Einstein's equation, E=mc^2, is valid in both relativistic and non-relativistic frames of reference. However, its implications and significance become more pronounced in the realm of special relativity.
In the context of non-relativistic physics, where speeds are much smaller than the speed of light (c), the equation reduces to the familiar relationship between energy (E), mass (m), and the speed of light squared (c^2):
E = mc^2
In this context, the equation is typically used to calculate the energy associated with a mass at rest or the energy released during a nuclear reaction, such as in nuclear fission or fusion.
However, the equation takes on a more profound meaning in the context of special relativity, which deals with objects moving at speeds close to the speed of light. In special relativity, energy and momentum are related through the equation:
E^2 = (mc^2)^2 + (pc)^2
where p is momentum. When an object is at rest (p=0), this equation reduces to E=mc^2. But when an object is in motion (p≠0), its total energy includes both its rest mass energy (mc^2) and its kinetic energy (pc)^2. As an object's velocity approaches the speed of light, its kinetic energy becomes significant and can even become dominant, leading to the well-known result that an object with mass cannot reach or exceed the speed of light due to its infinite energy requirements.
In summary, E=mc^2 is valid in both relativistic and non-relativistic contexts, but its full implications and significance are better understood and more relevant in the realm of special relativity when dealing with objects moving at significant fractions of the speed of light.