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In the Star Trek: Voyager episode The Omega Directive, Seven of Nine says that the Borg synthesized a molecule which was "kept [] stable for one trillionth of a nanosecond before it destabilized". That's $10^{-21}$ seconds, which is pretty brief.

Of course the point of that part of the script is to illustrate how unstable the molecule in question is. But this got me thinking: in our world, for how long must a molecule remain stable to be considered "stable"? Is there a generally applicable time limit or range (even order of magnitude)?

I did find Lifetimes of stable particles, but both the question and accepted answer talks about fundamental particles, whereas I am considering molecules.

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Useful vocabulary: "metastable". That said the speed of light delay across a molecule is on the attosecond ($10^{-18}\text{ s}$) scale, so it would be absurd to call anything that happens faster than that "stable" in a molecular context. Frankly, you should have expected that out of the Star Trek franchise (which has never bothered itself with good physics). – dmckee Apr 13 '13 at 22:58
@dmckee I'm sure the Borg used some sort of FTL sensors to observe what was going on, and there's a couple of really odd inconsistencies within that episode (and that's not the only episode that has such). That said, that part of the question was more background to my wondering than anything else; maybe it could have been left out. – Michael Kjörling Apr 13 '13 at 23:04
"I'm sure the Borg used some sort of FTL sensors" I rest my case, don't I? – dmckee Apr 13 '13 at 23:06
@dmckee I'm not saying that's "good physics" according to our current understanding of the laws of physics, but the in-universe quote is explainable (if you don't mind my using that word in this context) with in-universe physics and technology. Star Trek is entertainment, not hard sci-fi. – Michael Kjörling Apr 13 '13 at 23:10
In nuclear physics, "stable" is used in an absolute sense. If the half-life has any finite value, it's not considered stable. I don't know if this is also true in molecular physics. – Ben Crowell Apr 14 '13 at 0:30
up vote 5 down vote accepted

Molecules vibrate with frequencies in the range 10$^{12}$ to 10$^{14}$Hz. Although I don't know of any strict definition, I would take the view that a molecule must hold together for a few vibrations otherwise what you have is a collision not a molecule. That means the lifetime must be greater than 10$^{-14}$ to 10$^{-12}$ seconds, depending on the molecule.

To take Seven of Nine's claim, a vibrational period of 10$^{-21}$ seconds, i.e. $\nu$ = 10$^{21}$Hz, is an energy of around 4Mev, and this is far greater than any characteristic energy of molecules. It's more like the binding energy of nuclei. Perhaps Seven of Nine meant that they synthesised a new element that was stable for 10$^{-21}$ seconds.

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Absent an actual definition of "stable", this sounds to be about as close to a real answer as one can get. Thank you! As for the claim, if you have a few minutes and are curious I suggest heading on over to Memory Alpha for an episode summary. In short, yes, the molecule is presented in dialog as "the most powerful substance known to exist". – Michael Kjörling Apr 15 '13 at 7:25

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