How do I show the path to a file in Emacs mode?
First, you see the name of the buffer, not the name of the file. Try opening two files with the same name (in different directories) and see what I mean.
Secondly, yes, I'm sure it is possible - just configure
Third, it might not be such a great idea - the mode line is already quite crowded, and the long way just doesn't fit. I know it sounds great now, but the next day you will hate it.
Instead, put the path in the title bar:
(setq frame-title-format '(buffer-file-name "%b - %f" ; File buffer (dired-directory dired-directory ; Dired buffer (revert-buffer-function "%b" ; Buffer Menu ("%b - Dir: " default-directory))))) ; Plain buffer
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