Lorentz transformations

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$\gamma = \dfrac{1}{\sqrt{1 - v^2/c^2}}$ — and it is **always ≥ 1**.

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The time between two events measured by a **single clock present at both** — the **shortest** possible time.

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The length of an object measured **in its own rest frame** — the **longest** possible length.

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$\Delta t = \gamma\,\Delta t_0$. Since γ ≥ 1, **moving clocks run slow**.

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$L = \dfrac{L_0}{\gamma}$. Since γ ≥ 1, **moving objects contract** along the motion.

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**Multiply** the proper time by γ ($\Delta t = \gamma\,\Delta t_0$) — the time gets bigger.

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**Divide** the proper length by γ ($L = L_0/\gamma$) — the length gets smaller.

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$\gamma = \dfrac{1}{\sqrt{1 - 0.80^2}} = \dfrac{1}{\sqrt{0.36}} = 1.67$.

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Only the dimension **along the direction of motion**; width and height are unchanged.

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$u' = \dfrac{u - v}{1 - uv/c^2}$ — it always keeps the result **below c**.

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$\dfrac{1.00c}{1 + 0.25} = 0.80c$, **not** 1.0c.

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Time **stretches** (Δt = γΔt₀, multiply); length **shrinks** (L = L₀/γ, divide). Both use the same γ.