Modern_physics - Wikiparency

# Modern physics **Modern physics** is the body of physics founded on the two revolutions of the early twentieth century — [[Special_relativity|relativity]] and [[Quantum_mechanics|quantum mechanics]] — as against the [[Classical_physics|classical physics]] of [[Newton's_laws_of_motion|Newton's laws]], [[Maxwell's_equations|Maxwell's equations]] and [[Thermodynamics|thermodynamics]]. The split is not one of date or of subject matter but of regime. Classical mechanics is what quantum mechanics becomes when a system's action is enormous compared with [[Planck_constant|Planck's constant]] ħ, and what relativity becomes when speeds are small compared with the [[Speed_of_light|speed of light]] c. Every object in the universe sits somewhere on those two axes; *modern* names the territory where one or both of the classical approximations stops being good enough to use. In the microsim below the reader picks a system — or types in a mass, a speed and a size — and watches it land on a regime map. The horizontal axis is the dimensionless action `S/hbar = m·v·L/hbar` on a logarithmic scale; the vertical axis is the speed ratio `beta = v/c`. Two lines cut the plane into quadrants. The quantum line is drawn where ħ is one per cent of the action, at `S/hbar = 100`; the relativistic line is drawn where the Lorentz factor `gamma = 1/sqrt(1 − beta^2)` first exceeds 1 by one per cent, at β = 0.140 (derived). A baseball of 0.145 kg thrown at 40 m/s across its own 7.5 cm diameter lands at `S/hbar` ≈ 4×10³³ and β ≈ 10⁻⁷, deep in Newton's quadrant (derived). An [[Electron|electron]] in a [[Hydrogen_atom|hydrogen atom]] lands at `S/hbar` = 1 and β = 1/137, in Schrödinger's.[^raven-uncertainty] A navigation satellite at β = 1.3×10⁻⁵ is classical on both axes and still cannot be run classically. A 7 TeV proton in the [[Large_Hadron_Collider|Large Hadron Collider]] lands at β = 0.999 999 991 and, at the distances its collisions probe, at an action of order ħ — Dirac's quadrant, where relativity and quantum mechanics must be used together.[^raven-collider] The map is ILLUSTRATIVE: the one-per-cent boundaries are display choices, not measured thresholds, and a system's horizontal position moves with the length scale `L` the preset assigns it. On the [[Physics]] flagship this page serves Part II — Core theories, in the section *Distinction between classical and modern physics* (row P13). It is the hinge between the classical spine upstream — [[Momentum|momentum]], [[Angular_momentum|angular momentum]], [[Conservation_of_energy|energy conservation]] — and the quantum and relativistic sections downstream, and the same regime map reappears in reduced form wherever a downstream page has to justify which mechanics it is using. ## Hallmark experiments No argument settled the boundary; a sequence of experiments did, each one a measurement that classical physics predicted correctly right up to the point where it did not. Read in order they trace a path across the regime map: first down and to the left into small actions, where the quantum of action shows itself, and then upward into large β, where simultaneity and mass–energy have to be rebuilt. What follows is the short list that a physics course still uses to mark the crossing, with the numbers that each preset in the microsim carries. ### The quantum of action The first crack was thermal. A hot cavity radiates with a spectrum that classical [[Statistical_mechanics|statistical mechanics]] could not reproduce: dividing the energy equally among all the [[Electromagnetic_radiation|electromagnetic]] modes of a box makes the predicted power diverge at short wavelengths. In 1900 Max Planck fitted the measured [[Black-body_radiation|black-body]] curve by allowing the oscillators in the cavity wall to exchange energy only in units of `h·f`, and in 1901 published the distribution and the constant that carries his name.[^planck1901] The step was quietly enormous: it introduced a quantity, ħ = 1.054×10⁻³⁴ J·s, against which every mechanical action in nature can be measured, and so drew the vertical line on the regime map.