Physics¶

The laws of the universe, derived from first principles.

Mechanics¶

Newton's Laws - The definitions of motion (\(F=ma\)).
Centripetal Acceleration - Deriving \(a_c = \frac{v^2}{r}\) from geometric analysis.
Simple Harmonic Motion - Deriving the period formula \(T = 2\pi\sqrt{\frac{m}{k}}\).
Kinetic Energy - Deriving \(K = \frac{1}{2}mv^2\) from the definition of Work.
Gravitational Potential Energy - Deriving \(U = mgh\) and why lifting things makes you tired.

Coulomb's Law - Why electric force is inversely proportional to distance squared.

Measuring the Universe - How we weighed the Earth (\(G\)) and measured gravity (\(g\)) without satellites.

Schrödinger Equation - The fundamental equation of quantum mechanics (\(i\hbar \frac{\partial}{\partial t} \Psi = \hat{H} \Psi\)).
Heisenberg Uncertainty Principle - Fundamental limits on measurement precision (\(\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\)).
Rabi Frequency - Quantum oscillations between energy levels (\(\Omega_R = |\mathbf{d} \cdot \mathbf{E}_0|/\hbar\)).
Born Rule - The probabilistic interpretation of the wave function (\(P = |\langle \phi | \Psi \rangle|^2\)).

Doppler Effect - Why pitch and color shift with motion (\(f = f_0 \frac{v + v_o}{v - v_s}\)).

Minkowski Spacetime - Unifying space and time through the invariant interval (\(ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2\)).

Quantum Field Theory - Why particles are ripples in fields, derived from quantizing the harmonic oscillator.
Quantum Electrodynamics - How demanding local phase symmetry forces the photon into existence (\(\mathcal{L} = \bar\psi(i\gamma^\mu D_\mu - m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\)).
Quantum Chromodynamics - The non-abelian gauge theory of quarks, gluons, and the strong force.