For nearly two thousand years, astronomers tried to fit planetary motion into perfect circles.
Johannes Kepler abandoned that tradition after Tycho Brahe’s observations of Mars disagreed with the circular model by only eight arcminutes. In 1609, he showed that planets move in ellipses, with the Sun at one focus.
Kepler discovered the pattern from observation; Newton later explained it through gravity. The modern orbit equation unites circles, ellipses, parabolas and hyperbolas describing planets, comets, satellites and spacecraft with the same mathematical law.
“Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”
— Bertrand Russell
Johann Bernoulli challenged Isaac Newton with a 6 month deadline to solve the problem of the brachistochrone.
Newton got the message on Jan 26 at 4 pm and solved it going to bed that same night.
The Road Light Cannot Be Forced To Abandon
Ordinary light reflects when its path is blocked.
This light builds another path.
Inside a topological photonic crystal, light is governed by the two-component Dirac equation
i∂Ψ/∂t = [vᴅ(σₓpₓ + σᵧpᵧ) + m(x,y,t)σ𝓏 + V(x,y,t)I]Ψ.
Whenever the Dirac mass changes sign, a protected edge state appears. As moving defects and new topological domains emerge, the current bends, splits, reconnects, and assembles an entire photonic circuit without losing its path.
The optical probability density and current are
ρ = Ψ†Ψ,
jₓ = vᴅΨ†σₓΨ,
jᵧ = vᴅΨ†σᵧΨ,
with the luminous filaments transported by
v = j/ρ.
#TopologicalPhotonics #ChernInsulator #DiracEquation #EdgeStates #QuantumPhysics #PhotonicCrystal #ProbabilityCurrent #Mathematics #Physics
A Quantum Current Chooses a Path
A single electron enters a microscopic interferometer, but its wavefunction travels through two routes at once. One branch crosses a resonant quantum dot while the other moves freely around a ring threaded by magnetic flux.
The probability current is
j = (ℏ/m) Im(ψ*∇ψ) - (q/m)A|ψ|²,
while the enclosed flux creates the Aharonov-Bohm phase
Δφᴬᴮ = qΦ/ℏ.
The quantum dot adds the resonant phase
δ(E) = atan2(Γ, E - E₀),
producing Fano interference when the two paths recombine.
Wave packets split, become temporarily trapped, form circulating current vortices, reverse direction after a flux quench, and finally escape through the drain in a coherent burst. The glowing threads are material curves transported by
v = j/ρ,
revealing how invisible quantum phase controls the flow.
#QuantumMechanics #AharonovBohmEffect #QuantumInterference #QuantumDot #ProbabilityCurrent #MesoscopicPhysics #PhysicsAnimation #Physics
Adam Brown (@A_G_I_Joe) is back!
General relativity is said to be the most beautiful idea the human mind has ever produced.
Most of us will never get to fully appreciate its elegance by taking the 20-lecture graduate course Adam taught on it at Stanford.
But in the video below, Adam distills the key idea at its heart so clearly and compellingly that even I could keep up lol.
At the core of general relativity, Einstein is trying to figure out the principle behind a particular coincidence: that the mass that resists acceleration and the mass that gravity pulls on just happen to be exactly the same. Adam then leads us through the path of insight which Einstein called his “happiest thought.”
Then Adam lectures on black holes. First, by showing how even under special relativity you could create a perpetual motion machine if black holes weren't truly black. And then, by explaining why the observations of an infalling observer and a distant bystander to the black hole would be so radically different
Adam leads Blueshift, the team at Google DeepMind cracking science and reasoning.
Which gave us the opportunity to discuss at the very end how close we are to AIs that could rediscover general relativity from scratch. Stay till the close for some philosophy of science.
0:00:00 – The coincidence that led Einstein to general relativity
0:16:42 – Gravity is a consequence of curved spacetime, not a force
0:31:46 – Why black holes prevent unlimited energy extraction
0:47:12 – Black holes are the ultimate power plants
1:13:50 – What falling into a black hole would actually feel like
1:18:51 – The three ways we know black holes are real
1:24:21 – The first time we saw gravity bend light
1:29:33 – How far can AI get without experimental evidence?
Look up Dwarkesh Podcast on YouTube/Spotify to watch. Enjoy!