A note on frames: an inertial frame is one where a free body stays at rest or moves in a straight line at constant speed — i.e. Newton's first law holds and there are no pseudo-forces.
Postulate 1 — WHY it feels obvious yet is deep.
If you sip coffee in a smoothly flying plane, the cup pours normally. Galileo already knew this for mechanics. Einstein's leap was to extend it to all physics — including electromagnetism. Maxwell's equations predict light moves at c; if Postulate 1 is true, that prediction must hold in every inertial frame. This forces Postulate 2.
Postulate 2 — WHY it is shocking.
Everyday velocities add: walk 2 m/s on a 3 m/s train → ground sees 5 m/s. So shining a torch (c) from a fast rocket "should" give c+v. Experiment (Michelson–Morley, 1887) found no such addition for light. Light refuses to add. The only way to keep Maxwell consistent across frames is to declare cinvariant.
(1) Laws of physics are the same in all inertial frames; (2) speed of light in vacuum is the same for all inertial observers, independent of source/observer motion.
What is an inertial frame?
A non-accelerating frame where Newton's first law holds and no pseudo-forces appear.
Which experiment motivated Postulate 2?
Michelson–Morley (1887) — found no ether and no c+v addition for light.
Define the Lorentz factor and its range
γ=1/1−v2/c2, always ≥1 for v<c.
What does Δt=γΔt0 mean physically?
A moving clock (proper time Δt0) is measured to run slow by factor γ in any other inertial frame.
Why must Postulate 1 force Postulate 2?
Maxwell's equations give light speed c; if laws are identical in all inertial frames, all of them must measure c.
What classical idea did Einstein sacrifice to keep c constant?
The absoluteness/universality of time and simultaneity.
Relativistic velocity addition formula?
u′=(u+v)/(1+uv/c2); with u=c it gives c.
Why does Newtonian physics still work daily?
At everyday v≪c, γ≈1, so relativistic effects are negligible.
Recall Feynman: explain to a 12-year-old
Imagine you're on a super-smooth train and you drop a ball — it falls straight down, just like at home. You can't feel the train moving. Einstein said: no experiment you do will reveal you're moving — that's rule 1. Rule 2 is the weird one: light always zooms past you at the same speed, whether you chase it or run away from it. To make both rules true, moving clocks have to tick slower. Nature would rather slow down time than let light change its speed!
Dekho, Special Relativity ki neev sirf do postulates par tiki hai. Pehla: physics ke saare laws har inertial frame (jo accelerate nahi kar raha) mein bilkul same dikhte hain — yaani smooth chalti train mein baith ke koi bhi experiment kar lo, tum bata hi nahi sakte ki tum "rest" mein ho ya constant speed se move kar rahe ho. Doosra, aur sabse shocking: light ki speed c har observer ke liye same hai, chahe source bhag raha ho ya tum bhag rahe ho. Normal cheezein (train pe chalna) toh add hoti hain, par light kabhi add nahi hoti.
Yeh dono rules ek saath rakho toh purani "time sab jagah same chalta hai" wali soch tootti hai. Einstein ne kaha — agar c ko nahi badalna, toh time aur space ko bend hone do. Isi se time dilation nikalta hai: ek light-clock socho jisme photon upar-neeche bounce karta hai. Apne frame mein wo seedha 2L chalta hai. Lekin agar clock side mein move kar rahi ho, toh photon diagonal raasta lega — lamba path — par speed phir bhi c hi rahegi (Postulate 2!). Pythagoras lagao toh nikal aata hai Δt=γΔt0, jahan γ=1/1−v2/c2.
Yeh matter kyun karta hai? Kyunki γ humesha ≥1 hota hai, matlab chalti ghadi dheere chalti hai. Rozmarra ki speeds (car, plane) pe v, c ke saamne kuch bhi nahi, isliye γ≈1 aur Newton ki physics kaam karti hai. Par jab speed c ke kareeb pahunchti hai (particles, GPS satellites), tab yeh effect zabardast ho jaata hai. Yaad rakho: "Same Laws, Same Light" — bas yahi se poori relativity build hoti hai.
