Teleportation is when a physical object travels from one place to another without passing through the intervening space.

Teleportation is, at least to a first-order approximation, fictitious. However, when it does appear in fiction, it frequently has some kind of logical underpinning, and it becomes interesting to break down those various models. In fact we come up with a sort of taxonomical tree.

Wormholery

The subject travels through some sort of "exotic matter tunnel", "Einstein-Podolsky-Rosen bridge", "folded space" etc. etc., reaching a distant location through what essentially amounts to a shortcut. Examples: Stargate, Portal.

This is not teleportation. Although it is true that the subject did not travel through most of "the intervening space", there are numerous physical routes between locations in the real universe; a wormhole in the usual sense is nothing more than regular space, highly distorted or contorted or warped or compressed to present one route which is much shorter than all of the others. This is basically just walking.

"Printing"

The subject is physically scanned and dismantled; a signal representing the scanned information is transmitted to the destination, where nanobots assemble a copy from raw matter already present there. Example: Glasshouse. (I think?)

This, also, is not teleportation. The signal (the "transporter buffer", if you will) is not matter; the matter at the source stays where it is and the matter at the target was already there.

Note that this is already completely possible to a relatively low degree of fidelity, all you need to do is hook up a 3D scanner to the internet to a 3D printer. And, oh, make sure you break the original apart with a hammer once you're done.

Accidental duplication is absolutely a potential problem here. Preventing deliberate duplication is also a problem, as there's no serious reason why the transmitted signal can't be stored indefinitely and reused.

If used successfully on a human, this is simultaneously murder and something significantly more legally and ethically complicated; the production of a new living human from thin air, one who is unquestionably not the original. (Plus, the whole "souls" deal.)

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Alright, with those "fools' teleporters" discarded, we can break the remaining models down using a simple question: What happens at the destination?

"Nothing at all": Fraudulent Teleportation

What appears to be, and is popularly sold as, a "teleportation unit" is in fact merely a disintegrator. The receiver/reassembler technology does not exist, or exists but is not in use; smoke, mirrors and cajolery are used to conceal this fact from the victims. "Oh, the destination colony is four and a half light-years from here! You won't get a response for nine years... Unless you feel like following them?" The operator collects the victims' assets. Source.

This, again, is not teleportation.

Crowbar Teleportation

When the teleporter fires, a gap is somehow forced open at the destination and the source volume of matter is inserted. This probably leaves a vacuum at the source, which implodes noisily unless something prevents this. In this model, the crowbar effect is a direct result of using the teleporter — maybe the arriving "packet" of data forces everything out of the way as it descends/unfolds from some higher dimension. (As opposed to some secondary machine opening the gap deliberately to make room. More about that in a second.) Example: can't provide one off-hand; I used something similar in Ra, but that's really nanobot "printing".

Forcing air molecules or even grass or dirt out of the way at the destination probably isn't too much trouble, whereas teleporting into a volume of solid steel is cause for more concern; how much force does this take? How much force does the incoming matter exert to create this space? What happens if it isn't physically possible to force a large enough gap open? Does the source volume get compressed into a smaller space? Does it bounce back to the source somehow?

This has the interesting side-effect of turning teleportation into an effective way to selectively distort the internal structure of physical objects.

Telefragging

All the matter at the destination is annihilated to make room for the incoming matter from the source. Again, a vacuum is left at the source; again, the annihilation effect is considered to be a direct result of applying teleportation technology. There is NOT some secondary device which "clobbers" the target volume to prepare room for what is incoming. Example: Team Fortress 2 (sort of).

This, like the crowbar model, has an interesting side-effect: completely aside from the teleporter, you have just created a working, potentially arbitrarily far-ranged disintegrator. Just teleport fresh air over the top of whatever it is you want gone!

Real, live, working teleportation is, in all its forms, a colossal game-changer. Like time travel, it undermines and destroys fictional universes.

