Nigel's close.
You cannot directly start another app from your app, but you can launch a URI and have it open in the default handler for that URI. You can leverage this by having your app define a custom protocol which accepts the arguments you want to pass.
The caveats are that the user gets to choose the default handler, so your app cannot depend on launching a specific app, and your app won't pass certification if it has a strong dependency on an external app.
See: How to handle URI activation and
How to launch the default app for a URI
--Rob