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.

Most scientists do not have much need of numerology and consider the realm of sacred numbers quackery in spite of its association with Pythagorus and other notables.

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 wiki 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.

For reasons that will become apparent latter (
section 17 and Section 19) I consider Newton’s law of gravity fundamental, and that the theory of the curvature of space-time is correct but misleading. The problem is with light and how it is postulated to travel at one speed c in a straight line in free space.

DWT postulates that free space is a transmission medium for light. Furthermore this medium has an index of refraction that is a function of the density of gravitons present (you could also say density of the gravitational field). 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.

Its a subtle point, does mass curve space-time directly, or does mass cause a density gradient of gravitons which slows and curves light, making it look like mass curves space-time when in fact mass influences light via gravitons and not space-time. My bet is that our initial postulates about how light moves in free space are incorrect. Light (our primary tool for measurements) has been misbehaving and we have been blaming space-time as the culprit.  Experiments are needed, see section 21 Nitpicking General Relativity and section 19 DarkEnergy - Curved SpaceTime.

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 limits of the universe.  I can hear some of my readers saying “nonsense, there is no proof that these numbers are fundamental limits!”  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.

Conclusion:  The Planck Units are more than just a numerical curiosity.

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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