Theoretical Physics

How to read equations without fear

You don’t need to memorize everything. Focus on what a symbol means in words and what would change if you poked the system. If an equation has a derivative with respect to time, it’s about change. If you see a symmetry, expect a conserved quantity. If a result seems weird, try a limit: what happens when something is very small, very large, or zero?

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From pushes and pulls to a single action

Newton says $\mathbf{F}=m\mathbf{a}$. Lagrange says: choose a function $L=T-V$ and take the path that makes the action $S=\int L\,dt$ “stationary” (small wiggles don’t matter to first order). Same physics, cleaner math, easier coordinates.

Conservation laws you can feel

Time-shift symmetry → energy conserved. Space-shift symmetry → momentum conserved. Rotation symmetry → angular momentum conserved. When you spot a symmetry, you’ve found a constant of motion — a compass for problem solving.

Why “fields” are worth the mindset shift

Instead of forces that jump across space, EM treats space itself as filled with fields ${\bf E}$ and ${\bf B}$ that carry energy and momentum. Changes ripple as waves at speed $c$. That’s light! A field picture also plays perfectly with relativity and later with quantum fields.

From theory to devices

Antennas, fiber optics, spectrometers — all are Maxwell made practical. Interference patterns are theory you can see.

Why time dilates (without pain)

If the speed of light is the same for everyone, moving clocks must tick differently so the math stays consistent. It’s not a trick — it’s how spacetime keeps laws universal.

Gravity isn’t a pull — it’s a path

Mass and energy curve spacetime; free objects follow the straightest possible paths (geodesics) in that curved geometry. Light bends near stars; time runs slower in stronger gravity.

Superposition • adding possibilities

A system can be in a mix of options at once — and the phase matters. Two paths can add or cancel like waves. If you learn which path it took, the interference fades. Information changes the pattern.

Uncertainty is about spreads, not clumsiness

For position $X$ and momentum $P$, spreads obey $\Delta X\,\Delta P \ge \hbar/2$. It’s a property of the state and the math, not “disturbance.” You can know a lot — just not everything at once.

Correlations that outsmart classical guesses

Some joint states can’t be described as “part A is this, part B is that.” Bell tests show the pattern beats any local hidden-variable plan. No faster-than-light messages, just different logic for joint outcomes.

So… what “collapses”?

The math has smooth evolution and sharp outcomes. Interpretations explain that gap in different ways (Copenhagen, Many-Worlds, pilot-wave). You can do great physics without picking a side — but knowing the options helps.

Feynman’s idea in friendly terms

The amplitude for a process is a sum of contributions from many possible histories, each with a phase that depends on the action. Nearby histories line up; wildly different ones cancel. Diagrams are smart bookkeeping for this math.

Renormalization • scale honesty

Parameters “run” with energy scale. That’s not cheating — it’s acknowledging that a theory describes nature up to a certain resolution. Different systems can show the same big-scale behavior (universality).

Why averages beat chaos

You don’t track every molecule. You track distributions. The partition function $Z=\sum e^{-E_i/k_BT}$ is a master key: it builds averages and fluctuations without following each particle.

Why eggs break but don’t unbreak

Microscopic laws are reversible, but we start the universe in a low-entropy condition. From there, typical evolution increases entropy. That’s your everyday arrow of time.

Stretch tiny jitters into galaxies

A brief burst of accelerated expansion magnifies quantum fluctuations into the seeds of cosmic structure. The exact engine is debated; the general picture matches the sky remarkably well.

What we really know (and don’t)

We see gravity’s effects that point to dark matter and dark energy. We name them honestly and keep testing — separating measurement from guess.

Berry phase • a phase from the path

Slowly loop a system’s settings and the state can pick up a geometric phase that depends on the loop’s shape, not the speed. Shows up in polarization and solid-state physics.

Topological phases • edges that won’t quit

Some materials have edge states protected by topology (not by energy barriers). That’s why their responses are quantized and robust to messiness.

Decoherence-free subspaces

Store quantum information in subspaces the dominant noise can’t touch. This is a real strategy for quantum devices, not sci-fi.

Wigner’s friend (plainly)

Inside the lab, the friend sees one outcome. From outside, Wigner treats the whole lab as a quantum system. The lesson: be explicit about information — who has which record — and many “paradoxes” calm down.

QBism, relational views, and superdeterminism

Different ways to connect math and meaning. You don’t have to swear loyalty — but knowing the menu keeps you from reading more into equations than they say.

Return to the map

Skim the other learning routes and pick a new doorway.

See code bring ideas to life

Short, readable notebooks that turn equations into pictures.

How labs test theories

Instruments, noise, and honest uncertainty bars.