The folks who track Apple (AAPL) shares closely — and there are loads of them — watched open-jawed Tuesday morning as the stock, which had been climbing steadily all month, went into free fall.

After opening at $290.70, within $3 of its all-time high, the stock dropped $16.7 (5.7%) to $275 in less than three minutes, briefly shaving more than $15 billion off its market capitalization.

Shares recovered somewhat, and by mid-morning had drifted into a $283-$286 trading range, but nobody had come up with an authoritative explanation for what had just happened. Among the theories we’ve seen put forward:

• A wave of programmed profit taking.
• Reaction to the unveiling Monday of Research in Motion’s (RIMM) iPad competitor, the BlackBerry PlayBook.
• A Goldman Sach’s report that the next iPad — thinner and lighter with a mini USB port and built-in camera — won’t arrive before June, later than some had predicted.
• A two-week old rumor that Hewlett-Packard (HPQ) might try to tap Apple COO Tim Cook as its new CEO, the explanation that seems to have found favor among readers of the Wall Street Journal‘s Market Beat blog.

UPDATE: The Cook rumor is taking on a life of its own, as the usual suspects — with nothing more to go on — rush to put it on their sites: Henry Blodget at Silicon Alley Insider, Matt Phillips at Market Beat, Tyler Durdon at Zero Hedge. This is one story Apple PR ought to shoot down quickly, if they can.

UPDATE 2: Apple PR won’t comment on the record, which is their standard operating procedure, but Barrons‘ Eric Savitz reports that Tim Cook told Gleacher & Co.’s Brian Marshall over coffee this  morning that there is nothing to it.

“Tim Cook will not be going to HP, he loves Apple,” Marshall told Savitz that Cook told him.

That’s as good as we can do.

[Follow Philip Elmer-DeWitt on Twitter @philiped]