# A Study of Notation #67: Particle-Wave Duality

### The Numbers:

2.38509×10-15 meters: Not our common experience, but from the heart of today’s research

Overview: The 67th notation is one-third of the total notations. In the earliest stages of developing this model, the range of notations, 1-to-67, was called the small-scale universe. The next set of 67 notations, 67-to-134, were referred to as the human-scale universe, and notations 134-to-202 were considered the large-scale universe. Such labels, of course, are subject to review.

Notations 1-to-67 are the really infinitesimal. The 64th appears to be in the range of the limits to measurement and the start of particle-wave duality. Looked at one way, it’s a particle; another way, it’s a wave.
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67th Planck Length doubling: 2.38509×10-15 meters. This multiple of the Planck Length is in the area of measurement by CERN’s Large Hadron Collider. Going within to a smaller scale, the next step or notation is, of course, fifty percent smaller. Every facet within the next notation is fifty percent smaller.
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67th Planck Mass doubling: 3.211962×1012 kilograms. The mass for such a small space (3.211962×1012 kg) is beyond imagination. The mass of the earth is 6×1024 kilograms. In 1971 a team at Harvard, Baym, Pethick & Sutherland calculated densities could approach 4.3×1014kg/m3 before nuclear pasta and saturation densities are reached. Subsequently that figure has been further calculated to be ≃2.3×1017kg/m3 (nuclear saturation density). Although stretching beyond our comfort zones, we are eager to learn something as simple as the proper computations for meters-cubed (m3) so we ask, “In the progression of doublings, is it assumed to be m3 or should we be using another calculus within these mathematical transformations before we approach what is known as neutron drip densities, nuclear pasta and Coulomb crystals?”
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67th Planck Charge doubling: 276.7891 Coulombs. Equivalent to the discharge of a few average lightning bolts, in the International System of Units ( SI ), the coulomb (C) is the preferred unit of electric charge quantity.
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67th Planck Time doubling: 7.95630×10-24 seconds. Within the big bang theory, the Quark Epoch begins at 10−31 and runs down to 10−12 seconds. Within our Quiet Expansion model, this epoch would begin within Notation 41 and extend through Notation 107. At Notation 67, clearly halfway through the Quark Epoch, we propose that it be called the Quark Processes. Within that scope there would be multiple primes, all of which might initiate a special mathematics: 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, and 107. One might conclude there are many opportunities to develop the mathematics of the Standard Model of Particle Physics.
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From the Planck Temperature scale: Within our charts, the Planck Temperature is placed within the 203rd notation and divided by 2 over and over and over again. By the 67th notation it is approaching absolute zero at 3.25288×10-7 Kelvin. This is Zeno’s paradox all over again.

These numbers may appear to be difficult to interpret. Yet, there are many experts within every field who will see patterns, uniqueness, and new functions at each notation.

The big bang theory’s epochs…. According to the big bang theory, the Quark Epoch begins at about Notation 41 and ends with Notation 41 at about 10−12 seconds and might go up to Notation 136 where we project the Quark-Gluon Processes could begin because the Planck Temperature is now at 1.9201×1012 Kelvin. The Planck Time multiple is 4.6965×10-3 seconds.

An Open Question: What is the logical sequence, from the most simple to the most complex, and which would be required before another begins? Are there logicians and mathematicians, true scholars, who would be open to working with us, the neophytes? Remember this project originated from within a high school geometry class.
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Cycles, frequency and periodicity: The first prime numbers might tell a special story. Staying within the 202 notations, consider multiplying-by-2 the primes up to 101. Does this open a potential for many systems within systems within this model?