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It’s just another average day in the life of modern day earth. Suddenly a transmission from orbit washes over the planet! Oh no! An alien race, calling themselves the “Thull”, has suddenly arrived in their spaceship and declares war on our race, threatening genocide! They are undoubtedly real, as anyone with a moderately powerful telescope can see their ship in orbit, and there was an obvious effect as their ship “slowed down” or ”transferred from hyperspace” or method it used to travel.

Acting quickly and perhaps rashly, one of the governments of the world sends a nuke up. It has surprisingly good aim, and actually collides with the spaceship before detonating. To everyone’s surprise it obliterates the Thull spaceship and every one on-board. This is probably because the most advanced war-fighting technology the Thull had were steak knives and tinfoil shielding. North Korea claims responsibility.

Assuming that:

  1. By and large, it is accepted that the Thull were real
  2. And that their spaceship was real,used FTL, and didn’t sneak close to the planet
  3. All physical traces of alien technology are now useless bits of scrap
  4. Their method of ftl drive/travel doesn’t use handwavium or unobtainium (it can be built by things the people on the planet have available). Recovery of the scrap shows no traces of anything unobtainable.
  5. Humanity doesn’t self-destruct TOO MUCH at the reveal of other intelligent life out there.

What’s a realistic expectation for the collective of humanity for the length of time to determine the ftl method and build their own ftl ship/probe/test-bed?

Keep in mind, all they really have is the blatant demonstration that it’s possible and some of the outward observable effects, they have to work out ‘how’ on their own, with only the knowledge that its possible and within grasp (demonstrated by the general (lack of)advancement of the Thull).

Edit

Everyone, Thanks for the responses so far!

Most of what people are saying is that it’s not possible to determine, and if that’s the consensus then I can accept that, but I keep thinking back to an idea;

During World War 2, suddenly someone had a nuke and without question demonstrated it was possible to create that device. Where before places and nations only had theories, now they had proof, and within a relatively short period of time other places created their own nuclear devices. In-fact, most other places that had access to the brain power and materials figured it out.

Isn't this sort of example usually the case? It takes forever to make/invent the first one, but once people "know x is a thing," shortly everyone has it. Coming up with a working idea in the first place is hard for humans, but recreating it is "less hard". Or is this off base?

Edit2

Its seems the general consensus is "not enough information" which is fair. It leaves me a little freedom to work with the timeline, but for my use-case, ultimately what I'm hearing is I will have to decide on what timeline works best for the story, but probably a minimum time of a few years. If I could I would +1 everyone that contributed,but I feel Serban Tanasa provided the most useful answer because he elaborated out the different degrees of technological differences that could exist in a simple way.

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Comments are not for extended discussion; this conversation has been moved to chat. – Tim B Feb 17 at 22:35
    
I remember reading a short story about something sort of like that once already - aliens with anti-gravity warp drives arrive on Earth, get obliterated because their best weapons are glass jars full of gunpowder, and then humanity copies their warp drives and takes over the galaxy. – immibis Feb 18 at 1:35
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Nuclear weapons were basically invented once and then shared or stolen around the world. Though in many cases it is sufficiently motivational just to know that a thing is possible, this is not one of those cases. – Ryan Reich Feb 18 at 1:58
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@kasperd If time travel will be possible at some point in the future, some guys from the future will bring it back to us. – Alexander Feb 19 at 11:18
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@Alexander They might not. Also I recall at least one fiction where the range of possible destinations for time travel was limited to a fixed number of years in either direction from the moment of the invention/discovery of time travel (in other words, you could only go to dates that fell between, say, 38 years before its invention and 38 years after). Something like that would explain why it hasn't been "brought back to us". – Dan Henderson Feb 21 at 18:57

11 Answers 11

up vote 52 down vote accepted

It depends on how far from the current production possibilities frontier this technology is. There are several possibilities, depending on the technology gap:

  1. It is like the Apollo Moon mission to Stone Age hunter-gatherers. We (the hunter gatherers) can probably recover some debris, use it to bash stones or store berries, but we have neither the industrial base or the scientific framework to comprehend and replicate the technology.

