Question

Decoherence times can be estimated and are inverse functions of mass. Since there are no upper bounds on mass, can decoherence time be shorter than Planck time?

Answer 1

of course, the decoherence time may be - and quite often is - much shorter than the Planck time. There exists no law saying that "all quantities with the units of seconds have to be longer than the Planck time". The only genuine limitation is that "if you try to measure the timing of an event with the precision better than the Planck time, you will fail." This is an entirely different thing.

The decoherence time is the (approximate) time after which the off-diagonal elements of the density matrix between two macroscopically "different" states of a sufficiently macroscopic system decrease to a negligible fraction of its initial value. The processes that drive decoherence - that make the off-diagonal elements drop - are results of interactions of the macroscopic object with the environment. The more strongly the object interacts with the environment and the higher number of environmental degrees of freedom we are forgetting - i.e. tracing over - the more quickly the decoherence proceeds.

Of course that if you talk about Schr