FTL and Violating Causality

[Lord Torath]

A discussion in the Roleplaying forum got into FTL travel/communications and how it violates causality. Those of you who are experts in this field, can you explain how something like this could happen by allowing FTL communications?

For example, Person A sees Saceship B explode Planet C, then transmits this information instantaneously to Spaceship D traveling at Speed Ec, enabling someone on the spaceship to prevent the exploding. Assuming the light from the shooting reaches Person A before it reaches Spaceship D, of course.

[Max_Killjoy]

The past explanations I've seen have usually come down to "getting information to a place before light would get it there is bad because it's bad for information to get there before the light does", which is the "explanation" -- and/or presume that FTL travel in a setting automatically implies relativistic velocities are possible for vessels not traveling FTL.

[halfeye]

A discussion in the Roleplaying forum got into FTL travel/communications and how it violates causality. Those of you who are experts in this field, can you explain how something like this could happen by allowing FTL communications?

For example, Person A sees Saceship B explode Planet C, then transmits this information instantaneously to Spaceship D traveling at Speed Ec, enabling someone on the spaceship to prevent the exploding. Assuming the light from the shooting reaches Person A before it reaches Spaceship D, of course.

I think it's based on the idea that at c, no time passes, thus light doesn't exist for any time at all, so a FTL ship must travel backwards in time.

[CharonsHelper]

I think it's based on the idea that at c, no time passes, thus light doesn't exist for any time at all, so a FTL ship must travel backwards in time.

If that's all it is - then you couldn't ever stop something once you've seen it occur. Just the opposite - once you've seen it at light speed it happened long ago.

Now - you could communicate to someone so that they could dodge something - even a laser - since you can see it and then FTL ahead of it, but not once it's already hit home.

*shrug* But - I'm not a physicist.

[Anonymouswizard]

I'm not an expert, but as I remember it has to do with time cones (or how you view time), and how they skew as you're moving towards c (which I always think of as 'infinite energy' for anything with mass). So when your velocity gets to greater than c your time cone is skewed to the point where no part of it is aligned with an 'at rest' observer, and so something something information something something time travel.


Anyway, question for people who understand this stuff. Let's assume that we can make a wormhole so that point A (let's say the center of mass of the Palace of Westminster) is next to point B (let's say the highest atom on Olympus Mons) are next to each other through the wormhole. Am I right in thinking that although the Palace of Westminster and Olympus Mons are for all intents and purposes less than a metre apart through this wormhole, any information sent though it would still fall into the problem of travelling FTL and (at least conventionally) violating causality?

[Max_Killjoy]

I think it's based on the idea that at c, no time passes, thus light doesn't exist for any time at all, so a FTL ship must travel backwards in time.

There are two separate questions here.

One is, how is it that a particular form of FTL would enable you arrive back a location before you left that location? How that allows causality violations should be fairly obvious, right?

The other is, why would ALL forms of FTL allow causality violations?

[Max_Killjoy]

Anyway, question for people who understand this stuff. Let's assume that we can make a wormhole so that point A (let's say the center of mass of the Palace of Westminster) is next to point B (let's say the highest atom on Olympus Mons) are next to each other through the wormhole. Am I right in thinking that although the Palace of Westminster and Olympus Mons are for all intents and purposes less than a metre apart through this wormhole, any information sent though it would still fall into the problem of travelling FTL and (at least conventionally) violating causality?

There's a missing step there, that actually hits the big question... why is it that information arriving somewhere before "light" would get it there (across the normal span of space) a violation of causality?

[rs2excelsior]

As I said in my previous post, it's explained here better than I could. This is the source for my information and images.

It has to do with the fact that the speed of light is defined based on universal constants, meaning it will be the same for all observers. That one fact is what leads to all kinds of weirdness with space and time as you approach lightspeed, and why simultaneous events aren't really simultaneous.

