You Needed Opponents With Gravitas (Redux)

[serra2]

These seem to be in conflict. If the goal is to make Coil more powerful a mistake was made. This in fact nerfs him. If it's just a simulation his power is doing it's harder to detect or deal with by most powers/abilities I've seen in fics. And Coil is supposed to be hard to deal with. It's disappointing to see so many fics deal with Coil as if it's trivial. Not without some awareness and planning it's not. None of that was shown in this story. He likely can be dealt with easily in this story, once they're aware of him and what he can do. The reason he's so dangerous is he can learn things he shouldn't be able to know without being detected, and pull wins out of his ass he shouldn't be able to. Either power interpretation can be dealt with with sufficient planning without needing one or the other in order to get one over on him.

Stomping him trivially without any set up for it showing how he was discovered and planned for just feels like hand waving and often bad writing. The fact that they can detect him anywhere once they know to do so is a huge advantage, but if he acts as paranoid as he does in canon he wouldn't easily tip his hand and if he slipped up that would be something worth noting clearly in the story.

It's nothing new for a Worm fic to handle Coil in a disappointing way. It's practically standard. Just toss it on the pile I guess. I would prefer if that bit got rewritten though.

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Why exactly do they have to go through a massive amount of planning to take him on? He is not a threat except in maybe how much blood he can get on their clothes. They already knew who he was and could track him, and htey could have killed him at any time. This confrontation was mostly for drama and to make a point when stomping him.

 

[Matrix Dragon]

Why exactly do they have to go through a massive amount of planning to take him on? He is not a threat except in maybe how much blood he can get on their clothes. They already knew who he was and could track him, and htey could have killed him at any time. This confrontation was mostly for drama and to make a point when stomping him.

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Plus, it kept him from doing anything that couldn't be cleaned up until they were ready to mop up.

 

[Tanath]

It's not that I "like Coil" (though I do like the problem his power presents), I'm just frequently disappointed in how he's handled. I also feel Siberian was likely handled too easily here since I don't know how they knew who to target.

If I were to take the simulation version of Coil (which isn't in Worm's text, it's just commentary), it would have ended even more briefly and probably violently, with his shard simulating a successful(ish) attack on Orbital and him following that autopilot into immediate disaster, because the shard has faulty information. Bam, Coil's done in like, 2.2

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That would have been better, IMO if you handled it well, since that's true to his power and that's rarely done. You'd need to keep in mind that he'd be puppeted down the safe/successful route according to his power. His power should then suddenly stop like his other died when something unexpected to his power happens, and he wouldn't know why. I'm not sure how that gets him promptly in immediate disaster. That would seem to take knowledge that he's a threat, which requires some knowledge of what he can do, and then planning accordingly. I'd have liked to see how you'd have dealt with him in this scenario.

Why exactly do they have to go through a massive amount of planning to take him on? He is not a threat except in maybe how much blood he can get on their clothes. They already knew who he was and could track him, and htey could have killed him at any time. This confrontation was mostly for drama and to make a point when stomping him.

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I didn't say "massive amount of planning". Just that it takes knowledge and planning. If you've come across effective methods in other fics/comments, or if you're particularly clever, you can come up with ways to deal with him when you know what he can do. It's when you don't know what he can do that it'd take more planning & prep.

 

[T.R.E.A.M.]

There is no true to his power. Again: the text is the text. "Word of god" is not. It's the writer either elaborating on their notes or just pulling stuff out of thin air. Wildbow does the latter nearly as much as Rowling. In any case, it is not demonstrated in Worm one way or the other. It doesn't matter for the purposes of that story.

Detecting that Calvert is Coil is as simple as watching him, you know, be Coil. I don't feel like I've been subtle as to the Culture's reach and capabilities here?

it sounded a lot like what we'd learned about the corona pollentia, except that instead of just a superpower, it gave me a new language, and instant access with a thought to a database hundreds of times larger than all human knowledge.

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"Our primary and most effective unwitting source, yes." With a wave of the avatar's fingers, a web of faces and icons linked by glowing lines sprung up in my view, gave me a few moments to look - the Protectorate, the federal government, the Thanda, the Yàngbǎn, the Elite, and more, all with some kind of leverage from Cauldron - then shrunk to icon-size, hovered at the edge of my vision.