This model possibly violates the law of conservation of mass/energy, unless the matter at the destination is e.g. converted into energy (boom) or perhaps displaced into some other dimension. Or maybe, like the second domino, it is catapulted off to some third destination, where it displaces still more matter off to a fourth destination, and so on?

Splice Teleportation

Nothing happens to the matter at the destination; all of the particles of the source volume are interleaved with the particles at the destination. Example: that one issue of Top Ten (basically). Maybe The Fly?

This is almost certainly fatal for all living creatures, because there shouldn't be air inside all of your cells and organs, let alone solid matter.

The standard method to prevent this is for some kind of secondary machine (remember?) to deliberately open a hard vacuum at the destination prior to the arrival of the source matter.

Without these precautions, a person can end up phased through a wall or a floor or another human. Even if being riddled with unwanted oxygen and nitrogen molecules doesn't kill you — which maybe it won't, I'm no biologist, corrections will be along soon I'm certain — this is very bad news. You're going to lose that part of your body.

Some interpretations of this model hold that the inevitable result is a nuclear explosion, because the source atoms and target atoms end up close enough together for atomic fusion to occur. This... doesn't seem too likely to me? Atomic nuclei make up only a tiny fraction of a whole atom. And even if a few nuclei ended up genuinely interpolated into one another, creating a heavier nucleus and releasing some energy, why would that cause a chain reaction?

Free Exchange Teleportation

The matter at the target destination is sent back to the source. Effectively, using the teleporter near-instantaneously exchanges two (presumably identical) volumes of space.

This is the interesting one.

This model is elegant and effective, simple, non-fatal, plausible... and incidentally implies causality violations. At least one, possibly both of the volumes involved in this "instantaneous" exchange have travelled backwards in time from certain perspectives.

This model can perfectly adequately support quite a lot of really good stories in the same way that Newtonian mechanics can support quite a lot of really good physics, and it's only once you start actively pushing the extreme limits that the causality problem rears its head.

Note that if the target volume doesn't return to its destination instantaneously, then we have to revert to one of the prior models when that target volume does arrive. Something else has to happen: it has to obliterate the destination, interleave with it, or force it aside.

Simple variant: Three Exchange Teleportation: source arrives at target, target volume "disappears", matter from a MYSTERIOUS THIRD PLACE arrives at source.

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Good! What other ways are there to classify teleportation models?

Orientation conservation

It would be easy to conceive of models where the orientation of the teleported volume at the source and target have to match, so that when beaming down from a spaceship to a planet, you usually arrive upside-down or at some stupid angle. Conservation of spin, maybe?

What's less easy is conceiving of a useful in-story reason for this to be the case, which is why you generally don't see it.

Velocity conservation

Slightly more interesting is the question of retained velocity. Without something to match the relative velocities of the source surroundings and target surroundings, teleporting down from a spaceship invariably leaves you hurled into the nearest wall at several kilometres per second. To my knowledge, this never happens in Star Trek, even in that one episode where they were transporting in-flight bullets around. It gets employed to pretty great effect in the Discworld book Interesting Times, though.

Of course, if this isn't a fundamental feature of the science of teleportation, then presumably some secondary machine is helping you out here. Which is to say, modifying the velocity of a group of particles at will. What a useful machine that must be to have!

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Conclusions

Each teleportation model has its own little clutch of dangers, implications, ethical questions, obvious and non-obvious storytelling possibilities. I guess we already knew that. Teleportation can be central to a story or, if it wishes, it can — unbelievably — be entirely incidental.

It also seems that the existence of a working teleporter invariably implies the existence of one or more other fantastically powerful and dangerous technologies — disintegrators, momentum shunts, time travel. These other technologies often arise directly from teleportation science itself but equally often are simply separate, necessary prerequisites before any of this can work.

I wrote this mainly to clarify my own thoughts. I feel as if these are the primary colours. The next step is start mixing stuff up, like real stories do.