Postulates of SR: Question bank — Hinglish deep dive

2.3.26 · D5 · Physics › Modern Physics › Postulates of SR

Definition Is page par use hone wale symbols (pehle define kiye gaye)

$c$ — speed of light in vacuum, $\approx 3 \times 1 0^{8} m/s$ ; woh ek speed jis par sabhi agree karte hain.
$v$ — do inertial frames ke beech constant relative speed (ek observer doosre ke paas se kitni tezi se guzarta hai).
$L$ — light-clock ke do mirrors ke beech fixed height (woh vertical gap jisme photon bounce karta hai); ek length jo tum rest mein ruler se measure kar sakte ho.
$u$ — kisi cheez ki velocity (jaise bullet ya light beam) ek frame mein measure ki gayi, doosre frame mein switch karne se pehle.
$u^{'}$ — usi cheez ki velocity ek doosre frame mein measure ki gayi jo pehle frame ke relative speed $v$ par move kar raha hai; relativistic addition rule batata hai ki $u$ kaise $u^{'}$ banta hai.
$Δ t_{0}$ — proper time: ek duration jo ek clock apne rest frame mein measure karta hai, jahan clock move nahi karta. Yeh us pair of events ke liye possible sabse chhoti reading hai.
$Δ t$ — unhi do events ki duration ek alag frame se measure ki gayi jo clock ko move karte dekh raha hai. Hamesha $\geq Δ t_{0}$ .
$γ$ — Lorentz factor, $γ = \frac{1}{1 - v ^{2} / c ^{2}} \geq 1$ , woh exact number jo dono ko link karta hai: $Δ t = γ Δ t_{0}$ .

Intuition Neeche har trap ke peeche ek hi picture (the light-clock)

Ek "clock" ek photon hai jo do mirrors ke beech seedha upar-neeche bounce karta hai, mirrors $L$ height par hain; ek tick ek upar-neeche ka safar hai. Clock ke apne frame mein photon $2 L$ speed $c$ par cover karta hai, toh $Δ t_{0} = 2 L / c$ . Ek aise frame mein jahan clock sideways $v$ par slide kar raha hai, photon ko diagonal travel karna padta hai — ek zyada lambi distance — lekin phir bhi speed $c$ par (Postulate 2). Pythagoras se, ek-taraf ka path $= L^{2} + (v Δ t /2)^{2}$ hai, aur $c Δ t = 2 L^{2} + (v Δ t /2)^{2}$ solve karne par exactly $Δ t = Δ t_{0} / 1 - v^{2} / c^{2} = γ Δ t_{0}$ milta hai. Toh diagonal, vertical se precisely $γ$ factor se lamba hai — woh geometric stretch hi time dilation hai. Neeche har item ke liye is triangle ko dhyan mein rakho. Time Dilation dekho.

Figure below (s01): baaya (violet) arrow photon ka seedha-upar path hai length $L$ clock ke rest frame mein; daaya (magenta) arrow usi photon ka diagonal path hai ek aise frame mein jahan top mirror orange dashed leg $v Δ t /2$ se right mein khisal gayi hai. Magenta hypotenuse violet leg se exactly $γ$ se lambi hai — woh stretched arrow hi slowed tick hai. Jab bhi koi item diagonal mention kare, is triangle par wapas aao.

True or false — justify

Light from a fast rocket reaches me at

c + v

if the rocket flies toward me.

False — Postulate 2 ke anusaar, light ki speed har inertial observer ke liye

c

hai chahe source move kare ya nahi; sirf iska frequency (colour) Doppler ke zariye shift hota hai. Relativistic Velocity Addition dekho, jahan

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

collapse hoke

c

ban jaata hai jab bhi

u = c

hota hai.

Time dilation isliye hota hai kyunki motion physically clock ke mechanism ko jhatka deta hai.

False — yeh geometric hai, sirf

c

ki constancy se derived hai (upar wala diagonal-vs-vertical triangle); ek perfect ideal clock bhi (ya dhadakta dil, ya decay hota particle) dilate karta hai. Yeh time khud hai, device nahi.

Special Relativity ka pehla postulate ek aisi rocket par apply hota hai jo apne engines fire kar rahi hai.

False — Postulate 1 sirf inertial (non-accelerating) frames ko cover karta hai; ek accelerating frame pseudo-forces feel karta hai, isliye uske rules alag hain. Special relativity abhi bhi aisi motion describe kar sakti hai (jaise accelerated "Rindler" coordinates ke zariye) — tumhe General Relativity ki zarurat nahi — lekin Postulate 1 ki exact frame-equivalence ab apply nahi hoti.

