Ship in a Bottleneck

I've got this awesome idea. Check it out.

OK, you know how all across the globe there are time zones, and each time zone has a difference of one hour? We all know that this is essentially just a dictation from the man though, because in reality, there are no physical zones. However, the world is turning, and it actually is later in Arizona than it is in Los Angeles, for example.

But, it's also later in Long Beach than it is in San Pedro, again, for example, although they're only a few miles apart. The sun definitely sets slightly sooner in Long Beach, our neighbor to the east.
So here's my idea: Split up each of the current time zones into 60 smaller zones so that the time difference between each one is one minute. I figure if there are 24 time zones on earth and it's working out pretty well, then 1440 time zones would have to be even better.

Wouldn't that be awesome?