Twin Paradox

Introduction

The Twin Paradox is a famous thought experiment in special relativity. It involves a pair of identical twins: one stays on Earth, while the other departs on a high-speed journey into space and eventually returns. Upon reunion, the traveling twin is found to have aged less than the twin who remained on Earth. Though this outcome seems paradoxical, it can be explained by the effects of acceleration and the relativity of time.

Basics of Time Dilation

According to special relativity, a clock moving at a significant fraction of the speed of light appears to tick more slowly when observed from a relatively stationary frame. Mathematically, the relationship is given by:

where is the time interval observed in the moving frame, is the time interval in the stationary frame, and is the Lorentz factor defined as:

Here, is the velocity of the moving frame, and is the speed of light in a vacuum. As approaches , grows larger, leading to more pronounced time dilation.

The Core of the Paradox

During the outbound and inbound journeys, both twins see the other’s clock running slower. However, the experiences aren’t symmetrical because the traveling twin undergoes acceleration and deceleration when turning around. Special relativity’s core symmetry applies only to inertial frames—those moving at a constant velocity without acceleration. The Earth-bound twin remains in an inertial frame (neglecting Earth’s modest accelerations), while the traveling twin does not.

Resolution of the Twin Paradox

When acceleration is introduced, special relativity still works—though one must handle the journey in segments of constant velocity and account for the turnaround phase. Alternatively, general relativity provides a more comprehensive treatment of accelerating frames, illustrating that the traveling twin follows a different “world line” through spacetime. In either approach, the result remains: the traveling twin’s clock accumulates less elapsed time.

Conclusion

The Twin Paradox is a striking example of how relativity challenges everyday intuition about time. By recognizing the role of non-inertial motion (acceleration), we see there is no genuine paradox. Instead, the traveling twin’s accelerated journey leads to less proper time passing, which is why they return younger than their stay-at-home sibling.

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