What bogu said, PHP is server-sided and it can not find out what the local time of your visitor is. However, to achieve what you want, the best thing to do is have a menu/option somewhere in your script where users can set what time zone or major city they are in. (e.g. Chicago, New York, London, Amsterdam). You can put a cookie behind that script that sets the number of GMT they are in (e.g. -9, -8, +0, +1). Then use:
$localtime = date(H)+$_COOKIE['localtime'];
$showtime = date($localtime . ":M");