  Everyday experience supports the existence of physical properties independent
of observation in strong contrast to the predictions of quantum theory. In
particular, existence of physical properties that are independent of the
measurement context is prohibited for certain quantum systems. This property is
known as contextuality. This paper studies whether the process of decay in
space-time generally destroys the ability of revealing contextuality. We find
that in the most general situation the decay property does not diminish this
ability. However, applying certain constraints due to the space-time structure
either on the time evolution of the decaying system or on the measurement
procedure, the criteria revealing contextuality become inherently dependent on
the decay property or an impossibility. In particular, we derive how the
context-revealing setup known as Bell's nonlocality tests changes for decaying
quantum systems. Our findings illustrate the interdependence between hidden and
local hidden parameter theories and the role of time.
