Does the Poisson Bracket Always Equal Zero When Both Observables Start at Zero?

[tut_einstein]

Hello,

If you have two observables f and g both of which start off as: f =0 and g =0 and you evaluate their possion bracket:

{f,g}, will it necessarily be equal to zero?

Also, if just f=0 and g wasn't zero, would {f,g} =0?

Thanks!

 

[Physics Monkey]

What do you think?

Are f ang g identically zero? or zero at the "start" (= initial time?) only? or zero only when some constraint is applied?

 

[tut_einstein]

f and g start out being zero. so because the poisson bracket consists of derivatives of f and g, it need not necessarily be zero even if f and g started off being zero? this is what i would think.

but I'm reading a research paper that seems to suggest that if f anf g start off being zero, then the poisson bracket {f,g} is always zero.
but if only one of them started out being zero, {f,g} needn't be zero. i don't understand why this would be true.

thanks!