William Kingdon Clifford - Premonition of Relativity

Premonition of Relativity

Though Clifford never constructed a full theory of spacetime and relativity, there are some remarkable observations he made in print that foreshadowed these modern concepts: In his book Elements of Dynamic (1878), he introduced "quasi-harmonic motion in a hyperbola". He wrote an expression for a parametrized unit hyperbola, which other authors later used as a model for relativistic velocity. Elsewhere he states,

The geometry of rotors and motors ... forms the basis of the whole modern theory of the relative rest (Static) and the relative motion (Kinematic and Kinetic) of invariable systems.

Common Sense of the Exact Sciences (1885), page 193 (This is p.193 of the Dover reprint: it's p. 214 in the 1885 edition, and immediately followed by a section on "The bending of space". However, as the preface (p.vii) this section was written by Karl Pearson - so maybe some of the credit should be given to KP.)

This passage makes reference to biquaternions, though Clifford made these into split-biquaternions as his independent development. The book continues with a chapter "On the bending of space", the substance of general relativity. Clifford also discussed his views in On the Space-Theory of Matter in 1876.

In 1910 William Barrett Frankland quoted the Space-Theory of Matter in his book on parallelism. He wrote:

The boldness of this speculation is surely unexcelled in the history of thought. Up to the present, however, it presents the appearance of an Icarian flight.

Years later, after general relativity had been advanced by Albert Einstein, various authors noted that Clifford had anticipated Einstein:

In 1923 Hermann Weyl mentioned Clifford as one of those who, like Bernhard Riemann, anticipated the geometric ideas of relativity.

In 1940 Eric Temple Bell published his The Development of Mathematics. There on pages 359 and 360 he discusses the prescience of Clifford on relativity:

Bolder even than Riemann, Clifford confessed his belief (1870) that matter is only a manifestation of curvature in a space-time manifold. This embryonic divination has been acclaimed as an anticipation of Einstein’s (1915–16) relativistic theory of the gravitational field. The actual theory, however, bears but slight resemblance to Clifford’s rather detailed creed. As a rule, those mathematical prophets who never descend to particulars make the top scores. Almost anyone can hit the side of a barn at forty yards with a charge of buckshot.

Also in 1960, at Stanford University for the International Congress for Logic, Methodology, and Philosophy of Science, John Archibald Wheeler introduced his geometrodynamics formulation of general relativity by crediting Clifford as the initiator.

In his The Natural Philosophy of Time (1961, 1980) Gerald James Whitrow recalls Clifford's prescience by quoting him to describe the Friedmann-Lemaitre-Robertson-Walker metric in cosmology(1st ed pp 246,7; 2nd ed p 291).

In 1970 Cornelius Lanczos summarizes Clifford's premonitions this way:

with great ingenuity foresaw in a qualitative fashion that physical matter might be conceived as a curved ripple on a generally flat plane. Many of his ingenious hunches were later realized in Einstein's gravitational theory. Such speculations were automatically premature and could not lead to anything constructive without an intermediate link which demanded the extension of 3-dimensional geometry to the inclusion of time. The theory of curved spaces had to be preceded by the realization that space and time form a single four-dimensional entity.

In 1990 Ruth Farwell and Christopher Knee examined the record on acknowledgement of Clifford's foresight. They conclude "it was Clifford, not Riemann, who anticipated some of the conceptual ideas of General Relativity". To explain the backward attitude to Clifford, they point out that he was an expert in metric geometry, and "metric geometry was too challenging to orthodox epistemology to be pursued." In 1992 Farwell and Knee continued their study with "The Geometric Challenge of Riemann and Clifford" They "hold that once tensors had been used in the theory of general relativity, the framework existed in which a geometrical perspective in physics could be developed and allowed the challenging geometrical conceptions of Riemann and Clifford to be rediscovered."