[General Battuta]

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?

You got something wrong at a very early step in this example.

I'll see if you can spot what it is wrong in this passage:

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.

What is the period of time that passes between Person A pressing the detonator and perceiving the blast? You assert that it is 'an amount of time, however miniscule'. What's wrong with that assertion?

[The E]

Okay, once more. Special relativity states that any form of faster than light travel can be functionally equivalent to time travel. Meaning that the traveling object may arrive at its destination before it has left.

If it does, there is a chance that that arrival may interfere with the launch of the FTL object. The Bomb/Detonator example is one such possibility; The Spaceship travelling away from Earth communicating via FTL is another (in that example, an Astronaut aboard the ship sends a message containing a question back to base. Someone on Earth answers. Under certain conditions, the answer may arrive at the starship before the Astronaut sends his message to Earth).

In both cases, the arrival of the FTL message changes the conditions for sending the FTL message in the first place (The detonator shuts down before sending the detonation pulse, the Astronaut receives an answer before asking the question, thereby possibly changing the question). Both scenarios create infinite loops of paradoxa, where it becomes impossible to determine what the exact order of events is. This, it is assumed, is bad. 

[Aardwolf]

So yeah, Fermi's paradox.

I reckon Francis Drake screwed up. That, or the statistical anomaly isn't that we exist, but that in our galaxy, nobody but us exists.

[Shivan Hunter]

I'm surprised no one has linked this yet.

All this FTL discussion is interesting given that my dad posited a rather flawed proposition for FTL communication only this morning, which I promptly shot down, then told him to reconfigure the deflector array to emit an inverse tachyon pulse.

Anyway, Fermi's paradox- I think the alt-text for the comic has some value.

Firstly, the amount of EM communication we could actually detect is inversely proportional to the square of the distance between Sol and the other civilization's system- if it's on the other side of the galaxy entirely, it'd be completely indistinguishable from background noise.

Second, what range of frequencies do we actually look for? Another species might use higher-intensity or even lower-intensity frequencies than those we're listening on.

Thirdly, how exactly would we determine whether something is a 'message' or not? We may be hearing some civilization's Arecibo Message right now and interpreting it as random noise, because they encode it in a way that seems totally alien to us (because, well, it is).

(I'd actually like some sources for the second and third points, since I'm really just guessing that we don't listen on every frequency from radio to gamma rays, and an answer to the second question would be quite interesting.)

[watsisname]

The higher the frequency of the radiation, the less likely it is that a civilization communicates with it, because it requires more energy and effort to create and direct that communication.  Additionally, longer wavelengths are more capable of penetrating the interstellar medium, which tends to scatter shorter wavelengths (just like how our atmosphere scatters bluer light and not so much red light).  For these reasons, radio waves are the most logical ones to look for.  

However, there is also the possibility of interstellar communication via lasers, whether they function in visible light or otherwise.
Edit:  This is also a good point for trying to find/contact other civilizations, because lasers are extremely rare in nature.

Aardwolf:  I think Drake was just a bit too optimistic with the variables he chose.  However, it is still *highly* unlikely that we're the only life in the galaxy.  We know it didn't take long for life to show up on earth once conditions were favorable (and there's some evidence that life started on multiple/separate occasions).  We also know that there are hundreds of thousands of low-mass stars out there, which can potentially support habitable planets for many billions of years.  So that's one hell of a statistical anomaly for us to be the only life in the galaxy.  The existence of other "communicative" civilizations, however, is much more uncertain.  Afterall, we only have our own species to go on, and we've been a communicative civilization for less than 100 years.

unrelated edit:  Heh, spellchecker wants to replace your name with "Adolf".  I chuckled a little.  I'm a terrible person.

[Aardwolf]

Tell your spell-checker to get a ****ing dictionary. Seriously, the only reason I came up with this name is because I was looking at some of the first non-abbreviation words in the dictionary.

[General Battuta]

I'd just like to point out that the Drake equation postdates Fermi's paradox by about ten years and, while it is an attempt to attack Fermi's paradox, is not the root of the problem or the only way to look at it.

