Entropy, the Arrow of Time

ENTROPY — why time only points forward the single law of physics that can tell the past from the future. 1 · THE PARADOX fall rewind? An egg rolls off the table -> SPLAT. Happens every day. ✓ Play the film backwards: the splat leaps up and re-forms a perfect egg. You INSTANTLY know it's a fake video. ✗ THE SHOCK: physics fully ALLOWS the rewind. Every molecular collision runs backward fine. No law is broken. So why do we NEVER see it happen? 2 · NOT A FORCE — JUST ODDS ORDERED few ways to look like this · W small drifts to -> SPREAD OUT vast # of ways W astronomical A messy state isn't 'preferred'. There are just VASTLY more ways to be messy than tidy — so that's where things land. Same reason a shuffled deck never lands sorted: 1 sorted order 8 x 10^67 shuffles not forbidden — just 1-in-10^67. S = k · log W entropy = how many hidden arrangements look identical from outside. (this is carved on Boltzmann's gravestone) 3 · THIS *IS* TIME LOW ENTROPY (the past) HIGH (future) Time isn't a river flowing past you. Time is simply the DIRECTION disorder grows. 'Rewind' = entropy falling = the one thing nature never does. food (packed order) heat + waste (disorder) YOU are a pocket of low entropy. To stay alive & tidy you must dump MORE disorder into the world than you build inside. Same deal as your fridge or AC. BIG BANG freakishly TIDY start — the ONLY reason time has a direction HEAT DEATH all one temp, no events — the arrow STOPS. JARGON, DECODED Entropy (S) · how many hidden arrangements look identical from outside. High = messy. Micro- vs Macro-state · exact particle positions vs the blurry 'what it looks like'. W (multiplicity) · the number of those arrangements. Bigger W = more entropy. 2nd Law · a closed system's total entropy never falls. Lower it HERE only by raising it MORE elsewhere. WHY YOU REMEMBER THE PAST, NOT THE FUTURE: forming a memory increases entropy — so recording only works low -> high. Cause comes before effect for the very same reason.