In dual display: can I get both panes to work synchronously?

Scenario:
Dual display open
The directories in each pane are broasdly similar becasue one is a copy of the other.
If I click UP in the left pane I would like the right pane to follow in its directory.
Similarly if I drill down a directory in one pane I would like the other pane to follow.
It's a bit like an FTP program where the local and remote directories can be set to follow each other when one pane is naviagted up or down.

Can I do this in DO dual display?

You can. I'm not sure if the button to toggle it is in the default menus/toolbars but you can drag it out of the Customize dialog to add it where you want it.

In the Settings -> Customize dialog's Commands tab, it's in the Go category and is called Navigation Lock. It works pretty much as you describe.