[watsisname]

Tell your spell-checker to get a ****ing dictionary. Seriously, the only reason I came up with this name is because I was looking at some of the first non-abbreviation words in the dictionary.

Aggressive much?  It's not my spellchecker, and I wasn't attacking your name.  Calm yourself.

[General Battuta]

Tell your spell-checker to get a ****ing dictionary. Seriously, the only reason I came up with this name is because I was looking at some of the first non-abbreviation words in the dictionary.

Aggressive much?  It's not my spellchecker, and I wasn't attacking your name.  Calm yourself.

He's very sensitive about his name.

[Aardwolf]

No, I just forgot to use a smiley

@Shivan Hunter: I was pretty sure what it was going to be, upon reading "I'm surprised no one has linked this yet." Heheh.

[Scourge of Ages]

I hate to bump this off topic again, but, this whole FTL signals travelling back in time has got me in a brainlock.

I get 100% how FTL things going back in time would cause paradoxes, but I still don't understand how those things can actually make it.
With the cone of light examples, I don't get how anybody can see things that are in the future or in the past and would be able to tell them apart. I can only see things that are actually happenning. I can remember things in the past, or I can predict things in the future based on things I am observing in the present, but I can't actually SEE them, because I'm not a Tralfamadorian.

Here's the scenario I'm working off of:

Person A has an FTL radio, and Person B is exactly one light-minute away with the other FTL radio. For simplicity's sake, lets say that FTL is only 200% of c.
It's 8:00 pm when Person A calls Person B. The signal arrives at 8:00:30 (on watch A, but he doesn't know that), and Person B responds with a signal. Person A receives that signal at 8:01 by his own watch.

[The E]

Person A has an FTL radio, and Person B is exactly one light-minute away with the other FTL radio. For simplicity's sake, lets say that FTL is only 200% of c.
It's 8:00 pm when Person A calls Person B. The signal arrives at 8:00:30 (on watch A, but he doesn't know that), and Person B responds with a signal. Person A receives that signal at 8:01 by his own watch.

Here's the full math: http://en.wikipedia.org/wiki/Tachyonic_antitelephone

The actual speeds involved are very important here, not only the exact speed at which the signal moves, but also the relative movement of A and B. In this example, (if I did the math right) it means that A would have to be moving away from B at a speed greater than .8c. The faster the signal gets, the easier this effect happens, if the signal travels at 200c, the relative velocity of A and B would only have to be greater than 0.08c.

EDIT: If we take Voyager's assertion that Warp 9.9 equals roughly 21000c as true, the ship would cause paradoxa (meaning, arrive at it's destination before leaving) if the her starting and arrival points are moving away from each other faster than 9.524x10^-5c or greater (Or, in other words, 28.5 km/second, or roughly 100 million km/h, which translates to about 64 million miles per hour for our non-metric friends). While that may sound like much, it's also far below the canonical sublight speeds Star Trek vessels are capable of.

[Scourge of Ages]

????it. Math, my old nemesis. I had hoped we wouldn't meet again.

Seriously, I was trying to avoid weird math with variables and junk. For the sake of greater simplicity, how about A and B stay in exactly the same position relative to each other and the universe (really hard, I know). They are exactly one light-minute apart when A transmits, and still exactly one light-minute apart when A gets a response.

Oh, wait. You're saying that the signal only goes back in time if the two parts are moving relative to each other and the signal is moving significantly faster than c? So in my example with 0 relative motion, it really would come back at 8:01?

EDIT: Discussion page on the tachyonic thing linked to this: http://xkcd.com/660/

[The E]

Yes, what I'm saying is that as the speed of the signal increases, the relative speed at which A and B have to move away from each other decreases. Make the signal fast enough, and the relative speeds will stop to matter, as long as A and B move away from each other. If they move towards each other, it doesn't work (I think, not sure about that right now).

