A group of people displaced from their own world just so happen to have the knowhow to not only recreate their society's general level of technology, but to begin the march of innovation with little to no pause.
Basically, even cast into a society that's roughly at the equivalent of the Bronze Age, a group of a hundred or so usually randomly-assembled people (often military personnel) will be able to haul their new allies right into the midst of the Industrial Revolution within a year or two.
A sort of supertrope of Bamboo Technology... while that trope relies on using local, low-tech materials to roughly approximate "modern" inventions, when Stranded With Edison, a group will manage to make themselves the real thing... and possibly make it better.
See also Giving Radio to the Romans.
- Implied at the end of the movie The Time Machine (1960). When Wells leaves after telling his friend Filby about his adventures, he takes three books from his vast library. Filby asks the housekeeper (and the audience), "If you were going to start civilization over again, which three books would you choose?"
- This is a common essay question in English Lit class.
- Mark Twain's A Connecticut Yankee in King Arthur's Court (1889). After time traveling back to the 6th century, Hank Morgan uses his knowledge of manufacturing to build hidden factories that produce modern (1879) tools and weapons, thus industrializing King Arthur's kingdom. Justified in that Hank, while something of a drunk and a troublemaker, complains about losing his job as what would now be referred to as an industrial metallurgist and machinist. It is quite realistic that someone with that background and access to early iron-age materials and equipment would not find it terribly hard to produce steam-age technology and reproduce the relatively well-known and simple recipe for gunpowder; especially since he was transported to one of the regions where said technology originated, so he wouldn't exactly be short on raw materials or craftsmen with vaguely relevant expertise.
- In the Ciaphas Cain novel Death or Glory, their makeshift convoy/militia (made up from the rescued survivors/slaves of a town looted by orks) has just enough specialists to survive: a tracker to help them find water and supply dumps, a vet to serve as an impromptu doctor a technopriest to keep their vehicles running and enough former police, gang members and PDF troops to form a militia and a former not-so-Obstructive Bureaucrat to manage their supplies.
- Discussed, but averted, in Mostly Harmless: when Arthur Dent is stranded on a planet with an Iron Age culture, he initially thinks he can bring them civilization, before realizing that he doesn't actually know how to make anything... except sandwiches. A few months later, his adopted people are hailing him as their Sandwich Maker.
- In Destroyermen, the crew of two US naval destroyers just happens to have some engineers who have worked in oil fields so that they can drill new oil wells for fuel (there's also a geologist on board, who can tell them where to drill). Other experts are in abundance (pilots that can design planes), to the point that know-how isn't usually a problem, just materials and facilities. Only once or twice does someone mention they don't actually know how to make something they need, but it's sort of shrugged off with "We'll figure something out."
- In the first novel, the crew of the Walker wants to capture a Grik ship to gather intel. Since 20th-century destroyers aren't designed for boarding actions, The Captain uses his interest in ancient naval warfare to get the Lemurians to build him a corvus, a bridge of sorts designed by Romans to drop on the enemy ship's deck and embed itself there with a spike, allowing boarders to cross. It works at first, but the corvus breaks under the strain, as the Lemurians make it out of bamboo.
- In the Prince Roger series, the Bronze Barbarians do have the basic knowledge required to teach their allies how to manufacture moderately advanced guns. Semi-justified in that the characters are all military personnel who were selected in part for having potentially useful skills outside the standard ones required for their post and that while they know the theory they often have to rely on native expertise for the actual details. Additionally several of them have skills that are never actually needed (for example one is a reformed carjacker and another knows how to knit).
- The 1632 series involves a Mysterious Event teleporting a self-sufficient town from West Virginia into 17th century Germany. The town has a library and a school, so plenty of books, a coal power plant with fairly large stocks of fuel from the parts of the nearby coal mine that came with them, and oil wells. With advanced knowledge, they are able to make down-leveled for the 21st century, but up-level for 17th century, gear.
- Jules Verne's The Mysterious Island is pretty much entirely about this trope. In the book, a group of five Civil War era people, headed by an incredibly knowledgeable engineer, are trapped on an island in the Pacific. Within 4 years, they manage to re-create (at a small level) most aspects of 1860s technology while trapped on a deserted island, with (almost) no outside help. By the end of the book, they even manage to have a telegraph set up on the island.
- Done in Axis of Time, where there are hundreds (if not thousands) of "uptimers" (i.e. people from the 21st century) ending up in the middle of World War II. A number of them have hobbies that help in designing weapons and machines advanced for the time (but primitive for the uptimers). In fact, the uptimers are not able to replicate their own level of technology but merely upgrade what the 'temps already have with something from a few decades down the line. Instead of giving them a version of their own assault rifle that fires ceramic rounds and uses advanced electronic scopes linked with the HUD on the helmet, they instead make a version of the AK-47 fitted with an underslung grenade launcher. It also helps that they have computers aboard the ships with useful information in the cache (i.e. whatever people were downloading from the 'Net at the time of the Transition). Many people also get their hands on flexible tablets, but those cannot be replicated.
- Portuguese sailors and traders who got stranded in Japan by a stroke of bad luck in the early 1500s brought primitive firearms with them. In less than a generation, the Japanese used their skills in metalworking to mass produce and to improve the primitive matchlock musket, such that some were nigh-impervious to rain. While two European empires fought with armies of roughly 20,000 men each at Rocroi in 1643, 50 years before that Japan could project over the sea to Korea 160,000 men, of which over 40,000 were trained musketmen.