First off, when anyone says "velocity," your first question should be "velocity relative to what?" If you see me tearing along at .999c, you'd say I am moving pretty dang fast. In my frame of reference, I'm sitting still, and you're the one going .999c. Which of us is correct? As long as no one is accelerating, it doesn't matter which reference frame is used. All inertial reference frames give the exact same results.

At first, that doesn't seem like that meshes with the idea that the speed of light is constant. In the above example, if I fired a laser ahead of me, you would see the end of the laser going away from me at a piddly .001c. It's actual velocity relative to you is 1c, but I am also going close to 1c. From my perspective, that same laser beam is travelling away from me at 1c, despite the fact that the separation velocity I see is 1000x that which you see. That's because of space and time dilation.

If we construct a space-time diagram for an observer, we can do so as a simple x-y graph, considering only one spatial dimension (or compressing all 3 into one, same effect) as the x-axis and time as the y-axis. For convenience (you'll see why in a second), each mark on the x-axis (space) is one light-second, and each mark on the y-axis (time) is one second. Thus, an event that occurs 3 light-seconds to the left and one second before the observer's current time would be placed at (-3, -1) on the graph.


Event is at the @

If another observer, say moving along at 1/3c, passes by our initial ("stationary") observer at time t=0, their position would look something like this:



Because of the fact that light travels (by definition) one light-second in one second, light moves along 45 degree angles on this graph.


Things "inside" the light cone can either influence or be influenced by actions at t=0, since the observer there will see an event in the past or be able to send a signal to the point in the future. Things "outside" the light cone cannot influence or be influenced, since light cannot travel far enough in time. Observers later might argue whether events outside the light cone are simultaneous, but (if we restrict things to non-FTL) they will remain firmly in the past for both, so they cannot be influenced.

Again, because the speed of light is based on a physical constant, it moves along 45-degree lines on any space-time graph, not just the one for our "stationary" observer. So, we can construct axes for our moving observer as well, using methods which you can read about in the above link.


x' is the space axis for a moving observer, and t' the time axis (Remember this is relative--you could shift to a reference frame where our "moving" observer was stationary, and our "stationary" observer would be moving. Basically you rotate both sets of axes until our "slanted" ones are straight and our straight ones are slanted. Again, more detail on this in the link.) The event marked with an * is below the x axis (in the past for our stationary observer) but above the x' axis (in the future for our moving observer).


These are lines of constant space and constant time for our moving observer. Anything below the x' axis is in the past, and anything above it is in the future. Anything along a line of constant time is simultaneous for that observer. Note that there are events, such as our event earlier at (-3, -1), which are in the past for our stationary observer but in the future for our moving observer. This is where the problems come in.


Now, because this event is outside of the light cone, this normally isn't a problem. At t=0 when the observers pass, the light from the event hasn't reached them yet, so neither of them CAN KNOW about the event, nor influence it. Even for the moving observer, for whom the event has not happened yet, he cannot reach it in time to affect it, either by presence or information, since it is outside of the light cone--that would require travel or communication faster than light. Same for the stationary observer; even though it's in the past he hasn't seen the event yet so can't tell the mover about it. Later on, once it is in their light cones, they can argue about whether it had happened when they passed one another, but at this point it will firmly be in the past for all involved and thus the question can't cause a paradox.

But, if you have FTL communication or travel of any sort, this breaks down. Say the event is person C murdering person D. The stationary observer, person A, has an instantaneous video feed watching D, and sees D die. The body is there on the screen. A tells B (our moving observer) as they pass, and B sends an instantaneous message to his friends at (-3,-1) to kill C. Which they do. But, in B's reference frame, the instantaneous message was sent--and arrived--BEFORE C murdered D. Thus the cause of the event cannot occur, as C is dead. But what does A see? D was already dead for him. That is what a causality violation looks like.

