The illusion of causality (RAR)

[SMJB]

Am I using that right? I don't know what those initials stand for. Anyway, what I'm looking for is some critiques on an idea I have for a 'verse.

Now, you know what they say: Relativity. Causality. FTL. Pick any two.

I think you can guess which two I picked from the title. But of course to qualify as science fiction of the non-crap variety, the observed effects of causality have to be explained, such as the fact that we're not being constantly pestered by visitors from the future. I've got an idea for a "theory" that explains it, Apparent Causality:

Let's take your classic Grandfather Paradox. You go back in time and kill your grandfather before your father was conceived, thereby creating a timeline where you were nev3er born and therefore never went back in time, meaning your grandfather in fact lives, meaning you are born and kill your grandfather, so on and so forth in an infinite loop, thus creating a paradox right? Wrong.

Even ignoring such philosophically murky debates as free will, there are truly random elements in the universe, any of which can change in a derivative timeline in order to stop the paradox from happening in the first place. It doesn't matter how unlikely said paradox-thwarting event is (so long as it's nonzero), the universe is going to keep rebooting itself until it achieves equilibrium, and it's far easier to make your time machine blow up than to create a stable time loop, much like how a glass could in theory unshatter if all the vectors are just right but in reality is never going to.

And of course, doing anything that makes it possible for you to effect your past counts as affecting your past. Butterflies and whatnot.

That's how I intend to explain it in-universe, at any rate. One effect I see from it is that a limited sort of time travel is still possible; just, if your target star is ten lightyears away, you have to arrive less than ten years before when you departed. (Assuming someone from there from, say, two years ago doesn't come to your world before you leave, of course; really, time travel's not worth it.)

Now, this universe will (likely) use Alcubierre drives and wormholes and suchlike. Which require massive amounts of negative mass, something we're not likely to get our hands on in any meaningful way in the near future even if it exists, so basically what they do is stick a spigot into a neighboring universe that's made of the stuff. They can control the flow and direction, but can't use it for anything but the above and the odd weapon of mass destruction because, well, negative energy density. Hopefully this helps to curtail how ridiculously powerful these people would have to be to pull it off, not to mention the whole "OMG free energy forever!!!" aspect of it.

[Simon_Jester]

Have you sat down and done the math? I've been meaning to do that for years...

Anyway. The real trick here is that any FTL trick will appear to be equivalent to time travel in a certain frame of reference.

Imagine two spaceships are dueling with relativistic railguns. The bullets move at insane speeds, but still slower than light. And in any frame of reference, whether I'm aboard one of the ships, or standing on a nearby planet, or zooming by at 90% of the speed of light in some arbitrary direction, one important rule holds: I can still agree that each bullet was fired before it hit the target.

If the spaceships duel with laser beams, in most frames of reference it is still clear that the lasers were fired before they hit the target. In the laser beam's frame of reference, these events occur simultaneously, but even that is manageable.

BUT...

If the ships instead fight with tachyon beams that travel at twice the speed of light, we have a problem. Sure, in my frame of reference it may still look like the tachyon beam was fired before it hit the target. But there will exist at least one, and in practice many, frames of reference where an observer passing by the scene would observe the beam hitting the target before it was fired.

So we have a situation where causality violations appear to occur, or could appear to occur, even though you personally may not think causality has been violated in your own frame of reference.

That's what triggers paradoxes. As long as we can all agree who shot first, there's no paradox. But if, in the reference frame of some passing ship, the beam hits before it was fired, we are forced to ask:

"How did the second ship shoot back after being hit and blown up? It couldn't have. Therefore the hit didn't register on the first ship, which means it was in a different position when it fired the shot that blew up the second ship..." and the whole battle becomes a mass of paradox.
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What makes this really tough to unravel is that you can't just handwave it by saying "time machines blow up." It would be easy to do that in a universe where everyone occupies the same frame of reference. Your method of handling causality violation works brilliantly in a Newtonian universe, because there we can all agree on what constitutes time travel and what doesn't.

But doing this in an Einsteinian universe is tougher, and I must plead partial ignorance of the rules now.

[SMJB]

Well, damn.