  2. Helicopters to Leonardo. Leonardo understood the concepts of helicopters, but didn't know about internal combustion engines. Given the field of debris from a helicopter crash, Leonardo might infer a few advances, but will likely be unable to build a helicopter. It would still revolutionize technology, though.

  3. Nukes to Stalin. Russian scientists knew nukes were possible. There was even a nuclear program. Knowing that the Americans had done it and stealing American tech allowed the Russians to build the same project quickly, without the steep and costly learning process that the Americans had to undergo. If this is the case, we'd have FTL within one to three years of the 'attack'.

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#3 makes the excellent point that the reason any technological breakthrough is "replicated" by other parties in a relatively short period of time is that one people know something is possible and that somebody has the knowledge of how to do it, they do whatever is necessary to try to acquire that information. – Michael Feb 17 at 2:07
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I would argue that it is none of the above. Considering that the aliens did not display a knowledge of advanced weaponry or shielding, it is possible that their technologically development is completely imbalanced. See my answer for more details. – March Ho Feb 17 at 4:47
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@MarchHo: Unbalanced, or more likely stolen from another more advanced race. These guys remind me of the Ferengi from Star Trek. They know just enough about advanced technology to be able to operate it, but not build it on their own. (When first encountered, their most advanced weaponry was whips. Fancy electric whips maybe, but still - don't bring a whip to a phaser-fight.) I mean - steak knives? If they haven't even figured out basic firearms (or heck, even archery) yet, they probably were not the ones who designed the FTL they were using. – Darrel Hoffman Feb 17 at 14:37
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These analogies don't quite grasp the problem of FTL. Helicopters, moon missions... these are all pushing into the unknown: Leonardo had no working concept of aerodynamics; Hunter-gatherers had no idea of orbital dynamics. In contrast we have a solid and experimentally verified understanding of how the universe works that says FTL is not possible, or would require enormous energies to work around. FTL means breaking, or side-stepping, one of the most fundamental and well tested laws of the Universe: causality moves at the speed of light. – Schwern Feb 17 at 22:00
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@SerbanTanasa Time dilation is well understood, matches theory, and is not FTL; to an outside observer you're still going slower than light. Superluminal jets are not really superluminal, it's an optical illusion. Frame dragging was predicted by relativity and is not FTL, but the warping of space-time points at how FTL may be possible without violating causality: the warp drive and the wormhole. – Schwern Feb 17 at 23:52

Impossible to answer. I'm using the answer format rather than a comment to get enough space to explain.

  • FTL travel will probably require a paradigm shift in science. The necessary theoretical hints may or may not be observable. Imagine somebody like James Watt gets a tour of a nuclear power plant, but without a helpful tour guide. He might have recognized the turbine building, and concluded that turbines rather than reciprocating cylinders are the way to go for steam power, but guessing where the power comes from would be impossible.
  • Without the breakthroughs, who can tell what the manufacturing tolerances of the FTL drive are? If somebody had handed James Watt the blueprints of a jet turbine, he might well have concluded that it is a neat concept but utterly impractical, because he can't come up with the bearings and blades to take the strain.
  • We think that we understand nuclear fusion, but it has been "a couple of decades away" for a couple of decades.

Questions are supposed to be off-topic here if they are idea generation rather than specific stumbling blocks in your fictional work. Without knowing how your FTL drive works and what the observable side effects are, we can't help you.

Or to put it another way, decide what outcome you want for your story and then consider how to make it happen.

  • Can spectroscopic analysis of the attack tell us about unusual elements in the debris of the alien craft?
  • As a minimum, consider how long the development of an airliner or a jet fighter takes, both today and during major wars. Years to decades.
  • Can the FTL drive function on Earth or only in space? If we have to take the labs to a space station, add a decade or two.

Edit:

The Royal Navy deployed an AEW variant of the Sea King in 11 weeks. Both the helicopter and the radar were existing, they just had to integrate them.

