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An experimental investigation ofthe influence of an electrostaticpotential on electron mass aspredicted by Weber’s force law

Johann E. Junginger and Zoran D. Popovic

Abstract: Assis (J. Phys. Soc. Jpn. 62, 1418 (1993).) showed that Weber’s force law betweenmoving charges leads to the conclusion that the inertial mass of an electron depends onthe charges that surround it. The experimental confirmation of this effect was claimedby Mikhailov (Annal. Fond. Louis de Broglie, 24, 161 (1999).) who detected frequencychanges of a glow discharge lamp oscillator as a function of the voltage applied to theshield surrounding the oscillator. We carefully repeated the experiment employing an opticalrather than the electrical coupling, used by Mikhailov, to measure the oscillator frequencyas a function of shield voltage. Our results did not show any frequency changes associatedwith the change in shield voltage that could be interpreted as a change in the electron massinduced by the surrounding charges. As this effect is an inescapable consequence of Weber’sforce law, our experiment strongly indicates that this force law is not valid.

PACS No.: 41.20.–q

Résumé : Assis (J. Phys. Soc. Jpn. 62, 1418 (1993).) a montré que la loi de force deWeber entre des charges en mouvement mène à la conclusion que la masse inertielle del’électron dépend des charges qui l’entourent. Mikhailov (Annal. Fond. Louis de Broglie,24, 161 (1999).) déclare avoir détecté expérimentalement cet effet dans des déplacementsen fréquence d’un tube à décharge en fonction du voltage appliqué au blindage entourantl’oscillateur. Nous avons répété avec beaucoup de soins cette expérience, employant uncouplage optique plutôt qu’électrique, afin de mesurer le déplacement en fréquence enfonction du voltage sur le blindage. Nos résultats ne montrent aucun déplacement enfréquence avec le changement de voltage qui indiquerait une variation de la masse avec lescharges l’entourant. Puisque cet effet est un effet incontournable de la loi de force de Weber,nous devons conclure que cette loi de force n’est pas valide.

[Traduit par la Rédaction]

1. Introduction and theory

Electrodynamics as formulated by Weber’s force law is termed Weber’s electrodynamics in contrastto the better known electrodynamics of Maxwell. Renewed interest in Weber’s electrodynamics has been

Received 9 December 2003. Accepted 30 June 2004. Published on the NRC Research Press Web site athttp://cjp.nrc.ca/ on 20 August 2004.

J.E. Junginger and Z.D. Popovic.1 Xerox Research Centre of Canada, Mississauga, ON L5K 2L1, Canada.

1 Corresponding author (e-mail: zoran.popovic@crt.xerox.com).

Can. J. Phys. 82: 731–735 (2004) doi: 10.1139/P04-046 © 2004 NRC Canada

732 Can. J. Phys. Vol. 82, 2004

reported in the literature recently [1–6]. Cavalleri et al. [7, 8] presented theoretical arguments indicatingthat Weber’s force law is not valid, based on their conclusion that it cannot account for synchrotronradiation and also gives the wrong direction for the radiation field. This is in contrast to recent reports [5,6] claiming experimental observation of one of the critical consequences of Weber’s electrodynamics,which is not predicted by Maxwell’s theory. In this note, we will present an improved measurement toaddress, experimentally, the question of the validity of Weber’s force law.

Maxwell’s electrodynamics assumes a force law that does not satisfy the customary action/reactionlaw of classical mechanics [4]. Weber’s force law between two charged particles q1 and q2 separatedby a distance r is given by

F = q1q2

4πε0· r

r3 ·(

1 − r

2c2 + rr

c2

)(1)

where c is the speed of light in a vacuum and ε0 is the permittivity of free space [1–4].The alternative expression proposed by Weber satisfies the action/reaction law and gives identical

results as the accepted force law in the case of attraction between static charges (Coulomb’s law), theforce between two charges moving at constant velocity (Lorentz’law), and also explains the phenomenonof electromagnetic induction. A comprehensive overview of the subject matter can be found in Fukai’sbook [4].

