What isotope has the shortest half life?

Question:

What isotope has the shortest half life?

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One question at a time please. The question of half-life constantness has been addressed on the site already (see also the "related" question of the link), and redefining the time base would be a "discussion" and as such "not a real question". –  dmckee Jul 25 '12 at 15:17
@dmckee What SE site would you suggest for the redefining time question? Philosophy? (sounds wrong to me but....) –  Event_Horizon Jul 25 '12 at 15:46
All Stack Exchange site that I am familiar with ban "discussion" type questions, so I wouldn't suggest any of them. I'm not, however, intimately familiar with all of the sites so you could read their FAQ and look in their meta posts to figure it out. –  dmckee Jul 25 '12 at 15:50
@Event_Horizon: you could repose as something like "What would be the advantages/disadvantages of changing our time system?" and post it here. If you have specific changes in mind, that would help define the question further. –  AdamRedwine Jul 25 '12 at 18:14

The question is ill-posed.

To begin it should be "*What isotope has the..." and even then the answer is "We don't really know, as there are some we have produced too few times to have an accurate measure for but they sure don't live long." Looking at the low-mass end of the periodic table I find some described in terms of the linewidth---which means really short.

Isotopes with halflives measured in 10s of seconds have been put to use from time to time. And the shortlived low-mass isotopes are useful in calibrating underground neutrino detectors.

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I agree with dmckee in that there are isotopes with extremely short half-lives for which we do not have sufficient numbers to produce a reliable value of half-life. Additionally, for an arbitrarily small half-life, one could imagine an isotope that would theoretically have a half-life less than that (depending on which model you prefer); once you get a half-life below a second or so, the material is essentially useless anyway and it's just an academic question, except potentially in some astrophysics applications.

As to how to redefine time, there have been talks about that for a very long time. During the French revolution they even made clocks representing a 10 hour day with 100 minutes per hour and 100 seconds per minute. Honestly, I kind of like that setup, but it really is quite arbitrary and it is highly unlikely that any alternative time system than the current metric one will be adopted within our lifetime.

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Hey, but a kilosecond is close to 15 minutes, so a Megasecond day would be only a little longer than our day. SciFi for the win! –  dmckee Jul 25 '12 at 15:31
@dmckee: A megasecond is perhaps a _holy_day, composed of almost 12 ordinary days.... –  Arnold Neumaier Jul 25 '12 at 17:31
@ArnoldNeumaier Er...Yeah. You know how it is, trouble with things like basic multiplication. $24*4 \approx 100$ not $1000$. Thanks. –  dmckee Jul 25 '12 at 18:00