Quantum mechanics

Quantum mechanics is the physical theory that describes matter and energy at the scale of atoms and subatomic particles. It replaces the continuous quantities of classical physics with discrete quanta, allows systems to occupy superpositions of states at once, and predicts only the probabilities of measurement outcomes rather than definite results. It is among the most precisely tested theories in all of science.

#Origins

Quantum mechanics grew out of experiments that classical physics could not explain. In 1900 Max Planck accounted for the spectrum of black-body radiation by assuming that energy is emitted and absorbed in discrete packets, or quanta, introducing the constant now named after him (Nobel Foundation, Planck). Albert Einstein extended the idea in 1905 by treating light itself as quanta to explain the photoelectric effect, and Niels Bohr applied quantization to atomic orbits in 1913. These early results, now called the old quantum theory, worked in specific cases but lacked a unified framework. The full theory arrived in 1925 and 1926, first as Werner Heisenberg's matrix mechanics and then as Erwin Schrodinger's wave mechanics, soon shown to be equivalent. The history of quantum mechanics traces this development in detail.

#Core principles

Several features distinguish quantum mechanics from the classical physics it superseded.

Quantization. Certain quantities, such as the energy levels of a bound electron or the spin of a particle, take only discrete allowed values rather than a continuous range. The size of these steps is set by the Planck constant, an extremely small number, which is why quantization is invisible in everyday life.

Wave-particle duality. Matter and light display both wave-like and particle-like behavior depending on the experiment. Electrons produce interference patterns like waves yet arrive at a detector as discrete impacts. This wave-particle duality is exhibited most cleanly in the double-slit experiment.

Superposition. A quantum system can exist in a combination of distinct states at the same time, described by a wave function whose components carry complex amplitudes. A Qubit, the unit of quantum information, is a two-state system held in Superposition of 0 and 1 until it is read out.

The Born rule. Measurement does not reveal a pre-existing value. Instead the squared magnitude of an amplitude gives the probability of each possible outcome, a rule introduced by Max Born in 1926 and recognized with a Nobel Prize in 1954 (Nobel Foundation, Born). Quantum mechanics is intrinsically probabilistic: identical experiments on identically prepared systems can yield different results.

The uncertainty principle. Certain pairs of quantities, such as position and momentum, cannot both have precisely defined values at once. Heisenberg formalized this in 1927, and the uncertainty principle is a structural feature of the theory rather than a limit of any instrument.

Entanglement. Two or more systems can share a joint state that cannot be factored into independent parts, so measurements on them stay correlated no matter how far apart they are. Quantum entanglement has no classical analogue and underlies much of quantum information science.

#How the theory is expressed

The state of a quantum system is represented by a wave function, or state vector, that lives in an abstract space of possibilities. Between measurements this state evolves smoothly and deterministically according to the Schrodinger equation. The connection to what an observer records comes through the Born rule, which turns the state into probabilities for the values of observable quantities such as energy, position, or spin. Each observable corresponds to a mathematical operator whose allowed measurement results are its eigenvalues.

Three ideas make this machinery work together. Observable quantities that are quantized, such as energy in a bound system, take only the discrete eigenvalues of their operator, which is where the discreteness of atomic spectra comes from. States can be added together, the property called linearity, so any combination of allowed states is itself an allowed state, which is the mathematical source of superposition. And the amplitudes are complex numbers that can reinforce or cancel, so quantum probabilities interfere in a way that classical probabilities never do. Interference of amplitudes, not the mere existence of many possibilities, is what gives quantum systems their distinctive behavior.

#Characteristic scales

Quantum effects are set by the size of the Planck constant, about 6.6 times ten to the power of minus thirty-four joule seconds. Because this number is so small, the action of everyday objects, the product of quantities such as energy and time, is astronomically large by comparison, and quantum behavior is averaged away. For an electron in an atom the relevant action is comparable to the Planck constant, so quantization, superposition, and interference are decisive. This separation of scales explains why a theory so alien to daily intuition went undiscovered until sensitive experiments on atoms and radiation forced it into view.

#The measurement problem

The theory contains two different accounts of how a state changes: smooth deterministic evolution when the system is left alone, and an abrupt jump to a single definite outcome when it is measured. Reconciling these, and explaining why a superposition of many possibilities yields one observed result, is the measurement problem. Schrodinger dramatized the tension in 1935 with the Schrodinger's cat thought experiment, in which a cat would be placed in a superposition of alive and dead. Competing interpretations, including the Copenhagen interpretation and the many-worlds interpretation, agree on the predictions but disagree on what the formalism means (Stanford Encyclopedia of Philosophy).

#Correspondence with classical physics

Quantum mechanics does not discard classical physics; it contains it as a limiting case. For systems that are large, energetic, or otherwise far from the scale set by the Planck constant, quantum predictions converge on the familiar results of Newtonian mechanics, a relationship Bohr called the correspondence principle. This is why the discreteness, superposition, and uncertainty of the quantum world are not apparent in everyday objects. The regime where quantum effects dominate is sometimes loosely called the quantum realm.

#Reach and applications

The theory explains the structure of the periodic table, chemical bonding, the behavior of semiconductors, superconductivity, lasers, and the stability of matter itself. It is the foundation of modern electronics and of technologies from magnetic resonance imaging to atomic clocks. Extended to be consistent with special relativity, it becomes quantum field theory, the framework of the Standard Model of particle physics. It also underlies emerging fields that manipulate quantum states directly, including quantum computing, where Shor's algorithm threatens widely deployed public-key cryptography and motivates the shift to post-quantum cryptography.

#Status

Quantum mechanics has passed every experimental test attempted over a century, some to more than ten significant figures. No confirmed experiment contradicts it. What remains open is not the accuracy of the predictions but their interpretation, the reconciliation of the theory with general relativity into a full theory of quantum gravity, and the engineering challenge of controlling quantum systems at scale.