Classical Physics
This inescapable thermodynamic law establishes the "arrow of time," famously breaking the time-reversal symmetry otherwise present in Newton's and Maxwell's equations.
What is the Second Law of Thermodynamics?
The null result of this famous 1887 interferometry experiment provided the first strong evidence against the existence of the luminiferous aether, paving the way for Special Relativity.
What is the Michelson-Morley experiment?
Setting the first variation of the action integral to zero yields these fundamental differential equations, the cornerstone of Lagrangian mechanics.
What are the Euler-Lagrange equations?
Discovered accidentally by Penzias and Wilson as persistent radio noise, this nearly isotropic 2.7 Kelvin relic radiation provided the "smoking gun" evidence for the Big Bang model.
What is the Cosmic Microwave Background (CMB)?
This famous type of astronomical body, that was finally pictured in 2019, prevents anything from escaping by bending the curvature of spacetime so drastically that the geodesic paths remain in the body.
What is a black hole?
By adding this specific "current" term to Ampere's Law, Maxwell resolved a conservation of charge paradox and mathematically unified electricity, magnetism, and light.
What is the displacement current?
Max Born sparked a philosophical earthquake in physics when he proposed that taking the absolute square of a quantum wave function yields this, explicitly replacing classical determinism.
What is probability density?
This integral transform is the mathematical reason why position and momentum are conjugate variables, providing the foundation for the Heisenberg Uncertainty Principle.
What is the Fourier transform?
These spinning neutron stars emit radiation beams so precise they rival atomic clocks.
What are pulsars?
Discovered at CERN in 2012, this excitation of a ubiquitous scalar field is the mechanism by which the W and Z gauge bosons - and fundamental fermions - acquire their rest mass.
What is the Higgs Boson?
According to Liouville's theorem, as a classical, conservative system evolves over time, the "volume" occupied by a set of initial states in this 2N-dimensional abstract space remains perfectly constant.
What is phase space?
Einstein famously called it his "happiest thought:" this fundamental principle asserting that an observer in a closed box cannot distinguish between a uniform gravitational field and uniform acceleration.
What is the Equivalence Principle?
Physicists often evaluate difficult real-line integrals for scattering amplitudes or quantum field theory by extending into the complex plane and using this theorem to sum the enclosed poles.
What is the Residue Theorem?
Vera Rubin's observation that spiral galaxies maintain unexpectedly flat rotation curves provided the first robust dynamical evidence for this invisible, non-baryonic cosmic scaffolding.
What is dark matter?
By observing that these elusive leptons spontaneously change "flavor" during transit from the Sun or the atmosphere, physicists in the early 2000s proved they must possess a non-zero mass.
What are neutrinos?
While studying the gravitational three-body problem, Henri Poincare discovered that purely deterministic classical equations can still be completely unpredictable due to extreme sensitivity to these.
What are initial conditions?
By modifying the Schrodinger equation to make it compatible with special relativity, Paul Dirac found it provided negative energy solutions, which led to the first theoretical prediction of this.
What is antimatter?
Emmy Noether used the continuous "Lie" variety of this branch of abstract algebra to prove her famous theorem linking continuous symmetries to conservation laws.
What is group theory?
Originally introduced by Einstein as a "fudge factor" to maintain a static universe, this term in the field equations was resurrected in the 1990s as the leading explanation for dark energy and cosmic acceleration.
What is the cosmological constant?
First directly detected in 2015 from a binary black hole merger, these spacetime distortions are the primary observable consequences of a time-varying gravitational quadrupole moment.
What are gravitational waves?
Driven by the classical equipartition theorem, this dramatic failure of the Rayleigh-Jeans law to predict blackbody emission at short wavelengths signed the ultimate boundary of classical physics.
What is the ultraviolet catastrophe?
This 1964 theorem moved the Einstein-Podolsky-Rosen (EPR) paradox from philosophy into the laboratory, mathematically proving that quantum mechanics is fundamentally incompatible with any local hidden-variable theory.
What is Bell's Theorem?
Formulated heavily by Riemann and Levi-Civita, this branch of mathematics dealing with curved manifolds and tensors provided the exact machinery Einstein needed to describe gravity.
What is differential geometry?
Uniting general relativity, quantum field theory, and thermodynamics, this theorized thermal emission implies black holes are not completely black, but have a temperature inversely proportional to their mass.
What is Hawking radiation?
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