Tau Zero

A somewhat hard Science Fiction novel by Poul Anderson, written in 1970. It is based on a 1967 short story "To Outlive Eternity".

The starship Leonora Christine is supposed to carry its 50 colonists to a distant star. The journey should take 33 years, but due to Time Dilation at near-light speed, only 5 years will pass for the crew. Then things go to hell when the ship collides with a nebula (due to the mass of the ship and nebula at that speed, it's like hitting a solid object); the ship's decelerator system is damaged, so they can speed up (and steer) but can't slow down. The ship will keep getting closer and closer to light-speed, reducing the passage of time onboard (their "Tau") to nearly zero. In the time it takes them to repair the damage and stop the ship, billions upon billions of years have passed and the universe is reaching the point of imploding (a "Big Crunch") and starting over with a new Big Bang.

Tau Zero provides examples of:

 * A Father to His Men - Subverted with the captain, who starts off easy going and friendly but becomes more withdrawn from the crew after the disaster.
 * The Chessmaster - Reymont is a mild one. A member of his secret security force theorizes that Reymont's overall plan is to eventually make everyone on the ship either an official or secret deputy, in order to make sure everyone follows the rules and has something to do. After the disaster, he explains his theory on what people see as a Reasonable Authority Figure and makes sure everyone plays their part - he'll bully people into following the rules, and the first officer will be there to listen to people complain about Reymont.
 * Cool Starship - Practically the entire story takes place aboard Leonora Christine. And, let's face it, a starship that can circumvent the end of the universe has a lot going for it.
 * Historical In-Joke - The Swedish Empire, of all possible contenders, is the dominant world power.
 * Generation Ship - Leonora Christine nearly becomes this, when the occupants realize they might be stuck in interstellar space forever without a means of slowing down.
 * Inertial Dampening - At high relativistic velocities, some magical property of Anderson's universe allows for gravity nullification so that the starship can accelerate at 3g while only subjecting its passengers to 1g.
 * Info Dump - Many chapters have sections where Anderson takes a break from the story to explain the theories and math behind what is going on with the plot.
 * Jerk with a Heart of Gold - Reymont is very abrasive and is seen as a bully by most of the crew, but is genuinely interested in maintaining order and keeping the ship safe.
 * Last of His Kind - By the end of the book the universe has died and been reborn, with the crew the only remnants of the old one.
 * Married to the Job - One of the requirements for joining the crew was that you have no family or ties to Earth.
 * Mohs Scale of Sci Fi Hardness - So hard it makes diamonds look like a fluffy pillow. Even the ship's engine is based on a real world theoretical engine that was proposed shortly before Anderson wrote the book.
 * Unfortunately Science Marches On. The Bussard engine which is used in this novel (and many others during the time period) doesn't really work as advertised. In short, the enormous drag of collecting interstellar hydrogen limits the ramjet's speed to about 12% light-speed.
 * There are a few proposed solutions to the drag problem, though they require technology that doesn't currently exist. If it's possible to fuse the interstellar hydrogen while it's rushing through the engine at the same speed it's being gathered -- i.e. without slowing it down -- the drag could be minimized or eliminated. The Bremsstrahlung drag from the gathered hydrogen "swirling down the drain" is another matter, though.
 * Despite the novel's hardness, Anderson still uses Handwavium in a few places. The molecular interpenetration anchors that secure a boat to the docks on Earth are pure fantasy. The scoop field operates by "seizing hydrogen atoms by their dipoles -- no ionization needed," for which no current scientific basis exists. And then there's the Inertial Dampening that allows them to accelerate at upwards of 10g while near the speed of light, while the crew only experiences 1g.
 * That last point isn't really so far-fetched. All you need to do is subject the interior of the spacecraft to a constant, homogeneous force. Diamagnetic levitation, for example, could shave off a lot of the stress on the stuff on the interior without resorting to hypothetical at best gravity manipulation gizmos.
 * Given the strength of the magnetic field required for diamagnetic levitation, let's hope none of the crew members are wearing any metal belt buckles!
