An introduction to dual physics, part 2

According to the McGraw-Hill Dictionary of Physics, mass is “A quantitative measure of a body’s resistance to being accelerated; equal to the inverse of the ratio of the body’s acceleration to the acceleration of a standard mass under otherwise identical conditions.” This is because the ratio of two masses equals the inverse ratio of the magnitudes of the accelerations produced by the same force applied to each mass. By employing a reference mass, the mass of other bodies may be determined. That is:

m(X) / m(R) = a(R) / a(X)

for body X, reference R, acceleration a, and mass m. The reference mass may be set to one for simplicity. For the dual, we need to use the inverse of these quantities:

(1/m(X)) / (1/m(R)) = (1/a(R)) / (1/a(X))

= n(X) / n(R) = b(R) / b(X)

where b and n represent the dual acceleration and dual mass, respectively.

The duals of Newton’s laws of motion are referenced to space instead of time in the denominator, with the numerator’s directions in three dimensions of time:

(1) Every object with uniform dual velocity tends to remain in that state of motion unless an external dual force is applied to it.

(2) The dual force equals the dual mass times the dual acceleration, with the direction of the dual force vector the same as the temporal direction of the dual acceleration vector.

(3) If a given body A acts on a body B with a dual force, then B will also act on A with a dual force equal in magnitude but opposite in temporal direction.