Models.Behaving.Badly. by Emanuel Derman

Author:Emanuel Derman
Language: eng
Format: epub
Publisher: Free Press

Figure 4.3. Ampère’s Law: The magnetic forces that two current elements, I1 of length dl 1 and I2 of length dl 2, separated by a distance r21, exert on each other. Each element can point in an arbitrary direction, and they can be separated by an arbitrary distance. Ampère’s formula is shown boxed.

A SYMPATHETIC UNDERSTANDING

Ampère titled his paper “Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience.” But as Henri Poincaré remarked in 1905 about “Ampère’s immortal work,” Ampère’s laws could not have been deduced from experience, because he had no infinitesimal currents to experiment with. Only what Einstein called intuition or a “sympathetic understanding of experience” could have led him from observations of entire circuits to a law for infinitesimal current elements. In his encyclopedic A Treatise on Electricity and Magnetism, James Clerk Maxwell later wrote:

The experimental investigation by which Ampère established the laws of the mechanical action between electric currents is one of the most brilliant achievements in science.

The whole, theory and experiment, seems as if it had leaped full grown and full armed from the brain of the “Newton of Electricity.” It is perfect in form and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electro-dynamics.

The method of Ampère, however, though cast into an inductive form, does not allow us to trace the formation of the ideas which guided it. We can scarcely believe that Ampère really discovered the law of action by means of the experiments which he describes. We are led to suspect, what, indeed, he tells us himself, that he discovered the law by some process which he has not shown us, and that when he had afterwards built up a perfect demonstration, he removed all traces of the scaffolding by which he had built it.

Maxwell, who performed his own magic, recognized that miraculous discoveries seem to leap out of the mind’s invisible Dirac sea, elicited by intuition.

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