Short description: Open questions connected with quantum physics and modern theoretical physics

Quantum unsolved problems are open questions in modern physics, mathematics, and cosmology whose resolution would deepen the understanding of quantum mechanics, quantum field theory, matter, gravity, and fundamental interactions.

Although quantum theory is one of the most successful frameworks in science, several questions remain unresolved. Some are conceptual, such as the meaning of measurement. Others are mathematical, such as the rigorous construction of interacting quantum field theories. Still others are physical, such as the origin of dark matter, the smallness of neutrino masses, the mechanism of confinement, and the relation between quantum mechanics and gravity.

Unsolved problems in quantum physics connect measurement, fields, particles, gravity, information, and matter.

Overview

Open problems in quantum physics do not all have the same character. A useful distinction can be made between conceptual, mathematical, particle-physics, cosmological, and gravity-related problems.

Important examples include:

These problems are connected by the fact that they expose limits in current theories. They are not simply gaps in observation, but places where quantum theory, field theory, gravity, cosmology, and mathematical rigor meet.

Quantum measurement problem

The quantum measurement problem concerns the relation between quantum states and definite experimental outcomes. In the mathematical description of quantum mechanics, a system may evolve into a superposition of possible outcomes. In actual experiments, however, a definite result is observed.

The problem is not merely technical. It concerns how to understand the status of the wave function, the role of observers and apparatus, and the meaning of probability in quantum theory. Different interpretations of quantum mechanics address this issue in different ways, including collapse interpretations, many-worlds interpretations, hidden-variable approaches, and decoherence-based accounts.^[1]^[2]

Yang–Mills existence and mass gap

The Yang–Mills existence and mass gap problem is one of the Millennium Prize Problems of the Clay Mathematics Institute. It asks for a mathematically rigorous construction of quantum Yang–Mills theory in four-dimensional spacetime and a proof that the theory has a positive mass gap.^[3]^[4]

This problem is central to quantum field theory because Yang–Mills theories underlie the non-Abelian gauge theories used in the Standard Model of particle physics. The mass gap is also closely connected with the fact that strong-interaction physics produces massive bound states even though the underlying gauge fields are massless in the classical theory.

Confinement problem

The confinement problem asks why quarks and gluons are not observed as isolated particles under ordinary low-energy conditions. In quantum chromodynamics, quarks and gluons carry color charge and interact through the strong interaction. Experiments show hadrons rather than free quarks, but a complete analytic understanding of confinement remains one of the major open problems in strong-interaction physics.^[5]

Confinement is related to the behavior of the quantum vacuum, gauge fields, color charge, and the non-perturbative structure of quantum chromodynamics. It also connects to the Yang–Mills mass gap problem.

Quantum gravity problem

The quantum gravity problem is the problem of reconciling quantum theory with general relativity. Quantum field theory normally describes fields on a background spacetime, while general relativity treats spacetime geometry itself as dynamical.

A theory of quantum gravity would be expected to describe regimes where both quantum effects and gravitational effects are important, such as the early universe, black-hole interiors, and physics near the Planck scale. Approaches to this problem differ in how they combine the principles of general relativity with those of quantum theory.^[6]

Black hole information paradox

The black hole information paradox concerns the apparent conflict between quantum mechanics and black-hole evaporation. In ordinary quantum mechanics, time evolution is expected to preserve information. In semiclassical black-hole physics, Hawking radiation appears approximately thermal, raising the question of whether information about matter that formed a black hole is lost during evaporation.^[7]

The paradox links quantum mechanics, thermodynamics, general relativity, entropy, and quantum field theory in curved spacetime. It is one of the main reasons black holes are considered important testing grounds for quantum gravity.

Dark matter problem

The dark matter problem asks what unseen form of matter explains gravitational effects observed in galaxies, galaxy clusters, and cosmology. Dark matter does not emit, absorb, or reflect light in the usual way, but its gravitational influence is inferred from astronomical and cosmological observations.^[8]

Many proposed dark-matter candidates are quantum particles or fields beyond the Standard Model. Examples include axions, sterile neutrinos, weakly interacting massive particles, and other hypothetical particles. For this reason, dark matter is not only a cosmological problem, but also a problem in quantum particle physics.

Neutrino mass problem

The neutrino mass problem concerns the origin, size, and nature of neutrino masses. Neutrino oscillation experiments show that neutrinos have nonzero mass, but the mechanism behind these masses is not yet known.

Open questions include whether neutrinos are Dirac or Majorana particles, why their masses are so small compared with other fermions, and whether neutrino mass is connected with physics beyond the Standard Model. Neutrinoless double-beta decay experiments are important because they could help determine whether neutrinos are Majorana particles.^[9]

Matter–antimatter asymmetry

The matter–antimatter asymmetry problem asks why the observable universe contains much more matter than antimatter. Known particle physics includes processes that distinguish matter from antimatter, but the observed cosmic imbalance remains unexplained.

This problem is connected with baryogenesis, leptogenesis, CP violation, neutrino physics, and possible physics beyond the Standard Model. Heavy neutral leptons and sterile-neutrino-like particles have been studied as possible links between neutrino mass, dark matter, and the matter–antimatter asymmetry.^[10]^[11]

Relation to Millennium Prize Problems

The Millennium Prize Problems are seven mathematical problems selected by the Clay Mathematics Institute. The problem most directly connected with quantum physics is the Yang–Mills existence and mass gap problem.^[4]

Other Millennium problems, such as the Riemann hypothesis, the Hodge conjecture, P versus NP, the Navier–Stokes problem, and the Birch and Swinnerton-Dyer conjecture, are not quantum-physics problems in the narrow sense. However, they may become relevant as mathematical background in areas such as spectral theory, geometry, computation, fluid dynamics, and mathematical physics.