See this article by one William Gewirtz. I wrote the following response:
Occam’s razor is not a completely logical rule, but it is useful. Gewirtz’s theory makes too many assumptions, is too complicated, and is ultimately unsatisfying. I would like to offer an alternative explanation:
1. Accurate clocks were, until the modern era, a privilege of wealthy Europeans.
2. The idea that the day can be divided into 12 hours is ancient, and can reflect the use of the oldest timepiece: the sundial. The method of calculating the hours of the day attributed to Maimonides and the Vilna Gaon can be figured with a sundial and similar devices, and did not need to be explicated until later authorities started including hours before sunrise or after sunset in their halachic calculations.
3. It is also very easy to have a rudimentary sundial indicate the halachic times of Minha G’dola and Plag Haminha. Any opinions that would result in Plag Haminha being so close to sunset are self refuting, or as the Vilna Gaon would say, “contradicted by the senses.”
4. Boy scouts are taught how to make simple and accurate sundials
5. Anywhere in the world, a sundial will indicate X minutes after sunrise and X minutes before sunset by a shadow of length Y, equivalent to the distance between the center of the sundial and a concentric circle within the dial, every single day of the year, as long as X is no longer than half the the time between sunrise and sunset.
6. For our case, this means that in Jerusalem, every day of the year, a sundial can easily be made to indicate when 40 minutes have passed since sunrise, and when sunset will be in another 40 minutes. If the people using the sundial so choose, they can draw a concentric circle within the dial indicating a similar length of time before sunset or after sunrise up to five hours in length.
7. Further, the same time X after sunrise or before sunset will be indicated twice every day by the height of the sun in the sky. If there are landmarks of the right height to the east and west that mark enough of the horizon, it can be readily known to even the most uneducated observer when 40 minutes remain before sunset. If there is a line of palm trees far to the west, and they are all about the same height, and they cover enough of the horizon from the sun’s southernmost position at sunset to its northernmost position, then everyone knows that when the sun is at the top of those trees, then it will set in another 40 minutes.
8. 40 minutes is a nice round number that a community and its religious leaders can use if their goal is to find a length of time that allows for the early acceptance of the Sabbath so as to show communal resolve to add significantly to the Sabbath, but not so much so as to be futile.