Let me tell you about a word thats time has come.
First, though, hands up: Did that sentence bother you? If so, why?
Never mind. I know why. For the benefit of those it didn't bother — and there are more and more of you out there — it's this: "Thats is not a word!"
You probably assume that the word chosen should have been whose. But here's the deal: English has a person/non-person distinction in pronouns.
We have who versus what. We have he and she versus it. They is, of course, plural for non-persons and persons alike, but people who use they in the singular (Each one should do what they want) use it just for persons and keep it for non-persons.
For relative pronouns, on the one side we have "the person whom you met" and "the person who is coming;" on the other side, we have "the thing that you met" and "the thing, which you met." Some people can get very exercised about making sure that people don't write "the person that you met" because they want to make sure that and which are for things and who and whom are for people.
But. But! There is no non-person relative possessive pronoun. Not in standard English, anyway. It's "a person whose time has come" and "a thing whose time has come" — or "a thing for which the time has come," or "a thing the time has come for."
Perhaps unsurprisingly, this does not map out well for everyone. Quite a few people want to make the same kind of person/non-person distinction there as well. They write a thing that's time has come or a thing thats time has come.
They will prevail.
I'm not here to say you have to use thats as a relative possessive pronoun. I'm not even here to say you have to like it. But I am here to say it's inevitable. It's not going to be standard English this year or this decade. Maybe not even this century, though maybe it will. Changes of this type can take a long time. We'll see. But I predict that it will prevail. It's a word thats time is coming.
Here are the main objections to it, and why it will overcome them — or already has.
Whose works fine
It's not wrong to use whose to refer to inanimate objects. It's not! Erin Brenner, writing at Visual Thesaurus, has given a nice, tidy explanation of why it's historically well-founded, and she shows that experts have been explaining that for decades. But the very fact that they have to explain it over and over shows that it's not intuitive. It's an exception to an internalized distinction.
Unless it's not. Toss in the thats and it's all tidy. Think of thats as the Higgs boson of English relative pronouns. You know the Higgs boson — the subatomic particle whose existence is necessary to make the whole model work neatly. (Is that whose OK with you? Does it make the boson a person? Your results may vary.)
You can rephrase to avoid it
If you don't like the non-person whose, you can always rephrase: An idea for which the time has come. The subatomic particle the existence of which is necessary… um, or The subatomic particle such that its existence is necessary… hmm. All so wordy and ugly. Did your English teacher tell you not to load your prose up with unnecessary words and circumlocutions? Just because we can use more words doesn't mean we should. Perhaps thats is a necessary word that will avoid a whole bunch of unnecessary words.
It has no historical basis
It's true that if we bring in thats it will be an innovation. But we might help justify it by considering it atavistic. Linguist Jonathan Owen gives a good run-down of the historical development of our relative and interrogative pronouns. In Old English, the demonstrative that had a full set of forms, corresponding to modern he/she/it/they and him/her/it/them and his/her/its/their, that were also used as relative pronouns. There were equivalents of thats: þæs, þære, þara (the þ equals th). Over time the relative pronouns shifted to be based on the interrogative words — who and what and which. These had possessive forms too. But English gradually lost nearly all of its inflectional endings; its noun case system got stripped down. The only surviving relative pronoun was whose, and for centuries it covered singular and plural, all genders, non-persons as well as persons.
Well, its absolute reign may be ending. It's looking like it's going to have to share the throne. The person/non-person distinction has become important enough to make a difference.
No one is using it
This is typically presented as the capper when thats comes up. The thing is, though, people are using it. They're still in the minority, but they're there and have been for some time. In Google Books you can find "an idea that's time has come" in magazines and government records starting in the 1970s. In 1993 a contributor to the Linguist List declared thats prevalent in the UK (probably an overstatement). In 1995, Aimo Seppänen and Göran Kjellmer, two linguists at the University of Gothenburg, published a paper in which they noted its use in regional dialects and found that it was increasingly considered acceptable by some speakers of standard English.
More recently, in 2011, linguist Neal Whitman observed not only that his son used it without awareness that there was an issue, but that contributors to a discussion on the American Dialect Society email list found plenty of uses of it — and one of them even declared a personal preference for it. Last year, language blogger Stan Carey took note of it and doubted it was used enough to prevail, but he received responses indicating it was already fairly common. Earlier this year on Language Log, a post by Mark Liberman drew quite a few comments attesting to its use.
So people are using it, and the evidence suggests that its use is increasing. If, as Neal Whitman's experience suggests, younger users are tending to use that's more, it will become more widely accepted as the older users die out and the younger users pass it on. That's one of the main ways language change works. As Whitman observed, he and his son are speaking different languages; he didn't need to mention that his son's is likely to outlast his.
How about which's?
Some people use which's or even plain which for the relative possessive. But which's is not popular, probably at least in part because it's awkward to say, and which is less clear: an idea which time has come is like an idea that time has come, which could be read to mean that the idea is that time has arrived. I therefore think it is less likely to prevail. If you think either of these is uglier than thats, you can do your part to help forestall them by using thats.
Well, hey, it's probably going to win anyway. You might as well be pragmatic about it.
Does this mean that I'm going to start using thats? Hmm, no, not yet. It's not effective to use words that upset or distract or confuse many readers (unless that's the point of the article). But I may, in a few years, find myself working on content for a younger generation and going with thats precisely because it will be the least obtrusive choice.
One more thing: You may have noticed that I am preferring the version without an apostrophe, thats rather than that's. This is because possessive pronouns don't have apostrophes, even the ones with an s. Properly, it's his, hers, yours, theirs, whose, though many people get those wrong. We will know that thats has truly gained its place when the pedants correct people not for using it but for spelling it with an apostrophe.