[^raven-hbar] The constant is small enough to hide. A pendulum swinging through one metre carries an action some thirty-four orders of magnitude larger than ħ, so its energy levels are spaced too finely to detect and its motion is classical to any precision a laboratory can reach. The same arithmetic run backwards says where the quantum must appear: at atomic masses and atomic distances, `m·v·L` falls to ħ itself. ### The photoelectric effect Planck treated quantization as a property of the emitting matter. In 1905 Albert Einstein applied it to the [[Electromagnetic_radiation|radiation field]] itself, proposing that light of frequency f is absorbed in quanta of energy `h·f` and that a metal illuminated above a threshold frequency ejects electrons with a maximum kinetic energy `K_max = h·f − W`, where W is the work function.[^einstein1905pe] The prediction is starkly non-classical: raising the intensity of dim red light, which in a [[Wave|wave]] picture must eventually shake an electron free, never does, while faint blue light works at once. The [[Photoelectric_effect|photoelectric effect]] is now the standard laboratory route to h, since the slope of `K_max` against f is Planck's constant and the intercept is the [[Work_(physics)|work]] needed to escape the metal. ### Atomic spectra and the nuclear atom Classical mechanics gives no reason for an [[Atom|atom]] to have a definite size, and classical electrodynamics gives an orbiting electron every reason to spiral into the nucleus in a fraction of a nanosecond. Two experiments framed the problem. Ernest Rutherford's collaborators scattered α particles from a gold foil and found a few turning through more than 90°, which forced the positive charge into a nucleus thousands of times smaller than the atom.[^rutherford1911] Then [[Bohr_model|Niels Bohr]] quantized the orbits, reproducing the hydrogen [[Spectral_line|spectral lines]] with a single integer.[^bohr1913] The size the theory predicts is the Bohr radius a₀ = 5.29×10⁻¹¹ m, and it is exactly the length that makes the electron's action equal to ħ. Taking the ground-state orbital speed as αc = 2.19×10⁶ m/s gives `m·v·a_0/hbar` = 1.00 (derived), which is why the hydrogen preset lands on the quantum boundary rather than near it. The modern statement drops the orbit and keeps the scale: for the true ground state, Δx = (√3/2)·a₀ and Δp = ħ/a₀, so the product is (√3/2)·ħ, comfortably above the ħ/2 floor set by the [[Uncertainty_principle|uncertainty principle]].[^raven-uncertainty] ### Electron diffraction and the Stern–Gerlach beam If light carries momentum in quanta, matter should carry wave properties, and two experiments of the 1920s showed that it does in ways no classical model allows. In 1927 Clinton Davisson and Lester Germer fired low-energy electrons at a nickel crystal and recovered a diffraction pattern with the spacing a [[Wave_packet|wave]] of wavelength `lambda = h/p` would give.[^davisson1927] Five years earlier Otto Stern and Walther Gerlach had passed a beam of silver atoms through an inhomogeneous [[Magnetic_field|magnetic field]] and found it split into two, not smeared into a continuum: the [[Stern–Gerlach_experiment|Stern–Gerlach experiment]] showed that [[Spin_(physics)|spin]] angular momentum takes discrete orientations.[^stern1922] Neither result has a classical limit in which it becomes approximate; they are qualitative, and they are the reason the regime map's quantum axis is drawn as a boundary rather than a correction term. ### Time dilation in the field The relativistic axis was crossed first by a null result and then by clocks. Albert Michelson and Edward Morley, comparing light travel times along perpendicular arms in 1887, found no trace of the Earth's motion through a light-carrying medium.[^michelson1887] In 1905 Einstein took the constancy of c as a postulate and rebuilt kinematics on it, so that moving clocks run slow by the factor γ and simultaneity ceases to be absolute.[^einstein1905sr] The microsim's satellite preset makes the size of the effect concrete. At an orbital speed of 3.87 km/s, β = 1.29×10⁻⁵ and `gamma − 1` = 8.3×10⁻¹¹, which over one day of 86,400 s is a clock loss of 7.2 μs (derived). That is a rounding error to a stopwatch and a 2 km navigation error to a satellite system, which is why a global positioning constellation applies relativistic corrections continuously rather than as a refinement.