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Advanced Physics — Special Relativity

Lorentz transformations, time dilation, and relativistic mechanics

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lorentz_factor 22 terms Jan 3, 2026
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Terms 22

1
Postulates of Special Relativity
1) Laws of physics same in all inertial frames 2) Speed of light c constant in all inertial frames
2
Inertial Reference Frame
Frame at rest or moving at constant velocity; Newton's laws hold without pseudo-forces
3
Lorentz Factor (γ)
γ = 1/√(1−v²/c²); always ≥ 1; approaches ∞ as v→c
4
Time Dilation
Moving clocks run slower: Δt = γΔt₀; proper time τ measured in rest frame is shortest
5
Length Contraction
Moving objects shorter in direction of motion: L = L₀/γ; perpendicular dimensions unchanged
6
Relativity of Simultaneity
Events simultaneous in one frame may not be in another; no absolute simultaneity
7
Lorentz Transformation
x' = γ(x−vt), t' = γ(t−vx/c²); relate coordinates between inertial frames
8
Spacetime Interval
s² = c²t² − x² − y² − z²; invariant under Lorentz transformations; same for all observers
9
Lightlike Interval
s² = 0; events connected by light signal; on light cone
10
Timelike Interval
s² > 0; events causally connected; proper time exists between them
11
Spacelike Interval
s² < 0; events cannot be causally connected; simultaneity frame exists
12
Four-Vector
Four-component vector in spacetime: (ct, x, y, z); inner product is Lorentz invariant
13
Relativistic Momentum
p = γmv; momentum increases without bound as v→c
14
Relativistic Energy
E = γmc²; rest energy E₀ = mc²; kinetic energy = (γ−1)mc²
15
Energy-Momentum Relation
E² = (pc)² + (mc²)²; for massless photon: E = pc
16
Mass-Energy Equivalence
E = mc²; rest mass is form of energy; annihilation converts mass to photons
17
Twin Paradox
Traveling twin ages less than stationary twin; resolved by asymmetry of acceleration
18
Relativistic Velocity Addition
u' = (u−v)/(1−uv/c²); prevents exceeding c; Galilean addition breaks down
19
Doppler Effect (relativistic)
f_obs = f_source √((1−β)/(1+β)) for recession; includes time dilation
20
Aberration of Light
Direction of light depends on observer's velocity; angle transforms with Lorentz equations
21
Cherenkov Radiation
Radiation emitted when particle travels faster than light in medium (not c in vacuum)
22
Minkowski Diagram
Spacetime diagram with ct vs x; worldlines, light cone, simultaneity shown geometrically