The equation you mentioned, E = mc², is a key result of Einstein's theory of special relativity, where E represents energy, m represents mass, and c represents the speed of light in a vacuum. This equation establishes the equivalence of mass and energy and demonstrates the profound connection between the two.
In the context of the twin paradox and the relativity of motion, this equation is relevant because it highlights the concept of mass-energy equivalence and its consequences. The twin paradox is a thought experiment commonly used to explain the effects of time dilation in special relativity.
In the twin paradox, one twin (called the "traveling twin") embarks on a high-speed space journey while the other twin (called the "stationary twin") remains on Earth. According to the theory of special relativity, as the traveling twin moves at high speeds relative to the stationary twin, time will appear to pass slower for the traveling twin compared to the stationary twin.
The mass-energy equivalence comes into play when the traveling twin's energy changes due to their motion. As the traveling twin accelerates to high speeds, their kinetic energy increases. According to the equation E = mc², this increase in energy is accompanied by an increase in mass. Therefore, the traveling twin's mass increases as they approach the speed of light, and this increase affects the passage of time for them.
From the perspective of the stationary twin, who remains on Earth, the traveling twin appears to age more slowly due to time dilation. The traveling twin experiences less time compared to the stationary twin because their increased mass-energy affects their experience of time. When the traveling twin returns to Earth, they will be younger than their stationary twin counterpart.
The equation E = mc² encapsulates the understanding that energy and mass are intimately related in the theory of special relativity. It helps explain how changes in energy, associated with changes in mass, affect the experience of time and the relative aging of observers in different frames of reference, as observed in the twin paradox and other relativistic phenomena.