But it seems to me that with apparent causality effect would only have to follow cause in "relevant frames"--in this case, the frame of my ship and the frame of the ship I'm dueling with. Nothing is happening in any other frame that can affect the past of either frame in this battle, so a hypothetical observer can observe whatever the hell they want.

Alas, I've no equations for this. It's the funniest thing, when you start using things besides X, Y, and Z to denote variables, I'm suddenly dyslexic. I know the equation for calculating time dilation (by heart), and that's about it.

[Simon_Jester]

Ironically, you can do special relativity equations for transforming distances and times observed in one frame to those of another using... x, y, z, and t. Occasionally with primes on. Heck, the time dilation formula IS one of the relevant equations.

Anyway. The problem with your "apparent causality effect would only have to follow cause..." idea is that it creates privileged frames of reference. In other words, "causality" is a special quality that we decide by looking at one frame of reference, and if it exists in that frame then it "really" exists, no matter what anyone else observes.

I'm going to use time dilation to explain why this is a problem. Set up a standard twin paradox scenario, where one twin ages 15 years on the rocket, and the other ages 20 years before the rocket returns. Ask the question: "how much time has passed?"

One twin will answer "twenty years." The other will answer "fifteen years." Both can point to the evidence of their own personal clocks, and for that matter their own physical bodies. Who is right?

Answer: both, and neither. Both are accurately describing their own experience, but neither has any special privilege that lets them gainsay the other in terms of "absolute truth." The absolute truth is that neither of them has observations any more or less valid than the other's. Observations of time are relative, hence the name "relativity."


But as long as c is preserved as a universal speed limit, and no cause-effect relationship can travel faster than c, while we may disagree on the duration of the interval between events A and B, we can at least agree on which one happened first. This is no longer possible once the speed limit is broken. I may be in frame F-one and observe A happening before B, while a different observer in frame F-two may observe B happening before A.

Within any one frame, causality holds (or can hold) at superluminal speeds. Superluminal speeds can be measured within that frame without breaking causality in that frame. But other people in different frames observe the causality-breaking.

And since there is no privileged frame of reference, no one person or place or velocity setting whose observations 'outrank' all others, if causality breaks in one frame of reference, for practical purposes it breaks in ALL frames.

Or at least, causality cannot be said to hold true as a general rule of the cosmos.

[SMJB]

That's the thing, though--causality doesn't hold in this 'verse. It's an illusion created by the fact that if an effect in any given frame precedes a cause which is also in that frame, it'll change the cause, thus changing the effect, thus changing the cause...and on and on until equilibrium is achieved.

[Simon_Jester]

Remember that "frame of reference" is a thing which applies to the observer, not the events.

The problem then is that any FTL effect will cause this to happen in some frame of reference. Even if no physical moving object exists to have that frame of reference, the frame itself still exists. So every thing by which signals propagate FTL would

Really, to preserve any meaningful sense of causality, relativity, and FTL... I can't think of a way to do it except to create a privileged frame of reference in which 'cause and effect' are determined.

[SMJB]

But...then how do wormholes work? Surely there's a frame somewhere that'll see you come out of one end before it sees you enter the other.

[Borgholio]

But...then how do wormholes work? Surely there's a frame somewhere that'll see you come out of one end before it sees you enter the other.

If you sit at the exit of a wormhole and look at the entrance with a conventional optical telescope, then you in fact might see a ship entering the wormhole centuries after it exits right next to you, depending on the distance you are from the entrance.

[Simon_Jester]

There's more to it than that. The perceived time lag between two events is NOT a matter of "it is fifty light years away so it looks like it happened fifty years ago." It is an actual observed phenomenon that applies to all means of measuring time no matter how you compensate for them.

In other words, if two clocks at rest relative to you have their alarms ring at the same moment in your frame, they are simultaneous in your frame, whether they were five feet apart or five quadrillion miles apart.

On the other hand, if those clocks are moving relative to you, you will NOT perceive them ringing at the same time, whether they are close or far apart- the physical separation between them in your frame serves only to control the size of the separation in time, not whether one exists.

[Esquire]

Why does that break causality, and not simply illustrate that information doesn't travel instantaneously? I've always been a little fuzzy on that.

[Simon_Jester]

There's no causality break in that- the point is... hm.