It's not related to whether you have travel but not communication or vice versa, it's not related to how you get around the speed of light limitations (note I never said how these instantaneous messages were sent). It's a property of relativity and the distortions that occur in time and space. Again, the link I posted explains the concept in far more detail than I, but this is how it works in a nutshell. It's hard to get good, condensed answers, because frankly relativity is a complicated mess that does not at all work intuitively.

[rs2excelsior]

There are two separate questions here.

One is, how is it that a particular form of FTL would enable you arrive back a location before you left that location? How that allows causality violations should be fairly obvious, right?

The other is, why would ALL forms of FTL allow causality violations?

As I've said before, the particular form doesn't matter. At all. This is all due to the fact that simultaneous events aren't simultaneous in all reference frames, and something in your past might be in my future. Without FTL it's impossible to actually take advantage of that fact. With FTL, it becomes very possible.

[NichG]

It's not just the transmission delay, which is an additive offset. The problem is that in relativity, moving at relative velocity also leads to a difference in rate of time passage, so there's a multiplicative term as well. The simplest causality violation construction uses a third, moving relay to exploit that. Just going from site A to B and directly back to A at FTL doesn't do it I think, although you have to be careful about acceleration and GR effects (acceleration induced dilation breaks the symmetry in the twin paradox).

[Gray Mage]

As rs2excelsior said, when dealing with relativistic velocities you need to account for different time frames. When doing the math to convert the time frames considering speeds higher than c it results in the information arriving before the actual fact happened, thus it being non-causal.

Anyway, question for people who understand this stuff. Let's assume that we can make a wormhole so that point A (let's say the center of mass of the Palace of Westminster) is next to point B (let's say the highest atom on Olympus Mons) are next to each other through the wormhole. Am I right in thinking that although the Palace of Westminster and Olympus Mons are for all intents and purposes less than a metre apart through this wormhole, any information sent though it would still fall into the problem of travelling FTL and (at least conventionally) violating causality?

As far as I know, no, it wouldn't violate causality as you are not really travelling FTL, you just took a shortcut, thus it not taking as long for the information to get there.

[Max_Killjoy]

At least in the explanation posted above, it appears to come down to issues with going at higher fractions of C within "normal space", which is why I noted that there seems to be an assumption that FTL travel automatically implies that there is also relativistic travel, rather than being a completely separate thing.

[rs2excelsior]

I'm not an expert, but as I remember it has to do with time cones (or how you view time), and how they skew as you're moving towards c (which I always think of as 'infinite energy' for anything with mass). So when your velocity gets to greater than c your time cone is skewed to the point where no part of it is aligned with an 'at rest' observer, and so something something information something something time travel.


Anyway, question for people who understand this stuff. Let's assume that we can make a wormhole so that point A (let's say the center of mass of the Palace of Westminster) is next to point B (let's say the highest atom on Olympus Mons) are next to each other through the wormhole. Am I right in thinking that although the Palace of Westminster and Olympus Mons are for all intents and purposes less than a metre apart through this wormhole, any information sent though it would still fall into the problem of travelling FTL and (at least conventionally) violating causality?

As far as I know, no, it wouldn't violate causality as you are not really travelling FTL, you just took a shortcut, thus it not taking as long for the information to get there.

Strictly speaking it could. The issues arise when FTL communication/travel is used between points moving in different reference frames, and Earth and Mars aren't really moving at too greatly different velocities. So the potential would be small, but it exists. That said, the surface of neither planet is an inertial reference frame (as the planet's surface is spinning, and the planet itself is rotating around the sun) which introduces all kinds of complications. Plus gravity has further distortions, forcing you to get into general (rather than special, which assumes negligible gravitational effects) relativity. It's a lot more complicated and I don't know an exact answer for how it'd work.

[rs2excelsior]

At least in the explanation posted above, it appears to come down to issues with going at higher fractions of C within "normal space", which is why I noted that there seems to be an assumption that FTL travel automatically implies that there is also relativistic travel, rather than being a completely separate thing.