Agar do observers constant velocity par ek doosre se door ja rahe hain, toh har ek doosre ki clock ko slow chal te dekh ta hai.

True — situation bilkul symmetric hai kyunki na to "sach mein" move kar raha hai (Postulate 1); har ek ek valid inertial frame hai, toh har ek doosre ki clock ko

γ

se dilated dekhta hai.

Lorentz factor

γ

bahut tez objects ke liye 1 se kam ho sakta hai.

False — kyunki

v < c

v^{2} / c^{2} < 1

milta hai, square root

1 - v^{2} / c^{2}

0 aur 1 ke beech hai, toh iska reciprocal

γ

hamesha

\geq 1

hota hai. Time Dilation dekho.

Galilean velocity addition aur light ki invariant speed dono ek saath exactly sach ho sakte hain.

False — yeh logically contradictory hain;

c

ko invariant rakhne ke liye tumhe Galilean addition aur time ki universality dono chhodni padti hai. Galilean Relativity dekho.

Michelson–Morley ne prove kiya ki light ether se travel karta hai.

False — usne ulta prove kiya; koi ether wind detect nahi hua aur koi

c + v

effect nahi mila, yahi cheez physics ko Postulate 2 ki taraf le gayi. Michelson-Morley Experiment dekho.

v = 30

m/s par ek real clock measurably slow chalti hai.

Practice mein False —

γ \approx 1 + \frac{1}{2} (1 0^{- 14})

, ek correction jo everyday speeds par detect karne ke liye bahut tiny hai; relativity hamesha on hai lekin dikhai nahi deti.

Mere liye ek saath hone wale do events har observer ke liye ek saath hain.

False — simultaneity relative hai; mujhse relative move karne wala observer unhi do events ko alag-alag times par hota measure kar sakta hai. Yahi cheez Einstein ne

c

bachane ke liye sacrifice ki.

Spot the error

"Ek photon ka ek rest frame hai; usme photon bas wahan khada rehta hai."

Error — koi bhi inertial frame

c

par move nahi karta, toh photon ka koi rest frame nahi hai; jaise

v

c

ke paas jaata hai,

γ

unbounded badhta hai, toh transformation breakdown ho jaata hai. Light har frame mein

c

hai, kisi mein bhi rest mein kabhi nahi.

"Postulate 1 kehta hai ki sabhi observers har cheez par agree karte hain."

Error — yeh kehta hai ki physics ke laws sabhi inertial frames mein identical hain, yeh nahi ki measured values (times

Δ t

, lengths) agree karte hain. Observers famously durations aur lengths par disagree karte hain jabki laws aur

c

par agree karte hain.

Δ t = γ Δ t_{0}

, aur kyunki moving frame zyada time dekhta hai, main

γ

se divide karta hun."

Error — tum multiply karte ho:

Δ t_{0}

proper time hai (sabse chhota, clock ke apne frame mein measure kiya gaya), aur koi bhi doosra frame bada value

γ Δ t_{0}

measure karta hai. Divide karne se galat tarike se doosre frame ka time chhota ho jaata.

"Light ko ek medium chahiye, toh yeh us medium ke relative

c

par travel karta hai."

Error — sound ke unlike, light ko koi medium nahi chahiye; Maxwell's equations

c

dete hain bina kisi ether ke reference ke, aur Michelson-Morley Experiment ne confirm kiya ki koi exist nahi karta.

"Einstein ne time dilation assume kiya aur us se

c

ki constancy derive ki."

Error — logic ulti direction mein chalta hai:

c

constant postulate hai, aur time dilation ek derived consequence hai (light-clock triangle ke zariye). Tum kabhi conclusion assume nahi karte.

"Kyunki moving clocks slow down karte hain, moving observer apne liye time crawl karte feel karta hai."

Error — moving observer kuch bhi unusual feel nahi karta; unki apni clock unhe unke liye normally tick karti hai (unke apne frame mein

Δ t_{0}

). Dilation hamesha ek alag inertial frame dwara measure kiya jaata hai, kabhi bhi clock apne baare mein nahi.

Why questions

Postulate 1 Postulate 2 ko force kyun karta hai zyada ki independent hone ki bajaye?

