How physics got its right hand: The origins of chiral conventions in electromagnetism

How physics got its right hand: The origins of chiral conventions in electromagnetism Tyler McMaken∗ Department of Mathematics and Physics, University of Mary, Bismarck, ND 58504 (Dated: December 23, 2025) Abstract Why do physicists almost universally take the direction of positive rotation to be counterclock- wise, and three-dimensional coordinates to be right-handed? This paper traces the historical development of these chiral conventions, with an emphasis on the physical quantity whose di- rection became the focal point of this discussion in the mid-1800s, the magnetic field. Though these standards are often reduced to mere mathematical, inconsequential choices, an analysis of the impact of Newton, Maxwell, the London Mathematical Society, and others toward the subject can enhance classroom discussion, not only as a contextual sidebar, but also by emphasizing the influence conventions in physics can have on pedagogy, communication, and scientific advancement. ∗tcmcmaken@umary.edu 1 arXiv:2512.18040v1 [physics.hist-ph] 19 Dec 2025 I. INTRODUCTION In both mechanics and electromagnetism courses, a common question that often arises from students is related to the origin of right-handed coordinates and other similar conven- tions in physics: Why is counterclockwise rotation defined as positive? Who decided that magnetic fields and other axial vectors follow a right-hand rule and not a left-hand rule? Is there a physical reason behind it all, or at least a pedagogical or historical one? The answer usually given to these questions in textbooks and by many instructors is to brush them off as unimportant—they are merely conventions and have no bearing on physical observations, so one should take care only to be consistent and acquainted with the greater scientific community’s practices. Any further consideration would then be unproductive and take time away from the issues that really matter. Some go further to give speculative or even erroneous explanations for the origin of these conventions, like that right-handed coordinates became conventional because the majority of people are right-handed, or that counterclockwise angles have been the norm among mathematicians since at least the time of Babylonian astronomy. Readers may be surprised to learn that the aforementioned conventions were only fixed because of a vote of the London Mathematical Society in 1871 at the behest of James Clerk Maxwell. The goal of this work is to recount the fascinating story of the historical development of chiral conventions in physics, culminating in Maxwell’s efforts to understand and create a shared language for the axial vectors of electromagnetism. To help frame the discussion, consider Faraday’s law of induction, which states that an electromotive force E around a conducting loop is caused by a change in magnetic flux through a surface Σ enclosed by that loop (for example, when a bar magnet is moved toward a loop of wire to induce a current): E = −d dt ZZ Σ B · dA. (1) It is a useful exercise for students to reflect on how changes in underlying conventions would affect a given equation. Some conventions, like the choice of area vector dA as into or out of the loop, are completely arbitrary and must be decided for each given setup, while others, like the three outlined below, have been fixed in advance by scientific consensus. In particular, consider what would happen to the above form of Faraday’s law if (1) the 2 sign of electric charge (and therefore the direction of conventional current and the sign of E = dW/dq) were reversed, (2) the north/south polarity of magnetism (and therefore the conventional direction of B-field lines) were reversed, or (3) the right-hand rule were exchanged for a left-hand rule. In all three cases, the minus sign of Eq. 1 would become a plus sign. Nonetheless, for some problems in physics (e.g., Gauss’s law), the equations are com- pletely unaffected by the three above conventions. Often, this is the result of an internal cancellation of two sign changes; for example, students switching to a left-hand rule when using Eq. 1 will still obtain the same direction for the induced current if they also use a left-hand rule for Amp`ere’s law when determining the direction of the magnetic field from a source current. In this case, it becomes apparent that Lenz’s law is not encoded in the minus sign of Eq. 1. Even if the magnetic field direction were reversed such that E = +dΦB/dt, students can check that the induced magnetic field still opposes the original field, as a result of the relative sign difference between the two dynamical Maxwell equations (and ultimately from Lorentz covariance of the electromagnetic field tensor). The above enumeration of conventions baked into Eq. 1 will serve as an outline for the remainder of this paper as we proceed chronologically through history. To begin, Sec. II will discuss a mathematical convention that, like dA, is completely arbitrary (but, as will be seen, had a

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