The Mercury Project took a couple of years, based on existing rockets and a new capsule.

The B-2 took a more than a decade.

The F-35 went operational a decade after her first flight.

Does that mean a great sense of urgency can accelerate sluggy R&D, or does that mean modern aerospace craft are much more complicated than a wood-and-canvas biplane? I think so.

Wild guesstimate: At least a decade for theory, at least a decade for orbital infrastructure, at least decade to build a prototype, and that is optimistic.

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I'm tempted to downvote or flag this because, as you stated, you're not using an answer to answer the question. – Frostfyre Feb 16 at 18:41
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@Frostfyre, I'd call it a partial answer, and explanations why more precision isn't possible. Do you think are more complete answer is possible? – o.m. Feb 16 at 18:43
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It's not whether it's possible or not, it's that this is not an answer, and the whole point of SE is to provide answers, or remove questions that are not answerable ... On one hand I can clearly see that your input is valuable, on the other hand this is clearly a "long" comment, not an answer ... – AndreiROM Feb 16 at 18:44
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I would say that this is a complete answer, and one of the better ones here. Asking an unknowable question calls for the answer that the answer is unknowable, and that is an answer, especially when it's correct. – Dronz Feb 17 at 8:14
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One can argue that nuclear fusion is taking so long because it is significantly underfunded. Presumably, the threat of Thull would be enough to secure lots of funding. – svick Feb 18 at 21:50

During World War 2, suddenly someone had a nuke and without question demonstrated it was possible to create that device. Where before places and nations only had theories, now they had proof, and within a relatively short period of time other places created their own nuclear devices.

Comparing nukes to FTL is an incorrect analogy, and examining why will explain why simply knowing FTL is possible does not help determine how long it will be before we can do it.

During WWII it wasn't "suddenly someone had a nuke". The physics of nuclear fission was understood and published in 1939 and 1940 by the Germans and Soviets. We, meaning humanity, knew a nuke was theoretically possible, and we knew the basic mechanism by which it could happen. It was the engineering to make a practical device that was lacking, engineering that was far, far beyond anyone's expectations at the time. The Manhattan Project, the first successful nuclear bomb, was at a scale beyond anything previously.

What knowing FTL can work, plus the fear of someone else using it against us, does is get funding, so important for the practical implementation of an engineering project. Going back to the nuclear analogy, the Germans had their own nuclear program, but it was never at the scale of the Manhattan Project. The Manhattan Project got its funding, in part, because of the idea of the Germans getting a nuke first and the many scientists warning the government of that.

Underfunded hypothetical FTL projects on the drawing board like the Alcubierre drive will suddenly get funding. But they're still lacking a lot of basic physics to understand how to do it, much less get the energies involved down to something we can practically produce.


A better analogy is AI and the human brain.

We know from the human brain that you can make a computer which does the things humans can do. Since the 60s we've been predicting that computers which can think like humans are right around the corner... and it's remained right around the corner for the last 50 years. Even things like Siri and Deep Blue are still performing specialized tricks, they don't think.

What it comes down to is we still do not know how the brain works and how we build computers is fundamentally different from how the brain works. We know AI can work, we are thinking machines, but even with seven billion working examples we're still an unknown amount of time away from AI. It's not an engineering problem, we lack the basic understanding of intelligence, learning, and consciousness.


Furthermore, the other analogies of great technological leaps offered: pre-WWII nukes, Renaissance helicopters, Stone-Age Moon landing, even AI... these are all steps into the unknown. They wouldn't violate known and tested systems. Leonardo had no working knowledge of aerodynamics, and cavemen had no tested ideas about orbital dynamics. Those are all problems which were (or can be) solved with more research, more theory, and more experimentation (and more money).

In contrast, we have a huge body of theory and evidence which says not only that the speed of light is the fastest you can travel, but that the speed of light is the speed of causality. Breaking, or working around, the speed of light isn't like breaking the sound barrier. FTL isn't about more powerful engines or a better understanding of aerodynamics. If you go faster than the speed of light you break our fundamental and well tested understanding of how the Universe works. Watch this video to understand.