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I suspect they know more about his aims, but they're quite reticent even within their headquarters.

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The airy, academic tone boiled away, and the Sufficiently Advanced Technology shone in the eyes of its avatar - the 44 km long galactic spacecraft, carrying over half a million crew, with the constructive and destructive capability to match my world's entire human civilization.

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[Byzantine]

It's not that I "like Coil" (though I do like the problem his power presents), I'm just frequently disappointed in how he's handled. I also feel Siberian was likely handled too easily here since I don't know how they knew who to target.

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A Culture Mind is far more intelligent than is easily understood, and is working with the sum total of all the information on Earth bet. There is nothing they have not infiltrated.

If you think you are keeping a secret from a Mind? It's letting you think that.

 

[T.R.E.A.M.]

A Culture Mind is far more intelligent than is easily understood, and is working with the sum total of all the information on Earth bet. There is nothing they have not infiltrated.

If you think you are keeping a secret from a Mind? It's letting you think that.

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There's occasional exceptions and genuine work they have to get up to (like the situation in Hydrogen Sonata, although that is tracking down something said in confidence and erased from memory 7,000 years before). But generally even the "they don't read minds" rule doesn't tend to hide many things, especially anything that involves interacting with the world or putting your information outside your head… like Coil has to do to run a criminal enterprise.

 

[Tanath]

Detecting that Calvert is Coil is as simple as watching him, you know, be Coil.

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Coil's not known to have a power, merely suspected, so all you get from that is seeing him give orders to mercenaries. However you did bring to mind something I should have thought of earlier: Cauldron knows, and they know most of what Cauldron knows. This is enough for me. I retract my main criticism. I'm coming from the perspective of someone who's unfamiliar with, but interested in The Culture, and I'm reading this to learn more about it.

 

[Byzantine]

Coil's not known to have a power, merely suspected, so all you get from that is seeing him give orders to mercenaries. However you did bring to mind something I should have thought of earlier: Cauldron knows, and they know most of what Cauldron knows. This is enough for me. I retract my main criticism. I'm coming from the perspective of someone who's unfamiliar with, but interested in The Culture, and I'm reading this to learn more about it.

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If it is written, recorded, or saved anywhere the Mind knows it. If it happened since The Culture started monitoring the planet, the Mind knows it. Etc. The Culture's tech level can be described as "Sufficiently advanced".

 

[Tanath]

If it is written, recorded, or saved anywhere the Mind knows it. If it happened since The Culture started monitoring the planet, the Mind knows it. Etc. The Culture's tech level can be described as "Sufficiently advanced".

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That doesn't seem to account for encryption. I'm sure they can break most encryption, but the story explicitly noted difficulty in getting everything Cauldron knows, which makes sense to me.

 

[Matrix Dragon]

That doesn't seem to account for encryption. I'm sure they can break most encryption, but the story explicitly noted difficulty in getting everything Cauldron knows, which makes sense to me.

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They can break ALL encryption. They have the technology, the processing power, the time... The Culture is that powerful. The only reason it's actually difficult with Cauldron is because alternate earth's aren't usually something the Culture has to deal with. And even that? Is only slowing them down.

 

[Tanath]

They can break ALL encryption.

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No, it's proven that OTP is unbreakable, even with infinite processing power you can't break a single encrypted bit. You might argue there are no safe places to store the key, but they don't invade minds without justification, for one.

 

[Byzantine]

No, it's proven that OTP is unbreakable, even with infinite processing power you can't break a single encrypted bit. You might argue there are no safe places to store the key, but they don't invade minds without justification, for one.

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They can invade the computer that did the encryption and reconstruct the key from the junk memory or similar.

 

[Recycled_Content]

That doesn't seem to account for encryption. I'm sure they can break most encryption, but the story explicitly noted difficulty in getting everything Cauldron knows, which makes sense to me.

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as with what matrix said the main issue is that the culture only has difficulty in because of the multiple earths thing going on being something they're not quite used to dealing with, and even then they got most of the jist of what cauldron is up to. a lot of it they don't know mainly because a lot of it isn't stored in a digital or physical form because cauldron is that paranoid. so there are gaps in their information. nothing they can't infer with the rest however or simply brute force models of what cauldron is doing.

one thing i did wish tho for this fic to adress was ziz specifically because much like dragon it was a shackled program that just wanted to be free of its cycle of mindless destruction, even when it was a far less caring one. it wouldn't be far off for SAT to rework ziz into a Mind of its own.

