| Planck constant | |
|---|---|
| Name | Planck constant |
| Alternative symbols | ħ (reduced) |
| Quantity | action / energy·time |
| SI units | J·s |
| Exact value | 6.62607015×10^−34 J·s (defined) |
| Discovered by | Max Planck |
| Year | 1900 |
Planck constant
The Planck constant (symbol h) is a fundamental physical constant that relates the energy of a quantum to its frequency and sets the scale of quantum effects. It underpins the discrete nature of energy exchange in Quantum Physics and is central to the formulation of Quantum mechanics, quantum field theory, and modern metrology.
The Planck constant h is defined by the relation E = hν that links the energy E of a photon to its frequency ν, establishing energy quantization for electromagnetic radiation first hypothesized in black-body studies. The reduced Planck constant ħ = h/2π appears in canonical commutation relations [\[x,p\] = iħ] and determines the scale of the Heisenberg uncertainty principle Δx Δp ≥ ħ/2. As a constant of action, h sets the scale at which classical descriptions break down and quantum descriptions dominate, influencing phenomena from atomic spectra to tunnelling and quantum entanglement.
The Planck constant emerged from Max Planck's 1900 derivation of what became known as Planck's law for black-body radiation while working at the University of Berlin and the Physikalisch-Technische Reichsanstalt. To resolve the ultraviolet catastrophe predicted by classical Rayleigh–Jeans law, Planck introduced the hypothesis that oscillators exchange energy in discrete quanta proportional to frequency. This quantization idea influenced contemporaries including Albert Einstein, who used the quantum hypothesis to explain the photoelectric effect in 1905, and later shaped the development of Niels Bohr's atomic model and early quantum theory.
In canonical quantization the Planck constant appears explicitly: commutation relations, the Schrödinger equation iħ ∂ψ/∂t = Ĥψ, and the expression for angular momentum eigenvalues all involve ħ. The constant distinguishes quantum operators from their classical analogues in formalisms developed by Werner Heisenberg, Erwin Schrödinger, and Paul Dirac. The pair of constants h and ħ are used interchangeably depending on context: h for photon energy relations and ħ for angular momentum and wave mechanics. The value of h also determines the magnitude of quantum corrections in semiclassical methods such as the WKB approximation and appears in the expressions for fundamental scales like the Planck length and Planck time when combined with gravitational constant G and the speed of light c.
High-precision determinations of h have involved experiments linking electrical and mechanical quantities to quantum effects. Notable methods include measurements using the photoelectric effect, X-ray crystal density via the Avogadro project (silicon sphere), and most recently the Kibble balance (formerly Watt balance) that compares electromagnetic and mechanical power using the Josephson effect and quantum Hall effect. National metrology institutes such as the National Institute of Standards and Technology (NIST), Physikalisch-Technische Bundesanstalt (PTB), International Bureau of Weights and Measures (BIPM), and National Physical Laboratory (United Kingdom) have led precision campaigns. The progressive reduction of uncertainty required careful control of systematic effects including thermal expansion, lattice parameter measurements, and instrumental calibrations.
The Planck constant directly mediates the quantization rules in models such as the Bohr model (ΔE = hν for transitions), and underlies the particle-like characterization of light as photons introduced by Einstein. It sets the scale for energy level spacing in atoms and molecules described by quantum chemistry and the Born–Oppenheimer approximation. In solid-state physics h appears in band structure calculations, quantized conductance in quantum point contacts, and the quantization steps in the integer quantum Hall effect and Josephson junctions, where h links voltage and frequency via the Josephson relation. Concepts like wave–particle duality and de Broglie wavelength λ = h/p arise from h and inform technologies such as electron microscopy and quantum computing.
In 2019 the International System of Units (SI) was redefined to fix exact numerical values for several constants, including h, thereby making the kilogram dependent on h rather than a physical artefact (the International Prototype of the Kilogram). This change was based on results from the Kibble balance and the Avogadro project and implemented by the General Conference on Weights and Measures (CGPM). Fixing h ties mass measurements to quantum electrical standards via the Josephson effect (linking voltage to frequency) and the quantum Hall effect (linking resistance to h/e^2), strengthening traceability and reproducibility in international trade, industry, and research.
Beyond pure science, the Planck constant’s role in enabling technologies raises questions about equitable access to the benefits of quantum-enabled products and infrastructures. Quantum standards, precision metrology, and emerging quantum technologies (sensors, cryptography, computing) are concentrated in wealthy institutions and countries—entities such as NIST, PTB, CERN, and leading universities—risking unequal distribution of economic and security advantages. Ethical considerations include fair allocation of research funding, capacity-building in underrepresented regions, and inclusive policy frameworks to ensure technologies informed by h (e.g., quantum-secure communications) benefit marginalized communities. Philosophically, quantization prompted reevaluation of determinism and agency in science, influencing debates in philosophy of science about objectivity, measurement, and the societal framing of technological change.
Category:Physical constants Category:Quantum mechanics Category:Metrology