Thing is, there's nothing that prohibits relativistic travel. You pile on speed, and you'll be going at relativistic speeds eventually. Even two observers moving at low fractions of c relative to one another (say 0.01c), their time and space axes are still going to be slanted and there will still be opportunities to violate causality. There are less, perhaps, but they exist. You might just be putting a tiny hole in the can of worms, but it's still open and one still might crawl out.

[Max_Killjoy]

As I've said before, the particular form doesn't matter. At all. This is all due to the fact that simultaneous events aren't simultaneous in all reference frames, and something in your past might be in my future. Without FTL it's impossible to actually take advantage of that fact. With FTL, it becomes very possible.

So let's posit an FTL drive that allows the ship to enter a parallel space that corresponds in location to our space but also has an added "depth" such that the "deeper" one goes, the closer together the "correspondences" within that parallel space. The vessel has to be protected by a "bubble of normal space" while in this parallel space, and the bigger the bubble and/or the deeper the vessel goes, the more energy it takes to maintain it. Thus, there is no communication other than sending an actual vessel, as this would require punching a bubble through from the origin to the destination and holding it open for as long as it takes to send the messages.

NOTE -- there is no relativistic travel in this setting. The fastest ships don't even hit 0.1 c in normal space.

A vessel is traveling from point A to point B, one light year apart. It leaves A, an observer at A sees it "disappear" as it enters the parallel space, and time is still passing at A, regardless of any other consideration. Light has left A, and will arrive there in 1 year -- from the POV of the light? From the POV of A? From the POV of B?

Time is also passing at B, regardless of any other consideration. They do not have to be "the same time".

One hour later from the POV of the vessel, it arrives at B. No one has observed its travel across the intervening space (they can't, and it hasn't), and it has not communicated with anyone during that travel (it can't). It immediately turns around, disappears again, heading back to A. Time is still passing at B after it leaves.

One hour later from the POV of the vessel, it arrives back at A. No one has observed its travel across the intervening space (they can't, and it hasn't), and it has not communicated with anyone during that travel (it can't).

Time has been passing -- if from the ships POV it's been 2 hours, how long as it been at A? How long has it been at B?


Who in this scenario is experiencing relativistic effects such that they're noticeable?

At what point does anyone learn of an event from their future?

[exelsisxax]

I still can't buy the FTL time travel argument. There's too much handwavium, nobody ever explains how FTL sends anything back in time, and then conclude "FTL is time travel, time travel is impossible, ergo FTL is impossible" without ever demonstrating why time travel would be impossible in the first place.

Consider Bob. bob's dog was let off the leash and is now on the moon.

Consider Steve. Steve has a teleporter that can instantly take him to the dog's location.

Please explain how any use of steve's teleporter can bring bob's dog back prior to bob asking steve to go get his dog.

[Anonymouswizard]

There's a missing step there, that actually hits the big question... why is it that information arriving somewhere before "light" would get it there (across the normal span of space) a violation of causality?

Actually I'm not. My question assumes that an object moving FTL can potentially cause a violation of causality.

Unlike you I'm not attempting to get around the FTL-causality issue with technobabble, if I ever need to in a story I'll generally just say something along the lines of 'Edwards's Theory of Relative Causality stops information from arriving before it's left' or something to that effect, translating into 'I know it shouldn't work like this but I'm not smart enough to write this story another way'.

I'm saying 'let me check, in this specific instance of "shortcut through space" is causality still violated'. The setting which uses this system already exists under the assumption that it does, and allows information to travel back in time and appear with no source (which baffles scientists in-setting). The out-of setting reason is that the universe can split off (universes? timelines? realities? I'm sticking with timelines for the moment) that are 'behind' the one that sent the information, and with enough power you can move between the timelines. The source still sent you the information before it arrived, you just cannot sense the source.

Yes, I know that is bad physics and is not going to hold up to reality. But this is for a book and potentially game setting where I want 'messages from the future', and I want to have a bit of fun with cross-timeline travel later on as well.