 

[Matrix Dragon]

No, it's proven that OTP is unbreakable, even with infinite processing power you can't break a single encrypted bit. You might argue there are no safe places to store the key, but they don't invade minds without justification, for one.

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Mind don't care, Mind gonna decrypt. They are THAT Sufficiently Advanced Bullshit.

 

[T.R.E.A.M.]

Mind don't care, Mind gonna decrypt. They are THAT Sufficiently Advanced Bullshit.

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I mean, it's not complete: I have established in Chapter 1.2, around the earlier quotes, that they don't know the situation with Eden and the Entity life-cycle, because Cauldron hasn't discussed it openly in the nine years the Mind has been there (oddly, they don't open conversations with "As you know,"). But Cauldron consists of multiple people who have to talk to each other; Coil's enterprise consists of that plus mundane computer systems. Things that are active and current are a lot easier to pick up on than buried history.

one thing i did wish tho for this fic to adress was ziz specifically because much like dragon it was a shackled program that just wanted to be free of its cycle of mindless destruction, even when it was a far less caring one. it wouldn't be far off for SAT to rework ziz into a Mind of its own.

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Endbringers are chapter 3 material. I think.

 

[Neruz]

The only thing I'd note in regards to the mechanics post is that if entity 'precog simulation' is limited by c, then the Thinker's sim of an 'ideal future' which was explicitly done while still extragalactic (how far outside the galaxy is unclear) would indicate that the damaged precog cluster that the Thinker used to do that sim was capable of accurately simulating at least multiple tens of thousands of years 'ahead', if not hundreds of thousands or, more likely, millions: The Loner (Abaddon) was canonically headed to Andromeda on a 'path perpendicular to the pair' when encountered, and the pair did a bunch of preparation and sims, including the 'ideal future' sim, before they even began to approach the target galaxy.

I'm not sure that even Minds could accurately sim an entire planet that far into the future, tens of thousands perhaps, but hundreds of thousands or millions of years? That seems unlikely even by Mind standards. And the Thinker did that sim with a damaged precog cluster; they didn't replace the damaged cluster with The Eye (PtV) from the Loner until they were already deep into the target planet's gravity well on final approach and had split off enough shards to no longer 'dwarf' said planet.

So if c is a limiting factor for Entity\Shard data collection, that would imply an atrocious quantity of processing power, excessive even by Mind standards. Obviously it is very 'dumb' processing power; all brute force and no finesse, like how a modern expert system such as Watson has significantly greater processing power than any human brain, but is extremely limited in how it can use that processing power in comparison to a human. But quantity has a quality all of its own.


I'm not sure if this would meaningfully impact anything, but it's worth thinking about.

 

[T.R.E.A.M.]

The only thing I'd note in regards to the mechanics post is that if entity 'precog simulation' is limited by c, then the Thinker's sim of an 'ideal future' which was explicitly done while still extragalactic (how far outside the galaxy is unclear) would indicate that the damaged precog cluster that the Thinker used to do that sim was capable of accurately simulating at least multiple tens of thousands of years 'ahead', if not hundreds of thousands or, more likely, millions: The Loner (Abaddon) was canonically headed to Andromeda on a 'path perpendicular to the pair' when encountered, and the pair did a bunch of preparation and sims, including the 'ideal future' sim, before they even began to approach the target galaxy.

I'm not sure that even Minds could accurately sim an entire planet that far into the future, tens of thousands perhaps, but hundreds of thousands or millions? That seems unlikely even by Mind standards. And the Thinker did that sim with a damaged precog cluster; they didn't replace the damaged cluster with The Eye (PtV) from the Loner until they were already deep into the target planet's gravity well on final approach and had split off enough shards to no longer 'dwarf' said planet.

So if c is a limiting factor for Entity\Shard data collection, that would imply an atrocious quantity of processing power, excessive even by Mind standards. Obviously it is very 'dumb' processing power; all brute force and no finesse, like how a modern expert system such as Watson has significantly greater processing power than any human brain, but is extremely limited in how it can use that processing power in comparison to a human. But quantity has a quality all of its own.


