Theoretical Physics

The fundamental theory describing nature at the smallest scales, where energy, momentum, and other quantities are quantized. It replaces deterministic classical mechanics with probabilistic wave functions governed by the Schr\u00f6dinger equation.

Einstein's geometric theory of gravitation, which describes gravity not as a force but as the curvature of spacetime caused by mass and energy. It is expressed through the Einstein field equations relating spacetime geometry to the energy-momentum tensor.

Einstein's 1905 theory establishing that the laws of physics are identical in all inertial reference frames and that the speed of light in vacuum is constant for all observers. It leads to time dilation, length contraction, and the equivalence of mass and energy ($E = mc^2$).

A theoretical framework that combines quantum mechanics with special relativity, treating particles as excited states (quanta) of underlying fields. It provides the mathematical language for the Standard Model of particle physics.

The theoretical framework classifying all known elementary particles and describing three of the four fundamental forces (electromagnetic, weak nuclear, and strong nuclear) through gauge symmetries. It does not include gravity.

A candidate theory of quantum gravity proposing that the fundamental constituents of the universe are not point particles but one-dimensional vibrating strings. Different vibrational modes correspond to different particles. It requires extra spatial dimensions beyond the three we observe.

Noether's theorem establishes a deep connection between continuous symmetries of a physical system and conserved quantities. Every differentiable symmetry of the action of a physical system corresponds to a conservation law.

The principle that every quantum entity exhibits both wave-like and particle-like properties. Whether it behaves as a wave or particle depends on the experimental setup used to observe it.

The four-dimensional continuum combining three spatial dimensions with one time dimension into a single geometric entity. In general relativity, spacetime is dynamic: it curves in response to mass-energy and tells matter how to move.

Heisenberg's principle stating that certain pairs of physical properties, such as position and momentum, cannot both be known to arbitrary precision simultaneously. Expressed as $\Delta x \cdot \Delta p \geq \frac{\hbar}{2}$. This is not a limitation of measurement but a fundamental property of nature.