First posted: March 2015. A press release for science publications
Posted on March 2015 on the server that hosted the website of Small Business School, our television series on PBS-TV throughout the USA and VOA-TV (Voice of America) around the world.
Major thesis: By using Planck Length and Planck Time and the simplest mathematics (multiplication by 2), the speed of light is confirmed. That is a peculiar outcome from data that has been questioned since its introduction by Max Planck in 1899. The place of the Planck Units did not become a focus of the scientific community until Frank Wilczek (MIT, Nobel laureate, 2004) wrote a series of articles, Scaling Mt. Planck, for Physics Today back in 2001 and 2002 . Yet, even today, these numbers are still questioned by many. Notwithstanding, in a New Orleans high school geometry class, they study the Planck Units in light of the concepts of the continuum, continuity and tilings and tessellations.
Recently this group found a correspondence between data derived from experimentation and data derived purely by mathematics within the Planck Units, particularly Planck Length and Planck Time.
Please take a look at their chart (link opens a new window). Starting at the bottom of the first column, the Planck Time is doubled, then doubled again and again. At the 143rd doubling it is .6011 seconds. At the 144th doubling is 1.2023 seconds. In between the two is a single second. In the corresponding column, the Planck length is doubled then doubled again and again. By the 142rd doubling it is 180,212.316 kilometers. Doing the simple calculation of where the length would be at one second, it is found to be equal to the distance light travels in a second. That is, mathematically, extending the Planck Length using base-2 exponential notation (multiplying by 2), it is confirmed to be 299,792,458 meters, the distance light travels in one second.
Even though that statement seemed self-evident, it still begged the question, “Is this a first? Has the speed of light ever been confirmed using simple mathematics and the Planck Length and Planck Time?”
The initial observations were made while developing an entire Planck Chart based on doublings of the five basic Planck Units . Here, however, the focus on the Planck Length-and-Time have been going on since 2011. As a result, this team is trying to find other ways the Planck Units can be used to confirm experimental data as well as open basic questions about the nature of measurement, number theory, and the power of simple mathematics.
There are three facts of mathematics that have been particularly noted in the process of developing this base-2 chart of the basic Planck Units from their given value by Max Planck in 1899 to their largest known values, particularly the Age of the Universe and the Observable Universe.
Fact 1: The universe can be contained within 202 doublings of the Planck Length and the Planck Time. An initial fact of applied Planck mathematics is that the entire known universe can be ordered in 201+ necessarily-related groups by using base-2 exponential notation. The chart is simple to calculate; it was a project that started in a high school geometry class. Unlike Kees Boeke’s base-10 work in 1957 (also in a high school), this chart begins with the Planck Units and gets its order through the Planck Units (although it initially started with simple embedded geometries that adds another dimension of order ).
Fact 2: Between notations notation 143 and 144 is a light second. Experimentally defined over the years , here it is defined and confirmed by simple Planck-based mathematics. Discrepancies begin to arise quickly at a light minute between notations 148 and 149 and a Light Year, found between notations 167 and 168. In Google a light year is reported to be 9.4605284×1015 meters. In Wikipedia it is reported to be 9,460,730,472,580,800 meters exactly. Using simple mathematics the result is 9.4605362+×1015 meters. Using just the figures within the Planck Time-and- Length progression, it is 9.45994265715×1015meters. Each of these discrepancies will require more thoughtful analysis.
Fact 3: Either the Known Universe may not be as old as it has been calculated to be, or it is not as large as reported, and/or one (or more) of the initial Planck calculations is off, and/or there is more to learn about the nature of light.
Between notations 201 and 202 is the estimated Age of the Universe .
Though as noted earlier, the Planck Units were virtually ignored until MIT professor Frank Wilczek began his earnest study of them in Physics Today (June 2001). His first article in a three-part series came to the attention of a Minnesota chemistry professor, C. Alden Mead, who upon reading the Wilczek article commented in the “Letters” section about his work back in 1959 that argued for the use of the Planck Length. Wilczek acknowledged that Mead had been the first pioneer to advocate for the use of the Planck Length.
It also seems that this approach of the New Orleans high school geometry class is a first. Senior editors of Wikipedia told them that they could not publish an article on their site because it was “original research.” Though they readily admit that this work is rather idiosyncratic, they have persevered since December 2011. Using base-2 exponential notation first they found no less than 201 doublings or groups, then a small-scale, human-scale, and large-scale universe, and then so much more. Within each scale and within each group, they know that there is much more to be uncovered. They have just started to open this door and are working to discover more. In 2002, Wilczek reflects, “It therefore comes to seem that Planck’s magic mountain, born in fantasy and numerology, may well correspond to physical reality.”  Here the students and their teacher conclude, “The space-time continuum is really real even when using discrete steps.”
American Institute of Physics, New York, NY, PHYSICS TODAY, S-0031-9228-0111-220-2, 2001 p15