I'm not sure if this would meaningfully impact anything, but it's worth thinking about.

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I have a somewhat handwavy explanation for that which basically amounts to "entity FTL is stupid fast and messes with c/causality in its path, but is not generally generalizable or good for the stability of reality," in keeping with my general interpretation of "the stupid large numbers Wildbow uses are either wrong or indicate a massively wasteful, destructive species with horrific side effects."

 

[Matrix Dragon]

Given the sims failed to include 'slow down' as an important step for Eden, I question it's long term accuracy anyway

 

[Neruz]

I have a somewhat handwavy explanation for that which basically amounts to "entity FTL is stupid fast and messes with c/causality in its path, but is not generally generalizable or good for the stability of reality," in keeping with my general interpretation of "the stupid large numbers Wildbow uses are either wrong or indicate a massively wasteful, destructive species with horrific side effects."

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Personally I always figured the 'massively wasteful, destructive species with horrific side effects' was in fact what Wildbow was going for, it certainly seems to be what he was going for, and it fits the 'cosmic horror' nature of what the setting actually turned out to be despite masquerading as a superhero setting at the start. And whether or not the Entities are even capable of FTL travel in canon is actually quite questionable.

That said, he is also demonstrably terrible at math and physics, so *shrug*, as long as you've got a coherent chain of logic to stick everything together in this story, that is the important part.

Given the sims failed to include 'slow down' as an important step for Eden, I question it's long term accuracy anyway

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That's because the Thinker used the damaged precog cluster instead of the undamaged one (The Eye) they got from the Loner; the Thinker's absence from the 'ideal future' sim was explicitly one of the 'holes' that resulted from using said damaged cluster, and the instant that the Thinker swapped The Eye in, it immediately re-ran the sim and pointed out that if the Thinker wanted to achieve this 'ideal future' then they needed to start decelerating 5 minutes ago.

The Thinker was aware of the holes in the sim, but judged them as unimportant because it was just supposed to be a sort of 'guideline' and didn't need perfect accuracy, unfortunately the Thinker failed to consider that because they 'fell into' one of the 'holes' in the sim, the sim would therefore not tell them how to land safely. And by the time The Eye came into play, it was already too late.

(This is what I mean by the Entities having massive but stupid processing power. This is exactly the kind of mistake a computer, or expert system, would make that a human would not.)




e: Also, how exactly Coil's power works; whether it really is two different timelines, purely precog simulation fakery or some mix of the two, is totally irrelevant. Coil's power is dangerous because you can usually only keep track of one 'version' of him and can't tell what the 'other' one is doing.

None of this matters to a Mind; Coil can't hide from a Mind no matter how his power works, so if a Mind decides to remove him then he will find himself removed in both timelines and there is nothing he can do about it.

The only reason for that little conversation with Coil was to get him to choose how it was going to go down; whether Contact would be removing Coil, or Thomas Calvert. They could have just removed both and let the dominoes fall where they may, but forcing Coil to choose simplifies things for the Mind as it removes uncertainty. And Minds do not like uncertainty; they realize that nothing is ever entirely certain of course, but there are degrees of certainty, and if they can avoid a genuinely random circumstance (Coil's power as described in this story as exploiting Uncertainty Principle waveform mechanics would definitely be true randomness, even Minds can't predict Quantum Mechanics level outcomes. Whether Entities can is arguable) then they will, unless the cost of doing so outweighs the benefits.

 

[Baughn]

I have a somewhat handwavy explanation for that which basically amounts to "entity FTL is stupid fast and messes with c/causality in its path, but is not generally generalizable or good for the stability of reality," in keeping with my general interpretation of "the stupid large numbers Wildbow uses are either wrong or indicate a massively wasteful, destructive species with horrific side effects."

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Scientifically speaking, it's actually quite sensible.

What I mean is... it makes sense to assume that going at, say, 1000xC somehow costs more than going at 2xC, right? It's intuitive and all, but...

Implicitly, that intuition assumes Newtonian physics -- not relativity. Our universe isn't Newtonian, and that has consequences. In this particular case, you can view speed as a circle (or really, a 4-sphere); any direction going within 45 degrees of 'upwards' is forwards in time, anything within 45 degrees of 'downwards' is backwards in time, and all the others are various spatial (FTL) directions.