[^up3-relativity] The map marks such systems as classical in both coordinates and still flags them: being far from a boundary bounds the size of a correction, not its importance. ### Relativistic particles in the laboratory At the other end of the β axis the corrections stop being corrections. A proton's rest energy is 938.27 MeV, computed from its mass of 1.6726219×10⁻²⁷ kg.[^raven-proton] A beam of 7 TeV protons in the Large Hadron Collider therefore carries γ = 7,460 and β = 0.999 999 991 (derived), and two such beams meet at 14 TeV; the Tevatron's 980 GeV per beam gave 1.96 TeV.[^raven-collider] At these energies kinetic energy exceeds rest energy by a factor of thousands, [[Mass–energy_equivalence|mass and energy]] are interconvertible in every collision, and the accounting is done with [[Four-momentum|four-momentum]] rather than with `p = m·v`. The same books make the point about mass itself. The three valence quarks of a proton, scaled to grams in the same proportion as their masses, come to 2.2 + 2.2 + 4.7 = 9.1 g against the proton's 938 g — about one per cent.[^raven-quarks] Ninety-nine per cent of the mass of ordinary matter is the energy of the [[Nuclear_force|strong interaction]] binding those quarks, a statement that has no meaning at all in classical mechanics. ### The separation of energy scales A last hallmark is quantitative rather than conceptual, and it explains why classical [[Chemical_bond|chemistry]] and modern [[Nuclear_physics|nuclear physics]] can coexist without meeting. An excited state of the oxygen-16 nucleus sits 6.05 MeV above its ground state; a 450 nm photon of visible light carries 2.75 eV. The ratio is greater than 2×10⁶.[^raven-nuclear] Atomic and molecular processes therefore never disturb nuclei, and [[Radioactive_decay|nuclear decay]] is indifferent to the chemical state of the atom around it. The regime map's quadrants are separated in the same way: within a quadrant one set of equations suffices, and the boundaries are where the neglected terms grow past the precision being demanded. ### Where the classical limit is recovered The boundary is a limit, not a wall, and the [[Correspondence_principle|correspondence principle]] requires quantum results to reproduce classical ones where the action is large. The clearest worked case is the [[Quantum_harmonic_oscillator|harmonic oscillator]]. Its exact ladder is `E_n = hbar·w0·(n + 1/2)`, and the old Wilson–Sommerfeld quantization condition `oint p dx = 2·pi·hbar·(n + 1/2)` gives the same ladder — exactly, for this one potential.[^likharev-ladder] The semiclassical [[WKB_approximation|WKB approximation]] that generalizes it is valid only for n ≫ 1, which is the correspondence principle stated as an inequality.[^likharev-wkb] At large n the probability density of the quantum state piles up at the classical turning points, approaching the classical distribution it must reproduce.[^likharev-ladder] Reading the regime map from right to left is reading that limit backwards: the classical answer survives until the neglected ratio ħ/S grows past the tolerance a measurement demands, and modern physics is the set of theories written for what happens after it does. ## See also - [[Classical_physics]] - [[Correspondence_principle]] - [[Quantum_mechanics]] - [[Special_relativity]] - [[Atomic_physics]] - [[Standard_Model]] ## References [^planck1901]: Planck, Max (1901). "Ueber das Gesetz der Energieverteilung im Normalspectrum." *Annalen der Physik* 4: 553–563. [^einstein1905pe]: Einstein, Albert (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt." *Annalen der Physik* 17: 132–148. [^einstein1905sr]: Einstein, Albert (1905). "Zur Elektrodynamik bewegter Körper." *Annalen der Physik* 17: 891–921. [^michelson1887]: Michelson, Albert A.; Morley, Edward W. (1887). "On the Relative Motion of the Earth and the Luminiferous Ether." *American Journal of Science* 34 (203): 333–345. [^rutherford1911]: Rutherford, Ernest (1911). "The Scattering of α and β Particles by Matter and the Structure of the Atom." *Philosophical Magazine* 21 (125): 669–688. [^bohr1913]: Bohr, Niels (1913). "On the Constitution of Atoms and Molecules, Part I." *Philosophical Magazine* 26 (151): 1–25. [^davisson1927]: Davisson, Clinton; Germer, Lester H. (1927). "Diffraction of Electrons by a Crystal of Nickel." *Physical Review* 30 (6): 705–740. [^stern1922]: Gerlach, Walther; Stern, Otto (1922). "Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld." *Zeitschrift für Physik* 9 (1): 349–352. [^raven-hbar]: Raven, Will (2025). *Atomic Physics for Everyone: An Introduction to Atomic Physics, Quantum Mechanics, and Precision Spectroscopy with No College-Level Prerequisites*. Chapter 3, p. 58 (ħ = 1.054×10⁻³⁴ J·s) and Chapter 11, p. 244 (1 MeV = 1.602176×10⁻¹³ J). Portal Book 046, https://open.umn.edu/opentextbooks/textbooks/atomic-physics-for-everyone-an-introduction-to-atomic-physics-quantum-mechanics-and-precision-spectroscopy-with-no-college-level-prerequisites [^raven-uncertainty]: Raven (2025), *Atomic Physics for Everyone*, Chapter 11, pp. 229–230 (the hydrogen ground state as Δx = (√3/2)·a₀ and Δp = ħ/a₀, whose product (√3/2)·ħ exceeds the ħ/2 bound; a₀ = 5.29×10⁻¹¹ m). The value `m·v·a_0/hbar` = 1.00 for an orbital speed of αc is derived from those constants. Portal Book 046. [^raven-proton]: Raven (2025), *Atomic Physics for Everyone*, Chapter 11, p. 231 (a proton of mass 1.6726219×10⁻²⁷ kg has a rest energy of 938.27 MeV; the energy–time relation ΔE·Δt ≥ ħ/2 is re-derived on p. 230). Portal Book 046. [^raven-quarks]: Raven (2025), *Atomic Physics for Everyone*, Chapter 11, p. 229 (the quark-mass analogy: 2.2 + 2.2 + 4.7 g of quark mass against 938 g of proton, about one per cent). Portal Book 046. [^raven-nuclear]: Raven (2025), *Atomic Physics for Everyone*, Chapter 11, p. 232 (an oxygen-16 excited state at 6.05 MeV against a 450 nm photon at 2.75 eV, a ratio above 2×10⁶). Portal Book 046. [^raven-collider]: Raven (2025), *Atomic Physics for Everyone*, Chapter 11, p. 245 (Tevatron 980 GeV per beam for 1.96 TeV; Large Hadron Collider 7 TeV per beam for 14 TeV). The γ = 7,460 and β = 0.999 999 991 of a 7 TeV proton are derived from that figure and the 938.27 MeV rest energy of p. 231. Portal Book 046. [^likharev-ladder]: Likharev, Konstantin (2013). *Essential Graduate Physics, Part QM: Quantum Mechanics*. Chapter 2, §2.9, pp. ~96–99 (page to pin; the sub-manual records that the extract's own page labels for this subsection are inconsistent): `E_n = hbar·w0·(n + 1/2)`, the Wilson–Sommerfeld condition `oint p dx = 2·pi·hbar·(n + 1/2)` giving the same ladder exactly for this potential, and the approach of |ψ_n|² to the classical density at large n. Portal Book 047, https://open.umn.edu/opentextbooks/textbooks/part-qm-quantum-mechanics [^likharev-wkb]: Likharev (2013), *Essential Graduate Physics, Part QM*, Chapter 2, pp. 53–54 (the WKB approximation is valid only for n ≫ 1). Portal Book 047. [^up3-relativity]: Sanny, Jeff; Ling, Samuel (2016). *University Physics Volume 3*. OpenStax. Chapter 5 "Relativity", pp. 183–240 (page to pin) — time dilation by the factor γ, the relativity of simultaneity, and the relativistic corrections a satellite navigation system must apply. The 7.2 μs per day of motional clock loss at β = 1.29×10⁻⁵ is derived. Portal Book 079, https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3 ## Further reading - Raven, Will (2025). *Atomic Physics for Everyone*. Portal Book 046 — Chapter 11 carries the scales used on this page: the hydrogen uncertainty product, the proton's rest energy, the quark-mass analogy and the collider energies. - Likharev, Konstantin (2013). *Essential Graduate Physics, Part QM: Quantum Mechanics*. Portal Book 047 — Chapter 2 is the semiclassical limit in full, from WKB to the oscillator ladder. - Sanny, Jeff; Ling, Samuel (2016). *University Physics Volume 3*. OpenStax. Portal Book 079 — Chapter 5 for relativity, Chapters 6–8 for the quantum crossing. - Idema, Timon (2018). *Mechanics and Relativity*. Portal Book 080 — the classical side of the boundary, written so that the relativistic chapters follow from it.  **Microsim — three.js (Wikitube framework), pending deploy:** *Modern physics* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Modern_physics.html` is live.   ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Modern_physics) : [Wikitube](https://en.wikitube.io/wiki/Modern_physics) · pinned revision [1355568917](https://en.wikipedia.org/w/index.php?oldid=1355568917) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Physics]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Physics row P13 · sim pending (matter/Modern_physics).*