Note: This article was first published in March 2015. This version has been updated (2016). The original version is preserved within the website (where it was first published): Small Business School.
Précis. By using Planck Length-and-Time and the simplest mathematics (multiplication by 2), a speed of light can be determined within all 202 base-2 notations from Planck Time to the Age of the Universe. At one light second, it is off by 1% from the experimental data.
Planck Numbers. These most-fascinating, magical numbers have been questioned since their introduction in 1899 by Max Planck. The place of the Planck Base 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 (Physics Today) back in 2001 and 2002 [1].
Yet, even today, these numbers are still questioned by many.
Looking for some boundary conditions within which to work, a New Orleans high school geometry class used the Planck Base Units as a starting point to construct their model of the universe. Their primary operating assumption was that continuity and symmetry are the foundational concepts for universal constructions. As a geometry class they were looking to see how they could tile-and-tessellate the universe. This group found a bit of a correspondence between data derived from experimentation and data derived purely by mathematics using Planck Length and Planck Time.
Their first chart with Planck Time. This chart carried over an error (a notation was skipped between Notations 39 and 40) within the listing of the Planck Length. That error did not exist in the December 2012 chart of just the Planck Length. As of February 3, 2016, documents from March 2015 forward are being updated. Originals of each document will be preserved within the Small Business School website where each was first posted.
By the 142nd doubling the Planck Time is correctly posted as .6011 seconds. At the 143rd doubling, it is 1.2023 seconds. In between the two is a single second. In the corresponding column, the Planck length incorrectly reported within the 142nd doubling to be 180,212.316 kilometers and by the 143rd to be 360,414.632 km. Using the wrong length figure to do the calculation resulted in a number very close to the distance light travels in a second. In actuality, instead of 299,773.654587, that figure without any adjustments would be…
Back to the drawing boards.
There are three facts of mathematics that were particularly noted in the process of developing this base-2 chart of the basic Planck Units to their largest known values, particularly the Age of the Universe and the Observable Universe.
Fact 1: The universe can be contained within 201 to 202 doublings of the Planck Length and the Planck Time [4]. An initial fact of applied Planck mathematics is that the entire known universe can be ordered in 201 to 202 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 and the base-2 progression as well as the observed-and-imputed, simple, embedded geometries [5] which adds another dimension of order, i.e. symmetry.
Fact 2: Between notations notation 142 and 143 is a light second.
Experimentally defined over the years [6], here if we were to use the Planck Length as the determinant, light would be quite slow between the 142 and 143 notation. There will be three charts studied. As noted above, the original with the mistake will be preserved within the Small Business School website. The page with the correction from February 3, 2016 will be preserved as the “initial correction.” Additional charts will be constructed whereby a simple logic is imputed whereby adjustments are made to the model so experimentally-defined data is introduced. The small-scale and human-scale notations are in some manner of speaking archetypal. At one second we are looking at the raw universe just one second old. If the entire universe is dynamically adjusting itself, nothing is static, all notations are dynamic and active, we can begin to hypothesize at which notation the light makes its appearance and at which notations light begins to speed up.
Around notation 202 is the estimated Age of the Universe [8].
Though as noted earlier, the Planck Base Units were virtually ignored until MIT professor Frank Wilczek began his earnest study of them in Physics Today (June 2001) [9]. 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 [10] as part of experimental data.
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. By dividing the entire scale in half, they found themselves in the middle of the Human Scale universe. By dividing in thirds, there was a natural division between the small-scale, human-scale, and large-scale universe. 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.[11]
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.” [12] Here the students and their teacher conclude, “The space-time continuum is really real even when using discrete steps.”
Big Board-little universe 