[General Battuta]

Here's the scenario I'm working off of:

Person A has an FTL radio, and Person B is exactly one light-minute away with the other FTL radio. For simplicity's sake, lets say that FTL is only 200% of c.
It's 8:00 pm when Person A calls Person B. The signal arrives at 8:00:30 (on watch A, but he doesn't know that), and Person B responds with a signal. Person A receives that signal at 8:01 by his own watch.

There's an understandable error here. You used a simple Newtonian coordinate transformation to get from Person A to Person B. This only holds within their shared reference frame.

Specifically, you assumed that a signal traveling at 2xC would cross a distance of one light minute in thirty seconds. It could then be returned at 2xC to reach the sender one minute after it sent.

And this is true - within the reference frame of Person A (Alice?) and Person B (Bob).

But you're using Newtonian transformations, which don't reflect the way the universe actually works. Instead, you need to use a Lorentz transformation between two reference frames.

Now, you're correct to say that this shouldn't matter assuming that Alice and Bob are sending signals to each other, stationary, in the same reference frame. Keep this in mind: Alice and Bob share a common reference frame since there is no velocity difference between them.

But there's a problem.

What does an observer driving past at 3/5 lightspeed, moving away from Alice and towards Bob, see?

To this observer, Alice is receding at 3/5 lightspeed, and Bob is approaching at 3/5 lightspeed.

Let's say our observer, Charlie, sees Alice fire the 2xC signal at time 0 from coordinate 0 (we'll treat the line between Alice and Bob as a one-dimensional axis.)

In Alice's reference frame, the signal reaches Bob 30 seconds after she fires it. The coordinates of the reception, Event B, are, in Alice and Bob's shared reference frame, t = 1/2 minute, x = 1 lmin (since Bob is one light-minute away from Alice, and Alice is at x = 0 lmin.)

We can say that Event B, the signal reception, has coordinates 1/2, 1 in Alice and Bob's reference frame. Since the coordinates of Event A, the signal transmission, are 0,0, Alice and Bob agree that the reception occurred after the transmission. t = 1/2 is clearly after t = 1, right?

But what are the coordinates of the reception event to Charlie?

We need to use the Lorentz transformation to get the time of the event in Charlie's reference frame. Behold:

t' = γ(t - ux/c^2)

Gamma is going to be the Lorentz transformation constant. I'll just tell you that right here, it's 5/4.

We can treat the speed of light as '1' since that's what we're using as our velocity unit.

T = .5 minutes, the time coordinate of event B, the signal reception

U = 3/5, the speed differential between Charlie and Bob when Bob receives the signal (i.e. when event B occurs)

X = 1, since that's Bob's coordinates when event B occurs.

Work it out and we get t', the time of event B in Charlie's speeding reference frame, to be:

t' = -0.125

Remember that our time unit is in minutes, so we transform that to seconds and get...

t' = -7.5 seconds.

(The time coordinate of the original event at 0,0 transformed into Charlie's reference frame is still t = 0; I worked out the transformation to make sure.)

In your example, Alice fires a superluminal single to Bob at a speed of 2xC. It covers the distance of one light-minute in 30 seconds, and Bob and Alice both agree the signal reaches Bob 30 seconds after transmission.

But to Charlie, flying between them on a 3/5 C rocket...

...the signal reaches Bob 7.5 seconds before it is ever sent by Alice.

And remember, all reference frames are equally valid. There is nothing to say that Alice and Bob's shared reference frame is the correct one, since there is no single correct reference frame.

The upshot of this is that, for any given superluminal signal, an observer in a different reference frame can interpret that superluminal motion as motion back in time.

As a little demonstration, by the way, just change the value of T in the above equation from .5 to 1, indicating that it took the signal a full light-minute to reach Bob and therefore was only traveling at C instead of 2xC.

In Charlie's speeding reference frame, the time coordinate of the reception becomes

5/4*(1-(3/5*1)/1^2) = .5, which is perfectly sensible since it occurs after the transmission event which happens at t = 0 for Charlie.

[The E]

What General B didn't mention, because it was already mentioned several times, is that if something is valid in one reference frame, it has to be valid in every reference frame.