In relativity, the "distance" between two points can only be measured accurately in terms of the "spacetime interval" between two events. Events occur at a specified position in space and a specified time.

The "interval" between two events is equal in all frames- but the amount of elapsed time, and spatial distance, between the events are NOT equal. Thus, for example, the length contraction you observe in a bar flying past you at relativistic speeds.

However, if you have a way to judge the exact separation in time of events at either end of the bar (say, blinking lights) an interesting thing happens. In the bar's frame of reference, the events take place, say, five meters apart and at the same moment in time. In YOUR frame, the events take place less than five meters apart (due to length contraction), but they must also take place some nonzero amount of time apart, in order to preserve the "interval" measurement.

In other words, "interval" in spacetime takes the place of our intuitive measurements of spatial distance and temporal duration.


The issue here is that if two frames are traveling faster than c relative to one another, they may disagree about whether the time difference between events A and B are positive or negative. Which translates into not knowing which event has taken place first. Thus, causality goes out the window. There is no consistently observable cause and effect.

[gigabytelord]

I have a question regarding timeflow in and around a galaxy.

First: Gravity effects time as well not just traveling at relativistic speeds correct?

Second: Is it possible that time 'flows' at slower rates the closer you get to the center of a galaxy compared to it's far reaches? Or are the time dilation effects of the increased mass present at the center of the galaxy balanced out by the higher speeds that the outer edges of the galaxy travel at compared to areas closer to the center?

Third: Is it possible that time travels at a different rate outside of a galaxy than inside the galaxy, or in two galaxies of differening total masses and speeds?

I'm asking because I genuinely don't know. I have a basic understanding relativistic physics but I'm certainly not on the same level as some of those on this very forum.

[Esquire]

What are you thinking of time as, just for clarity's sake?

Simon - thanks for the explanation. Essentially, it's an issue because we assume there's neither a privileged frame of reference nor an absolute measurement of time, yes?

[Simon_Jester]

It's an empirical fact that there is no absolute measurement of time; we've checked that relativity does distort time as predicted.

It is a philosophical assumption of the underlying model that there is no privileged frame of reference so far as I know, but that may be due to my own ignorance.

[gigabytelord]

What are you thinking of time as, just for clarity's sake?

You know it's taken me a while to come up with an answer, and frankly I honestly don't know. When most people think of time they think of it as linear. Flowing smoothly from point A to point B, but even I know that's not the case.
Figuring out a different way to ask the same question escapes me unfortunately.

I mean on the face of it, it's really a very simple question. Does time flow at different rates inside galaxies (ie: near large collections of mass) than outside the galaxy?

[Simon_Jester]

Any differences in the observed rate of time passing depend on one of two things:
1) The relative velocity of the observers (time dilation from special relativity)
2) Curvature of spacetime caused by the presence of mass (which is entirely from general relativity)

Spacetime in and around galaxies is slightly curved by their mass, which does create small distortions compared to ideal 'flat' spacetime in deep intergalactic void. However, this effect is really really really tiny because galaxies have a very low density, and most of the mass in a galaxy is so far away from you that its gravitational effect on the place you're standing on is stupidly tiny. It exists, it's measurable over huge astronomical distances, but it is small when treated as a percentage effect.

Spacetime is much more strongly curved for us by the presence of the sun 150 million kilometers away than it is by the galactic core 474 thousand million million kilometers away, even though the galactic core contains billions of solar masses of matter including a giant monster black hole with enough gravity to make whole SUNS do kooky hairpin turns.

Therefore, any distortion of the passage of time caused by galactic mass is going to be relatively tiny and trivial, very hard to measure even with scientific instruments and impossible to measure by crude means such as "the twin between galaxies aged X years, and the twin in the galaxy aged by X plus or minus one year."

There are a few people on this site who could do the math in detail- Kuroneko and Surlethe being the ones that come to mind. My knowledge of general relativity is pretty sparse and rusty.

[Simon_Jester]

Addendum: the main reason we perceive the passage of time travelling at different rates is always going to be special relativity unless we decide to go skinny dipping in a black hole's accretion disk. It is this kind of different elapsed time for different observers that presents problems with FTL motion and observers disagreeing about cause and effect.