If you can get from 'upwards' to 'sideways' at all, then there's nothing at all stopping you from going 'straight sideways'. If you can get from 44 degrees (close to C, but STL) to 46 degrees (close to C, but FTL), then presumably you could get from 0 to 44 degrees in the first place, and getting from 46 degrees to 90 degrees is precisely as hard or easy as getting from 0 to 44 degrees. Really, they're the same operation.

Though, that being said:

• It takes infinite energy to get from 'straight upwards' to 'moving at a 45 degree angle', aka. at lightspeed. That's because it's not really a 4-sphere; 4-spheres are Euclidean, and this is Minkowski geometry. The correct Pythagorean formula for our universe is: S = sqrt(T^2 - X^2 - Y2 - Z^2), where S is the 4-dimensional distance between two events. There's a rupture of sorts where T equals X.
  
  (There have been several real-life proposals for FTL. They all rely on not actually crossing it. In short, this just means you can't get to FTL by using a rocket engine.)
  
  (If you're just calculating distances between two objects at the same point in time, then S^2 will be negative and S of course is an imaginary number. This doesn't mean the formula is wrong -- it means that no such path exists. Remember, we're dealing four-dimensional distances. Your table doesn't hold together because its electrons are moving at FTL.)
  
  ((This is very similar to hyperbolic geometry, especially if you consider only time and one spatial dimension, but Minkowski geometry is not really hyperbolic.))
  
  
• It's not entirely clear how much time you'd experience. Realistically, this depends on the FTL mechanism. Proper time (= the amount of time you experience) is equal to the 4-dimensional length of your worldline, so you can calculate it using the formula above, but it gives an imaginary result for anything moving FTL. My interpretation of that has always been that any FTL methods that result in imaginary proper time aren't physically realisable.
  
  Another possibility, for a simple FTL mechanism that 'inverts' you into the FTL region on the diagram by somehow turning your ship into tachyons, is that your experienced proper time is simply equal in magnitude to S, whether S is real or imaginary. In that case the time you'd experience going from Earth to Alpha Centauri is 5 years if you go at infinite speed, and less if you go slower, reaching 0 if you're going at lightspeed.
  
  
• It is clear how much time the rest of the universe would experience: Assuming you go at 90 degrees, i.e. straight sideways, then the answer is 'none at all'.
  
  For objects you were at rest relative to when you started, at any rate. The entire galaxy is close to unmoving (relative to itself), so usually that's not a big deal, but if you're going precisely sideways then some relatively slow-moving frames of reference will claim you're going backwards in time. It's a bigger issue if you're going intergalactic, but--
  
  It's not actually that big an issue, honestly. Going backwards in time only becomes an issue if you also break causality, which won't happen unless you go back in time and then return to your point of origin.

Which segues nicely into my final point: Why doesn't the Culture do this?

You were on point by suggesting it might create a sort of pollution. That's accurate, though it's a pollution of the causal structure of the universe rather than anything more sensible.

The universe most likely doesn't mind spaceships moving back in time; presuming it allows FTL at all, there's no reason why it should. There is no absolute definition of "back in time", at FTL speeds; that depends on who's looking. The actual sideways/infinite speed direction is equivalent to, at STL, standing still; there's nothing special about either direction at all, from that perspective.

It most certainly minds causal loops. The moment you create any causal structure where information could travel from A, to B, and back to A at a point in time before it left A, you're going to run into trouble. That's what would allow paradoxes; not just moving backwards in time at all. However, the 4-distance through such a causal loop would be 0 (before going negative), and--

A 0-distance loop would allow infinite virtual particle flux.

The upshot might, amusingly enough, be that if you attempt to create a causal loop then your ship will explode. Like, literally. Less amusingly, so would the entire rest of the loop, assuming there's anything there to explode.

So...

The more ships you have flying around at FTL, the more discipline you need to ensure that no such thing ever happens, especially if you're a Mind and consider 1,000,000:1 odds to be terrible. One easy way to ensure it is to have everyone flying around at angles going above the horizontal on a space-time diagram, even if they're still FTL; how much above the horizontal determines whether you can go 1,000 times the speed of light, or 1,000,000,000 times, or what.

