Copyright 2004 - 2013 David V Connell.

Theoretical Considerations.
    Curvilinear motion may be described as the curved path of a moving particle which is not part of or attached to another body, often in a circular path. The latter is of interest here.
    The possible effects of rotation on the mass of a particle at a radius r from the center of rotation are considered to be from three sources :-
    ( i ) the tangential speed of the particle,
    ( ii ) the centripetal force causing the path of the particle to be circular, and
     (iii ) the centrifugal force caused by the rotation.
    We now consider a charged particle of mass M moving at speed V in a particular direction, in a chosen FoR, free from any significant effects of gravity. A constant external force is then applied to the particle by a uniform magnetic or electric field perpendicular to the direction of motion, causing it to take a circular path in a plane perpendicular to the magnetic or electric field.
    In experiments of this type, a magnetic field H causes a curvature of the path of electrons to a radius r, where the transverse force generated by the motion in the magnetic field is equal and opposite to the centrifugal force, according to the relation HeV = MV²/r, where e is the charge on the electron and M is its effective mass,
giving                                                     Hre = MV = p                                                            (1)
    A radial electrostatic field X has a similar effect according to the relation
                                                                Xre = MV²                                                                  (2)
    Equations (1) and (2) were expected to be used as simultaneous equations to solve for mass and speed, to confirm the SR equation, hence the following were derived from the above,
the mass ratio                                    M/Mo = (e/Mo)(Hr)² /Xr                                              (3)
and the speed                                            V = Xr / Hr                                                            (4)
    It is considered that the deviation from a straight line caused by the magnetic field is analagous to a fast moving body in gravitational free fall - a reduction in mass and a gain in speed (since a magnetic field cannot supply any energy), resulting in a reduction of the gradient of the line on a chart of M/M0 versus V²/c² (The Chart).
    An electric field is an energy field and does transfer energy to charged particles, but since motion in the direction of the electric potential is blocked by the centrifugal force it is postulated that an energy transfer is in the form of an increase in mass, and conservation of momentum could cause a reduction in speed. These effects are opposite to those from the application of a magnetic field, causing different values for the resulting mass and speed. Any differences in the values of M or V from applying the two types of field invalidates the use of eqs. 3 and 4, which would then produce strange results.
    Using both fields simultaneously would not avoid this problem as the two forces are additive and combine to oppose the centrifugal force,
hence                                          HeV + Xe = MV²/r                                                (5)
and eq.5 has the same two unknowns.

    Two published experiments accurate enough to detect the difference between NR and SR predictions were investigated and their underlying theories were discovered to be faulty.

   1. The Geller and Kollarits Experiment (1972).
    This experiment [1] used only a magnetic field, on Beta particles, but measured the final KE, and used a radius of curvature of 2 inches (0.0508m). It was used by students at Drexel University, Philadelphia and demonstrates relativistic mass changes with KE, without attempting to solve for the speed. Only the gradient of the line on a chart of mass -v- kinetic energy and the intercept on the mass axis were of interest.
    The kinetic energies T were obtained by a relative calibration method and also by an absolute method. Not all experimental values were given in their text for T (MeV) and H (Gauss), some were obtained from their chart (having axes (Hre)² , and T ).

( i ) From M = p²/2T, where 2T = MV², the masses are calculated and a chart of  p²/2T vs T plotted.
    Examination of the experiment theory reveals that an SR equation, E2 = c²p² + Eo2   (which is another form of the Lorentz/Einstein mass-ratio equation) was combined with their eq.(3M = Mo + T/c² where each equation predicts the mass ratio to be different for the same speed! Therefore their resulting eq.(4), p²/2T = Mo + T/2c² cannot be valid.
    Avoiding their invalid eq.(4) and using their eq.(3) instead, results in an increase by a factor of 2 on the theoretical gradient, from 1/2 to 1/, on the chart.
    As the experimental points fitted the original theoretical line quite well, the gradient of the line must have been reduced to half its new theoretical value by the reduced mass and the increased speed.

(ii ) This experiment confirms a relativistic change of mass with KE, but not the SR version, producing in this case a reduction from the corrected theoretical gradient of the line by a factor of two (within experimental limits), probably due to the small radius of curvature, and possibly encouraging the experimenters to match this with a strange piece of mathematical manipulation to produce agreement with the value of c.
    From 2T= MV², which is valid for unrestricted and restricted motion, the values of V² are obtained from the values of T and M, and are independent of the 'adjustment' to the expected gradient of the line on the chart. The experiment values of T, M, and M/Mo are shown in columns 1, 2, 3, 4, and the resulting values of V²/c² in column 5 of Table I.

Table I. Experimental Data and Calculated Results
     T          T(10-14)     M(10-30)    M / Mo      (V/c)²
  (MeV)     (Joules)        (Kg)          (4)              (5)
   .690        11.04          1.526          1.673          1.607
   .612          9.79          1.452          1.592          1.498
   .542          8.67          1.379          1.515          1.397
   .482          7.72          1.316          1.443          1.303
   .420          6.72          1.262          1.384          1.183
   .350          5.60          1.220          1.338          1.020
   .274          4.39          1.156          1.267          0.844
   .235          3.76          1.123          1.231          0.744

    Values of V/c greater than 1.0 are quite normal for Beta particles in Natural Relativity, but are declared to be impossible in SR.
         SR is proved to be wrong at relativistic speeds by these experimental results

2. The Rogers' et al Experiment (1940).
    In this other modern-type particle experiment [2], possibly useful for investigating the Curve Effect (found in the Geller & Kollarits experiment), both magnetic and electric fields were applied separately to obtain data for analysis. This experiment was very similar to the Geller and Kollerits experiment, but produced very different results, which could be due to the use of an electric field (see eq.2 above), instead of measuring the KE. The calculated results lie near the SR curve on the above chart, whereas those from [1] lie well away from it.
    From the above theory, the use of an electric field would cause different values for mass and speed, invalidating the use of the simultaneous equations. In fact they were used to calculate the resulting three pairs of values, which, by coincidence, agreed with the predictions of SR (within experimental uncertainty). Strange results were to be expected!
    Questions arise. Would particles in a different range of energies, or data obtained using a different radius, (or both) have agreed with SR? Would Rogers'-type experiments have been published if they produced strange results? Does no one check the physics theory and mathematics of papers before publication ?

Future Investigation.
    The effects of magnetic and electric fields on charged particles needs to be investigated further. It is hoped that these experiment can be repeated using, as appropriate, magnetic and electric fields separately, a KE detector, a wider range of known source speeds, and hopefully some different radii. Pulses of accelerated electrons fed into, or through, a magnetic field containing a time of flight measuring system and a KE detector could produce very useful data, if practicable.
    Knowledge of the initial and final velocities are necessary to properly analyze the above experiments, but the author has been unable to obtain that information, but hopes that investigation into these effect will be made not too long in the future. No other modern experiments of this type have been found for investigation and/or to supply better data. There appears to be extremely few published experiments in this field. The answers to the above questions could explain that. Could there be some unpublished ones filed away that could be useful in this endeavor? The data the author was unable to obtain could be useful too.

  1. K.N. Geller and R. Kollarits, "Experiment to Measure the Increase in Electron Mass
    with Velocity", Am. J. Phys 40, 1125-30 (1972).
  2. M.M.Rogers, A.W.McReynolds and F.T.Rogers,Jnr, "A Determination of the Masses
    and Velocities of three Radium B Beta-Particles", Phys.Rev. 57, 379-83 (1940).

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