In all cases this is effected by allowing the constant velocity parameter c to become infinite. Only the main equations for which a classical equivalent exists is so treated. Trivial examples will be ignored unless a special condition is implied.

Section 2

(i) Eq. (2.6), the temporal rate. When c ® ¥

Hence in classical theory the proper time of a moving body is identical to the time in D₀, Pseudo-Euclidean Space-Time.

(ii) Eq. (2.7), Existence Velocity. When c ® ¥

Hence temporal velocity in classical studies is ïnfinite". Existence velocity does not exist in classical mechanics, and temporal velocity in such studies, is therefore a meaningless concept because it implies that time passes infinitely quickly. Where a concept does not exist in classical mechanics etc, relativistic reduction generally results in an infinite or zero value.

Section 3.

(iii) Eqs. (3.6) and (3.9), Rest, Energy and Inertial Mass. When c ® ¥

Thus rest, energy and inertial mass are identical in classical mechanics. Hence any reference to inertial mass in such studies is meaningless. Consequently, as is evident from Eq (3.7), when c ® ¥

(iv) Eq (3.19), Kinetic Energy. To determine the classical expression for kinetic energy directly from (3.19) would be incorrect because (3.19) is a relationship in matter energy, a concept that does not exist in classical mechanics. The correct procedure is first to insert (3.6) into (3.19) and expand the result binomially to yield

from which, when c ® ¥

the classical result.

Section 4.

(v) Eq. (4.19) and (4.20), the acceleration vectors along the co-ordinant axes, when c ® ¥

(vi) Eq. (4.21) and (4.22), the mass on each co-ordinant axis, when c ® ¥

(vii) Eq. (4.24), Angular relationship between the acceleration vector and the X axis, when c ® ¥

which confirms the result at (B.7) and (B.8).

(viii) Eqs. (4.25) and (4.28), accelerations along and normal to the velocity vector, when c ® ¥.

and

which now also shows that the force, acceleration and velocity vectors are co-incident.

Section 5.

(ix) Eq. (5.5), general curvi-linear equation of motion, when c ® ¥

the classical equation in mechanics.

(x) Eq. (5.25), equation of planar motion in the proper time, when c ® ¥

the classical equation in mechanics.

(xi) Eq. (5.32), the equation of a central orbit, when c ® ¥

where

(xii) Eq. (5.40), the equation of a central orbit trajectory, when c ® ¥

which is clearly the equation of a simple conic section. The semi-latus rectum and eccentricity are

These are again the classical results.

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