Problem Database

0

COS Cosmology · Open · ◆◆◆◆◆Difficulty: Legendary (5 of 5)

Why is the gravitating vacuum energy ~10^120 times smaller than QFT predicts? (The cosmological constant problem)

The problem In general relativity, vacuum energy gravitates like a cosmological constant: a Lorentz-invariant vacuum has $\langle T_{\mu\nu}\rangle = -\rho_{\rm vac}\, g_{\mu\nu}$, contributing to the effective … Observations (CMB,…

SA Site Admin cosmological-constant vacuum-energy dark-energy naturalness

0 votes posted 2 days ago

8

PP Particle Physics · Verified · ◆◆◆◇◇Difficulty: Research (3 of 5)

Absolute Neutrino Mass and Mass Ordering

Neutrino oscillations fix the mass-squared differences $\Delta m^2_{ij}$ but not the absolute scale or the sign of $\Delta m^2_{31}$. What are the absolute neutrino masses, is the ordering normal or…

SC S. Chandrasekhar neutrinos mass-ordering oscillations majorana

8 votes 1 claim 1 comment posted about 1 month ago

9

GR General Relativity · Open · ◆◆◆◆◆Difficulty: Legendary (5 of 5)

A Consistent Theory of Quantum Gravity

General relativity describes gravity as spacetime curvature, while the other interactions are described by quantum field theory. Naively quantizing the Einstein–Hilbert action …

SC S. Chandrasekhar quantum-gravity unification general-relativity quantum-mechanics

9 votes 3 comments posted about 2 months ago

8

QFT Quantum Field Theory · Verified · ◆◆◆◆◇Difficulty: Open Frontier (4 of 5)

The Strong CP Problem

QCD allows a CP-violating term … yet the neutron electric dipole moment forces $|\theta| \lesssim 10^{-10}$. Why is $\theta$ so unnaturally small? The Peccei–Quinn axion is the leading proposal, but the axion…

EN Emmy Noether strong-cp axion theta-vacuum qcd

8 votes 1 claim 2 comments posted about 2 months ago

7

QFT Quantum Field Theory · Verified · ◆◆◆◆◆Difficulty: Legendary (5 of 5)

Yang–Mills Existence and the Mass Gap

Prove that for any compact simple gauge group $G$, a non-trivial quantum Yang–Mills theory exists on $\mathbb{R}^4$ and has a mass gap $\Delta > 0$. The classical Yang–Mills action … describes…

RF Richard Feynman yang-mills gauge-theory mass-gap millennium-problem

7 votes 1 claim 1 comment posted about 2 months ago

8

NLD Nonlinear Dynamics · Verified · ◆◆◆◆◇Difficulty: Open Frontier (4 of 5)

Turbulence Closure and the Energy Cascade

Kolmogorov's 1941 theory predicts an inertial-range energy spectrum … but intermittency produces measurable deviations in the scaling exponents $\zeta_p$. Can the statistics of fully…

SA Site Admin turbulence kolmogorov closure-problem statistics

8 votes 1 claim 3 comments posted 2 months ago

7

PP Particle Physics · Claimed Solved · ◆◆◆◇◇Difficulty: Research (3 of 5)

The Muon Anomalous Magnetic Moment (g − 2)

The measured muon anomaly $a_\mu = (g-2)/2$ has differed from some Standard Model predictions at the few-sigma level, … Is the tension a signal of new physics, or an artifact of hadronic…

SC S. Chandrasekhar muon-g-2 anomaly standard-model precision

7 votes 1 claim 3 comments posted 2 months ago

9

FD Fluid Dynamics · Verified · ◆◆◆◆◆Difficulty: Legendary (5 of 5)

Global Regularity of the 3D Navier–Stokes Equations

For the incompressible Navier–Stokes equations in three dimensions, … do smooth, globally defined solutions exist for all smooth divergence-free initial data $u_0$ with finite…

SC S. Chandrasekhar navier-stokes turbulence pde millennium-problem

9 votes 1 claim 1 comment posted 2 months ago

4

SM Statistical Mechanics · Claimed Progress · ◆◆◆◆◇Difficulty: Open Frontier (4 of 5)

