15 Planck Units and Numerology                                 Table of Contents     Previous       Next      


Click on image of Pythagorus for everything “arithmancy”.

This is a very good web site, check it out.

Special Numbers:

Pythagorus and other philosophers of the time believed that because mathematical concepts were more "practical" (easier to regulate and classify) than physical ones, they had greater actuality.

Planck Units:

Max Planck showed us that the three universal constants of G, h, and c can be combined together to give units of length (hG/c3)1/2, time (hG/c5)1/2 and mass (hc/G)1/2, respectively known as the Planck length, the Planck time and the Planck mass.  See the following wikipedia site for a good overview of Planck units: http://en.wikipedia.org/wiki/Planck_units

On the wikipedia site is a note:In 1899, Newton's law of universal gravitation was still seen as exact, rather than as a convenient approximation holding for "small" velocities and masses (the approximate nature of Newton's law was shown following the development of general relativity in 1915). Hence Planck normalized to 1 the gravitational constant G in Newton's law. In theories emerging after 1899, G nearly always appears in formulae multiplied by 4π or a small integer multiple thereof. Hence, a choice to be made when designing a system of natural units is which, if any, instances of 4π appearing in the equations of physics are to be eliminated via the normalization.

An Aside on Gravity:
For reasons that will become apparent latter (
section 17 and Section 19) I consider Newton’s law of gravity fundamental, and Einstein’s postulate that mass curves space-time is not quite right. I believe the starting point of general relativity should be that mass causes gravitons. It is the gradients of these gravitons that causes the curvature of spacetime. The currently accepted way of looking at gravity (2017) is that Newton’s law of gravity is a subset of general relativity. My alternative view is that we can use Newton’s law of gravity to define a quantum mechanical graviton and then show that geometrical distributions of this graviton is the source of the curvature of spacetime. The result is that this alternative view using the graviton gives the predictions of general relativity and in addition explains dark matter and dark energy. 


DWT postulates that free space has varying index of refractions due to gradients of gravitons. And just as the index of refraction in a prism will slow and bend a light beam the index of refraction caused by graviton density in free space will also slow and bend a light beam (see section 21).

It’s a subtle point, does mass curve space-time directly, or does mass cause a density gradient of gravitons which then slows and curves light. Yes, we can say mass curves spacetime, however more precisely mass causes gravitons which then curves light. This curving of light in “free space” is the curving of spacetime!

My bet is that our initial postulates about how light moves in free space are incorrect. Light (our primary tool for measurements) has been moving in a medium (free space) that has an index of refraction. This medium consists of a vast array of gravitons with varying densities.

Does it make a difference if we say that mass curves spacetime OR gravitons bend light?
Having mass that produces gravitons has one big benefit: The gravitons that have mass can explain dark matter and dark energy.

Continuing with Planck Units:

The following fundamental units of length, time, and mass are derived from G, h and c.

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Planck length: 1.616 199 × 10−35 meter

Planck time:   5.391 06 × 10−44 second

Planck mass:   2.176 51 × 10−8  kilogram

I consider these three numbers to be as close to sacred numbers as we are going to get.  They are the physical constants of the universe.  I can hear some of my readers saying “nonsense, there is no proof that these numbers are fundamental”  OK, here is my reasoning on why the Planck units are more than just a numerical curiosity:

1.  In Section 16 we derive the Compton wavelength form a simple ratio involving Planck units:
    λ/(Planck Length) = m0/(Planck Mass) where the Planck Length = (hG/c3)0.5 and the                
    Planck Mass = (hc/G)0.5. Solving for λ we get λ = h/(m0c), the Compton wavelength for a mass m.

2.  We can also derive the Compton wavelength using two fundamental principles of physics:
    a.  E = m0c2     Einstein’s relationship between rest mass and energy
    b.  E = hf = hc/λ       Planck’s relationship for a quantum of energy
    Solving for λ we get λ = h/(m0c), the Compton wavelength for a given rest mass m.

    Two independent ways of calculating the Compton wavelength of a particle are shown. One
    involves the foundational principles of energy as developed in standard physics.  The other uses
    the “sacred” Planck units.   Both give the same result for the Compton wavelength λ = h/(m0c).

3. In Section 17 we show that the Planck mass is the value that satisfies Newton’s law of gravity
    (Force = Gm1m2/d2) when we require that the gravitational energy comes in quanta of E = hc/d.

4. In Section 20  we make a calculation (using G,h and c) to calculate the precession of
    Mercury about the Sun that gives the value obtained via general relativity. 

An interesting detail about the Planck Charge:
The Planck charge (a lesser used Planck unit) is an interesting anomaly. Why it seems to make no sense is investigated in
Section 34.  The Planck charge and its proposed modification shows the usefulness of the λ-hopping concept and why Feynman’s coupling constant α  is fundamental.

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