Achieving FTL means either throwing out our understanding of the Universe and somehow constructing a whole new one. Alternatively we'd need to build one of several hypothetical work-arounds which warp space-time such as the Alcubierre Warp Drive which require tremendous amounts of negative energy. Negative energy has only been produced at quantum scales and quantum things tend to not scale up well.


This is why just knowing FTL can work, and having the motivation to fund its development, doesn't mean we can predict when it will happen. We only have untested hypotheses about how FTL might work, but there's a lot of basic science we don't understand. What can be said is we'll achieve FTL faster than we would otherwise.

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Seems to me the nuclear weapons example was not a case of "oh we know it can be done so we'll figure it out independently", but mostly a case of studying in as many ways as possible (including espionage) how the US did it. That's nothing like "oh look, an alien ship just zoomed in, then was destroyed - let's try to invent an FTL drive of some sort now". – Dronz Feb 17 at 8:11
    
@Dronz Somebody still had to do the work of actually figuring it out, even if others later copied it. The point made in this answer seems to me to be very much valid. – Michael Kjörling Feb 17 at 23:17
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The point is more that by WWII nukes were inevitable. If the US hadn't done it, somebody else would have. We had all the theory, it "just" needed engineering, engineering that was just inside what a single nation was capable of. With FTL we not only lack the theory, but current theory says its nigh-impossible. And the engineering requirements for building the hypothesized FTL starships might optimistically require energies like the entire mass-energy (as in E=mc^2) of a small asteroid, something we're no where near capable of producing. – Schwern Feb 17 at 23:58
    
I understand that, and I don't mean to disagree with the answer, which I upvoted. I just wanted to add that in contrast to the original question and some of the other answers' apparent thinking, I think it's important also to keep in mind that the effort by later nations also involved using technical details of how the US did it. Most of the world is still struggling to achieve that technology, and the efforts that succeeded or are anywhere near close, require borrowing a lot, not just inferring from the fact it was done, as some of the other thinkers seem to think would occur right away. – Dronz Feb 18 at 1:34
    
Damn, you beat me to the AI example. Though some would argue that we do have a decent understanding of how intelligence works and that the recent success of the old concept of neural networks shows that strong AI might only be a question of increasing computing power and data availability. – BlindKungFuMaster Feb 18 at 15:19

This idea has actually been explored in the short story The Road Not Taken by Harry Turtledove.

In the story, the aliens invading Earth had FTL technology but lacked any other significant military technology, much like the aliens in the question. Having discovered FTL in their Age of Sail, they travel in conquistador-style submarine-like spaceships, and attempt to invade Earth with black powder weapons.

While their ship was not actually destroyed in the story and could be directly reverse-engineered, the idea that such travel is even possible would quickly galvanise scientists to work on the idea.

Since the aliens described in the question are similarly under-developed in their war-related technologies, it is highly likely that their early discovery of FTL has therefore stunted their scientific expenditure in fields such as engineering and weaponry, and that humans have far surpassed them in these other fields. As a result, humans should be technologically far more advanced than the aliens in non-FTL fields. Any engineering feats that the aliens can create would be trivial by human standards.

Current scientific theories imply that FTL travel is impossible, and scientific inertia is an important factor in the advancement of science. Max Planck famously quipped that:

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it

A clear demonstration that FTL is in fact possible would mean that the vast majority of scientists capable of working on such an idea would immediately begin to obtain massive amounts of funding and resources and research FTL. Turning FTL from a scientific pariah into the most militarily and economically important question would likely result in billions to trillions of dollars being poured into its research.

If the aliens could discover FTL with pre-industrial levels of population and scientific expenditure, it is not unreasonable to think that humans would be able to do the same relatively quickly with millions of times more resources at their disposal. All humanity needs is to think along different lines from previously established science, as flaws in previous theories had likely led to the stagnation of FTL research.