As far as I know, no, it wouldn't violate causality as you are not really travelling FTL, you just took a shortcut, thus it not taking as long for the information to get there.

Strictly speaking it could. The issues arise when FTL communication/travel is used between points moving in different reference frames, and Earth and Mars aren't really moving at too greatly different velocities. So the potential would be small, but it exists. That said, the surface of neither planet is an inertial reference frame (as the planet's surface is spinning, and the planet itself is rotating around the sun) which introduces all kinds of complications. Plus gravity has further distortions, forcing you to get into general (rather than special, which assumes negligible gravitational effects) relativity. It's a lot more complicated and I don't know an exact answer for how it'd work.

Thank's for your help, I understand that it's complicated. I've been working under the assumption that it did, but I'm unsure because of the entire 'didn't travel FTL, just took a shortcut' stuff that's true in that most annoying way (that is, only if you look at it from the right frame of reference).

[Max_Killjoy]

Me, in the original thread:

"Roughly, as I understood it, with two things:

1) We have four dimension. 3 space relative, 1 time relative. Take place A and B, happening at the same relative time in relative space. Now FTL from a to B and you will land in the past of B. Why? Because Time is the constant with which space is measured, you're faster than that, this will also affect the fourth axis, time.

2) Now indent of movie-like straight "zoom!", let's make FTL maneuverable. Start at A, go full force FTL and head straight back to A. You'd be back before you started."

So with "light" being the yard-stick to measure physical reality, which in term deals with time, FTL... well, guess it.

This would appear to assume that you are actually traveling faster than light within spacetime as your vessel passing through it -- rather than either distorting spacetime ("warp drive") while remaining STL relative to the space immediately surrounding your vessel, or bypassing spacetime entirely while still traveling along the same bypass.

It would also appear that part of the confusion in these conversations is between those instances of FTL which also cause actual issues with time, and those instances which might for other reasons risk a violation of causality. In some instances, FTL is literally time travel, in other instances FTL may risk time travel.

[rs2excelsior]

Who in this scenario is experiencing relativistic effects such that they're noticeable?

Anyone else who happens to me moving at a different speed.

Causality effects don't have to be on behalf of the ship actually doing the FTL travel. In my previous example, instead of communicating with one another, D could send a ship making an FTL hop to A, and B send another such ship back to C. That situation will still violate causality, even though the ships themselves do not experience the relativistic effects. Even though you aren't moving through real space. As soon as you combine FTL travel OR communication with people moving in different reference frames, you have events which are in the past of one observer but the future of another, and which are accessible for information transfer via FTL. You have to look further at lower speeds, but they exist.

If you disallow "relativistic" travel by imposing an arbitrary speed limit (which physically doesn't make sense), you still don't fix the problem. There is no such thing as "Newtonian" and "relativistic" speeds, there are speeds where relativistic effects are noticeable and where they are minor enough you can ignore them and the answers you get will be good enough. We have taken extremely precise clocks up in airplanes, and when they came back they had recorded very slightly different times elapsed. Even at what we consider everyday speeds, relativistic effects do exist and there exist situations where FTL can violate causality. You have to look rather hard, but they're there.

As I said before, "FTL violates causality" doesn't necessarily mean every use of FTL will automatically cause a paradox. But any form of FTL can cause a paradox under the correct circumstances. Because for any two observers not moving at exactly the same speed and exactly the same direction, concepts like "simultaneous" and "future" and "past do not exist on a universal scale.

Again, the best thing I can tell you to do is read over the link I posted. My explanation wasn't complete, and that site goes into far more detail than I can. But this is because space and time don't actually work the way we think, not related to simply an object moving along faster than light.

Spoiler: Aside regarding in-universe FTL

Show

Physics breaks in other ways if you allow FTL travel simply by accelerating. Any object at lightspeed has infinite energy and infinite mass, which by definition cannot be obtained. Time dilation would mean an observer watching someone moving at c relative to them would experience no time passing, and space dilation means if you are moving at c all points along the direction of travel coalesce into a single point--the trip takes no time whatsoever from your perspective. Going faster simply doesn't make sense. Many of the equations start to give imaginary numbers as answers when you plug in speeds faster than c.

