For example, how safe is it to assume that a general reader of SF will have some idea about matter/anti matter reactions, including pair production and annihilation? With Feynman diagrams? How about chaos? Or the way NASA uses near chaotic gravitational environments for navigation and course definition?

If you don't want the explanations to be dull there are a few options. A basic rule, as I see it, is to not have a long textbook like excerpt in your story.

Introduction of a less knowledgeable character learning about these things for him/herself is sometimes a good ploy, but be careful not to make it seem contrived.

Or you could try explaining things in small chunks, interspersed with action, each chunk building on the one before. (This wno't work for all concepts and you do have to make it seem natural.)

In the latest Phobos anthology (edited by OSC) there's a story called RUWATTU8 that has as its major obstacle a damaged space craft with too much mass and not enough fuel to make it into an orbit that will carry them to a safe haven. The author seems to know what he is talking about when it comes to orbits and rocket propulsion, but it could just be that I don't know enough to judge. As a reader, I'm fairly satisfied with broad assertions. If a writer says there's not enough fuel, fine, sure, I don't need to see the math. In the same story, the writer claims that one of his robots is powered by bio-fuel. He eats organic matter, bacteria in his guts digest it, and in doing so energy is released. Again, fine, one sentence is more than enough explanation. However, the same story bothered me with something it didn't explain. In the story its important to keep the biofuel robot alive because it has vital knowledge about how the space craft was damaged. And, since it was a robot, even a biopowered one, I was never given an explanation as to why it was important to keep it alive instead of just backing up its knowledge to a floppy, or burn a cd, or even just telling what it knew to a tape recorder, or, god forbid, just WRITING IT DOWN! Ahem, excuse me while I wipe off the spittle. Now, admittedly, the story in retrospect provides a motive why the robot wouldn't do this, but the fact that it is never even discussed bugged me in what was for all other purposes a terrific little story.

Did I have a point? What was I talking about? Oh, yeah. Readers will accept most of your major SF concepts as simple assertions without detailed explanations. The items that will trip you up are the simple things you might ignore or fudge to make your story work.

--James Maxey

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For example, how safe is it to assume that a general reader of SF will have some idea about matter/anti matter reactions, including pair production and annihilation? With Feynman diagrams? How about chaos? Or the way NASA uses near chaotic gravitational environments for navigation and course definition?

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I don’t know about the true lovers of hard science fiction (I’m just not one of them), but for a general reader I’d agree with James about what people require as far as explanation. Certainly, "pop culture" sorts of science would be pretty safe – matter/antimatter annihilation and basic chaos theory from your list above. Others I can think of would be basic heredity rules and the uncertainty principle.

You run the risk of loosing people if you go more specific and you don’t explain a bit. I can’t say I would know that you are talking about if a story started referring without explanation to Feynman diagrams (and after looking them up online, I understand what they show, but I can’t say I’ve ever seen one, even in the course of getting a science B.S.) and I am not familiar with NASA navigation techniques (although a more serious science fiction reader may be, and it sounds interesting).

Know whether your more advanced stuff is actually contrary to current science, and provide justification within the story for this (for instance, if you have have FTL communication or travel, casually drop a referance that lets us know that it is discovered to be possible in the future).

As James points out, you should also anticipate alternate possible applications of your science that readers are likely to think up (the "why don't they just...?" questions). Put the answers to those challenges in the text as the characters try to find solutions. Even if all you say is, "that would be about as smart as doing X (X being known to all the characters to be an exceptionally dumb idea)."

Most importantly, write the story so it works for you. Where you feel comfortable reading about a postulated technology without technical explainations, write it that way. Where you feel that exposition is clunky and distracts from the story, don't put it in. Where you would feel confused by a posited technology without some pointers, give a few pointers.

For instance, let’s say an accountant is traveling by spaceship to the planet Oberon. Like a travel writer describing a part of the country, you want to give the reader some idea what the ship is like. So you describe the hallways, living spaces, and dining room. Throw in a tour of the engine room (since it will become important later on), but give only the most cursory explanation of the antimatter engine, one suitable for an accountant. Add a couple of minor points if you need to, but have the accountant ignore them. Then go on with the back story.

Suddenly, the reactor shields break, flooding the passenger compartments with radiation. The accountant is the only one who is not immediately incapacitated. Now both the accountant and the reader need to know a lot more about how the engine works. How is the antimatter contained? What are the dangerous particles created by the reaction? How does he shield himself from them? How does the bloody thing really work??

Science and technology is boring only as long as it is not important. When it becomes vital for the character to know about it, then it becomes interesting to him and the reader. So discuss the science when the character needs to know about it.

And only discuss the amount the character needs to know to solve his dilemma--with maybe with a bit more thrown in to make it realistic and provide some red herrings. But don’t load the story down with everything you know. For instance, why exactly would the character need to know about “near chaotic gravitational environments for navigation and course definition?” Is it really important to the plot? Like everything else in writing, if the story doesn’t need it, throw it out.

Critique groups would be good to discover how much the “average” reader knows about a subject. I would venture to guess that you should write to a high school educated reader who has seen some episodes of
Star Trek. But show it around to some members of your potential audience. If it confuses almost all of them, then it probably should be reworked.

In a story I'm working on, I needed faster than light travel (absolutely required for the plot, which involves people travelling from Earth, to a habitable world outside of the solar system, back again, and then returning...). So I made up a system, based around my not-so-in-depth knowledge of the issues of both General and Special relativity that would turn up in this case.

I was aware that it wouldn't be entirely inconsistent for a region of space to exist that has a different scale to 'normal' space.

Obviously it couldn't interface particularly well with normal space because it wouldn't fit in properly. Things attempting to pass into or out of it would get stretched around badly, unless they entered in a controlled manner.

As the story progressed I used this implication... at an early stage I show what kind of things happen when this drive system fails (the ship crashes into a wall between the two pockets of reality, which tears it apart at a subatomic level).

At a later point in the story I use this in a couple of action scenes - at one point I move a ship using this drive across in front of another ship that isn't; the one that isn't is destroyed as it passes through the modified region of space (NB: the drive doesn't have to be faster than light, it just can be...). Later still, two ships end up in the same packet, one chasing the other. This isn't particularly useful for the one doing the chasing as it is suddenly trapped and can't get out...

You can do all kinds of fun things with made up science, as long as you think carefully about the implications of your 'theory'. I think the best example of this is probably Larry Niven's Ringworld, which is a spectacularly good book.

Now I've finished rambling, back to the original topic... I would guess that most (but not all) SF readers understand the absolute basics of matter/anti-matter reactions, and the general principle of chaos theory. Pair production/annihilation is probably a little beyond the scope of the majority, but you'll still find a comfortable proportion who understand it. Feynman diagrams are technical and are right out. I doubt many people who haven't actually studied physics understand what they are. Similarly for any actual applications of chaos theory. Many will understand that it is involved somehow in weather modelling (largely because that is the context it is most often explained in), but won't actually know what any of the implications of that are.

I would say that if you really want to guage what an average SF reader knows, the easiest thing to do is pick up a few SF books that might cover it and see what they assume. As well as real science there are genre conventions, like warp drives or hyperspace or force fields that you can reasonably expect people to understand without an explanation.