280 Chapter 18
“ melting temperature, ” Nambu thought of them as strings. Then, “ since the external
hadrons should also be strings, I formed a pictu re that the scattering is a process of two
incoming strings joining ends and separating again. ”^19 In his description, the strings seem
to come into physical existence as the analogy with simple harmonic oscillators coheres
with more and more facets of the argument. Nambu moved between a hypothetical, math-
ematical view and emergent physical insights about strings joining and separating.
Thus, the relativistic string began as an analogy of an analogy of an analogy, first to the
quantum-mechanical harmonic oscillator (via Planck, Heisenberg, and Schr ö dinger),
which is an analogical extension of Newtonian mechanics, which itself was a bold (and
in certain respects counterintuitive) mathematical representation of ordinary physical
strings. Yet in Nambu ’ s thinking, and in many developments since then, this analogic
hybrid has increasingly been treated as a candidate model of physical reality. The striking
accord between the features of the Veneziano amplitude and the dynamics of a hypothetical
string led to physical pictures of such strings inhabiting 26-dimensional worlds whose
degree of “ reality ” remains hotly debated.^20
Though several degrees removed from everyday experience, these analogies can only
operate by disclosing perceptible resonances between the terms they connect. For instance,
the experimental detection of a high-energy particle requires the observation of what is
still called a resonance , namely finding in particle data the same bell-shaped response
curve first derived from a glass resonating at its natural frequency (see figure 18.4, ♪ sound
example 18.2).^21 Thus, music continues to link vibrating bodies and particle physics, for
resonance is the hallmark of musical tone. Every effort of quantum field theory, string
theory, or loop quantum gravity (different as they are) ultimately may be traceable,
however distantly, to vibrating bodies and their sonorous mathematics. We must weigh the
continuity of that connection as well as how far it has been stretched. As with Wheatstone ’ s
Enchanted Lyre (figure 13.3), the faintness of the sound transmitted from its hidden source
is far less significant than the wonder of hearing it at all, however faintly. Indeed, the
mysterious faintness of that sound augments its wonder and its beauty; distance lends
enchantment to a sound heard from afar, no less than to a distant view. So too, I think, the
stretch to connect vibrating bodies and resonant particles intensifies the felt power of an
analogy that can sustain itself so far.
Long ago, Pythagoras ’ s younger contemporary (and critic) Heraclitus expressed this
important yet deeply surprising aspect of harmony: “ The unapparent harmony is stronger
than the apparent one ” ( Harmon í ē aphan ē s phaner ē s kre í ss ō n ).^22 His words compress
several senses: hidden (or invisible, a-phan ē s , un-apparent) harmony is stronger ( kre í ss ō n ),
more powerful, better than what is visible ( phaner ē s ) or apparent. The ever more hidden
harmonies that science seeks indeed have ever greater power (with all its promise and
danger) but are also may be more excellent, more beautiful, if Heraclitus is right.^23
For this and many other reasons the harmonic presuppositions of modern physics remain
subject to question. Kepler ’ s harmonic astronomy excluded the diverse, unrelated solar