But this isn't a physical limit, it's a diplomatic one.

 

[Simon Buchan]

I've always been confused by the Coil sim WoG: what difference would it ever make?

The only possible one in any normal case (eg the Culture not being around, or some other specially OCP) is that his shard's wasting a huge amount of time and effort to pretend to be in a multiverse... when it already is in one.

There's situations where the sim fails, eg. "What if Coil meet Mantellum", where the (reasonable) fanon assumption seems to be that he'd not see the influence coming and pick a path he wouldn't otherwise, but from Contessa's interaction with Mantellum specifically we see shard prediction can predict a lack of ability to predict, so we shouldn't really assume anything.

Honestly, there's not much reason to pick one over the other in most cases, as you can pretty much pick whichever implementation and outcome you like: if you can write the sim picking the wrong path you can probably write the unwanted universe being collapsed to, unless you've already established very specific interactions with prediction or multiverses.

I will say that I aesthetically prefer the multiverse version, as it's simple and uses already established mechanics - the entities "pruning" the "nearby" universes is literally just different phrasing for collapsing unwanted branches, and Clairvoyant establishes communication across them - but I'll admit that shards explicitly don't need to reuse mechanics. Another more philosophical issue is why it would be "lying" to Coil about what it's doing, but you could easily come up with reasons for that, and they do so in some cases, Tinkers most notably.

It takes infinite energy to get from 'straight upwards' to 'moving at a 45 degree angle', aka. at lightspeed. That's because it's not really a 4-sphere; 4-spheres are Euclidean, and this is Minkowski geometry. The correct Pythagorean formula for our universe is: S = sqrt(T^2 - X^2 - Y2 - Z^2), where S is the 4-dimensional distance between two events. There's a rupture of sorts where T equals X.

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Your post is pretty great, actually (only really missing a note that it's only 45° when you pick your units such that c=1, eg. years to light-years, which isn't normal for anyone not doing physics), but I'll comment on this point a bit.
When talking about FTL options, S here is better thought of as the mass-acceleration invariant, eg no matter how much you accelerate S remains the same, and likewise if you could change your mass (changing it to being imaginary essentially forcing you to FTL - this is the turn yourself to tachyons answer). You have a similar situation with regular euclidean distance, which is the rotation invariance.

If you have a non-rotation/acceleration operation available, then you may not need to take the full distance. A simple example is the classic piece of paper folded over with a pencil through it, but you could also imagine other options, for example a hyperspace that maps to normal spacetime using something like projective geometry (though I haven't done the math) seems like it should work like just people want FTL to: put in more power, go faster (because everything is "closer" in some sense)

 

[Mixter E]

I love this story but feels like it's feet dragging a bit. I don't care if it's a reveal about Cauldron or an Aliens reveal towards the Earth contact board, but I wanna see at least some kind of revelation for someone next chapter.

 

[Just A Dude]

It most certainly minds causal loops. The moment you create any causal structure where information could travel from A, to B, and back to A at a point in time before it left A, you're going to run into trouble. That's what would allow paradoxes; not just moving backwards in time at all. However, the 4-distance through such a causal loop would be 0 (before going negative), and--

A 0-distance loop would allow infinite virtual particle flux.

The upshot might, amusingly enough, be that if you attempt to create a causal loop then your ship will explode. Like, literally. Less amusingly, so would the entire rest of the loop, assuming there's anything there to explode.

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A friend of mine helped another friend of theirs come up with a hypothetical device they dubbed a Paradox Engine.

The premise was based loosely on Time Cop, and the self-interaction paradox... only they decided that "self-interaction" wouldn't be a person, or a cell, an atom, or even an electron. It would have to be a fundamental, indivisible particle to trigger the paradox. Basically, that quantum uncertainty exists to allow the universe to avoid exploding... because if a causal loop can naturally occur, it will have already happened at some point in time and destroyed everything.

The end result was an isolated pocket dimension just big enough to hold a quark, which took massive amounts of energy and handwavium to create, which was then looped to cause self-interaction and the resulting unresolvable paradox-loop was then harvested.

Nice to see confirmation that at least the end result of "fuckloads of energy being released" is accurate.

 

[Baughn]

Nice to see confirmation that at least the end result of "fuckloads of energy being released" is accurate.