 * The recent discovery of Dark Energy pretty much seals the coffin on having a "big crunch" at the end of the universe, like the Big Crunch described in the novel. Even at the time the book was written, though, Anderson's cosmology didn't line up with real cosmology. He described the material in the universe falling inward to a single point in space (which he called a "monobloc"), and Leonora Christine flying around it in a circle. In the real Big Crunch model, though, it isn't the stuff inside the universe that infalls into a single point, spacetime itself contracts to a point. There would be no space outside the "monobloc" to fly around in.
 * Even so, Anderson's handwave in the book still more or less applies: The characters have to hope that a single point is just an abstraction that makes the math easier, and the universe won't actually shrink quite as small as that. It's a rounding error in the size of the universe, but a million-mile rounding error makes all the difference for a spaceship in the vicinity.
 * Multinational Team - The crew is from all over the world.
 * Ramscoop - Leonora Christine is one. It's how they get so close to the speed of light.
 * Really Gets Around - A lot of the crew. Justified in that the situation doesn't really allow for long-term commitments. Many of the crew that fall into this category plan on settling down when they reach their destination.
 * Not that monogamous procreation would be an option for several generations, with fifty individuals trying to form the genetic base for a species.
 * Secret Police - Security officer Reymont has his known deputies, and a number of deputies that no one knows about (including other members of his covert security force). A mild case since there is no real crime aboard the ship, and the security force is just there to keep the peace when tensions get too high.
 * Reasonable Authority Figure - Reymont explains how everyone views their immediate superior as an unreasonable authority figure, but their superior's superior as a Reasonable Authority Figure.
 * Shown Their Work - See the Info Dump entry. Anderson even takes the reader through the mathematical formula for "tau". Unfortunately Anderson is also the only person on Earth who calls it tau - most others use the letter tau for proper time, and would call Anderson's tau 1/γ. Nevertheless, it's a real relativistic quantity.
 * Take a Third Option - Right before breaking the news to the crew that they have no hope, someone comes up with a possible way of stopping the ship.
 * Time Dilation - It keeps increasing, to the point where years are going by for every second the ship experiences. Unfortunately, he does it wrong. Time dilation is a distinctly tricky phenomenon to understand without digging deep in special relativity -- to a spaceship traveling close to the speed of light, the rest of the universe appears to be travelling past while the spaceship is stationary, therefore the spaceship would see time pass normally for itself and time pass more slowly for the rest of the universe. Things would only change (and the effect become prominent) upon deceleration.
 * Wham! Episode - Chapter 7 is when the disaster hits. Before that is was a lot of info on what the ship was doing, introducing the crew, and showing their daily lives.

Tau Zero averts or subverts the following common Science Fiction tropes:
 * Artificial Gravity - The crew experiences gravity due to acceleration, however they board the ship weightless and again when the ship ceases to accelerate while moving between galaxies.
 * Casual Interstellar Travel - Leonora Christine is monstrously expensive, and will take over five years of proper time (over 30 years for the people back on Earth) to carry its 50 inhabitants to Beta Virginis.
 * Creator Provincialism - While Anderson is American, few of the characters are. Nationality doesn't come up much in the book, but it's established that Sweden is the dominant power.
 * Faster-Than-Light Travel - The ship gets infinitely close to the speed of light, but never passes it.
 * Latex Space Suit - While the crew doesn't wear any kind of space suit normally, when bracing for the impact of the nebula, they are all fitted with very bulky suits.
 * Sci-Fi Writers Have No Sense of Scale - Anderson does understand just how big the universe is.
 * Space Clouds - The nebulina they run into, which damages their decelerator, is more rarefied than a laboratory vacuum. It's only because they slam into it at 99.9-some-odd percent of the speed of light that it's dangerous.
 * Space Friction - which allows for infinite acceleration (but not infinite velocity).
 * Space Is an Ocean - none of the sub-tropes come into play.