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Well, warp travel (or w/e these aliens use) may well be physically possible, but keep in mind that nuclear power was always possible as well - it just wasn't achievable by mankind until the 50's (aka at least 70 thousand years after we climbed out of trees in dear, ol' Africa).

In the short term what would happen is that anyone who would be able to get their hands on a piece of the alien craft would do so. They would analyze the heck out of each piece, and conflicts between nations may very well arise over who owns them, or who gets access to them.

A lot of research groups and think tanks would be established in order to examine everything about the aliens. "Experts" and other know-it-all types would probably declare that it's now only a matter of (short) time until humanity is interstellar, and make all sorts of crazy predictions. A lot of professors would be applying for grants in order to "analyze" the problem, that's for sure.

Quite probably an international space defense coalition would be formed, which would give the US a great excuse to put nukes in orbit. You know, to keep us all safe. Cough.

Other than that? Quite frankly it would serve as a great boost to humanity's confidence that we could one day spread to other stars, but without significantly more to go on we won't be discovering the alien's way of travel any sooner than we might have otherwise.

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The US is already on that path. As of Jan. 7, NASA has a Planetary Defense Officer. – Frostfyre Feb 16 at 18:50
    
@Frostfyre - the US has been on that path since they first launched a satellite. unfortunately for them, however, they signed treaties with the Ruskies that they wouldn't. The same way they signed treaties not to encroach on Russia's sphere of influence, cough, Ukraine, cough. It's not even certain if the US doesn't already have armed satellites or not - it would certainly be in their interest. So, in the end, who knows? The only certain thing is that such an incident would provide them with an excellent excuse to publicly launch (more?) armed satellites – AndreiROM Feb 16 at 18:54
    
I'm struggling through the borderline conspiracy theories in this answer and comments to really like it. – Ellesedil Feb 17 at 17:56
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Sigh. At best, it distracts from the core of your answer. At worst, it invites questions and discussions that ultimately have nothing to do with the core of your answer. Right now, all of the questions I have for this answer are about your opinions on US politics. – Ellesedil Feb 17 at 18:02
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@Frostfyre Sounds like it's time to phone Batman and ask him to fund the Justice League watchtower. – TylerH Feb 17 at 20:42

I would say that it would take a very short time (months, 2 or 3 years at most), for the following reasons:

  • You mention that: "and there was an obvious effect as their ship “slowed down” or ”transferred from hyperspace” or method it used to travel." -- The obvious effects would have to include various easily measurable phenomena using current technology. Including various electromagnetic traces with unusual spectra, exotic particles, and various gravitational effects due to the sudden appearance of additional mass in earth orbit out of seemingly nothing. Consider how much Galileo, Copernicus and Newton were able to learn from observing the movement of the planets with 18th century telescopes, and now imagine what 21st century scientists would be able to figure out once they measure the effects of an alien ship coming out of FTL.
  • Humanity has typically been able to achieve a lot scientifically when driven by war: Look at the technological development that occurred because of WWII and the Cold War. Now imagine what will happen if we were under threat of an alien invasion.
  • Historically, once something is shown to be possible, others figure out how to achieve it very quickly. The very fact that the mind set switches from "Is it possible" to "When will it happen" changes the way people approach the problem.
  • There is already a theoretical framework for FTL called the "Alcubierre Drive" (This is legitimate theoretical physics, not pie-in-the-sky sic-fi proposals). Wormholes are also a theoretical possibility according to general relativity (Physicists call them Einstein-Rosen bridges). Chances are, if aliens suddenly showed up in orbit, this would allow physicists to quickly fill any gaps in the above mentioned theories and create workable FTL devices.
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While I suspect years not months, I agree that with "obvious" observable effects we would be able to deduce exactly what form of FTL actually works, SO LONG as it's one we have considered theoretically possible or @ least have a basic understanding of... – MER Feb 16 at 22:46
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Even if those obvious observable effects would in principle give lots of information, it's likely that we'd fail to measure those accurately enough. Measurements of something completely new and unexpected are usually pretty vague, only by fine-tuning experiments do you narrow down the uncertainties. – leftaroundabout Feb 17 at 0:18
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— Then: I think you're overrating the boost of science through military need. Sure it helps for actual implementations if you throw in tons of money for projects like Manhattan, but still this wouldn't have succeded if they hadn't had a whole pile of groundbraking theory to work with, which had been established in the preceding 50 years. — Whereas the Alcubierre Drive is hardly a “theoretical framework”. It's an idea, brought forth seriously and perhaps visionary... or perhaps garbage, who knows! It doesn't have any of the experimental confirmation that nuclear physics had mid 1930's. – leftaroundabout Feb 17 at 0:18
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There are a few difficulties in answering this question, so let's go through them in order:

