The circumnavigator paradox seems like a contradiction but it is real. It has been known since the middle ages and continues to influence us today, what happens is that now we are not very aware because we all see the time and date on our mobile and it automatically adjusts to the local time and date. But before it was not like that and time was measured by suns.
The paradox could be stated as follows: three friends who do not have a watch or a cell phone meet in a city on January 1. One of them, whom we are going to call the sedentary one, stays in the same place waiting for her companions to go around the world to meet the three at the starting point. Another of the friends, whom we see called the melancholy, travels west chasing the sunset, just as Saint-Exupéry’s Little Prince did. The other, more optimistic, always travels east looking for the new day. That is, one stays at the starting point, another goes around the world traveling west and the other always travels east.
We are going to consider that when they meet again, two days have passed for the sedentary woman who has not moved from the starting point, so for her it is January 3. However, when her gloomy friend arrives she thinks it is January 2nd because she has only seen one night since she left. And the optimist thinks it is January 4 because she has seen three nights in the same time.
The explanation is that, due to the rotational movement of the Earth, when you travel completely around the planet you rotate more or less with respect to people who do not move, depending on whether you travel with the rotation of the Earth or against it. That is, the combination of the rotation of the Earth with the movement of the person traveling changes the length of his solar days. This change can be very noticeable if the trip is very fast, it is clearly seen on transoceanic flights, for example, or it can go unnoticed if you travel more slowly, on a train or a ship. But in any case, all solar days are going to be four minutes shorter for every degree of longitude you travel east, and four minutes longer for every degree you travel west. And this means that in all cases there is one day more or one day less than the sedentary friend, regardless of how long the trip lasts.
The circumnavigation of the world can last three years like the Magellan-Elcano trip in which this paradox was confirmed for the first time, it can be done in eighty days like the one Jules Verne devised, it can be measured in hours like the non-stop flights of the B- 52B in 1957 or it can be almost instantaneous travel. In all cases there will be a variation of 4 minutes more or less for each degree of longitude and when multiplying the 4 minutes by the 360º of the complete return to the planet, there will be a difference of 24 hours, more or less, with respect to the point of departure.
The practical consequences of this paradox are appreciable. For example, for centuries there was a day difference between the cities of Macao and Manila despite being quite close. The reason was that in the 16th century the former traded with the Portuguese who always traveled to it from the east, surrounding Africa, while Manila traded with the Spanish who traveled the western route. For the merchants there was no problem because they returned by the same way they were going and thus the day they had won or lost by going, they recovered it by returning.
But actually, this problem still exists today because the circumnavigator paradox is a real thing. To avoid this, the convention of having a time standard exists, a way of operating that allows activities and communications to be synchronized between different points on the planet. For this, Coordinated Universal Time (UTC), the International Date Line, drawn over the Pacific Ocean and close to the 180° meridian, and time zones were defined. These conventions are useful and solve many problems, but they are not easy to understand and they maintain some paradoxes, such as the need for the International Date Line.
To do battle with the circumnavigator paradox and our current conventions for dealing with it, here’s some fun Sunday afternoon entertainment. It consists of going around the imaginary world simulating the purchase of plane tickets between the cities of Madrid, New York, Los Angeles, Tokyo, Abu Dhabi and Madrid. It can be done to the east and to the west, that is, round trip. If you look at the duration of each flight and layovers, correct with time zones, and compare what you get with local arrival times, you can find where date corrections are being made to avoid the paradox. It’s complicated but it’s fun.
Maria Belen Munoz Garcia She is a doctor in Geology, professor and researcher at the Faculty of Geological Sciences of the Complutense University of Madrid.
Question sent via email by Paul Mager
Coordination and drafting: victory bull
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