Postulates of SR — Hinglish notes

2.3.26 · Physics › Modern Physics

WHAT hain ye postulates?

Frames ke baare mein ek note: ek inertial frame woh hota hai jahan ek free body rest mein rehti hai ya ek seedhi line mein constant speed se move karti hai — yaani Newton's first law hold karta hai aur koi pseudo-forces nahi hoti.

WHY har postulate? (Apni intuition ko steel-man karo)

Postulate 1 — WHY yeh obvious lagta hai phir bhi deep hai. Agar tum smoothly urte huye plane mein coffee peete ho, toh cup normally pour hota hai. Galileo yeh mechanics ke liye pehle se jaanta tha. Einstein ki leap thi ise sabhi physics tak extend karna — including electromagnetism. Maxwell's equations predict karti hain ki light $c$ par move karti hai; agar Postulate 1 sach hai, toh woh prediction har inertial frame mein hold karni chahiye. Yeh Postulate 2 ko force karta hai.

Postulate 2 — WHY yeh shocking hai. Rozmarra ki velocities add hoti hain: 3 m/s ki train par 2 m/s chalo → ground 5 m/s dekhta hai. Toh ek fast rocket se torch ( $c$ ) jalaane par "should" $c + v$ milna chahiye. Experiment (Michelson–Morley, 1887) ne light ke liye koi aisi addition nahi paai. Light add karne se mana karti hai. Maxwell ko sabhi frames mein consistent rakhne ka ek hi tarika hai — $c$ ko invariant declare karo.

HOW postulates physics ko rebuild karte hain (mini-derivation)

Hum formulas dump nahi karte; hum Postulate 2 se seedha pehla consequence — time dilation — derive karte hain.

Worked example Time dilation ki Light-clock derivation

Setup: Ek "clock" ek photon hai jo height $L$ se separated do mirrors ke beech vertically bounce karta hai. Ek tick = upar + neeche.

Clock ke apne (rest) frame mein: Photon $2 L$ door $c$ speed se travel karta hai. $Δ t_{0} = \frac{2 L}{c}$ Yeh step kyun? Apne frame mein clock sideways nahi move kar raha, toh light sirf seedha upar-neeche jaati hai — pure vertical distance $2 L$ .

Us frame mein jahan clock $v$ speed se right move karta hai: Jab light upar jaati hai, top mirror aage khisak jaata hai, toh photon ek diagonal travel karta hai. Moving-frame tick ko $Δ t$ maano. Half-tick mein horizontal distance $= v \frac{Δ t}{2}$ ; vertical $= L$ .

Pythagoras se, diagonal path length (ek taraf) hai $L^{2} + (\frac{v Δ t}{2})^{2}$ Yeh step kyun? Mirror physically sideways move kiya, toh light ka actual path lamba hai — lekin uski speed abhi bhi $c$ hai (Postulate 2!), $c$ plus kuch nahi.

Photon puri path $2 \times (diagonal)$ $c$ speed se cover karta hai: $c Δ t = 2 L^{2} + (\frac{v Δ t}{2})^{2}$ Yeh step kyun? distance = speed × time, aur speed $c$ honi forced hai.

Dono sides square karo: $c^{2} Δ t^{2} = 4 L^{2} + v^{2} Δ t^{2}$ . $Δ t$ ke liye solve karo: $Δ t^{2} (c^{2} - v^{2}) = 4 L^{2} \Rightarrow Δ t = \frac{2 L}{c ^{2} - v ^{2}}$ Ab $2 L = c Δ t_{0}$ substitute karo: $Δ t = \frac{Δ t _{0}}{1 - v ^{2} / c ^{2}} = γ Δ t_{0}$

Worked numerical examples

Common mistakes (Steel-manned)

Flashcards

SR ke do postulates batao

(1) Physics ke laws sabhi inertial frames mein same hain; (2) vacuum mein light ki speed sabhi inertial observers ke liye same hai, source/observer ke motion se independent.

Inertial frame kya hota hai?

Ek non-accelerating frame jahan Newton's first law hold karta hai aur koi pseudo-forces appear nahi hoti.

Postulate 2 ko kis experiment ne motivate kiya?

Michelson–Morley (1887) — koi ether nahi mila aur light ke liye koi

c + v

addition nahi mili.

Lorentz factor define karo aur uski range batao

γ = 1/ 1 - v^{2} / c^{2}

v < c

ke liye hamesha

\geq 1

Δ t = γ Δ t_{0}

physically kya matlab rakhta hai?

Ek moving clock (proper time

Δ t_{0}

) kisi bhi doosre inertial frame mein

γ

factor se slow run karta hua measure hota hai.

Postulate 1 ko Postulate 2 force kyun karna padta hai?

Maxwell's equations light speed

c

deti hain; agar laws sabhi inertial frames mein identical hain, toh sabko

c

measure karna padega.

Einstein ne

c

constant rakhne ke liye kya classical idea sacrifice kiya?

Time aur simultaneity ki absoluteness/universality.

Relativistic velocity addition formula?

u^{'} = (u + v) / (1 + uv / c^{2})

;

u = c

ke saath

c

deta hai.

Newtonian physics rozmarra kyun kaam karti hai?

Rozmarra ke

v ≪ c

par,

γ \approx 1

hota hai, toh relativistic effects negligible hain.

Recall Feynman: 12-saal ke bachche ko samjhao

Socho tum ek super-smooth train mein ho aur tum ball drop karte ho — woh seedha neeche girta hai, bilkul ghar ki tarah. Tum train ko move karta feel nahi kar sakte. Einstein ne kaha: koi bhi experiment jo tum karo woh reveal nahi karega ki tum move kar rahe ho — yeh rule 1 hai. Rule 2 weird wala hai: light hamesha tumhare paas se same speed par zoom karti hai, chahe tum uska peecha karo ya ussse door bhaago. Dono rules ko sach rakhne ke liye, moving clocks ko slower tick karna padta hai. Nature time ko slow karna zyada prefer karta hai bajaaye light ki speed badalne ke!

Connections

Time Dilation — upar derive kiya gaya direct consequence.
Length Contraction — spatial partner: $L = L_{0} / γ$ .
Lorentz Transformations — dono postulates encode karta full coordinate map.
Relativistic Velocity Addition — kyun light $c$ rehti hai.
Michelson-Morley Experiment — Postulate 2 ka experimental seed.
Maxwell's Equations — $c$ predict karti hain, invariance demand karti hain.
E=mc² — usi postulates ka baad ka fruit.
Galilean Relativity — classical limit jise SR generalize karta hai.