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Twin Paradox

This paradox highlights the counterintuitive effects of time dilation.
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The statement of the theorem

Consider two observers, A (staying in an inertial frame) and B (accelerating and returning to A's frame). The proper time τ\tau elapsed for B, relative to the coordinate time tt measured by A, is governed by the time dilation factor γ(v)\gamma(v): \nΔτB=∫tstarttend1−v(t)2c2 dt\Delta \tau_B = \int_{t_{start}}^{t_{end}} \sqrt{1 - \frac{v(t)^2}{c^2}} \ dt \nThe paradox is resolved by recognizing that the integral for ΔτB\Delta \tau_B must be calculated using the non-inertial path (acceleration) taken by B, leading to ΔτB<ΔτA\Delta \tau_B < \Delta \tau_A.
Source: Wikipedia