Step 1: Maxwell's Equations mein constants

ε_{0}

aur

μ_{0}

hain aur wave speed

c = 1/ ε_{0} μ_{0}

predict karte hain — ek single fixed number, bina kisi observer ki motion ke reference ke. Step 2: Postulate 1 kehta hai ki wahi equations (aur wahi number) har inertial frame mein identical hone chahiye. Step 3: isliye har inertial frame, wahi Maxwell's equations apply karke, wahi numerical

c

compute karta hai — yahi exactly Postulate 2 hai.

Einstein ne physics ke laws ki bajaye time ki universality sacrifice kyun ki?

Laws chhod dene se poori physics collapse ho jaati; time aur absolute simultaneity woh "saste," kam foundational assumptions hain jo laws aur

c

ko intact rakhte hue surrender ki ja sakti hain.

Moving light-clock ka photon zyada lamba diagonal path kyun travel karta hai, aur yeh exactly

γ

se zyada kyun hai?

Jab tak light height

L

tak uthti hai, mirror sideways

v Δ t /2

slide kar leta hai, toh Pythagoras se ek-taraf ka path

L^{2} + (v Δ t /2)^{2}

hai — ek right triangle ka hypotenuse jiska vertical leg

L

hai.

c Δ t = 2 L^{2} + (v Δ t /2)^{2}

solve karne par

Δ t = (2 L / c) / 1 - v^{2} / c^{2} = γ Δ t_{0}

milta hai, toh diagonal vertical se precisely

γ

factor se lamba hai. Time Dilation dekho.

Relativistic velocity addition hamesha

c

kyun return karta hai jab ek speed

c

hoti hai?

u = c

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

mein plug karne par

(c + v) / (1 + v / c) = c

milta hai; denominator exactly scale karta hai excess cancel karne ke liye, jo Postulate 2 enforce karne wala algebra hai.

Newtonian physics 200 saal ki engineering ke liye abhi bhi kyun kaam karta hai?

Everyday speeds par

v ≪ c

γ \to 1

aur Lorentz Transformations Galilean ones tak reduce ho jaati hain; relativity Newton ko apne low-speed limit ke roop mein contain karta hai. Galilean Relativity dekho.

c

sirf "light ki speed" nahi balki ek limiting speed ke roop mein kyun appear karta hai?

Kyunki

γ

bina bound ke badhta hai jaise

v \to c

, kisi bhi massive object ko

c

tak pahunchne ke liye infinite energy chahiye;

c

spacetime ki geometry mein built-in universal speed limit hai, aur light sirf uske saath chalta hai. Mass-Energy Equivalence dekho.

Edge cases

v \to c

par

γ

ka kya hota hai?

v^{2} / c^{2} \to 1

, toh

1 - v^{2} / c^{2} \to 0

aur

γ \to \infty

— time dilation unbounded ho jaata hai, yahi reason hai ki massive objects kabhi actually

c

tak nahi pahunch sakti.

v = 0

par

γ

kya hai?

γ = 1/ 1 - 0 = 1

, toh

Δ t = Δ t_{0}

— koi dilation nahi, aur har relativistic formula classical wale par collapse ho jaata hai, jaise hona chahiye.

Kya time dilation ek particle par apply hota hai jo move karte hue decay ho raha hai, jaise muon?

Haan — ek fast muon ki internal decay "clock" lab frame mein slow chalti hai, toh yeh itne der tak jeeta hai ki ground tak pahunch sake; yeh real experimental confirmation hai, koi device artifact nahi.

Agar do observers ek doosre ke paas se guzarte hain, kisi ki clock "sach mein" slow hai?

Kisi ki bhi nahi — yeh sawaal meaningless hai kyunki dono equally valid inertial frames hain (Postulate 1); har ek sahi taur par doosre ki clock ko slow measure karta hai. Sirf agar ek accelerate kare mile ne ke liye (symmetry todkar) tab ek absolute comparison exist karta hai.

Kya koi bhi inertial observer kabhi bhi vacuum mein light ko

c

se slow ya fast measure kar sakta hai?

Nahi — vacuum light speed har inertial frame mein exactly

c

hai; beam ke peeche bhagna ya usse bhaagna frequency badal deta hai lekin kabhi bhi measured speed nahi.

Postulate 1 ek aise observer ke baare mein kya kehta hai jo feel kar sakta hai ki ek force unhe sideways push kar rahi hai?

Woh ek accelerating (non-inertial) frame mein hain, toh Postulate 1 ki exact frame-equivalence apply nahi hoti; feel kiya gaya pseudo-force precisely woh signal hai ki frame non-inertial hai (abhi bhi SR ke andar describable, GR ki zarurat nahi).