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Momentum

Momentum is identified by Sir Isaac Newton, pictured here, as a central idea in mechanics.

Momentum is the modern English word used for translating the phrase “quantity of motion” that Sir Isaac Newton uses on the very first page of his great book, the Principia1Isaac Newton, Mathematical Principles of Natural Philosophy, page 639. Translated by A Motte and F Cajori. University of California Press, 1934.. So to understand motion EthnoPhysics starts by using sensation to define the momentum as follows. Consider some particle P characterized by its wavevector  \overline{ \kappa } and the total number of quarks it contains  N. Report on any changes relative to a frame of reference F which is characterized using  \widetilde{ \kappa } the average wavevector of the quarks in F. We define the momentum of particle P, in reference frame F, as the ordered set of three numbers

\overline{p} \equiv      \dfrac{h}{2\pi} \left( \overline{\kappa}^{\mathsf{P}} \! - N^{\mathsf{P}} \, \widetilde{ \kappa}^{\mathsf{F}} \right)

where  h and  \pi are constants. The norm of the momentum is marked without an overline as p \equiv \left| \, \overline{p} \, \right|. If p=0 we say that P is stationary or at rest in the F-frame. Alternatively, if p \ne 0 then we say that P is in motion.

Momentum is traditionally understood as a product of the mass and a velocity. But the premise of EthnoPhysics frowns on the naive acceptance of spatial concepts. And we require some extensive discussion of ideas like dynamic equilibrium and Planck’s postulate before getting to the velocity. But after logically disecting various entwined concepts, we ultimately show how the foregoing sensation-based definition of momentum is equivalent to the traditional definition.

Sensory Interpretation

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The momentum is defined by a difference between the wavevector of P and a scaled-down version of the frame’s wavevector. Recall that the wavevector has previously been interpreted as a mathematical representation of somatic and visual sensation. So momentum is like the audio-visual contrast between a particle and its reference frame. This striking juxtaposition is a signal for attention! So the EthnoPhysics definition of momentum directs our awareness to the reference sensations of seeing the Sun, seeing blood and seeing gold.

De Broglie’s Postulate

In a perfectly inertial frame of reference  \widetilde{ \kappa } ^{ \mathsf{F}}= \left( 0, 0, 0 \right). Then the momentum of P is given by

\overline{p} = \dfrac{h \overline{\kappa}}{2\pi}

And recall that for particles in motion, the wavelength is  \lambda = 2 \pi / \kappa. So taking the norm of the momentum and eliminating the wavenumber obtains Louis de Broglie’s statement about the inverse relationship between momentum and wavelength

\lambda = \dfrac{h}{p}

Thus de Broglie’s postulate notes a conditional proportionality between  \overline{p} and  \overline{ \kappa } that is just built-in to the definitions for these characteristics.

Momentum is Conserved

Recall that quarks are conserved. So if some free particals \mathbb{X}, \mathbb{Y} and \mathbb{Z} interact like \mathbb{X} + \mathbb{Y} \leftrightarrow \mathbb{Z} and are otherwise isolated, then

N ^{ \mathbb{X} } +  N ^{ \mathbb{Y} } =  N ^{ \mathbb{Z} }

Also, as shown earlier, wavevectors are combined as \overline{\kappa}^{\mathbb{X}} + \overline{\kappa}^{\mathbb{Y}} = \overline{\kappa}^{\mathbb{Z}}. Then by the foregoing definition, momenta are related as

\overline{p}^{\mathbb{X}} + \overline{p}^{\mathbb{Y}} = \overline{p}^{\mathbb{Z}}

Thus we say that momentum is conserved when compound quarks are formed or decomposed. Newtonian mechanics is based on this relationship. It is important but not unique. Recall that we also have conservation laws for seeds, quarks, charge, lepton number, baryon number and enthalpy. All of these conservation rules follow from the logical requirements of our descriptive method. EthnoPhysics depends on mathematics. Therefore we are constrained by the law of noncontradiction and the associative properties of addition. So any characteristic defined by sums of quark coefficients will necessarily be conserved.

Momentum conservation is like counting the beads in this textile from Kalimantan.
Baby Carrier panel, Basap people. Borneo 19th century, 39 x 20 cm. Photograph by D Dunlop.
References
1Isaac Newton, Mathematical Principles of Natural Philosophy, page 639. Translated by A Motte and F Cajori. University of California Press, 1934.