The Twin Paradox is a thought experiment in the realm of special relativity, proposed by Albert Einstein. It illustrates the effects of time dilation, a phenomenon predicted by the theory of relativity, where time is experienced differently for observers in different frames of reference, particularly when they are moving at significant fractions of the speed of light.

In the classic scenario, there are two twins: Twin A and Twin B. Twin A remains on Earth, while Twin B travels on a spaceship at a substantial velocity to a distant star and then returns. Due to the effects of time dilation, when Twin B returns to Earth, they will be younger than Twin A. This outcome seems paradoxical because, from Twin B's perspective, it could be argued that Twin A is the one moving away and then back, suggesting that Twin A should be the younger twin. However, the key lies in the fact that Twin B experiences acceleration and deceleration during the journey, breaking the symmetry of the situation.

Understanding Time Dilation

According to Einstein's theory of special relativity, the time experienced by an observer in motion is slower compared to an observer at rest. The equation that describes time dilation is:

T' = T / √(1 - v²/c²)

Where:

• T' is the time interval measured by the moving observer (Twin B).
• T is the time interval measured by the stationary observer (Twin A).
• v is the relative velocity between the observers.
• c is the speed of light in a vacuum.

Example Calculation

Assume Twin B travels to a star 4 light-years away at a speed of 0.8c (where c is the speed of light). The time taken for the journey as measured by Twin A can be calculated as follows:

Distance = Speed x Time

Thus, the time for the round trip as measured by Twin A is:

Time = 4 light-years / 0.8c = 5 years (one way)

The total round trip time for Twin A is 10 years. However, for Twin B, we need to account for time dilation:

T' = T / √(1 - v²/c²) = 10 years / √(1 - 0.8²) = 10 years / √(1 - 0.64) = 10 years / √(0.36) = 10 years / 0.6 ≈ 6.67 years

Thus, Twin B experiences approximately 6.67 years of time during the journey, while Twin A ages 10 years. When Twin B returns, they are younger than Twin A.

Resolving the Paradox

The resolution to the Twin Paradox lies in the fact that Twin B undergoes acceleration and deceleration during the trip, making their frame of reference non-inertial. Twin A, remaining on Earth, is in an inertial frame throughout the scenario. This difference in experiences leads to the asymmetry that results in Twin B aging less than Twin A.

References

• Einstein, A. (1915). Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik.
• Rindler, W. (2006). Relativity: Special, General, and Cosmological. Oxford University Press.
• Hawking, S. (2001). The Universe in a Nutshell. Bantam Books.

In conclusion, the Twin Paradox serves as a fascinating illustration of the implications of relativistic physics, demonstrating how our understanding of time and space can differ dramatically depending on relative motion.