More than 24 time zones

You know how they say there are 24 time zones? That's one time zone for each hour of the day, right? Well, if it worked like that wouldn't there be more than 24 time zones? For example, within those time zones, wouldn't there be 60 more time zones for each minute? So you drive east or west and every few miles and you have to change your clock by one minute. Even beyond that, wouldn't there be a time zone for any measurement of time that exists? So as your walking down the street, and for each step you take, you have to set your clock one millisecond later.

ALIENS WILL ABDUCT YOU IF YOU DON'T EAT YOUR BROCOLLI!!!