What isotope has the shortest half life?

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.

I think it is hyrdrogen-7 which is 4n decay, half life is 21x10^-23 seconds

One of the more important short half life isotopes which actually occurs (we strongly believe) in nature is $^8Be$ which is part of the helium burning, or tri-alpha, process of fusion in older stars. The half life is about 67 as, so after two alphas fuse, a third one must quickly interact, and apparently it does.

This isn't the shortest lived Be, however. $^6Be$, extremely neutron-deficient, has a half life of about 5 zs.

Hydrogen-7 ( about 23x10E-24) has the shortest half life. Hope you got your answer. You can also check out wiki page of half life of elements. .................................