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2

Just to complete Hritik Narayan's answer: the lifetime of an unstable particle is by definition the average time before it decays in its rest-frame. So whatever the frame used, the lifetime remains the same. Now, as already mentioned, what you measure experimentally does depend on the frame and thus on the velocity of the particle. You do have to correct for ...

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One thing that you have to remember is that the laws of physics are the same in all reference frames. Lets say there exists some particle $A$ which is stable for $t_o$ seconds when it is at rest. From its own reference frame, its lifetime HAS to be $t_o$ seconds regardless of the velocity with which it travels, because the laws of physics which apply to it ...

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If the pencil were at absolute zero it would necessarily assume its lowest energy state, which is not the vertical state. If the pencil were modeled as a quantum rotor with an infinite potential barrier covering half its solid angle space (i.e. the table) then there are certainly excited but stable states where the pencil remains in a more or less vertical ...

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GIVE IT A SPIN, with the max possible rpm for such massive object. Do the experiment at the ISS, well above Earth surface. Unconstrain the problem from the 'surface' issue. Remove the 'surface' below the atom tip -- where is bellow without gravity? -- or approximate the surface as much as you can but without contact (the atom's electronic cloud prevent this, ...

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