The Duality of Time Theory

The Principia was published in 1687, with encouragement and financial help from Edmond Halley (1656-1742 AD). In this book, Newton stated the three universal laws of motion which describe the relationship between the object and the acting forces that caused their motion. This science later became to be known as classical mechanics, to distinguish it from its modern extension introduced by the theory of relativity and Quantum Mechanics, as it will be described in chapter III.

The three laws of Newton are:

1.In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force. 2.In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object:. 3.When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

In these three laws, objects are considered as single point masses; ignoring their size and shape. The laws also hold only with respect to inertial reference frames; that are not moving with respect to the observer.

The second law can also be stated in terms of the rate of change of momentum, instead acceleration which is the rate of change of velocity:

(2.3)

This means that the force corresponds to the time derivative of the momentum, which could change either in magnitude only, to produce acceleration, or in direction only, such is the case with uniform circular motion, or both together. When the momentum does not change at all, the second law reduces to the first law.

Therefore, the second law implies that momentum is conserved when the net force on the body is zero, and any net force is equal to the rate of change of the momentum. The Duality of Time will introduce a critical generalization of this essential equation which will allow direct derivation of the equivalence principle that is required to introduce General Relativity. According to this generalization, that will be discussed in details in chapter V, momentum is always conserved for all inertial and non-inertial frames alike. This critical idea will convert the concept of force into the dynamic space-time geometry that is equivalent to gravity. Unlike General Relativity, however, in the resulting genuinely complex-time geometry, gravity will be granular and Euclidean at the same time. The new quantum gravity will reduce to General Relativity when we consider space-time to be real, and thus expressed as non-Euclidean Mankowski space, which then reduces to the Euclidean Mankowski space if we ignore the effect of gravity, as it is the case in Special Relativity, which in turn reduces to this Newtonian laws for normal low speeds.

As we noted in section 11, the laws of motion were clearly stated by many Muslim scholars more than seven centuries before Newton, but they were not formulated in mathematical equations. Ibn Malaka al-Baghdadi distinguished between velocity and acceleration, and showed that force is proportional to acceleration rather than velocity Gutman (2003). He also suggested that motion is relative: “there is motion only if the relative positions of the bodies in question change.”, and he also stated that “each type of body has a characteristic velocity that reaches its maximum when its motion encounters no resistance.” Langermann (1998).