Vibration: 'Everything Vibrates' as Fourier Analysis and Wave Mechanics

BY NICOLE LAU

The third Hermetic Principle, from The Kybalion:

"Nothing rests; everything moves; everything vibrates."

For over a century, this has been read as mystical insight—a poetic claim about the dynamic nature of reality.

But what if it's not mysticism at all?

What if it's mathematics—a precise statement about Fourier analysis, the mathematical theorem that any function can be decomposed into a sum of periodic vibrations?

In this article, I'll prove that the Hermetic Principle of Vibration is mathematically equivalent to Fourier analysis, wave mechanics, and the fundamental wave nature of reality discovered by quantum physics.

Not metaphorically. Exactly.

The Mathematical Translation: Fourier Analysis

Hermetic Version:
"Nothing rests; everything moves; everything vibrates."

Mathematical Version:
Any function f(x) can be expressed as a sum of sine and cosine waves:

f(x) = a₀/2 + Σ(n=1 to ∞)[aₙcos(nx) + bₙsin(nx)]

Where:
• aₙ = (1/π)∫f(x)cos(nx)dx
• bₙ = (1/π)∫f(x)sin(nx)dx

This is the Fourier series—the mathematical proof that everything can be decomposed into vibrations.

Same claim. Different language.

What Fourier Analysis Actually Says

Joseph Fourier (1768-1830) discovered something profound:

Any periodic function—no matter how complex—can be built from simple sine and cosine waves.

Think of it like music:

• A complex chord = sum of pure tones
• A complex waveform = sum of simple sine waves
• Any vibration = combination of fundamental frequencies

This isn't approximate. It's exact. Given enough terms in the series, you can reconstruct any function perfectly.

The Fourier Transform extends this to non-periodic functions:

F(ω) = ∫f(t)e^(-iωt)dt

This transforms a function from time domain to frequency domain—revealing its vibrational components.

Everything Vibrates: Quantum Mechanics

The Hermeticists claimed "everything vibrates." Quantum mechanics proved it.

1. Wave-Particle Duality

All matter has wave properties. De Broglie wavelength:

λ = h/p

Where:
• λ = wavelength
• h = Planck's constant
• p = momentum

Even massive objects have wavelengths. Everything is a wave. Everything vibrates.

2. The Schrödinger Equation

Quantum mechanics describes particles as wave functions:

iℏ ∂ψ/∂t = Ĥψ

The wave function ψ is literally a vibration in quantum field. Particles are excitations (vibrations) of quantum fields.

3. Zero-Point Energy

Even at absolute zero (0 Kelvin), quantum systems vibrate:

E₀ = ½ℏω

Nothing is ever truly at rest. Everything vibrates, even in the ground state.

The Hermetic principle, proven by quantum mechanics.

Everything Vibrates: String Theory

String theory takes "everything vibrates" to the ultimate level:

All particles are vibrating strings.

• Electron = string vibrating one way
• Photon = string vibrating another way
• Quark = string vibrating yet another way

Different particles = different vibrational modes of the same fundamental string.

Mathematical description:

X^μ(σ,τ) = x^μ + p^μτ + i√(α'/2) Σ(1/n)[α_n^μ e^(-inτ) + α̃_n^μ e^(inτ)]

This describes a vibrating string in spacetime. All of reality = vibrations.

The Hermetic principle, taken to its logical conclusion.

Specific Examples of Universal Vibration

Example 1: Light

Light is electromagnetic vibration:

• Red light: ~430 THz (430 trillion vibrations per second)
• Green light: ~540 THz
• Blue light: ~670 THz
• X-rays: ~10^18 Hz
• Radio waves: ~10^6 Hz

All light = vibration at different frequencies. The entire electromagnetic spectrum = vibrations.

Example 2: Sound

Sound is pressure wave vibration:

• Middle C: 261.6 Hz
• A above middle C: 440 Hz
• Human hearing range: 20 Hz - 20,000 Hz

Musical notes = specific vibration frequencies. Harmony = mathematical ratios of vibrations:

• Octave: 2:1 ratio
• Perfect fifth: 3:2 ratio
• Perfect fourth: 4:3 ratio

Music is applied mathematics of vibration.

Example 3: Matter

Atoms vibrate:

• Molecular vibrations: ~10^13 Hz
• Atomic vibrations in solids: ~10^12 Hz
• Electron orbital frequencies: ~10^15 Hz

Solid matter isn't solid—it's vibrating particles held together by vibrating fields.

Example 4: Brain Waves

Thoughts are neural oscillations:

• Delta waves (sleep): 0.5-4 Hz
• Theta waves (meditation): 4-8 Hz
• Alpha waves (relaxed): 8-13 Hz
• Beta waves (active): 13-30 Hz
• Gamma waves (focus): 30-100 Hz

Consciousness = synchronized neural vibrations. Even thoughts vibrate.

The Harmonic Series: Universal Pattern

When something vibrates, it doesn't just vibrate at one frequency. It vibrates at multiple frequencies simultaneously—the harmonic series:

f, 2f, 3f, 4f, 5f, ...

Where f is the fundamental frequency.

