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Email: Walter Babin
Relativistic Dynamics
Walter Babin

A thorough analysis of the kinematics of relativity showed that A. Einstein’s first postulate precluded any modifications in the measurement of time and space. The Einstein-Lorentz transformations were identified as applying to the wavelengths and frequencies of light waves rather than any underlying metric. Consistent with these findings, the reduced velocities of the early mass spectrometric experiments are obviously the result of induced fields and field couplings. This is evident in the equations. Furthermore, the concept of masses whose magnitude varies with speed is superfluous since there are fields which exhibit that property and which are completely ignored in relativistic doctrine.

Relativistic dynamics found confirmation in the early experiments with mass spectrometry and the bending of electron trajectories in a magnetic field. The standard formula is,

eveB/c = mov2/r: The term on the left equals e2vevb/c2r2 which equals movevb(v2)/c2r (1)

where e = charge, mo = electron rest mass, B = magnetic field, (fundamental units), ve and vb are the electron and magnetic field source velocities (Bohr equivalence, mov2r = e2). Note that the magnetic field is identified as a conservative (potential) force.

The initial equality in (1) is not dimensionally correct or is at least simplistic, since there is a magnitude [v2/c2] that is not accommodated. The dimensions are that of an induced electric current and not of the principle force. However, the experimental result is known and is attributed to an incremental increase in the mass of the electron, whereas it is clearly a field configuration. The proper formulation for the experiment is found in the equations of relativity itself

Kinetic energy in relativity theory is defined as,

(m - mo)c2 = ½mvk2 = K (2)
mo/m = 1 – (vk2/2c2) = b1 (3)

As indicated, the presumed relativistic "mass" increase must be attributed to the incremental induced field - an increase in potential. This however, should be viewed as a displacement between fields. If this is the case, mass is unaffected and should drop out of the relativistic momentum-energy equivalence equations,

(Pc)2 +(moc2)2 = (K+moc2)2 (4)

and the equality,

b = (1-vm2/c2)1/2 = b1 = (1-vk2/2c2) (5)

where P = momentum, K = kinetic energy, vm and vk are the velocities of the momentum and kinetic energy equations.

m2vm2c2 + mo2c4 = m2vk4/4) + mmovk2c2 + mo2c4 (6)

m2vm2c2 - m2vk4/4 = mmovk2c2 (7)

mvm2 - mvk4/4c2 = movk2 (8)

movm2 - movk4/4c2 = movk2 - movk4/2c2 (9)

movm2 = movk2 - movk4/4c2 (10)

vm2 = vk2 - vk 4/4c2 (11)

Equation (11) is the proper configuration for the mass spectrometry of (1) as well as the transfer of any gain or loss in potential due to accelerations or deceleration. It involves a primary field, an induced (inertial) field and their issue. The [b1] formulation provides the same end result, but obscures the actual field configuration. In particular, relativistic velocity is a result of some impulse and cannot in any way contribute to the internal modifications. In view of the above, it should be patently obvious that special relativity is redundant since the experimental results are completely explained within the parameters of classical electrodynamics.

Walter Babin