1, If it uses an engineering concept radically different from ours, I would say the possibility is nil. Consider this scenario: A modern F16 crashed during World War 1. What is the possibility of the Germans replicating that technology based on the remains? Exactly zero percent, as they do not understand the advanced electronics or the concepts used in micro-controllers and their software.

2, If it uses exotic materials, then the possibility is close to zero. Like making an F35 with World War I technology.

3, If crucial components auto-destruct, then the possibility is zero. Most military hardware is rigged so that it can be disabled to prevent leaking sensitive information to the enemy.

If none of these difficulties arise, then the only question is time required. I would say in the magnitude of a few decades...

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The OP's question was about FTL in general, not FTL identical to that used by the aliens. If an F16 crashed into the middle of WW1, the Germans wouldn't know how to recreate it, but they would certainly learn enough to create a jet aircraft. – Alex Kinman Feb 16 at 23:51
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@AlexKinman Metallurgy advanced after WWI. This is important to creating a functioning jet engine - you would struggle to create one using WWI era materials. Conceptually the jet engine uses the same principles as a gas turbine. IMHO lessons in aerodynamics would be more significant than the engine design. – Taemyr Feb 17 at 10:01
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@Taemyr a jet engine is a gas turbine engine. Also in reference to the first point, in WW1 German engineers were only 20ish years from building a jet engine, which was developed from steam turbines that had been around since the late 1800s. Seeing a modern jet would tell them to use axial designs rather than radial compressors and reverse-flow combustion, but they figured that out for themselves by 1943-44 anyway. – anaximander Feb 18 at 12:19

I'd agree that knowing that something is possible can change everything. When you know that it's possible, the question shifts from "if" to "how". It leads to a totally different mindset.

That said, the Atom Bomb example is flawed. Scientists had been building up atomic theory for literally thousands of years -- the ancient Greeks had discussed the idea of atoms. Yes, they never identified what the real elements were and got tripped up on important points, but they had the fundamental idea. Universities all over the world taught facts and theories very close to what was needed. It was just a matter of going one more step. Even if the U.S. had never built an atom bomb, I think it's likely that someone else would have built a bomb or a reactor within a decade or two.

But in the case of FTL travel, it's not a matter of the basic theory being there and we just need one more piece of the puzzle. No one has the vaguest idea how to build an FTL drive.

I guess if we had proof that FTL was possible, scientists would start revisiting all the reasons why we presently think it's not possible, and maybe they'd find the mistake.

If the alien visit left one solid clue -- if examining the wreckage revealed that the ship was fueled with lithium chloride or that the engines emitted charmed quarks or whatever -- that might give more hope.

Otherwise ... I'd say we'd still be looking at centuries. One could always postulate an inspired genius who figures it out, another Kepler or Newton or Einstein, in which case the key breakthrough could be tomorrow. I'd expect it would still take many years to get from the theoretical breakthrough to a working model.

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I believe the time would be relatively short (though my WAG is between 5 and 15 years, so partial agreement with @Alex Kinman).

