Repeating the Words of Power: Hamiltonian Dynamics and Physical Speculation in Late Nineteenth Century Britain

“It is remarkable how slow natural philosophers… have been to make use of [Lagrangian and Hamiltonian] methods… [But] now the feeblest among us can repeat the words of power and take part in dynamical discussions” (Maxwell, 1879). Through their work in the 1860s and 70s, James Clerk Maxwell and his influential friends William Thomson and Peter Guthrie Tait strongly promoted the power of Hamiltonian dynamics to coordinate macroscopic observations without reference to underlying physical structures. The outcomes — their development of thermodynamics and electromagnetism — are well known. But Hamiltonian dynamics also presented an epistemic challenge, as underlying structures were, in principle, indeterminate. The issue became particularly acute after 1877 when the Cambridge mathematician Edward Routh highlighted that some of the coordinates describing the structures might be cyclic, not explicitly entering the Hamiltonian expression of the system. This rendered them unobservable and hence unknowable. Rather than viewing this as a problem, this paper explores the ways in which the removal of underlying structures from precise empirical study may have been liberating, helping to explain the exploitation of Hamiltonian methods by men such as Tait, Balfour Stewart, Joseph John Thomson, Oliver Lodge, and Joseph Larmor. Hamiltonian dynamics provided a space in which speculative mechanisms became conceptual objects that could be explored mathematically. These mechanisms were heuristically valuable precisely because they were physically intelligible without requiring belief in their empirical reality. Such speculations were crucial, for example, in Thomson’s and Larmor’s development of corpuscle/electron concepts, and arguably of Tait and Stewart’s anti-materialist “Unseen Universe”.