The most correct form is "We are no longer in the 20th century". But saying "We are no more in the 20th century" or "We are in the 20th century no more" is also correct? Is it possible to use "no more" with periods of time in formal, semi-formal and informal speech as well as writing?
no more can have the same the meaning as no longer and, up until 1840, it was more widely used. Here is a typical example:
He instantly determined to be no more a slave. - The works of Hannah More, Hannah More, 1804
We are no more in the 20th century.
This sentence is therefore grammatically correct, though dated. There is a further problem: no more is often used in modern formal writing and rhetoric in the set phrase no more ... than. In your sentence, we expect a than-clause, and it doesn't come. Here is an example:
He is no more a simple soul than Tolstoy's Levin is a peasant. -Modern poetry studies, 1974
We are in the 20th century no more.
This avoids the expectation of a than-clause, but sounds to me like anastrophe (literary inversion).
For modern formal writing, no longer is perfectly clear, and would be my preferred option.
We are no longer in the 20th century.
For informal speech, you would be more likely to use any more (UK) or anymore (US):
We aren't in the 20th century any more.
Love don't live here anymore - Song lyrics, Rose Royce, 1974
Instead of your "We are no more in the 20th century" I would suggest we should use the sentence
"We are not in the 20th century any more" (the 20th century has ended)
as an alternative to
"We are no longer in the 20th century" (we are not in this time period)
Why we may be tempted to use " more" in the way you describe is because of the similarities with "any more" (us anymore) meaning any longer and the use of More to form the comparative of many adjectives and adverbs: In the second case we would need something to compare. The comparison maybe obvious or implied
He finds physics far/much more difficult than other science subjects.
She couldn't be more beautiful
Therefore the following sentence would be correct.
"We are no more in the 20th century than.."
However we are actually substituting more for longer. This we cannot do, more means greater or larger not longer. It can mean increasingly but again this makes no sense in this context.
What we really need to do is rearrange the sentence.
"We are not in the 20th century any more"
To clarify my point
Longer is related to time
we no longer have eggs
at this time and maybe forever (who knows) we have no eggs.
More is related to quantity, (increasingly, larger or extra number or amount).
we have no more eggs
We do not have any eggs, the eggs have stopped, egg production has ended.
In essence the result is the same No eggs but the meaning is very different
anymore C.E.D. adverb [ not gradable ] US (used esp. in negative statements) any longer: (UK usually any more)
more; C.E.D. determiner, pronoun, adverb
a larger or extra number or amount:
used to form the comparative of many adjectives and adverbs:
It is not possible to use "no more" with periods of time in formal, semi-formal and informal speech as well as writing? In this relation we would use, if needed, the alternative
any more or anymore (us)
anymore adverb;(also any more):C.E.D.(used esp. in negative statements) any longer:
The original form in the question was
"We are no longer in the 20th century".
no longer (also not any longer) C.E.D. ; in the past but not now:
yes we can use any more instead of no longer
It is not advisable to use the form
"We are no more in the 20th century".
Why! try it in shortened form.
"We are no more"
This means we have ceased, stopped, it is not related to time it is an action "Stop". In fact it is already established on this site that no more means cessation. (He is no more, means he is deceased).
This usage of no more to mean cease, stop or end, has be documented since Shakespearian times (sigh no-more) and remains so today.
Shakespeare obviously did not mean "Sigh in the past but not now ladies",
What he meant was "Cease/stop your sighing ladies",
However his version is so much better but alas we art nay longeth'r in the 16th century.
Sigheth nay m're ladies, sigheth nay m're, men w're deceiv'rs ev'r, one foot in flote and one on sh're,