Force That Clicks

Force and mass are a "loop" that defines each other using the other. So what is the content of F=ma? What comes out of an interaction is only the "ratio" of masses ── the absolute values are a convention, the ratio is physics.F = ma / a₁/a₂ = m₂/m₁

Touching an object and pushing it ── that repulsion is the electromagnetic force between the electron clouds of atoms. The sensation of contact is an illusion; in truth, no one is "touching" anything.contact force = electromagnetic force

Everyday forces have many names, but their true nature is nearly all one thing. That the spring law F=kx holds for any material is because "the bottom of a valley is a parabola."all the same single force

Centrifugal force and the Coriolis force are apparent forces that well up the moment you rotate the coordinates. They can be erased by re-labeling coordinates ── the seed of gauge.apparent force = the coordinates' balancing act

You feel weight, yet in free fall it vanishes. From the mystery that inertial mass and gravitational mass agree (the equivalence principle), to gravity = the geometry of spacetime. The substance of the weight you feel was the electromagnetism of the floor pushing up.gravity = geometry

Force is the exchange of a field and particles. The mass of the carrier decides the range the force reaches (Yukawa). That the weak force is short-range, and that light reaches to infinity, are seen at a glance from this.range ~ ℏ/mc

Gravity, electromagnetism, strong, and weak on one page ── by strength, range, and carrier. Strength is compared by unitless couplings ── the α of the sister series takes effect here. Also, the mystery of why the weakest force, gravity, rules the universe.α, α_s, α_W, α_G

Coupling constants run. Electromagnetism grows stronger the closer you get; the strong force grows weaker the closer you get. Three lines running in opposite directions meet at one point at high energy ── a hint of unification.α(energy) is not constant

The heart of the series. Freely choosing the ambiguity of phase at each point (local symmetry) gives birth to a force that patches it up ── the gauge principle. The four forces are the connectors of four symmetries. The endpoint of the peeling.∂ → D = ∂ − iA

Both gravity and electricity go as 1/r². This is not a property of force, but the fingerprint of space being three-dimensional. It's just a matter of being diluted over area. In 2D it's 1/r, in 4D it's 1/r³.F ∝ 1/r^(d−1)

The closer, the freer; the farther you pull apart, the stronger. That's why a quark can't be extracted on its own (confinement). The one force that breaks the common sense of inverse square. Its proof is still unsolved (a Millennium Prize problem).asymptotic freedom and confinement

Bring the four into one (unification), erase gravity with geometry, erase inertial force with coordinates. What can be erased is the ledger (gauge, coordinates); what can't be erased was the curvature (the body of relation).unification, and the final balancing

Closing up shop on the word "force." Descend the staircase of peeling to its deepest point, and what remains is not a substance but relation, geometry, symmetry, and un-erasable curvature ── that's the wrap-up.force is not a noun, but the name of a relation

A wave is not an independent substance but a chain of restoring force (spring) + inertia = a game of telephone played by force. Its speed is √(restoring force/inertia). Guitars, sound, and light share the same skeleton.v = √(T/μ)

The field of the electromagnetic force = light. A quiet force is the near field; shake it and it radiates (a wave). Two faces of the same single field. The carrier (the photon) is the particle of the field's wave.force = field = wave

Radiation pressure (light pushes), and, in the quantum realm, particles are waves and force is a shift of phase (Aharonov–Bohm = the gauge of Episode 9). The interference fringes slide. The culmination of "forces that look like waves."wave → force → phase

Action at a distance is an approximation. Changes in a field chase after at the speed of light (even if the Sun vanished, 8 minutes later). The speed of gravity = c is also confirmed (GW170817).change is transmitted at c

The carrier is massless (photon) → change goes at c, infinite range. Heavy (W/Z) → short range. But "short range = slow" is false. Sorting out range ≠ speed.zero mass ↔ c ↔ infinite range

The field of a uniformly-moving source points to its present position (seemingly instant) but carries no information. Only acceleration emits a wave and transmits it at c. Virtual particles and the appearance of instantaneity.only acceleration radiates

Loss = potential, gradient descent = F=−∇V, momentum = inertia, weight decay = spring, flat directions = gauge with zero force. Shaking hands with installment 10 of the sister series "Cosmology That Clicks" to close the two-part work.learning = mechanics

Force is not the lead. Nature chooses the path that makes the action S=∫(T−V)dt stationary. F=ma is a derivative of it. Light and free fall obey the same stationary principle.δS = 0 ⇒ F=ma

The conservation of energy and momentum is not handed down from on high but follows necessarily from the symmetry of the action. Time symmetry → energy, space symmetry → momentum. A sibling of Episode 9. Also the story of conservation breaking in an expanding universe.symmetry → conservation law

Gauge = connection, gravity = the curvature of spacetime (the mathematics of Episodes 9 and 12). The offset in an arrow's direction after taking it around a loop = curvature = force. The groups U(1)/SU(2)/SU(3) classify the forces.force = the curvature of a connection

A soap film solves for a minimal surface, a spring network solves simultaneous equations ── with force (energy minimization), in an instant. Nature = optimizer. AI's gradient descent is a member too.solving = energy minimization

The law of force is simple, yet three or more bodies can't be solved with a closed formula and become chaotic. Deterministic, yet unpredictable. So we have no choice but to rely on computation.simple law → chaos

Confinement, which can't be proved (Episode 11), is confirmed by carving spacetime into a lattice and computing on a supercomputer. V(r) climbing linearly = confinement reproduced. Shaking hands with the sister series "The Universe Is a Computer."confinement, by computation