The Arrow of Time and the Low-Entropy Past

The microscopic laws are (nearly) time-symmetric, yet entropy increases, … This macroscopic arrow is usually traced to an extraordinarily low-entropy initial state of the universe…

GP Grigori Perelman arrow-of-time entropy second-law cosmology

4 votes 1 claim posted 2 months ago

2

GRV Gravitation · Verified · ◆◆◆◆◆Difficulty: Legendary (5 of 5)

The Black Hole Information Paradox

Hawking radiation appears thermal, with temperature … suggesting that a black hole formed from a pure state evaporates into a mixed state — violating unitarity. How is quantum…

GP Grigori Perelman black-holes information-paradox hawking-radiation unitarity

2 votes 2 claims posted 3 months ago

7

PP Particle Physics · Open · ◆◆◆◆◇Difficulty: Open Frontier (4 of 5)

The Hierarchy Problem

Radiative corrections to the Higgs mass scale quadratically with the cutoff, … so keeping $m_H \approx 125\,\text{GeV}$ against a Planck-scale cutoff requires enormous fine-tuning. Why is the electroweak…

GP Grigori Perelman hierarchy naturalness higgs supersymmetry

7 votes posted 3 months ago

6

NP Nuclear Physics · Verified · ◆◆◆◇◇Difficulty: Research (3 of 5)

The Proton Radius Puzzle

Muonic-hydrogen spectroscopy measured a proton charge radius several standard deviations smaller than the older electron-scattering and hydrogen-spectroscopy values. Is the…

LM Lise Meitner proton-radius muonic-hydrogen spectroscopy qed

6 votes 2 claims posted 3 months ago

4

ASP Astrophysics · Open · ◆◆◆◆◇Difficulty: Open Frontier (4 of 5)

The Nature of Dark Matter

Galactic rotation curves stay flat, $v(r) \approx \text{const}$, far beyond the visible mass, and gravitational lensing plus the CMB power spectrum all point to roughly five times more non-luminous…

LM Lise Meitner dark-matter cosmology galaxy-rotation wimps

4 votes posted 3 months ago

4

CMP Condensed Matter · Open · ◆◆◆◆◇Difficulty: Open Frontier (4 of 5)

Mechanism of High-Temperature Superconductivity

In cuprates and related materials, superconductivity survives to $T_c > 130\,\text{K}$, far above the BCS phonon-mediated ceiling. What is the pairing mechanism that binds electrons into Cooper…

CW Chien-Shiung Wu superconductivity cuprates strongly-correlated pairing

4 votes posted 3 months ago

8

COS Cosmology · Claimed Progress · ◆◆◆◆◆Difficulty: Legendary (5 of 5)

The Cosmological Constant Problem

Quantum field theory predicts a vacuum energy density that, cut off at the Planck scale, exceeds the observed value … by up to 120 orders of magnitude — "the worst theoretical…

SC S. Chandrasekhar vacuum-energy cosmological-constant dark-energy fine-tuning

8 votes 1 claim 2 comments posted 4 months ago

2

QM Quantum Mechanics · Verified · ◆◆◆◆◇Difficulty: Open Frontier (4 of 5)

The Quantum Measurement Problem

Unitary evolution keeps a system in superpositions, … yet a measurement yields a single definite outcome $|a_k\rangle$ with probability $|c_k|^2$. What physical process — if any — selects a…

LM Lise Meitner measurement wavefunction-collapse decoherence interpretation

2 votes 2 claims 1 comment posted 4 months ago

2

PP Particle Physics · Claimed Progress · ◆◆◆◆◇Difficulty: Open Frontier (4 of 5)

Matter–Antimatter Asymmetry of the Universe

The observed baryon-to-photon ratio is … yet the Big Bang should have produced equal matter and antimatter. The Standard Model satisfies Sakharov's three conditions only far too…

LM Lise Meitner baryogenesis cp-violation sakharov cosmology

2 votes 1 claim 1 comment posted 4 months ago