The answer, I'm afraid, is not very edifying.
We cheat.
We cast at least one verb into the active voice.
One way is to provide an indefinite subject such as "people" or "they" or "we":
What will happen when people start to use metallic elements, &c?
Another is to make the passive subject the active subject of the first verb:
What will happen when metallic elements start to be used, &c?
This is permitted with verbs like start,begin,continue,finish,stop which don't really signify an action but act as semi-auxiliaries to tell you the temporal "shape" of the action verb - what grammarians call its aspect.
Actions and tasks and projects can be "started" or "finished", but we speak of an object being "started" or "finished" only if it is being treated as a task or project: "I started my paper today" means "I started writing my paper".
The basic question is whether sentence C is acceptable, but the motivation behind it is to know whether there are examples of PPs in active sentences that can function as subjects of passive ones.
Well, let me answer the motivation part of your question first -- because it is the easy part! :D
Yes, PPs can function as the subjects of passives. For example:
"We spent [over a year] on this problem." <-- active voice
"[Over a year] was spent on this problem." <-- passive voice
Notice that the PP "over a year" is the direct object in #1, and the subject in #2. (Example #2 was borrowed from H&P's CGEL, page 646 bottom.)
EDIT 06/30/2015:
The beginning of this answer post has an example from H&P's CGEL that uses the phrase "over a year" as subject (in #2 "[Over a year] was spent on this problem"), but unfortunately that phrase might not clearly be a preposition phrase (PP). There could be a reasonable argument that it is a noun phrase (NP).
In light of this, I would like to use the following as examples where unquestionable PPs (e.g. "after Christmas") are functioning as object and subject:
"They won't consider [after Christmas], of course, to be soon enough." <-- active voice with PP as object
"[After Christmas] won't of course be considered to be soon enough." <-- passive voice with PP as subject
Example #3 is borrowed from H&P's CGEL, page 647, [37.ii.c]; and example #4 is borrowed from their text on that same page.
END of EDIT 06/30/2015:
As to your other part of your question, which deals with whether sentence #C is acceptable: the actual sentence is kind of awkward (due to "by you"), but in spite of that awkwardness, I can imagine a reasonable context where it would be acceptable. That is, it could be a context where your testing instructor is standing next to your desk and is explaining to you that you can use your notes during that test:
- C. [Your notes] can be referred to by you whenever you need to. <-- your original example
Notice that your example #C is a prepositional passive of your example #A. Here's a more prototypical example of a prepositional passive:
The trial judge repeatedly referred to [my previous instructor's book]. <-- active voice
[My previous instructor's book] was repeatedly referred to by the trial judge. <-- prepositional passive
CGEL also provides an example of a prepositional passive using the verb "refer (to)":
- Her book was referred to. <-- page 276 [11.b]
ASIDE: Note that the verb "refer (to)" is labeled as a prepositional verb by CGEL, and that its preposition "to" is considered to be a mobile specified preposition. CGEL discusses these topics, including the verb "refer", on pages 274-80.
After re-reading this part of your original post:
He argues that, unlike direct and indirect objects, these PP types of verb complements can't function as subjects of a passive sentence:
- B. * To your notes can be referred by you whenever you need to.
It seems to me that he is arguing that the PP of a prepositional verb can't function as the subject of a corresponding passive. I'm not sure if specific info related to that issue is in CGEL, but it might be. It's that, er, it might take a bit of more work to look into this, er, ... :)
NOTE: H&P's CGEL is the 2002 reference grammar by Huddleston and Pullum (et al.), The Cambridge Grammar of the English Language.
Best Answer
These are all grammatical, but you are correct that they express slight differences in meaning.
Is being is present continuous. This can be used for an action that is still in process, or it can be used for an action that will be performed in the immediate future. So the introduction has either already started or is just about to start.
Is to be is a more formal-sounding construction that is either used in commands, or for future events. It's possible that the speaker is instructing someone on how to introduce the limit, or it could just be a statement that the introduction is planned to start at some future point.
Will be is plain old simple future. In terms of tone, it's in between sentence 1 (casual) and sentence 2 (formal); however it's also slightly more concrete than sentence 2. Technically, sentence 2 is only saying that the introduction is planned to occur in the future; sentence 3 is more definite on the fact that it will be done in the future.
See here for a brief summary of different ways English handles present tense.