I'm reading the sci-fi novel Saint Leibowitz and the Wild Horse Woman, and in the story a pope in the post-apocalyptic future moves the prime meridian from England to the U.S. It is an unpopular decision, because according to the author not only would it confuse navigation, but it would decrease the amount of time until it is necessary to drop a day to keep in line with planetary movement. I'm trying to understand the logic of this, but I don't get at all why this would happen.
I don't know the book and the quality of fiction are rarely in the facts. However, it is always nice to think about the spinning of our planet and how our theories and methods relate to the actual astronomic observations.
Historically there have been a number of prime meridians, sometimes used simultaneously and sometimes to large confusion. However, what reference you use doesn't change the duration of day and year. The calendars clearly described by Fred and kingledion are there to synchronize the day of year with the astronomic reasons for seasons. Farmers as well as priests plan the year according to the calendar dates and expect equinox at same day every year and the harvest to be in the same month.
You can think of the prime meridian as the offset and the calendar as the frequency of our time units. Even when we refer the time zone to Greenwich it is still only a way to express the relation between time zones. With a US prime meridian the sun would still rise about 6am at equinox all over the world unless the evil pope in the book also forced a time zone of choice to people living near other meridians. However there might be situations where it's practical or politically motivated to use the same time across meridians, even if it means that some people will have sunrise well into lunch time at equinox. Technically, by moving the prime meridian some 30° to the west while keeping the Gregorian calendar would only delay the correction dates with a few hours, but on the other hand, people living just East of the International Date Line will get their correction a day earlier, and might appreciate the new cardinal coordinates, if they have an extremely strong sense for daylight and time.
The Gregorian calendar was an important step to adjust the supernatural believes to actual observations. A year that is 365.2425 days long suggests a more complex universe than any simple cogwheel mechanics. If the evil pope really would like to suppress logic and perception, he or she should change the length of our time units rather than just relocating the coordinate system.
There is no basis in logic to have to subtract a day due to a change in the prime meridian.
Both the Julian & Gregorian calendars require days to be added, not subtracted. It's why we have leap years.
Also, both the Julian & Gregorian calendars were established centuries before the prime meridian was set in the 19th century. The formula for adding days & creating leap years was set long before the prime meridian was even contemplated.
To give a fuller explanation, the current calendar is the Gregorian calendar, which was introduced in 1582 to address the inaccuracies of the older Julian calendar. The Julian calendar gains a day every 128 years because the year is 365 with a leap day every 4 years for an average of 365.25 days long (the actual year is 365.24217 mean solar days). By the time of pope Gregory, the one day every 128 years translated into a 13 day discrepancy between the calendar ad the seasonal cycle.
The Gregorian calendar drops the leap year every 100 years (but keeps it every 400 years) for an average of 265.2425 days per year, so it gains a day only every 3030 years.
So, changing the number of days before you need to 'drop' a day to keep the calendar in place is done by adding or removing leap days. The Prime meridian has nothing to do with that.