[Max_Killjoy]

Unlike you I'm not attempting to get around the FTL-causality issue with technobabble,

It's not technobabble (meaninglessly throwing techy-sounding words as a smokescreen), unless all speculative fiction featuring what-if scenarios is "technobabble".

[rs2excelsior]

I still can't buy the FTL time travel argument. There's too much handwavium, nobody ever explains how FTL sends anything back in time, and then conclude "FTL is time travel, time travel is impossible, ergo FTL is impossible" without ever demonstrating why time travel would be impossible in the first place.

Consider Bob. bob's dog was let off the leash and is now on the moon.

Consider Steve. Steve has a teleporter that can instantly take him to the dog's location.

Please explain how any use of steve's teleporter can bring bob's dog back prior to bob asking steve to go get his dog.

For the fourth time: this guy does (and, for that matter, so did I). This isn't just something that a bunch of people decided they didn't want to deal with, and so came up with a BS excuse. This is mathematically verifiable according to relativity, which best explains how objects moving at speed behave and has been verified over and over by experiment.

[Max_Killjoy]

I still can't buy the FTL time travel argument. There's too much handwavium, nobody ever explains how FTL sends anything back in time, and then conclude "FTL is time travel, time travel is impossible, ergo FTL is impossible" without ever demonstrating why time travel would be impossible in the first place.

Consider Bob. bob's dog was let off the leash and is now on the moon.

Consider Steve. Steve has a teleporter that can instantly take him to the dog's location.

Please explain how any use of steve's teleporter can bring bob's dog back prior to bob asking steve to go get his dog.

There's a hierarchy of questions.

It's very possible for in-universe FTL to end up with a vessel arriving back at its starting point before it left, the verifiable math works out that way.

The more interesting questions arise with more esoteric "workarounds".

[halfeye]

Spoiler: Aside regarding in-universe FTL

Show

Physics breaks in other ways if you allow FTL travel simply by accelerating. Any object at lightspeed has infinite energy and infinite mass, which by definition cannot be obtained. Time dilation would mean an observer watching someone moving at c relative to them would experience no time passing, and space dilation means if you are moving at c all points along the direction of travel coalesce into a single point--the trip takes no time whatsoever from your perspective. Going faster simply doesn't make sense. Many of the equations start to give imaginary numbers as answers when you plug in speeds faster than c.

Okay, something that bugs me. What happens to a probe fired at a large black hole? we're told that a particle initially at rest at infinity would arrive at the event horizon travelling at exactly c. So, it has an acceleration due to gravity, What if we work out that acceleration and find it's speed at a given point, then accelerate some probe so that at that point it is going faster toward the black hole? I think I'm told that it doesn't achieve c before arriving at the black hole, but I do not understand why not, the accelerating force is gravity, and there's no limit on the supply of gravity that I understand.

[Douglas]

NOTE -- there is no relativistic travel in this setting. The fastest ships don't even hit 0.1 c in normal space.

A) Relativistic travel is possible. Full stop. That's a completely undisputed aspect of real world physics. It may not be practical, but it is possible.
B) Limiting non-FTL speed just makes a causality violation more difficult to set up, the math behind it can be made to work with any non-zero speed.

Let me dig up my explanation post from a previous time this subject was discussed here:

The core principle of (special) relativity is that, no matter how fast you're traveling and in what direction, if you measure the speed of a light beam (in a vacuum) relative to yourself you will always get the same result. If this requires the physics of the universe to contort in weird ways in order to produce that result, then guess what? The universe does, in fact, contort in exactly those weird ways.

