had a relatively good grasp of physics, but this just is't lining up, and I'm beggining to get a headache from working it over.  So I'll just trust that people who have spent a lot more time than me thinking about this stuff know what they are talking about.

[The E]

Okay... I have read the posts and still don't understand this whole faster than light=back in time thing.  How is it any different from seeing lightning before you hear thunder?  I remember that if you accelerated something to FTL by conventional means that it would go back in time, because you need to "steal" velocity from the time dimension in order to move in the spatial ones.  But that is impossible anyway because an object reaches infinite mass at the speed of light and cannot be  further accelerated.  So any method of FTL will be disregarding the speed/mass limit, and likely the speed/time limit as well.

The problem is that it's hard to find analogies for this behaviour that do not involve FTL travel, and decades of FTL in sci fi that treat FTL as being just really, really fast.
The easiest analogy to understand is the light cone one. Two cones, both centered on a single point. One cone includes everything that definitely happens after the event the point represents and everything that definitely happens concurrently with the event represented by the point. The other one includes everything that definitely happened before the event represented by the point. Everything that is outside these two cones may happen at the same time, before, or after the event. It's impossible to determine.

Now, the naive model, the one lazy SF writers use, makes both the "future" and "past" cone infinitely large, meaning that there is an absolutely reliable global causality chain. FTL travel is possible, the Enterprise can reach Alpha Centauri in an hour, and Captain Kirk can romance the hotties.

Special relativity makes this a bit more complicated. In special relativity, if something moves faster than light, it breaks out of the light cone that is caused by the start of the FTL object. This means that it enters a realm of uncertainty, where it is possible to affect things that lie in the past of the "starting" event. Once that happens, the "past" light cone of the starting event is irreversibly altered, which will affect the starting event in some way. And then, a paradox is created, because it becomes impossible to determine just what happened in the past light cone, since it gets overwritten over and over again by altered versions of the FTL object.

[General Battuta]

What I don't get is how moving faster than light is the same as moving back in time.

Something to do with the whole (1-v²/c²)^0.5 ?

Waiiiiiiit... diagramming it. I'll get back to you

I finally walked Aardwolf through the math on this, and I think he gets it.

I did a few Lorentz transformations to demonstrate that a 5xC signal being transmitted and bounced back to/from a ship receding at 3/5C would return to the sender 5 minutes or so before it was first transmitted.

[Aardwolf]

After a drawn out conversation on IRC, and then after me trying to describe it in writing, ... I'm confused. Bleh.


Ooo, an animation!

[Scotty]

Now let me address a specific and particularly asinine misconception you have:

An object moving back in time appears identical to, and for all intents and purposes is equivalent to an object moving forward in time in the opposite direction.

Really. Is that so.

Why are you talking about objects instead of worldlines? Why are you ignoring the relative position of the ends of the object's worldline?

First off, in whose reference frame? The telltale sign of a relativity novice is their failure to identify reference frames. You keep assuming that there is a 'correct' IRF where things 'actually' happen.

In the above example, describe to me what you see from the standpoint of the hapless victim.

Before you ever touch the detonator, the explosives spontaneously detonate. You die. Just after that moment, a signal appears from the explosives, moves along the wire to your detonator, and enters the detonator, which is no longer there because it has exploded.

Yet the detonator

is the cause and the signal is the effect.

The biggest thing that has always confused me about this is best summed up in one question:  Why does perception have to line up with the order of events?

[General Battuta]

Whose perception?

The reason it's a problem for effect to precede cause has nothing to do with anybody's perception.

It has to do with the fact that the effect (explosion) may prevent the cause (detonator sending signal; billiard ball entering wormhole) from ever occurring.

[Scotty]

Okay, back to the bomb example.

Person A triggers the detonation of a bomb at Site B using a transmission that is faster than light.  Person A is caught in the explosion.  Person B observes the explosion from a different Site C.

Obviously, the explosion happens.  To Person A, an amount of time, however miniscule, will still pass between the trigger and detonation.  To person B, however, it seems as if the explosion occurs first, and the transmission moves backwards, as in your example.  However, obviously the transmission occurred, or the explosion would not have taken place, and to Person A, that's also what the perception is.

I started off with a good question for the end of this, but I can't remember it right now.  So I'll ask a different one.  Why does it matter what Person B's perception of events is?

[The E]

Perception, in this case, is everything. Using the original example of the chair and the detonator that is shut down by the FTL pulse, the bomb "perceives" the detonation signal. It reacts (by exploding), sending the FTL pulse to the detonator. The Detonator "perceives" the FTL pulse, and shuts down. But since it's shut down, it doesn't send the detonation signal, which means the FTL pulse isn't sent out, which means the detonator works and sends the detonation signal, etc etc.

If you perceive something, you are changed by it. That is (one of) the basic rule(s) here.

[Scotty]

But the detonator has to perceive sending the signal before the FTL pulse arrives.

It may still be shut down by the perception of the FTL pulse, but the detonation has already occurred.

I don't get it, obviously, and I doubt I will.  It just seems so contradictory.  I can accept that an object can't be accelerated to c or past it, but the rest just confuses me.