The equation E=mc², which is a fundamental equation in physics, relates energy (E) to mass (m) and the speed of light (c). It expresses the equivalence between mass and energy. This equation is compatible with both time and time dilation, as they are all interconnected within the framework of special relativity.
In special relativity, time is not absolute but instead depends on the relative motion between observers. Time dilation occurs when there is a relative velocity between two observers, causing time to appear to pass differently for each observer. This effect is a consequence of the constant speed of light in all inertial reference frames.
The equation E=mc² incorporates the concept of energy, which includes both the mass energy and the kinetic energy of an object. When an object is in motion, its total energy includes both its rest mass energy (mc²) and its kinetic energy. As an object's velocity approaches the speed of light, its kinetic energy increases significantly, approaching infinity as the speed approaches c.
Time dilation arises due to the relativistic increase in an object's energy as it approaches the speed of light. As an object accelerates to high velocities, its energy increases, and according to E=mc², its mass also increases. This increased energy and mass have implications for the passage of time.
The faster an object moves, the greater the time dilation effects it experiences. As an object's velocity approaches the speed of light, time dilation becomes more pronounced, and from the perspective of a stationary observer, time appears to slow down for the moving object.
In summary, the equation E=mc² is compatible with time and time dilation as it encompasses the relationship between energy, mass, and the speed of light. Time dilation arises due to the relativistic increase in energy and mass as an object approaches the speed of light, as described by the equation.