Let \alpha be an “action”, and consider the two processes \alpha \star and \alpha .\varnothing + \alpha \star .
We have \mathbf {Traces}{\mathopen {}\left (\alpha \star \right )\mathclose {}} = {\mathopen {}\left \{\varepsilon , \alpha , \alpha .\alpha ,\ldots \right \}\mathclose {}}=\mathbf {Traces}{\mathopen {}\left (\alpha .\varnothing + \alpha \star \right )\mathclose {}}.
But the process \alpha \star can never get stuck, whereas \alpha .\varnothing + \alpha \star gets stuck if it proceeds along the left branch.
Thus trace equivalence is highly un-physical. To deal with this, we generalise the information order to a category in which bisimulation can be expressed. Idea: non-determinism must be modelled by a van Kampen colimit (e.g. disjoint coproduct).
See Joyal, Nielsen and Winskel (1996) and Cattani and Winskel (2005).