Index | Normal Realism | You Don't Have to Be Einstein to Know that Time is Relative | Einstein From Galileo And Newton By Pythagoras | Pope's Unifying Angular Momentum Equation | Philosophical Contribution to Theoretical Physics | List of Publications by N.V. Pope

The straight-line, so-called 'inertial' motion, or momentum *mv*, envisaged
by Galileo and Newton was seen, by Pope, as counter-empirical. As he saw it,
straight-line motion is purely theoretical, being a special, ideal case of angular
momentum of magnitude *mvr* with *r* at theoretical infinity (a straight
line and a circumference of infinite radius being one and the same). But with
*r* at infinity, the magnitude of the angular momentum *L* = *mvr*
is also infinite, which is unreal. It follows, then, that for all real (*i.e*.,
finite) angular momentum *r* is finite, hence the motion naturally curved
or orbital, without having to postulate invisible *in vacuo* 'forces' being
responsible for these curved trajectories.

Moreover, angular momentum is a naturally paired and balanced (*i.e*.,
non-local) relation between masses according to the equation

By this relation, the motions of the masses *m* and *M* are automatically
linked, so that any forced change in the motion of either of the masses immediately
affects that of the other, that is, directly, in accordance with Newton's third
law of instantaneous and reciprocal action-reaction. This, of course, is without
any need to postulate mediation by the fictitious and invisible 'forces', of
classical conception, such as those of 'gravitation', 'electrostatics' and 'magnetostatics'.

Pope's unifying angular momentum formula (stated simply, for orbital motion assumed circular and in the same plane *) is therefore:

(4) *L* = *mvr* = 2(*K*O
+ *K*X) *r/v = G
mM/v *

where *L* is the orbital angular momentum, *K*O
is the orbital kinetic energy and *K*X is some
extra-orbital kinetic energy such as, for example, spin or some other convoluted
form of angular momentum. *G* (call
it 'curly gee') is a variable which, when *K*X
is negligible, is equivalent to the usual 'gravitational' constant G (= 6.67259
× 10-11 N m2 kg-2).

* This simple, ideal formula, for magnitudes only and ideally circular motion, was later developed, by A.D. Osborne, to include the more real, elliptical orbits and angular momentum vectors. This development became the basis of the Pope-Osborne Angular Momentum Synthesis, or POAMS (see website www.poams.org ).

When *K*X is made equal, in mechanical units
of joules, to the so-called 'electron charge' in coulombs (*q* = 1.602 ×
10-19C) multiplied by the ionisation potential for
elementary hydrogen (13.595 volts), then *K*X
is 2.179907344 × 10-18 joule. The orbit defined
in these purely mechanical terms, with G
= 1,5141474 × 1029 N m2 kg -2,
then becomes that of the electron mass *m* = 9.1094 × 10-31
kg around the proton mass (*M* = 1.6725 × 10-27
kg) in Bohr's 'electrodynamical' model of the hydrogen atom.

In this way, with suitable step-changes in the value of G, the free orbits of 'electric' and 'magnetic' particles are included with 'gravitation' in the unified angular momentum equation. (For details see Publications Nos. 18, 28, 30, 31)

In this way, all forces become real, *i.e*., *measurable* forces.
For instance, the only 'gravitational' force it makes sense to speak of is that
which a body exerts on the earth's surface (*e.g*., on a weighing-scale)
when that surface prevents the body from orbiting where it should according to
the angular momentum equation for the free-motion case of *G*
= *G*. The real force pressing on the earth's surface is therefore:

where *m* is, say, a standard kilogram mass, *M* is the mass of the
earth and *r* and the radius of the earth's surface at that point. In this
case, *G* has the value, from (4):

(6) G
= *Lv/mM*

where *L* is the angular momentum of *m* at that point due to the
earth's rotation and *v* is the rotational speed at that same point. (For
details of this see, again, Publications
Nos. 18, 28, 30, 31).