One worldwide clock.
Dawn will be 0600 somewhere, but 1300 hours somewhere else. So fuggin' what? It's just a number. After a period of adjustment everyone on earth will know what will be the usual time to rise and retire where they live, based on their natural body clocks. Businesses will reset the numerical opening and closing times based on market demand - as they do now - which will ultimately be based on our body clocks.
Schedule a meeting with a client in Moscow. What time is the meeting? Same numerical time in both places - and what's convenient for both - simple.
Board a plane in New York, what time does it arrive - the math for the flight duration will be simple because the time basis will be the same.
Simple. No more 'local' time. No more Greenwich Meridian Time. Screw those arrogant limeys anyway.