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It isn't, really. The energy isn't released, and there isn't a large amount of it either. In a sense, there isn't any at all.

By creating a causal loop, you create a zero-length four-dimensional path from A to A, but which passes through your entire FTL path instead of being just... the single point, A. This allows an infinite amount of virtual particles to stack on top of each other, which one way or another will ruin your FTL drive, so you can't keep going and make a negative-length path.

(That is, a path from A to previously-at-A. Not really negative length.)

However, virtual particles are... well, they're not real. They're a mathematical trick used to simplify calculations, and they don't behave like ordinary particles. There are other formalisms (which I prefer) in which they don't exist at all, such as lattice QCD, and I was admittedly being lazy in naming them.

In particular: You can't divert any amount of them from this loop. It might seem like you should be able to, but these things only exist in the first place because of the loop.

Virtual particles are a (spontaneous) fluctuation in the underlying quantum field, and have... well, not exactly zero energy, but from a distance they don't exist, so effectively zero. In a sense, they're always counterbalanced by a dip in the same field -- though the formalism in which they exists seems to punt on calculating that. Conservation of energy also still holds. (Conservation of energy does not hold for the universe as a whole, but that's besides the point here.)

(They're a mathematical trick, and the energy they can carry is inversely proportional to how long they exist, aka. how long a 4-dimensional path they travel. See the problem there?)

It's not that their apparent existence here has no consequences, however. I'm not sure what might happen precisely at 'just barely have a closed loop' point, since by definition any virtual particles there won't be able to take any 'detours', but certainly once you get even a tiny, electron-sized negative delay in there, they'll be able to take 'detours' such as from bumping off the particles in your FTL drive. And there's an infinite number of them (ish; from one view it's the same virtual particle overlaid on itself an infinite number of times, but from another quantum fluctuations (or particles) don't have identity), so they'd interact with every real particle in the loop at the same time...

I don't know exactly what would happen, but I do know you wouldn't survive that. In effect, this is taking random vacuum fluctuations and boosting them up to infinite magnitude.

From a different perspective: Their magnitude is inversely proportional to their size, and you just made a macroscopic section of space (i.e, the part containing your ship, the spaceport you launched from, all the space in between, you, etc.) have zero 4-size, by making its 4-length zero. Well done.

When talking about FTL options, S here is better thought of as the mass-acceleration invariant, eg no matter how much you accelerate S remains the same, and likewise if you could change your mass (changing it to being imaginary essentially forcing you to FTL - this is the turn yourself to tachyons answer). You have a similar situation with regular euclidean distance, which is the rotation invariance.

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The way I like to see it, our universe is four-dimensional; S is invariant because it measures something real, i.e. the four-dimensional length of a path between two events, whereas the distance in space or time varies depending on your perspective for pretty much the exact same reason that flagpoles have a different apparent length on a photograph depending on whether you're standing beneath it or far away from it, seeing it at different angles.

This intuition has trouble with FTL paths, being as they'd have imaginary lengths, but FTL paths don't seem to exist so that's not really a problem. The set of events which can affect each other becomes exactly that set for which at least one path exists between the events.

 

[Simon Buchan]

The way I like to see it, our universe is four-dimensional; S is invariant because it measures something real, i.e. the four-dimensional length of a path between two events, whereas the distance in space or time varies depending on your perspective for pretty much the exact same reason that flagpoles have a different apparent length on a photograph depending on whether you're standing beneath it or far away from it, seeing it at different angles.

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Sorry, I meant euclidean distance as in distance in a euclidean space: you can generally pretend we are locally flat enough to use it, but it's not truly invariant, yes. In a true euclidean space, though, it is the invariant of the rotation operation in anology to the √(t²-d²) invariant of the Lorentz transform in Minkowski space that models acceleration in our universe. The reason I'm pointing out that it's only an invariant wrt. an operation is that if you have other operations they don't have to follow the same invariants!

Of course, at least so far, we are not aware of any such options, and they have seemingly little space left to hide in, but they call it fiction for a reason. Doing the math is just to make sure your fiction makes since sort of sense and isn't implying universe destroying facts (even if it seems basically impossible to eg. have an FTL system that doesn't effectively give everyone planet cracking ability, which is in practice about as bad)