Scientific thoughts about the New Year

At midnight, many people will celebrate the passage of a year in the Gregorian calendar. As always, there are many festivities planned in different locations all over the world, with celebrations in each inhabited time zone. The first places to celebrate New Year’s Day were Kiribati and the Line Islands, as their time zone of UTC+14:00 puts them ahead of everyone else in the world. The last places to celebrate the beginning of 2013 will be American Samoa, Niue, and Midway Atoll, with a time zone of UTC-11:00. (While the time zone UTC-12:00 exists, it is used only for two islands that are currently uninhabited, as well as the International Date Line.)

But for a scientist, this is a time to reflect upon the arbitrary nature of New Year’s Day in particular and our methods of keeping time in general. Let us consider the number of moments that we could choose to celebrate. We can choose any day of the year to be the end of one year and the beginning of another year. We can choose any moment within that day as well. While the number of moments that we could choose out of a year is unimaginably large, it is a finite value. This is because the speed of light is finite, and it is impossible for mass or energy to move faster than light in normal space. There is a quantization of length that is related to the Planck length, a quantity derived from the speed of light, Planck’s constant, and the universal gravitational constant. According to the generalized uncertainty principle, the Planck length is in principle, within a factor of order unity, the shortest measurable length. The smallest measurable time, called the Planck time, is the time it takes for light to travel one Planck length.

The NIST value of the Planck length is 1.616199 x 10^-35 ± 9.7 x 10^-40 meters, a value many orders of magnitude smaller than what can currently be measured directly. The speed of light in a vacuum is 299,792,458 meters per second, so a unit of Planck time is 5.39106 x 10^-44 ± 3.2 x 10^-48 seconds. If we invert this, we find that there are 1.85492 x 10^43 units of Planck time per second. If this quantization of time is correct, then we may think of the universe as being “animated,” with a “frame-rate” of 1.85492 x 10^43 frames per second. There are 31,556,926 seconds in a year, so we have a total of 5.85356 x 10^50 moments to choose from when deciding when to mark the boundary between years. To put this number into perspective, Drew Weisenberger of Jefferson Lab estimates that the number of individual atoms on Earth is about 1.33 x 10^50. So from the standpoint of quantum mechanics, New Year’s Day is not so special.

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