The term "hard" science fiction is used for sf that corresponds to our currently understood science models of the universe. The exact definition of what counts as hard science fiction is too subjective for this site. What are the common ways of determining relative hardness?
There are some elements that immediately disqualify a work as hard SF.
- telepathy, telekinesis, other psychic stuff. Perhaps this could be given some kind of pseudo-scientific explanation, and therefore interesting constraints, but too often this just turns into a my-specialness vs your-specialness kind of thing, and seems completely arbitrary.
- magic, not the sufficiently advanced technology kind, but the hocus-pocus kind. this is just completely too unconstrained, anything can happen, it has to be fantasy.
- time travel - specifically, going backwards in time. this is one of those things that allows anything to happen, with no semblance of any rules. Note however, "travel" forward in time is fine, as relativity allows you to slow your clock relative to the universe by chasing after light for a while.
But then there are some other elements that, depending on whether the author tries to maintain consistency, could be hard SF or might not be. For example
- FTL - looks impossible now. probably is impossible. but you can suspend disbelief (somewhat) if there are rules such as "only works in relatively flat space between stars"
- macroscale teleportation - again, sort of plausible if it only works between locations that have the same gravitational potential and relative motion.
As with any kind of fiction, there has to be a willingness of the reader to set aside disbelief. With SF, it seems that some works require us to set more science than others, and the less you have to do this, the 'harder' the SF. But even fantastical elements like FTL can work, so long as you don't have to set aside the 'feeling of science'.
Wikipedia actually has quite a good definition:
Hard science fiction, or "hard SF", is characterized by rigorous attention to accurate detail in quantitative sciences, especially physics, astrophysics, and chemistry, or on accurately depicting worlds that more advanced technology may make possible.
It's worth noting that some hard SF takes liberties with science, such as faster-than-light travel; the term "hard" can be a little blurry.
I think it helps to look at this as part of the same question as to how fantasy and sci-fi can be differentiated. A story with spaceships can be fantasy, and a story with putative magic can be hard sci-fi.
This broader division is determined (in my mind, at least), by who is the master. In science fiction, people (be they human or whatever) are the masters of the technology; in fantasy, the people have no understanding of the technology, they are merely users. In other words, fantasy has artisans (e.g., wizards) making use of a poorly-understood phenomenon; sci-fi has scientists learning how the world works, and devising technology to take advantage of it.
In this context, some things that look like sci-fi are really fantasy. The latter Star Wars movies (episodes 1-3) are like this: their focus on midi-chlorians is no different from a wizard with magic dust. Frederic Pohl's Gateway novels are similar: the blind use of alien artifacts is no different from Bilbo Baggins finding that the ring makes him invisible. This is why the setting for so many fantasy stories is a decaying, once-great society: in ages past the people understood their creation, but the knowledge has been lost.
Anyway, hard sci-fi is necessarily science fiction, which means that there's a systematic, scientific understanding of technology evinced in the story. But the theme or setting isn't what makes it hard or soft.
In soft sci-fi, the technological aspects are simply a backdrop, something that the story takes for granted without delving into. The space opera sub-genre is almost always soft sci-fi, because the story is all about the action. The ray guns, spaceships, and the like simply exist. There's no textual support for the actual science involved.
By contrast, in hard sci-fi, the science is an important aspect of the text. The author actively considers the science behind the technological aspects. For example, Vinge's treatment of the ubiquitous networking in A Deepness in the Sky is clearly hard.
While I'm only half way through the book, I'm actually inclined to label Sanderson's Mistborn as hard sci-fi, because of the way he fleshes out the abilities of allomancers. This might seem odd, because the author really makes it look like magic. But the way they invoke their powers, the limitations on its usage and strict adherence to the framework of physical laws that we the readers are already familiar with, strike me as less magical, and more of an empirically-discovered science, and thus some form of sci-fi rather than fantasy. And the fact that it's a big part of the story (through Vin learning about her powers) makes it, more specifically, hard sci-fi.
So, to sum up a long-winded answer:
- Hard sci-fi is science fiction in which the scientific aspects are explicitly addressed as part of the story.
- Soft sci-fi just has a high-tech background without giving us any understanding of how or why it works.
- In fantasy there is little or no understanding of the "magic", even by those inside the story (let alone us readers).
I've been reading sci-fi since I was a young lad in the 50s, and I've enjoyed all of it. Hard, soft, and fuzzy as well. If it's well-written, why quantify?
I remember being in a bookstore and several people were discussing various authors. I mentioned that I liked Harlan Ellison. One fellow actually sneered..."I don't read SOFT science-fiction!" Well, good for you, Skippy. I do. I like Jack Vance and Neil Gaiman and China Miehville along with Larry Niven and Greg Bear and those sorts of folks as well. It's a rare ability to combine cutting-edge science with a good, entertaining story.
This is sort of halfway between a comment and an answer:
The Mohs scale of hardness for minerals has inspired the addictive TV Tropes website to have a page called the Mohs Scale of Science Fiction Hardness numbering various works from 1 to 6 according to the hardness of their science:
Science in Genre Only: The work is unambiguously set in the literary genre of Science Fiction, but scientific it is not. Applied Phlebotinum is the rule of the day, often of the Nonsensoleum kind, Green Rocks gain New Powers as the Plot Demands, and both Bellisario's Maxim and the MST3K Mantra apply. Works like Futurama, Star Wars, Tengen Toppa Gurren Lagann, The DC and Marvel universes, and The Hitchhiker's Guide to the Galaxy fall in this class.