According to Assis [1, 2], there are experimental conditions under which Weber’s force law givesdifferent predictions from Maxwell’s electrodynamics. One specific experimental geometry that leadsto this distinctly different result is the motion of a test charge within a uniformly charged sphericalshell. According to Weber’s electrodynamics the inertial mass change of the charged particle q insidethis shell is given by

mw = qQ

12πε0c2R= qV

3c2 (2)

where Q is the uniformly distributed total charge on the enclosing spherical shell, R is the shell diameter,and V is the shell surface potential referenced to infinity. This mass difference, mw, is termed Weber’sinertial mass. Verifying Assis’prediction under these experimental conditions represents a critical test ofthe validity of Weber’s electrodynamics. Mikhailov reports experimental results [5, 6], which, if correct,would represent the evidence in favour of Assis’ theorized inertial mass effect. This paper discussesan experiment that is similar to Mikhailov’s experiment [5] but which fails to show any evidence insupport of the theorized Assis effect. The authors will propose an explanation as to why Mikhailov’sobservations may have been incorrectly attributed to the theorized Assis effect.

2. Experimental set-up

This investigation was inspired by the work of Mikhailov [5]. The experiment involves measure-ment of the oscillation frequency of a neon-glow-lamp oscillator placed inside a conductive sphericalenclosure biased to high voltage. Briefly, Ton ∼= k1Ron where Ton is the on time of the neon glowlamp, Ron is the differential on resistance of the neon glow lamp, and k1 is a proportionality constant.Also, Ron ∼= k2me where me is the electron mass and k2 is a proportionality constant. As such we haveTon ∼= k1k2me or �Ton ∼= k1k2�m, if the electron mass changes. Assuming that �m = mw and using(2) we obtain

�Ton

Ton

∼= mw

me= eVbias

3mec2 (3)

With a 10 kV bias potential and with mec2 = 511 keV, we have mw/me = 6.52 × 10−3. In our

experiment, it is the total period T that is measured, where T = Ton + Toff and Toff is the time in the

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Junginger and Popovic 733

Fig. 1. Schematic diagram of the experiment.

Power Supply(±10 kV)

9V

Vbias

Voltageregulator - 5V

10KHV DC-DCConverter

~200 V RC

Neonlamp

Fibre optic cable

Conductive Enclosure~ 40 x 40 x 40 cm

PulseShaping Circuit

PulseCounter

out

out

out

out

out

in

gnd

com

in

com

in

in

gnd

gnd

gnd

Vc

Oscillator circuit issuspended in the center ofthe enclosure.

R = 1.0M-Ohm, C = 10nFgives frequency ~700 Hz

Photodiodeand Amplifier

cycle during which the lamp is off. Given that the duty cycle, fduty = Ton/T , of the neon lamp used forthis experiment is 21%, we have a predicted �T/T ∼= fduty ×mw/me = 1.4×10−3. Mikhailov did nottake into account the duty cycle of the oscillator in his experiment [5]. This is equivalent to assumingthat electrons in the rest of the circuit behave in an identical manner as those in the neon glow dischargetube. This changes the magnitude of the predicted effect but qualitatively the effect remains the same,i.e., the oscillator frequency depends on the voltage applied to the conductive enclosure.

A neon lamp oscillator circuit as shown in Fig. 1 was constructed. The circuit was designed to bepowered by a battery to ensure the circuit is electrically isolated from the environment. The outputof a 9 V battery is regulated to 5.0 V by a manufactured solid-state voltage regulator. The 10 k�

potentiometer adjusts the voltage delivered to the input of the high-voltage DC–DC converter (SpellmanMM0.5P1.5/12). The potentiometer is adjusted to give ∼200 V at the output of the DC–DC converter.During the charging portion of the cycle the neon lamp (Chicago Miniature A1B) is off and the high-voltage output charges capacitor C through resistor R until the ignition voltage of the neon lamp isreached. During the discharge cycle, the lamp is on, rapidly discharging C until the turn-off thresholdis reached. R = 1.0 M� and C = 10 nF were chosen to give a frequency of oscillation of ∼700 Hz.

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734 Can. J. Phys. Vol. 82, 2004

Fig. 2. Light pulses from oscillator (counted for 100 s) versus measurement start time. The continuous linerepresents a linear fit to data points obtained at zero enclosure bias. The broken lines above and below thedata points are the Weber’s-law predictions for enclosure biases of +10 kV and −10 kV.