Though my answer depends primarily on one very important thing:
The obvious observable energy signature(s) of the FTL exit occurrence, MUST align with one of our existing theories for FTL, otherwise I doubt we would make much additional headway.
(Another point to support quick development of FTL in your scenario:
I would take it as evidence that the technology level required for FTL may not be that far from our own based on the fact that a nuke was able to get to, and destroy their ship.)

Reasoning:
If we are in any position to understand the FTL drive used by the Thull, AND in any position to produce said drive, our level of understanding of the universe must be deep enough to include the idea. If, on the other hand, there is some theory that must later supplant the Theory Of Relativity, and/or our general understanding of physics, prior to us being able to understand and build an FTL drive, then us being able to get there any time soon is not very likely (to agree with @AndreiROM).

Some possible support for the idea:
There are enough theoretical concepts of how FTL might be possible with current understanding:
Warp Drive
EmDrive
Wormholes
And a wikipedia article on FTL in general

Hope that helps.

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Why must it? I find it rather presumptuous to think that all possible FTL theories have been explored by human scientists. It could be the case that existing (flawed) human theories contradict the alien FTL theory, and therefore were not explored by human scientists. In fact, if we assume the EM drive will turn out to work as advertised, it is currently violating a number of key physical principles. – March Ho Feb 17 at 4:39
    
@MarchHo Hmmm I'll have to change the way I wrote that, if you read in the reasoning section I'm saying it must in order for us to be able to re-produce it quickly. If it does not then I'm agreeing with AndreiROM that it might increase our interest and focus but wouldn't be likely to get us noticeably closer otherwise... so thanks, I'll try to fix the answer to make it more clear. – MER Feb 17 at 8:43
    
@MarchHo modified the answer to clarify my point that I believe, given the scenario, we would fairly quickly develop FTL... SO LONG as it fits into some theory we already have, but if it DOES NOT, then I doubt we would develop FTL appreciably any faster. – MER Feb 17 at 9:07

Not really an answer, but some thoughts for the sake of completeness.

1) Given that Thull ship was in the Earth orbit, most of the debris which are not evaporated by the nuke would enter the atmosphere and burn. So I see no way for direct proof that there was no unobtainium involved.

2) However, those remaining debris would probably be hunted for (there goes reusable rocketry!) and examined scrupulously. This alone would take a year or two. Regardless of what was found, some nukes and more telescopes would end up in orbit (bye bye radiophobia, and more rocketry).

The mere signal that "FTL is possible" implies a major review of general relativity which currently forbids FTL. However, GR is extremely robust - it has been under constant scrutiny for a century now, and held. Building a viable alternative would probably take a generation or two.

The whole situation would be a huge boost for physics-related science in general (just as the Cold war was, but at a greater scale since the adversary is so far ahead), but training a modern scientist takes like 10 years (and real scientists would argue that it's more like "the whole life") so it won't pay off quickly.

Generally, the encounter will be beneficial for mankind, but not quite enough to discover FTL unless it's really, really close.

3) Now a couple possible events that could speed things up:

3.1) The entrance of the Thull ship may have been accidentally recorded by human telescopes. Even though one data entry is not much data, it would be a good boon. Especially if it somehow gets noticed by something like LIGO.

3.2) The collected debris may turn out to be not as advanced as expected. Say they use bare transistors and not chips, or barrel-loaded guns, or something like that. This may encourage the scientists even further.

Still it looks like years to tens of years... Maybe the Thull aren't coming because they are equally scared...

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Let's look at some other examples:

Birds wing -> heavier than air flight

Depending on how you look at it - hundreds of years to all of human history. We didn't understand the concept of the aerofoil, or know how to achieve propulsion. We could see birds flying, but only had handwavy ideas as to how they were achieving it.

US Nuke -> Russian Nuke

The concept of nuclear fission was public knowledge. There were scientific papers in the public domain. The Russians knew how it might work, the challenges were to do with measurement and engineering.

Alien FTL -> Human FTL

Without a theoretical framework, I would say this is more in the bird wing category. It would certainly spur scientists into action, but they would have little idea what avenues to explore.

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