Ontological Inertia

"Anything in existence will continue to exist until a sufficient force acts against it."

Ontological Inertia acts as a buffer against changes to the cosmic status quo: You cannot (well, not completely) undo something that already exists.

Writer Fritz Leiber agreed with this trope in his Change War series of stories involving time travel, and devised the "Law of Reality Conservation" as a way to show how things couldn't just un-happen. In that context, it states that you can change the past (in fact he named one of the stories in the series, "Try and Change the Past"), but Fate will force a coincidental event to ensure that history proceeds down its intended path without paradox; every time you try to prevent one historical trend or event, a similar one will take its place in history.

On the other hand, what can happen instead is if you do change something in history that is significant, the time line "fractures", a whole new universe is created at that point, and you and the new event are in a completely different reality with the change you caused. So either you go back to your universe where the change never happened, or you end up going forward to the equivalent time in the new universe with the change that you made propagating from that point. If you don't like the result, you can try to go back and change time again, in which case, guess what, time "fractures" again to compensate for that new incident, and the cycle starts all over again.

Simon Hawke's Time Wars has a similar Law of Historical Inertia, and any change you make will be like a stone dropped in the river of time: History will simply flow round it and, for the most part, end up exactly where it was before (so if you wanted to actually change it, you'd essentially need a really big "stone" to divert the river, the consequences of which could be disaster).

A particular case of You Can't Fight Fate. See also In Spite of a Nail. Contrast with (but not the exact opposite of) No Ontological Inertia. May explain Hitler's Time Travel Exemption Act.

Anime & Manga

 * Used in Higurashi no Naku Koro ni.
 * And in the Kai finale,.
 * A defining trope of Shakugan no Shana. When a person's existence is eaten by a Rinne, they are gone but replaced by a "Torch", who acts as a shock absorber; they look the same, and even have the original's memories. As their flame burns out over time, their presence and impact on the world lessens - they become apathetic and do little, people overlook them - until they disappear completely. When this happens, no one remembers them, and it is as though they never had existed, ever. This happens all the time.

Films

 * Explored in the 2002 version of The Time Machine, with the time traveler's fiancée Emma acting as fate bait.
 * It's a singularly interesting example. If she doesn't die, he doesn't invest the time and effort into creating the time machine. Her death CANNOT be changed, or he CANNOT go back to change. Down to the particular time limit (read: that very night, no matter what he tries). It's not like going back in time and stepping on a mosquito, the flow of time CANNOT continue if she does not die. Paradox, anyone?
 * Of course, all that's really important is that he believes she died. He could go back in time, fake her death and bring her into the present with him.
 * In the first three Terminator movies, good terminator androids, bad terminator androids, and one human are sent back in time to either prevent the upcomming apocalypse or kill off the future leader of the human rebellion. As each successive movie shows, attempts to change the future by either side will inevitably fail as long as there exists a demand for more Terminator movies.

Literature

 * The plot of Terry Pratchett's Thief of Time deals with this kind of idea. When the Procrastinators (which are sort of spindles that regulate the flow of time in Discworld) slip out of control and time starts moving in weird ways, the History Monks attempt to re-regulate everything by dumping the excess time into various places (like the ocean, for example, which is "always big and wet" no matter what the time, and nobody cares if fishermen are suddenly drawing up a catch of weird fish that they've only ever seen as fossils). In fact, the entire history of the Discworld
 * To clarify, even the History Monks aren't sure why the Disc's history seems to keep the same general shape in spite of various things messing with time. Some ideas include the Theory of Narrative Causality (the Trope Namer) and the Historical Imperative, which appears to be equal parts this trope and a pun on Kant.
 * The Discworld books also bring up the alrady-discussed concept of "steam engine time", which shows that human society tends to avert No Plans No Prototypes No Backup (i.e., if Thomas Savery hadn't invented the steam pump, one of his contemporaries who were working on the same subject would have patented roughly the same thing, and history might have been back on track just in time for James Watt to make the engine efficient enough to use portably, and no boiling-over tea kettle need be involved).
 * Played and justified in exactly so many words in Terry Pratchett's Mort. As Death's assistant, Mort attempts to, changing the predestined course of history. Historical inertia pushes back,.
 * In To Say Nothing of the Dog by Connie Willis, it is discovered that any change that someone tries to make in the past will be automatically rectified by the time-stream. For instance, if a bucket is removed from a historically significant bucket brigade, it will be replaced with a convenient barrel. By the end of the book, it turns out that
 * More than that, sometimes the time stream simply won't allow changes to be made. People who tried to go back and take out Hitler were deposited far enough away (time-wise) that they couldn't do it.
 * In Poul Anderson's Time Patrol series of short stories/novellas, there is a principle of "temporal inertia" which acts like this. It is very difficult to make substantial changes to the time-line, since most likely subsequent events will coalesce in a way that maintains the overall historical status quo. However, the flip side of the principle is that once changes are made to the time-line, it is similarly very difficult to undo those changes and return the time-line to its original status.

Live Action TV

 * Lost plays with this in Season 5. For example, when handling a nuke, Daniel assures them that it can't explode because the island still exists in the future they came from.
 * The Legendary Adventures Of Hercules had an episode where they were worried about how their time travel might affect the present, but Hercules assured them that Time would correct itself, so nothing would change.
 * In the final episode of Kamen Rider Decade, when Big Bad Apollo Geist is defeated, his forcible merger and destruction of the multiverse continues unabated. In fact, if anything it actually speeds up. This leads to Decade receiving a What the Hell, Hero? speech from his predecessors.

Tabletop Games

 * The Dragonlance Saga even uses the stone in a time-stream example. You cannot do anything to severely change the future, unless you are a kender, gnome, or a Dwarf.

Video Games
"But supposing you toss a coin enough times. Supposing one day, it lands on its edge..."
 * Spoilers for the Infocom Interactive Fiction game Trinity:
 * Mentioned in Shadow of Destiny (aka Shadow of Memories).
 * The conclusion of Final Fantasy I is a version of this:
 * In Command & Conquer: Red Alert, Einstein tries to erase Hitler from history to prevent World War II. He succeeds and an even worse war between Russia and the Allies takes the place of World War II.
 * It's implied that the Einstein that did the erasing will not see any changes. All he has done is create a divergent timeline which exists simultaneously with ours. Otherwise, he wouldn't be able to go back to his lab in 1946.
 * Ontological Inertia is such a strong force in the Legacy of Kain series that the titular vampire spends most of his immortal life looking for a way to thwart it at a key point in his past. This is the origin of Kain's memorable "edge of the coin" speech:

Western Animation

 * Strangely used in Code Lyoko. Although there's a Reset Button that the heroes can use to travel into the immediate past and undo most of the damage the Big Bad causes, if anyone dies before they use it, they'll stay dead, even after the past is changed; their death still possesses ontological inertia in the new time-line. Presumably they'd just drop dead from no apparent cause, but since the heroes never allowed anyone to die in the course of their adventures, the viewer never really saw how it'd work.
 * Additionally, the heroes, (and only the heroes, even if someone else were brought into the fold of this whole "XANA" shenanigan for this particular problem of the week) would remember the events of the erased day, presumably so someone would know the world had been saved to begin with.
 * One of the flashback episodes demonstrates that you retain your memory if you've been scanned into the supercomputer.