World of Phlebotinum: The universe is full of Applied Phlebotinum with more to be found behind every star, but the Phlebotinum is dealt with in a fairly consistent fashion despite its lack of correspondence with reality and, in-world, is considered to lie within the realm of scientific inquiry. Works like E. E. “Doc” Smith's Lensman series, Neon Genesis Evangelion, Star Trek: The Original Series, and StarCraft fall in this category.
A subclass of this class (arguably 2.5 on the scale) contains stories that are generally sound, except the physics aren't our own. Plot aside, they are often a philosophical exploration of a concept no longer considered true (such as Aristotelian physics), or never considered true in the first place (e.g. two spatial dimensions instead of three, like Flatland). Some of Arthur C. Clarke's stories fall here. However, given the overlap with fantasy, it can prove tricky to even classify a story as SF.
Physics Plus: Stories in this class once again have multiple forms of Applied Phlebotinum, but in contrast to the prior class, the author aims to justify these creations with real and invented natural laws — and these creations and others from the same laws will turn up again and again in new contexts. Works like Schlock Mercenary, David Weber's Honor Harrington series, David Brin's Uplift series, and Battlestar Galactica (2003) fall in this class. Most Real Robot shows fall somewhere between Classes 2 and 3.
One Big Lie: Authors of works in this class invent one (or, at most, a very few) counterfactual physical laws and writes a story that explores the implications of these principles. James Blish's Cities in Flight stories fall squarely into this category, courtesy of the "Dirac Equations" leading to the "spindizzy motor" and instantaneous communication. Most works in Alan Dean Foster's Humanx Commonwealth series, the Ad Astra board games and Robert A. Heinlein's Farnham's Freehold fall in this category, as do many of Vernor Vinge's books.
This class also includes a subclass (4.5 on the scale) we call One Small Fib, containing stories that include only a single counterfactual device (often FTL Travel), but for which the device is not a major element of the plot. Many Hal Clement novels (e.g. Mission of Gravity, Close to Critical) and Freefall fall within the subclass.
Speculative Science: Stories in which there is no "big lie" — the science of the tale is (or was) genuine speculative science or engineering, and the goal of the author to make as few errors with respect to known fact as possible. The first two books in Robert L. Forward's Rocheworld series and Robert A. Heinlein's The Moon Is a Harsh Mistress fall in this class.
A subclass of this (5.5 on the scale) is Futurology: stories which function almost like a prediction of the future, extrapolating from current technology rather than inventing major new technologies or discoveries. (Naturally, Zeerust is common in older entries.) Gattaca, Planetes, Transhuman Space and the more Speculative Fiction works of Jules Verne fall in this subclass.
Real Life (aka Fiction in Genre Only): A Shared Universe which spawned its own genre, known as "Non-Fiction". Despite the various problems noted at Reality Is Unrealistic, it is almost universally agreed that there is no other universe known so thoroughly worked out from established scientific principles. The Apollo Program, World War II, and Woodstock fall in this class.
While genre distinctions are in general not susceptible to rigid definition, there is a high degree of agreement on what science fiction is "hard" and what is not. Some criteria that seem useful:
Hard science fiction respects known facts about the universe. Typically readers will allow a small and fixed set of variations to the laws of physics in order to allow a plot to proceed. These should be known early on ("since Dr. Subhramian's discovery of the hyperphototachyonic drive, humanity had been able to visit and colonize neighboring stars") and should work on reasonable and fixed rules (an FTL drive might require some rare mineral or some particular computations, but it should not require the blood of a virgin). Science fiction that introduces massive variations (ie, magic) or changes the rules at whim is typically not seen as hard science fiction. (though it can still be excellent SF - for example, Philip Dick does not generally concern himself with consistency, but nobody doubts his importance to the field)
Hard science fiction respects engineering. Once we know what the rules of the universe are, structures built in the world should not surprise an engineer. Space ships should not have wings, unless they're expected to operate in atmosphere, and in that case, you got some 'splaining to do. Science fiction which disregards engineering considerations at whim is typically not regarded as hard science fiction, nor is "science fiction" which requires massive retcon work to bring its engineering into conformance. (I'm looking at you, Star Wars)
Hard science fiction typically is concerned more with grand arcs and less with the fates of individual characters. (though obviously writers of hard science fiction can and do use the fates of individual characters to engage readers) As a corollary, hard science fiction is usually not "about" the hard science, any more than computer science is "about" computers or astronomy is about telescopes. Classic examples would include Heinlein (who mostly wrote about political systems, but got the physics right), Clarke (lots of psychology and sociology, but also got the physics right), Asimov (likewise psychology and sociology, but handwaved the physics so charmingly that we give him a pass).
Hard Science Fiction can consist of the following
Space Opera sized plot and scope.
FTL drives of different sorts.
Giant Spaceships (different classes like Gangster class)
Collapsing wave function
Super advanced technology
Weird languages (that are invented as weapons)
Super exotic weapons (blackhole destroyers, hell class weapons, sentient inhibitors)
Exotic current, retired, ascended super intelligent races of Aliens.
Unknown quantum effects.
Unimaginably vast distances travelled quickly.
Adapted humans to live places other than Earth, like the Sun.
This list is incomplete. Bob.