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.