Course review

A.5 Galilean and special relativity

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Learning objective

A.5.2 (HL)—Galilean relativity

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• Galilean relativity: Newton’s laws are identical in all inertial frames.

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Learning objective

A.5.3 (HL)—Galilean transformations

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• Galilean transformations: x′=x-vt and t′=t.

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Learning objective

A.5.4 (HL)—Galilean velocity addition

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• Galilean velocity addition: u′=u-v.

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Learning objective

A.5.5 (HL)—Two postulates of special relativity

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• Two postulates of special relativity.

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Learning objective

A.5.6 (HL)—Lorentz transformations

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• Lorentz transformations relate event coordinates between inertial frames. • Use γ and the two inertial-frame coordinates x, t and x′, t′.

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Learning objective

A.5.7 (HL)—Relativistic velocity addition

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• Relativistic velocity addition: u′=(u-v)/(1-uv/c^2).

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Learning objective

A.5.8 (HL)—Space-time interval

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• Space-time interval is invariant: (Δs)^2=(cΔt)^2-(Δx)^2.

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Learning objective

A.5.9 (HL)—Proper time interval and proper length

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• Proper time interval and proper length.

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Learning objective

A.5.10 (HL)—Time dilation

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• Time dilation: Δt = γΔt0.

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Learning objective

A.5.11 (HL)—Length contraction

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• Length contraction: L = L0/γ.

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Learning objective

A.5.12 (HL)—Relativity of simultaneity

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• Relativity of simultaneity.

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Learning objective

A.5.13 (HL)—Space-time diagrams

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• Space-time diagrams.

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Learning objective

A.5.14 (HL)—World lines and speed

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• On space-time diagrams, world-line angle relates to speed: tan θ = v/c.

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Learning objective

A.5.15 (HL)—Muon decay evidence

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• Muon decay is experimental evidence for time dilation and length contraction.

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