OSX spaces - how to switch space on another monitor

I cannot for the life of me figure this out. I have two monitors. If I'm focused on the left monitor, I cannot use a shortcut to switch spaces on the right monitor. Or (as often happens) I click my right monitor to focus it instead of alt tabbing, and then I cannot switch the left monitor space with my keyboard without clicking on that screen.

Is there not a way to control the space of another monitor with your keyboard?

Ctrl-Left Arrow/Right Arrow let you scroll through spaces from the keyboard in Mavericks.

Spaces are only independent if you have "Displays Have Separate Spaces" enabled under System Preferences > Mission Control -- with this option enabled, you should be able to switch workspaces on each monitor independently. The monitor that switches when you use the keyboard shortcut should be the monitor where the pointer currently resides.

Yes, if you know applescript.

For example, to switch to Space 1 on the Secondary Display. Note:

1) Primary/Secondary Display is defined by where the Menu Bar is (i.e. System Preference -> Display -> Arrangement), not by cursor focus.

2) This script switches to Space 1, whether it's a Desktop or fullscreen app. If you want to switch only to Desktop 1, it can be done, but not with this script as it is.

3) If you don't mind flashing, remove delay 0.5 line.

4) The script cannot do without the animation/transition.

5) Enable Accessibility and all the standard applescript spiel.

6) Modify button number to switch to a different Space on that Display. Modify list number to switch a different Display.

7) Switching to a non-existent Space, e.g. Space 100, would leave the UI at mission control. Nothing bad is going in bad to your computer. It just stays there, and user will have to manually drop back to current Space.

8) No relative switching, i.e. move left or right a space. Just absolute switching.

9) Cursor focus doesn't switch display after running this script. That's a plus.

10) No simultaneously switching Spaces on both displays.

tell application "System Events"

    do shell script "/Applications/Mission\\ Control.app/Contents/MacOS/Mission\\ Control"
    delay 0.5
    tell process "Dock" to tell group 1 to tell list 2 to tell button 1 to click

end tell