iSoul In the beginning is reality

Mass and vass

In Isaac Newton’s Principia, Definition 1 states:

Quantity of matter is a measure of matter that arises from its density and volume jointly. (The Principia: The Authoritative Translation and Guide, Bernard Cohen, Anne Whitman, and Julia Budenz. University of California Press, 2016, p.403)

Today density is defined as mass per unit volume, which would make this definition circular. However, when Newton wrote, density was expressed as a relative quantity. (p.90) If we look at mass as the product of density and volume, a complementary measure arises: vass.

Density is a ratio, and ratios may be expressed as fractions in two ways: the ratio of nonzero quantities A:B is equivalent to either A/B or B/A. So instead of density as mass per unit volume we could just as well define its inverse, rarity, as volume per unit of mass. (See Max Jammer’s Concepts of Mass in Classical and Modern Physics, p.27.)

Then the rarity per unit of volume equals the vass, which is the inverse of mass. In SI units, that equates to (m³/kg) / m³ which equals 1/kg.

Mass is also defined as the ratio of force to acceleration, reflecting Newton’s second law. Force is the time rate of change of momentum. A complementary definition would be the space rate of change of fulmentum, which equals the vass.

Inertial mass is the resistance of an object to a change in its state of motion when a net force is applied. A complementary concept is the nonresistance of a subject to a change in its condition of movement when a net surge is applied.

If mass is the “quantity of matter,” what is vass the quantity of? Quantity of matter means how much of a material object there is. Vass answers how much of a material subject there is, which is measured inversely to the mass as subject and object are inverses.

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