Weber-type Laws of Action- at-a-Distance in Modern Physics

Recent data indicate that the law of action between electric current elements proposed by Ampere is notably superior to the Lorentz (Biot-Savart) law in its ability to describe laboratory observations of currents flowing in single circuits. Ampere's law conforms to Newton's third law and thus cannot be covariantly expressed. Since all field theories of retarded action violate Newton's third law in describing nonstatic situations, it appears that the observational evidence in question weighs against all field theories as applied to the description of force actions. A reexamination of force instant action-at-a-distance modes of description is therefore indicated. We investigate here the possible revival of such a formulation proposed by W. Weber before 1850. The virtues of this approach are (a) mathematical simplicity, (b) rigorous conformity to Newton's third law, and (c) agreement with Ampere's law of action between current elements—hence with the observations just mentioned. Two different " modernizations " of Weber's approach are examined, dependent on whether energy or force methods are viewed as more fundamental in mechanics. Implications for plasma physics are touched upon.