Yup, that way of doing it is protocol-agnostic.

is this officially accepted syntax? does it work in all browsers? (I'd really love both these answers to be yes so I can start doing this on my sites)

Yes and yes, since 1995.

More specifically: http://www.ietf.org/rfc/rfc3986.txt

Via: http://stackoverflow.com/questions/3583103/scheme-relative-u...

thanks :)

Which is interesting since Google doesn't serve a 404 over HTTPS as far as I can tell.

Try this: https://mail.google.com/asdfasdf

But they're clearly doing their best to minimise file size, and so using // cuts down on a few characters.

Well maybe they will...?