The Bohr Atom of Glueballs

Recently Buniy and Kephart made an astonishing empirical observation, which anyone can reproduce at home. Measure the {\it lengths} of closed knots tied from ordinary rope. The ``double do-nut'', and the beautiful trefoil knot are examples. Tie the knots tightly, and glue or splice the tails into a seamless unity. Compare two knots with corresponding members of the mysterious particle states known as ``glueball'' candidates in the literature. Propose that the microscopic glueball mass ought to be proportional to the macroscopic mass of the corresponding knot. Fit two parameters, then {\it predict} 12 of 12 remaining glueball masses with extraordinary accuracy, knot by knot. Here we relate these observations to the fundamental gauge theory of gluons, by recognizing a hidden gauge symmetry bent into the knots. As a result the existence and importance of a gluon mass parameter is clarified. Paradoxically forbidden by the usual framework, the gluon mass cannot be expressed in the usual coordinates, but has a natural meaning in the geometry of knots.