The equation you mentioned, E = mc², is a fundamental result of Einstein's theory of special relativity. It relates energy (E) to mass (m) through the speed of light (c). This equation has significant implications for the twin paradox and the relativity of motion.
The twin paradox is a thought experiment that involves two twins: one stays on Earth while the other travels at a high speed to a distant star and then returns. According to special relativity, time is not absolute but depends on the relative motion between observers. When one twin is in motion at a significant fraction of the speed of light and eventually returns, they will have experienced less time passing compared to the twin who remained on Earth. As a result, the traveling twin would be younger than their sibling.
The equation E = mc² is relevant to the twin paradox because it shows the equivalence between mass and energy. As an object accelerates to high speeds, its kinetic energy increases, and according to the equation, its effective mass also increases. This means that the mass of the moving twin increases as their velocity approaches the speed of light.
The increased mass affects the passage of time for the moving twin. According to special relativity, time dilation occurs, which means that moving clocks appear to run slower from the perspective of a stationary observer. The increased mass of the moving twin contributes to this time dilation effect, resulting in the difference in the aging of the twins.
In summary, the equation E = mc² is a fundamental result of special relativity and is relevant to understanding the twin paradox. It demonstrates the equivalence between mass and energy, and the increase in mass at high speeds contributes to the time dilation effect observed in the twin paradox.