This appears everywhere:

• Musical instruments (overtones)
• Quantum mechanics (energy levels: E_n = nℏω)
• Electromagnetic cavities (resonant modes)
• Vibrating strings (standing waves)
• Atomic orbitals (quantum numbers)

The harmonic series is a universal pattern of vibration.

Fourier Analysis in Action

Let's see Fourier analysis decompose a complex waveform:

Square Wave Decomposition:

A square wave (alternating +1 and -1) can be built from sine waves:

f(x) = (4/π)[sin(x) + (1/3)sin(3x) + (1/5)sin(5x) + ...]

Add more terms → better approximation → perfect square wave at infinity.

This proves: Complex vibration = sum of simple vibrations.

Applications:

• Audio compression (MP3): Remove inaudible frequencies
• Image compression (JPEG): Fourier transform of image blocks
• Signal processing: Filter noise, extract signals
• Quantum mechanics: Solve Schrödinger equation
• Heat transfer: Fourier's original application

The Mathematics of Vibration

1. Simple Harmonic Motion

The fundamental vibration:

x(t) = A cos(ωt + φ)

Where:
• A = amplitude
• ω = angular frequency
• φ = phase

Differential equation: d²x/dt² + ω²x = 0

This describes: pendulums, springs, atoms, electromagnetic waves, quantum particles.

2. Wave Equation

Vibrations propagate as waves:

∂²u/∂t² = c²∇²u

This describes: sound, light, water waves, quantum waves, gravitational waves.

Same equation, different phenomena. Universal vibration.

3. Quantum Harmonic Oscillator

Energy levels:

E_n = (n + ½)ℏω

Where n = 0, 1, 2, 3, ...

Even the ground state (n=0) has energy ½ℏω—zero-point vibration.

Nothing rests. Everything vibrates. Proven.

Why Everything Vibrates

Reason 1: Quantum Uncertainty

Heisenberg uncertainty principle:

Δx Δp ≥ ℏ/2

You can't have zero position uncertainty AND zero momentum uncertainty. Something must fluctuate. Everything must vibrate.

Reason 2: Field Theory

In quantum field theory, particles are excitations (vibrations) of fields:

• Photon = vibration of electromagnetic field
• Electron = vibration of electron field
• Higgs boson = vibration of Higgs field

All matter and energy = vibrations of quantum fields.

Reason 3: Energy Conservation

Energy can't be destroyed, only transformed. In quantum systems, this means perpetual vibration—energy oscillating between kinetic and potential forms.

Practical Applications

1. Spectroscopy

Identify substances by their vibrational frequencies:

• Infrared spectroscopy: Molecular vibrations
• NMR spectroscopy: Nuclear spin vibrations
• Raman spectroscopy: Molecular rotations and vibrations

Every substance has a unique vibrational signature.

2. Medical Imaging

• MRI: Detect hydrogen atom vibrations
• Ultrasound: High-frequency sound vibrations
• X-rays: High-frequency electromagnetic vibrations

3. Communication

All wireless communication uses electromagnetic vibrations:

• Radio: ~MHz
• WiFi: ~GHz
• 5G: ~30 GHz
• Fiber optics: ~200 THz (infrared light)

4. Energy Harvesting

Convert vibrations to electricity:

• Piezoelectric materials
• Vibration energy harvesters
• Ocean wave power

Objections and Responses

Objection 1: "Solid objects don't vibrate."

Response: They do. Atoms in solids vibrate at ~10^12 Hz. You can't see it, but it's happening. Temperature is literally average kinetic energy of atomic vibrations.

Objection 2: "Not everything is periodic."

Response: True. But the Fourier transform handles non-periodic functions too. Any function (periodic or not) can be decomposed into frequency components.

Objection 3: "This is just wave mechanics, not mysticism."

Response: Exactly! That's the point. The Hermetic principle IS wave mechanics, expressed in pre-mathematical language. The convergence validates both.

The Hermetic Insight Validated

The Hermeticists claimed:

"Nothing rests; everything moves; everything vibrates."

Modern physics has discovered:

• Fourier analysis: Any function = sum of vibrations
• Quantum mechanics: All matter has wave properties
• Zero-point energy: Nothing is ever at rest
• String theory: All particles are vibrating strings
• Field theory: Reality is vibrating fields

The convergence is exact:

"Everything vibrates" = "All phenomena can be decomposed into periodic functions"

Same claim. Different language. Perfect convergence.

Conclusion

The third Hermetic Principle—Vibration—is not mysticism.

It's a precise mathematical claim validated by:

• Fourier analysis: f(x) = Σ[aₙcos(nx) + bₙsin(nx)]
• Wave-particle duality: λ = h/p
• Schrödinger equation: iℏ ∂ψ/∂t = Ĥψ
• Zero-point energy: E₀ = ½ℏω
• String theory: All particles = vibrating strings

Everything vibrates because:

• Quantum uncertainty forbids absolute rest
• Particles are field vibrations
• Energy oscillates perpetually

The Hermeticists discovered wave mechanics 2,000 years before Fourier, Schrödinger, and de Broglie.

Hermetic Mathematics, validated.

What's Next

Next: Polarity—"Everything is dual; everything has poles."

We'll show this translates to symmetry group theory—the mathematics of complementary pairs and transformations.

Three principles down. Four to go.