Now, take that as given and start imagining scenarios. Let's start with two spaceships a light year away from Earth, one stationary and the other traveling towards Earth at 50% the speed of light. They are at the same location, and they each notice a light beam at their location that is traveling towards Earth. The stationary one will, of course, calculate that this light beam will reach Earth one year from now. From the moving one's perspective, however, the Earth is moving towards him at 50% c (remember, all motion is relative). In his view, part of the distance will be covered by the Earth's movement, so the light beam will have less distance to travel, but the light is still traveling at the same speed as per relativity's core principle so it will take less than a year for the light beam to reach Earth.

So, these two aliens disagree about how much time will pass before the light beam reaches Earth, and this disagreement happens because one of them is moving differently from the other. And, importantly, this disagreement is a fundamental aspect of how the universe really works, not just a perceptual artifact.

Now, the aliens will obviously agree that the light beam passed each of them at the same moment because they were both there together (however briefly) when it happened. If they start calculating time as measured on Earth, they will also agree that the moment of the light beam reaching Earth happens at the same Earth time for each of them. Now consider what result each alien will get for the question "what time is it on Earth right now". The stationary alien will calculate that "now" on Earth is "one year before the light beam hits". The moving alien will calculate that "now" on Earth is "significantly less than one year before the light beam hits". Again, this result is a fundamental part of how the universe works, not merely a perceptual artifact.

Now imagine that both aliens and the Earth have infinite-speed communication devices. The stationary alien sends a message to Earth, which arrives immediately - as per the previous paragraph, it arrives one year before the light beam does. Earth forwards this message to the moving alien, and the message arrives immediately. The message was sent from Earth one year before the light beam hits, so it arrives one year before the light beam hits. But in the moving alien's frame, the light beam hitting Earth is less than a year away, which means "one year before the light beam hits Earth" is in the past! Earth's forwarded message arrives back at the observer location before it was sent!

Tada, the FTL communication device has now violated causality by sending a message into the past.

Infinite speed is an extreme case, used to make the illustration clearer, but any communication speed faster than light can be used to set up a similar scenario. As message travel speed decreases towards the speed of light, the required combination of observer speed and message distance to produce a causality violation increases, but it's always possible if the message travels at all faster than light.

Incidentally, if your FTL travel operates in an absolute reference frame, that would prevent causality violations. It would also break one of the foundational principles of relativity, but you could handwave that in your story if you want.

[exelsisxax]

For the fourth time: this guy does (and, for that matter, so did I). This isn't just something that a bunch of people decided they didn't want to deal with, and so came up with a BS excuse. This is mathematically verifiable according to relativity, which best explains how objects moving at speed behave and has been verified over and over by experiment.

Yes, and I cannot accept the explanation as it has not convinced me that the position it purports is sufficiently supported. It reaches a point where it simply says that X violates causality by going back in time, without ever actually demonstrating that to a level that would convince me. It goes on and on at great length about everything must be consistent across different reference frames, then the situation it constructs swiftly ignores most of them and its conclusions appear, to me, to seriously violate that same stipulation. In the example, can you explain what O, Op, the guy who gets shot, and observer 3 all see from -10 to +10, on what Op's FTL vessel is doing, both what they see based on emitted light and an actual timeline without respect to observability? Because i'm not accepting a message going back in time unless you can show Op recieving a message from itself shortly into the future.

So again, can you show me how Steve goes back in time? There's a lot of light cone nonsense in most explanations, this avoids that.

[Anymage]

If you don't want to read through all of rs2excelsior's link, here's a youtube video that covers a lot of the same questions. The whole channel is good for the sorts of people who like asking these questions.

To repeat the basic points:

-Simultaneity gets really messy when you start talking about relativity. While I may see two events happening at the same time, someone else may see A happening before B while someone else sees B happen before A. This isn't just the part where photons have to travel for a certain amount of time to reach my eyes, this is the actual nature of the universe being really weird.