68 850

68 900

68 950

69 000

69 050

69 100

69 150

69 200

69 250

0 5 10 15 20 25 30 35

Measurement Start Time (min)

Cou

nts

per

100

s-10 kV bias0V bias+10 kV biasFit - 0V Bias

Such choice permits frequency measurements to five significant digits within a reasonable time period(100 s) using a pulse counter.

The circuit is suspended with nylon line in the center of an approximately 40 × 40 × 40 cm3

enclosure completely covered in conductive foil, forming a Faraday cage. The output of a high-voltageDC power supply (Trek 610D) is connected to the enclosure to provide the bias. A cubic geometry waschosen for the simplicity of implementing the experiment. This change in geometry would change theproportionality constant between the applied bias and mw (2) somewhat but cannot reduce the effect tozero.

As shown in Fig. 1, pulses of light from the neon glow lamp are transmitted through a fibre-opticcable to an external photodiode electrically isolated from the experimental enclosure. The photodiodecircuit triggers a digital pulse-shaping circuit (Stanford Research Systems DG-535) with every flashof the neon lamp. The pulses are then counted over a span of 100 s by a counter (Princeton AppliedResearch 1109).

3. Experimental results and analysis

It was observed that the frequency of the oscillator was drifting in a small but predictable fashion(∼3 Hz/h). This drift was compensated for by performing repetitive measurements at 0, +10 kV, 0,−10 kV, …, etc., at constant 2 min time increments.

The results are plotted in Fig. 2. The effect predicted for Weber’s electrodynamics (0.14% changeunder 10 kV bias) is also plotted. We observe a negative result — the oscillation frequency drifts linearlyand predictably for the duration of the experiment but there is no change as a function of bias voltage.

The 0 and ±10 kV data shown in Fig. 2 are linearly fitted using the method of least squares under theassumption of a common slope. The intercepts are identical within one count which is 1 part in 69 100,i.e., the relative error in measuring the possible influence of applied voltage on oscillation frequency is1.4 × 10−5, which is 100 times smaller than the expected magnitude of the effect (1.4 × 10−3).

Our results, therefore, show that the expected change based on Weber’s electrodynamics is notobserved, suggesting that Weber’s force law is not valid.

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Junginger and Popovic 735

A possible cause of Mikhailov’s positive result may be due to his choice of coupling the signalsfrom the neon-glow-lamp oscillator to an external counter through a capacitor rather than through anelectrically isolated optical fibre, as done in the present work. Any small leakage current through thecapacitor will impact the frequency of the oscillator and this leakage will change as a function of thebias voltage.

4. Conclusion

We have measured the frequency dependence of a glow discharge oscillator placed within a Faradayenclosure biased to different potentials. Weber’s theory predicts that biasing would induce changes inthe inertial mass of the electron and, therefore, the frequency of the neon discharge oscillator. We usedoptical coupling to measure the oscillator frequency for different cage biases and found no frequencychanges. As, according to Assis, the change of inertial electron mass in the described system is aninescapable conclusion of Weber’s electrodynamics, we feel that our negative result provides strongevidence that Weber’s force law is not correct.

Acknowledgements

The authors would like to acknowledge helpful correspondence withV.F. Mikhailov andA.K.T.Assisduring the design phase of this experiment and the subsequent preparation of this paper. In particular,we would like to thank A.K.T. Assis for encouraging us to publish this work.

References

1. A.K.T. Assis. J. Phys. Soc. Jpn. 62, 1418 (1993).2. A.K.T. Assis and A. Torres Silva. Pramana J. Phys. 55, 393 (2000).3. T.E. Phipps. Phys. Essays, 5, 425 (1992).4. J. Fukai. A promenade along electrodynamics. Vales Lake Publishing, Pueblo West Colo. (2003).5. V.F. Mikhailov. Annal. Fond. Louis de Broglie, 24, 161 (1999).6. V.F. Mikhailov. Annal. Fond. Louis de Broglie, 26, 633 (2001).7. G. Cavalleri, E. Tonni, and G. Spavieri. Hadronic J. 21, 459 (1998).8. G. Cavalleri, G. Bettoni, E. Tonni, and G. Spaviery. Phys. Rev. E, 58(2), 2505 (1998)

© 2004 NRC Canada