Five Equations, Told as One Story
July 2026
Original clip: @21xooaes on X, 2026-07-27, reposting a video by Ali Alqaraghuli, PhD — a NASA Postdoctoral Program fellow (ASTHROS balloon telescope project) — from his own channel, “99% of physics explained in 5 equations.” If the embed above doesn’t load, everything it covers is written out below from a full transcript and the chalkboard itself.
The move that makes this worth featuring
Most “N equations you need to know” videos present a list. This one deliberately doesn’t — Alqaraghuli picks five equations and tells them as a single throughline, each one handing off to the next, from everyday mechanics to the edge of quantum physics. That structure, not just the equations themselves, is the actual teaching technique worth studying.
The five equations, in the order he builds them
1. Newton’s second law, rewritten as cause and effect
$$a = \frac{F}{m}$$
He’s deliberate that this is not the same equation as $F=ma$ read the usual way — written as $a = F/m$, it reads as “force causes acceleration,” which he frames as the real content of all three of Newton’s laws in one line: no force, no acceleration (inertia); force in, acceleration out (the second law); and the reaction pair, worked out with his own knuckles against a chalkboard eraser (the third law).
2. Newton’s law of gravitation
$$F \sim \frac{Gm_1m_2}{d^2}$$
Two masses pull on each other, weakening with the square of the distance between them — twice the distance, a quarter the force. He drops the constant $G$ from the argument (it just makes the units work) to focus on the shape of the relationship itself, and points out gravity is only attractive — as far as anyone has observed.
3. Coulomb’s law
$$F = \frac{kq_1q_2}{d^2}$$
The same inverse-square shape as gravity, but for charge instead of mass: same-sign charges repel, opposite-sign charges attract, unlike gravity’s exclusively-attractive pull. His real point is sharper than the rule itself — it’s strange that nature reuses the identical mathematical form for two completely different forces, one strictly attractive, one capable of both. He’s honest that nobody fully knows why, and that repulsive gravity hasn’t (so far) been observed either.
4. The Ampère–Maxwell law
$$\nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0\varepsilon_0\frac{\partial \vec{E}}{\partial t}$$
A magnetic field can be produced two ways — by an electric current ($\vec{J}$), or by a changing electric field — and the equation says either is sufficient, not that both are required. This is where the video shifts from single-particle forces to fields, the concept that carries into everything after it.
5. The wave equation
$$\frac{\partial^2 u}{\partial t^2} = c^2\frac{\partial^2 u}{\partial x^2}, \qquad c = \sqrt{\frac{1}{\mu_0\varepsilon_0}}$$
Combine the Ampère–Maxwell law with Faraday’s law (its mirror image — a changing magnetic field induces an electric field) and the wave equation falls out, with the wave speed pinned to $1/\sqrt{\mu_0\varepsilon_0}$ — which is the speed of light. Two constants measured in totally unrelated lab experiments (a capacitor’s permittivity, a coil’s permeability) combine to predict a number nobody put in by hand. He then notes, correctly, that Schrödinger’s equation is itself a case of the wave equation — the same mathematical object that describes a plucked string also sits underneath quantum mechanics.
Catalog status: Proven Systems
All five equations are standard, extremely well-tested physics — Newtonian mechanics confirmed at everyday scales for centuries, Maxwell’s equations confirmed to extraordinary precision (this is the derivation showing electromagnetism predicts the speed of light), and the wave equation a direct mathematical consequence of the other two. None of this is a claim under test; it’s the settled backbone the video is built on.
Where this touches PBT
This is closer to home than most Math Applications Simplified entries. Paper 1 reframes gravity (equation 2 above) as an emergent push/shadowing effect between particles in an aether medium rather than a fundamental force in its own right, and Paper 3 does the same for magnetism and the Lorentz force (adjacent to equation 4). So two of these five equations sit directly in territory PBT is trying to mechanically re-derive from a different starting point. What PBT doesn’t currently offer is its own derivation of the Ampère–Maxwell law, the wave equation, or the specific value $c = 1/\sqrt{\mu_0\varepsilon_0}$ — those stand here exactly as mainstream electromagnetism defines them, with no PBT-specific claim attached.