You can find a way to translate different frames of reference. But one of the key translation factors is 1/sqrt(1-v²/c²). For all subluminal velocities, (c²/v²) is less than one, so you can get a nice normal number out. At c exactly you get 1/0, which is why all values at c tend towards either 0 or infinity. When v>c, you start getting imaginary numbers and stop getting nice, simple math.

-This isn't simply superman pushing past c and time starts to flow backwards. "Time slows as you approach c and flows backwards once you're past the point" is an oversimplification. What does happen is that you get different observers in different reference frames disagreeing as to what events they can or cannot influence. According to some perspectives, my FTL trip would take exactly the amount of relative time I perceived. To other perspectives, I'd appear to have gone back in time. Again, the translation factor that works at subluminal speeds breaks down after a point.

[Max_Killjoy]

A) Relativistic travel is possible. Full stop. That's a completely undisputed aspect of real world physics. It may not be practical, but it is possible.
B) Limiting non-FTL speed just makes a causality violation more difficult to set up, the math behind it can be made to work with any non-zero speed.

Poor wording on my part, yes, what I should have said was "even fractional values of C are incredibly impractical such that they can be ignored for the purposes of this what-if scenario".

[rs2excelsior]

Okay, something that bugs me. What happens to a probe fired at a large black hole? we're told that a particle initially at rest at infinity would arrive at the event horizon travelling at exactly c. So, it has an acceleration due to gravity, What if we work out that acceleration and find it's speed at a given point, then accelerate some probe so that at that point it is going faster toward the black hole? I think I'm told that it doesn't achieve c before arriving at the black hole, but I do not understand why not, the accelerating force is gravity, and there's no limit on the supply of gravity that I understand.

That's ANOTHER can of worms, involving both relativistic effects and extreme gravitational forces (to the point that physics just breaks). Think of it in terms of energy instead of acceleration. As you fall toward an object, you're converting gravitational potential energy into kinetic energy. As your velocity approaches c, that additional kinetic energy equates to less velocity, as your relativistic mass increases. Of course, this is all from the perspective of an outside observer stationary relative to the black hole. From the perspective of the falling object, a light beam would still move away from you at c, and you'd have a black hole accelerating toward you at a significant fraction of c.

The object would never actually break the speed of light, because doing so requires infinite energy. (An object at rest at infinity technically has infinite gravitational potential energy, but the force of gravity would also go to zero at infinity. Plus, you can't put an object "at infinity."

Black holes have all kinds of weirdness related to limits as things go to zero and as things approach lightspeed. Stuff gets weird, and the math you need to describe them gets a lot more complex than I personally understand.

[Douglas]

Poor wording on my part, yes, what I should have said was "even fractional values of C are incredibly impractical such that they can be ignored for the purposes of this what-if scenario".

Give me some numbers for your ship speeds, both in normal space and FTL, and I'll modify the scenario in my quoted explanation to use them.

[rs2excelsior]

Yes, and I cannot accept the explanation as it has not convinced me that the position it purports is sufficiently supported. It reaches a point where it simply says that X violates causality by going back in time, without ever actually demonstrating that to a level that would convince me. It goes on and on at great length about everything must be consistent across different reference frames, then the situation it constructs swiftly ignores most of them and its conclusions appear, to me, to seriously violate that same stipulation. In the example, can you explain what O, Op, the guy who gets shot, and observer 3 all see from -10 to +10, on what Op's FTL vessel is doing, both what they see based on emitted light and an actual timeline without respect to observability? Because i'm not accepting a message going back in time unless you can show Op recieving a message from itself shortly into the future.

So again, can you show me how Steve goes back in time? There's a lot of light cone nonsense in most explanations, this avoids that.

You can't avoid the "light cone nonsense." That "nonsense" is the entire crux of the issue. Normally, events which are in the past for one observer but not the other are not observable by either until they are in the past for both, due to speed of light restrictions. Once you allow FTL, that goes out the window. If you cannot accept being clearly shown that an event in the past for one observer is in the future for another observer at the same point but moving relative to the frame of reference, then I cannot help you.