Resonance: Joining and Knitting Together

All that is known owes its renown to the splendour of Thy Name, the Most Manifest, and every object is deeply stirred by the vibrating influence emanating from Thine invincible Will.

(The Bab, Selections from the Writings of the Bab: 195)

In this post and the next, through the phenomenon of resonance, I will propose a way to look at how the bonding, the joining and knitting together, of the spiritual worlds and material worlds may take place.

Briefly, because the spiritual and the material are exact counterparts, resonance operates or can operate between the spiritual and material realms.  When they are joined and knit together these realms are coherent at every level, like fractal spun yarn or large scale symmetry between levels of matter.  Resonance, the harmony of frequencies effected by the “vibrating influence” of the divine Will calling into being a new creation, is the mechanism of joining and knitting.  When coherence is achieved between the spiritual and material they become a resonant structure.  The finding of equivalent material vibration to manifest a vibrating spiritual reality is the creation of harmony between these two realms (the treble and bass, so to speak) and is, I believe, the basis of the phenomenon of manifestation.  First, what is resonance?

The word resonance comes from Latin and means to "resound"—to sound out together with a loud sound: an apt metaphor when linked with metaphors of creation by uttering the Word.  Resonance phenomena occur with all types of vibrations or waves.  Resonance needs a medium for waves and vibrations to travel through.  Resonance is the reinforcement or prolongation of sound by reflection from a surface or by the synchronous vibration of a neighboring object. 

There is resonance as the harmonics of interplay between interacting things, the vibratory frequencies that combine harmoniously to create, enhance and reinforce the equilibrium of living things.  The concept of resonance captures the interplay of the qualities of the field and all its interacting parts.  It is a fundamental quality of creation.

Resonance works in auditory harmonics as vibratory resonance.  In music, the natural frequencies of a musical instrument are sometimes referred to as the harmonics of the instrument. An instrument can be forced into vibrating at one of its harmonics if another interconnected object pushes it with one of those frequencies. When one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion that is resonance.  Resonance only occurs when the first object is vibrating at the natural frequency of the second object. 

In physics, resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at a specific preferential frequency.  Frequencies at which the response amplitude is a relative maximum are known as the system's resonant frequencies. At these frequencies, even small periodic driving forces can produce large amplitude oscillations, because the system stores vibrational energy.

That means that acoustic resonance can result in catastrophic breakdown of the object at resonance with too much positive feedback. The classic example of this is breaking a wine glass with sound at the precise resonant frequency of the glass.  Soldiers tramping across abridge in lockstep can set up such a vibration that it can shake the bridge down, whereas if they break stride and go over with separate steps all is well, for individual vibrations cancel out.

In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists—similar to the breakdowns in acoustic resonance. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance.

Resonance also occurs not only between structures or things but also within structures when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a pendulum). However, there are some losses from cycle to cycle, called damping. When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies. The exact response of a resonance, especially for frequencies far from the resonant frequency, depends on the details of the physical system, and is usually not exactly symmetric about the resonant frequency.  This is like Dissipative structures.

In chemistry, resonance is a way of describing delocalized electrons within certain molecules where the bonding cannot be expressed by one single Lewis Structure. (A Lewis Structure is a kind of diagram or formula that shows the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule.)  A molecule or ion with such delocalized electrons is represented by several contributing structures, also called resonance structures or canonical structures.  The greater the number of contributing structures, the more stable the molecule.

In Lewis formulas, electrons are paired between atoms to form covalent bonds.  In molecules or ions that have a combination of one or more single and multiple bonds, often the exact position of the respective bonds cannot be indicated by a single Lewis structure. (Indeterminancy is a basic quantum principle.) That is, the bonded electrons appear to occupy an intermediate position between molecules. To solve this problem, the concept of resonance is used, and the molecule is represented by several contributing structures, each showing a possible distribution of single and multiple bonds. The actual structure has a lowered overall energy and an intermediate bond order.  The molecule is said to be "stabilized by resonance" or "resonance-stabilized".  The Lewis Structure is a visual image to try and capture what is really this shared, resonance energy. 

Every structure is associated with a certain quantity of energy, which determines the stability of the molecule or ion--the lower the potential energy, the greater stability because more of the potential energy has become manifest in form. The actual structure of a molecule in the normal quantum state (the molecule with its contributing structures) has the lowest possible value of total energy. This shared structure of the molecule and all its contributing structures is called the "resonance hybrid" of that molecule.

The resonance hybrid has a structure that is we can say is “intermediate” between the contributing structures; the total quantity of potential energy, however, is lower than the intermediate and hybrids are therefore always more stable than any of the contributing structures would be, because they are all together in balance or equilibrium.   The difference between the potential energy of the actual structure (the resonance hybrid) and that of the contributing structure with the lowest potential energy is called the "resonance energy.”

It is important to remember that resonance structures—the totality of connected molecules mapped by Lewis structures—are not transient states between stable contributing states, a form oscillating between stable states or existing as a temporary equilibrium between them.  Resonance-stability is a hybrid state existing in only one form, the form of a balance of forces.  Since no actual form of the resonance-hybrid can be observed to be resonating it can be said to be nonlocalized, or delocalized. Resonance energy would, too, be delocalized energy existing not in a field but as a field of which any particular molecule would be a concretion and configuration of that energy.

Quantum mechanics requires that the wavefunction of a molecule obeys its observed symmetry. If a single contributing structure does not achieve this, resonance is invoked.  Thus resonance is associated with symmetry.  If contributing structures have equal energy, they are equal contributors to the overall structure.  But this need not be the case. The symmetric combination gives the ground state while the antisymmetric combination gives the first excited state.

Hence, as we read with the breakdown that can occur with acoustic resonance and in celestial mechanics, chemical and molecular resonance is not just about achieving stability, symmetry, and balanced structure, but is also connected with freedom and creativity.  A physical system can have as many resonant frequencies as it has degrees of freedom, each degree of freedom can vibrate as a harmonic oscillator.  But there is the potential for instability, disequilibrium and new harmonics built into the system.  Here we transition to resonant intervals.  That is the topic of the next post.