The Speed of Light Is “Close Enough” Using Just the Planck Units, then applying Base-2 Exponential Notation to Planck Time and Planck Length

Note: This article was first published in March 2015. This version has been updated several times in 2017 and 2018. The original version is preserved within the website (where it was first published): Small Business School.

Précis. By using Planck Length-and-Planck Time and the simplest mathematics (multiplication by 2), a speed of light is determined within each of 202 base-2 notations from Planck Time to the Age of the Universe. The experimentally-defined speed of light is 299,792,458 meters/second in a vacuum. Planck Length divided by Planck time equals 299,792,422.79 meters/second (using the SI units — these new SI base units were redefined in 2019 — where Planck Length  is 1.616255(18)×10-35 meters and Planck Time is 5.391247(60)×10-44 seconds). At one light second, the Big Board-little universe data is off by less than .1% from the experimental data.

Calculations. Yes, to date, the simple calculation, dividing Planck Length by Planck Time, renders 299,792,422.79 meters/second. In our initial count, over 160 notations are over 299,793,000 meters/second. The lowest calculation is within notation 76 which is 299,759,426.55 meters/second.

The fastest or highest calculation is within Notation 16 where it is at 299,982,157.27 meters/second.   The variable range, from a high of 299,982,157 to a low of 299,759,426, is just 222,720.72 m/second.

Ten percent of the total is 29,979,245.8 m/second. One percent is 2,997,245.8 meters per second. One-tenth of one percent is 299,724.58 meters per second.

Conclusion: The variations on the speed of light throughout all 202 notations is less than .1% of the speed of light measured in the laboratory in a vacuum.

Planck Numbers. These most-fascinating, magical numbers have been questioned since Max Planck introduced them in 1899. Largely ignored, 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, our New Orleans high school geometry class engaged the Planck Base Units as a starting point to construct their model of the universe [2]. 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 [3]. Our group found a bit of a correspondence between data derived from experimentation and data derived purely by mathematics using Planck Length and Planck Time.

There are three calculations 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.

 1: The universe can be contained within 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 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.

2: Between notations notation 143 and 144 is a light second.

Experimentally defined over the years [6], 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 visible light makes its appearance and then study the simple mathematics to discern why light speeds up or slows down within each notation.

3: There is much more to learn about the nature of light.

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 an early pioneer to advocate for the use of the Planck Length [10] as part of experimental data.

It also seems that this approach of our New Orleans high school geometry class is a first. Senior editors of Wikipedia told me that they could no longer publish an article on their site because it was “original research.” Though readily admitting that this work is idiosyncratic, we have persevered since December 2011. By applying base-2 exponential notation, first we found no less than 202 doublings or groups. By dividing the entire scale in half, we found ourselves right in the middle of it all, a 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, we know that there is much more to be uncovered. We 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 our students and teachers conclude, “The space-time continuum is really real even when using discrete steps.”


[1] PHYSICS TODAY, 2001 & 2002
[2] https:/
[3] https:/
[8] https:/
[10]…/Alden-Repsonse323.pdf From American Institute of Physics, New York, NY, PHYSICS TODAY, S-0031-9228-0111-220-2, 2001 p15
[12] , PHYSICS TODAY, August 2002

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