Cell execution timer continues even after kernel is shutdown

[mbektas]

Steps to reproduce:

1. Run a notebook cell which takes long to execute
2. Close and reopen the notebook
3. Notice that the timer still ticks, even if kernel is shut down after reopening.

I would expect timer to not tick after reopening the notebook.

[krassowski]

While it is easy to solve for the case of a dead kernel, in general if kernel is still running when re-opening we would not know if any given cell has already completed execution. We are exploring something to fix that in jupyter-server/jupyter_server#990 (comment)

[krassowski]

I looked a bit more into this and because the timer is a function of cell metadata, even a hot fix would not be trivial (unless we store kernel/session ID in the cell metadata which would be rather noisy; this way we could compare if the currently running kernel - if any - is the kernel in which the cell execution started). Again, it looks like the best solution would be adopting jupyter-server/jupyter_server#990 (comment).