Let the time of the signal being sent be t. In Alice's and Bob's shared reference frame, if they compare their notes, they will arrive at the conclusion that the signal was sent at t and received at time t+x. Since this is valid in that reference frame, it has to be valid in all reference frames. But Charlie, spoilsport that he is, says "Hey, wait a minute! You guys are wrong! The signal was sent at t, and received at t-7.5 and I have the math to prove it!".
So, in conclusion: In Alice' and Bob's reference frame, Alice sends the signal, and Bob receives it some time later, which has to be true in every reference frame.
In Charlies' reference frame however, Bob receives the signal 7.5 seconds before Alice sends it, which again, needs to be true for every reference frame.

Now, the basic point here is that the order of events has to be preserved globally. In all reference frames, Alice has to send the message before anyone (including Bob) can receive it. But since Charlie disagrees, the reference frames can not be reconciled, and paradoxa appear.
A more complete summary why this has to be this way can be found here: http://en.wikipedia.org/wiki/Inertial_frame_of_reference

[General Battuta]

Specifically, while it's okay for reference frames to disagree on how long passes between two events, they must agree on the order of the events.

Event A must precede Event B in all reference frames or causality is violated. When the signals go superluminal, order is no longer preserved in all subluminal reference frames.

[Scourge of Ages]

Thanks, Battuta. That long post helped me to reconcile the math quite a bit.

So now my questions are:

1. Doesn't it only appear to violate causality if Charlie is observing things at the speed of light? If Alice sent two signals, one to Bob and one to Charlie, wouldn't Charlie then get notification of sending before observing or being notified of receipt by Bob (Assuming he doesn't pass Bob before the signal would arrive)?

2. Does the scenario placing the effect before the cause still apply if Charlie is only moving at 2/3c?

3. Why does it matter if one observer sees causality violated? We see the effects of things before the causes all the time, like a bullet impact being seen before the gunshot is heard. If the effect arrives faster than the cause, what does it matter if anybody thinks it's backwards? In other words, just because you observe an effect before a cause, why should it indicate that time has flip-flopped, wouldn't it make more sense that your observation is just slow?

Extra credit: And doesn't this negate the example of the superluminal billiard ball, and the self exploding bomb paradoxes? Since the bomb and detonator occupy the same frame of reference, and the billiard ball carries it's frame with it.

EDIT: Remember, please explain as if I couldn't do the math myself if I wanted to am a total higher-math noob.

[The E]

Okay, I tried to do that, but people seem to be ignoring my posts here.

You see, SoA, the problem here is that according to the theory of special relativity, there are infinitely many reference frames in the universe. If something is true in one of these frames, it must be true in every reference frame, because the laws of physics are the same in every one of them.

The message that travels faster than light, through a combination of the actual message speed and the relative speed of the reference frames involved, travels back in time in one reference frame (Charlie's) and appears to be moving normally in another. Since according to the rules of special relativity, if something happens one way in one reference frame it needs to happen that way in every reference frame, a paradox is created, since there is one reference frame (Charlie's) that sees things differently.

So, in more general terms. If an event A happens that causes another event B to happen, every observer, regardless of where he is or how fast he is moving, needs to see A before B. If he doesn't, something is very, very wrong with the universe.

And yes, some of the examples General B chose were not examples of paradoxa caused by FTL travel, but rather examples that demonstrate temporal paradoxa in general.

And, well, the problem is that it's hard to explain this adequately without resorting to Math, so just take it as truth from those of us who can do the math, at least until someone proves that special relativity is wrong.

[Scourge of Ages]

And, well, the problem is that it's hard to explain this adequately without resorting to Math, so just take it as truth from those of us who can do the math, at least until someone proves that special relativity is wrong.

There. That! That's exactly what I needed.

So. My understanding is: FTL travel and the current theory of special relativity cannot coexist. And since as far as anybody can tell, special relativity is true, that makes FTL impossible.

Now I can sleep at night again, thanks.