I. Core Identity & Value

• Symbol: \( m_e \)
• Mass Energy: \( 0.51099895000(15) \text{MeV}/c^2 \)
• Mass Value: \( 9.1093837015(28) \times 10^{-31} \text{kg} \) (2018 CODATA)
• Relative Mass: \( \frac{m_e}{m_p} = \frac{1}{1836.15267343(11)} \)
• Fundamental Role: Determines atomic scale, chemical behavior, and quantum stability

II. Historical Discovery

Thomson’s Apparatus: Cathode ray tube with magnetic/electric fields to measure deflection ratio e/m_e.

III. Theoretical Significance

1. Quantum Mechanics

• Schrödinger equation for hydrogen:
  \[ \left[ -\frac{\hbar^2}{2m_e} \nabla^2 – \frac{k_e e^2}{r} \right] \psi = E \psi \]
• Atomic size scale:
  \[ a_0 = \frac{4\pi\epsilon_0 \hbar^2}{m_e e^2} \approx 0.529 \text{Å} \]

2. Quantum Electrodynamics (QED)

• Anomalous magnetic moment:
  \[ a_e = \frac{g-2}{2} = \frac{\alpha}{2\pi} – 0.328\frac{\alpha^2}{\pi^2} + \cdots \]
• Electron self-energy corrections proportional to m_e

3. Relativistic Quantum Mechanics

• Dirac equation:
  \[ \left( i\gamma^\mu \partial_\mu – \frac{m_e c}{\hbar} \right) \psi = 0 \]
• Predicts antimatter (positrons)

IV. Precision Measurement Techniques

V. Role in Fundamental Physics

1. Standard Model Parameters

• Yukawa coupling to Higgs field:
  \[ m_e = \frac{y_e v}{\sqrt{2}} \]

  v = Higgs vacuum expectation value (246 GeV)

2. Hierarchy Problem

• Electron vs. Planck mass ratio: m_e/m_P ≈ 10^-23
• Requires fine-tuning of Higgs coupling

3. Lepton Universality

• Tested via decay rates: Γ(μ→eνν)/Γ(τ→eνν) ∝ (m_μ/m_τ)⁵
• Confirms Standard Model mass generation

VI. Cosmic Significance

1. Stellar Evolution

• Chandrasekhar limit for white dwarfs:
  \[ M_{\text{Ch}} \approx \frac{1.44}{m_e^2} M_{\odot} \]

2. Big Bang Nucleosynthesis

• Determines neutron-proton freeze-out ratio
• Affects primordial helium abundance

3. Anthropic Constraints

• If m_e > 2m_e^current: No stable atoms
• If m_e < 0.5m_e^current: No covalent bonding
• Life-permitting range: 0.8-1.2 × current value

VII. Unsolved Mysteries

1. Why This Value?

• Yukawa coupling y_e ≈ 2 × 10^-6 has no theoretical explanation
• String theory landscape predicts possible values

2. Temporal Variation

• Oklo reactor constraint: |Δm_e/m_e| < 10^-8 (1.8 Gyr)
• Quasar spectra: |Δm_e/m_e| < 10^-5 (z=3)

3. Mass Generation Mechanism

• Is Higgs mechanism fundamental or emergent?
• Connection to dark matter mass scale?

“The electron: the universe’s perfect compromise – massive enough to form bonds, light enough to enable chemistry.”

– Freeman Dyson

References

1. Thomson, J.J. (1897). “Cathode Rays” (Philosophical Magazine)
2. Hanneke, D., et al. (2008). “New Measurement of the Electron Magnetic Moment” (Phys. Rev. Lett.)
3. Fan, X., et al. (2023). “Precision Electron Mass via Penning Trap” (Nature Physics)
4. Mohr, P.J., et al. (2016). “CODATA Recommended Values” (Rev. Mod. Phys.)
5. Barrow, J.D. (2002). “The Constants of Nature” (Vintage)
6. PDG (2022). “Review of Particle Physics”