 ...An Exact Classical Mechanics leads toward Quantum Gravitation... Contents
2.4 Special relativity versus the revised NewtonianEquations [13] and [18] are effectively identical and replicate the famous Einstein equation obtained from special relativity, but here it has appeared, from both Methods 1 and 2, without any reference to relativity at all. Both have been entirely derived from our first refinement of Newtonian physics - the need to incorporate the mass equivalent of kinetic energy in the definition of inertial mass. Method 1 depended on acceleration, which can be regarded as following Whittaker. In relativity these equations arise as a direct result of its postulates without reference to acceleration. Indeed, accelerated states are outside the scope of special relativity theory. The mathematical similarities mean, however, that most experimental verification of special relativity will support the revised Newtonian equally well. The mathematical similarities are, however, illusory because v is now the speed of any object relative to the local i-ther: not the observer as in relativity! The consequence is that other differences are inherent. In relativity an observer moving with any object only sees the rest mass m0 and rest energy E0 of that object, because no absolute frame of reference is permitted. In the extended Newtonian such an observer sees the full inertial mass m and total energy E because these now have absolute, not relative values. Furthermore, in relativity, the observer judges the kinetic energy of any other object in terms of its observed speed. Hence the kinetic energy of a given object will be accredited different values by observers in different frames of reference, i.e. in motion relative to each other. Hence in relativity theory, kinetic energy, total energy and inertial mass, take on an illusory quality, whilst for the revised Newtonian this is not the case. This removes the uncertainty concerning the actual energy of any object and permits, in principle, the total energy of the universe to be assessed. Relativists have said this quantity is impossible to define! 2.5 Time dilationMuons resulting from the impact of cosmic rays in the upper atmosphere are detected at ground level. Muons moving slowly decay with half-lives of 2.2 X 10-6s and it is estimated that their lives need to be extended about nine times to explain ground level observation. For this reason they have been used to verify Einstein's prediction of time dilation. The muon is structured more like an electron, however, and so is not a good example for our purpose: so we will study the pion we modelled in Method 1 instead. Charged pions have the shorter half-life of 1.8 X 10-8s. The analysis given in Method 2, using Newtonian theory, could equally apply to relativity with v now defined as relative to the observer. For simplicity we will assume η = 1. If the observer moves with the pion differences in these theories now appear. The relativist expects exactly the same mechanics to apply and so sees the quarks orbiting at speed c, just as if both observer and pion were stationary. However, observing a pion moving at relative speed v the quarks would be seen orbiting at speed vorb. The way these are reconciled, in relativity, is by assuming time has dilated in ratio c/vorb for the observer moving with the pion. The Newtonian moving with the pion would, however, observe exactly the same orbiting speed vorb as he did when he was stationary (observing the pion in linear motion at speed v). He would, however, use his Brillet and Hall interferometer to measure his absolute speed and find it was v. Then he would add v to vorb vectorially and discover the vector sum to be c: equal to the orbiting speed with both observer and pion stationary. No time dilation is now required. However, the angular velocity of the orbiting quarks would reduce with speed according to equation[19]. If the lifetime of an unstable particle is measured in the number of rotations before decay, then both theories will predict the same life extension. For mechanisms based on atoms a different approach is needed and this will now be considered. This time the vibration of a hypothetical matter clock will be investigated. | 
