Gravitational Mass

Bead panel from a baby carrier, Kayan or Kenyah people. Borneo 20th century, 27 x 27 cm. Photograph by D Dunlop.

Let P be characterized by its quark coefficients n and energies U.

Definition: the number M is called the gravitational mass of P.

$\mbox{\fontsize{10}{12}\selectfont $ M \equiv \left| \sum_{\zeta =7}^{10} {\Delta}n^{\zeta} U^{\zeta} \right| $}$

Note that the sum is over the baryonic quarks only.

Sensory Interpretation: gravitational mass represents the net magnitude of thermo-acoustic sensation. If the magnitude of audio-visual sensation is negligible compared to thermo-acoustic sensation, then inertial and gravitational masses are indistinguishable.

Definition: we say that Ω is a helical orbit about the w-axis if

$\mbox{\fontsize{12}{14}\selectfont $ \overline{I}^{\,\sf{\Omega}} = \left( \ 0,\ 0,\ I_{w} \ \right) $}$

By the definition of inertia this is obtained when

$\mbox{\fontsize{12}{14}\selectfont $ \Delta n^{\mathsf{E}}=\Delta n^{\mathsf{G}}= \Delta n^{\mathsf{A}}=\Delta n^{\mathsf{M}}=0 $}$

The inertia vector of a helical orbit about the w-axis is always

$\mbox{\fontsize{12}{14}\selectfont $ I = |I_{w}| $}$

because the weak component of the quark metric κ_ww is always one by definition.

Theorem: equivalence of gravitational and inertial mass. By definition, the enthalpy H can be written as

$\mbox{\fontsize{10}{12}\selectfont $ H &\equiv \sum_{\zeta =1}^{10} {\Delta}n^{\zeta} U^{\zeta} = \left( \sum_{\zeta =1}^{6} {\Delta}n^{\zeta} U^{\zeta} \right) \pm M $}$

If P is in a helical orbit about the w-axis then $\mbox{\fontsize{10}{12}\selectfont $ I = |I_{w}| $}$ and

$\mbox{\fontsize{10}{12}\selectfont $ \Delta n^{\mathsf{E}}=\Delta n^{\mathsf{G}}= \Delta n^{\mathsf{A}}=\Delta n^{\mathsf{M}}=0 $}$

So that

$\mbox{\fontsize{10}{12}\selectfont $ H = {\Delta}n^{\mathsf{U}} U^{\mathsf{U}} \pm M = I \pm M $}$

and

$\mbox{\fontsize{10}{12}\selectfont $ m = \sqrt{H^{2} - I^{2} } = \sqrt{M^{2} \pm 2MI } = M\sqrt{1 \pm 2I/M } $}$

So for particles in helical orbits, if M ≫ I then m = M.

Le Sage & Gravity

Fatio & Gravity

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page_revision: 46, last_edited: 1246428360|%e %b %Y, %H:%M %Z (%O ago)

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