The native datepicker is weird, at least in Chrome. I was playing around with it, and if you give it milliseconds it will render a millisecond picker in intervals of 100. If you give it a nice round minute, then ms and s disappear from the UI. There's no attribute to control this.

I also want a non-local time picker. Let me specify a time that the server can properly interpret as a moment in time. i.e specify an offset somehow.