History of Quantum Mechanics and Relativity

In the early 19th century, most phenomena could be explained by classical (or Newtonian) mechanics. By the turn of the century, however, many anomalous observations emerged that could only be explained through two revolutionary theories: Relativity and Quantum Mechanics.

Birth of Quantum Mechanics

Quantum mechanics emerged from several groundbreaking discoveries:

  • Max Planck's solution to blackbody radiation (1900)
    E=hfE = hf

    where h is Planck's constant and f is frequency

  • Einstein's explanation of the photoelectric effect (1905)
    E=hf−ϕE = hf - \phi

    where φ is the work function of the metal

  • Niels Bohr's model of the atom (1913)
    En=−13.6 eVn2E_n = -\frac{13.6\text{ eV}}{n^2}

    where n is the principal quantum number

  • Louis de Broglie's matter waves (1924)
    λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}

    relating wavelength λ to momentum p

  • Schrödinger's wave equation (1926)
    iℏ∂∂tΨ=H^Ψi\hbar\frac{\partial}{\partial t}\Psi = \hat{H}\Psi
  • Heisenberg's uncertainty principle (1927)
    ΔxΔp≥ℏ2\Delta x\Delta p \geq \frac{\hbar}{2}

Development of Relativity

Einstein's theory of relativity came in two parts:

  • Special Relativity (1905): Mass-energy equivalence
    E=mc2E = mc^2
  • Length contraction
    L=L01−v2c2L = L_0\sqrt{1-\frac{v^2}{c^2}}
  • Time dilation
    t=t01−v2c2t = \frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}
  • General Relativity (1915): Einstein field equations
    Gμν+Λgμν=8πGc4TμνG_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}

These theories revolutionized our understanding of space, time, and the universe itself.

Relationship with Classical Mechanics

Both Quantum Mechanics and Relativity contradict Newtonian Mechanics in fundamental ways:

  • Quantum Mechanics introduces uncertainty and probability at the microscopic level
  • Relativity shows that time and space are not absolute, but relative to the observer

However, both theories reduce to classical Newtonian results when applied to everyday scales, explaining why Newton's laws work so well in our daily experience.

Modern Applications

These theories form the foundation of modern physics and technology:

  • Quantum Mechanics: Semiconductors, lasers, and quantum computers
  • Relativity: GPS systems, particle accelerators, and understanding black holes