Extension for systems in motion




Unlike a system's energy in an inertial frame, the relativistic energy () of a system depends on both the rest mass () and the total momentum of the system. The extension of Einstein's equation to these systems is given by:note

or

where the term represents the square of the Euclidean norm (total vector length) of the various momentum vectors in the system, which reduces to the square of the simple momentum magnitude, if only a single particle is considered. This equation is called the energy–momentum relation and reduces to when the momentum term is zero. For photons where , the equation reduces to .

Comments

Post a Comment

Popular posts from this blog

Efficiency

Image
In some reactions matter particles can be destroyed and their associated energy released to the environment as other forms of energy, such as light and heat. One example of such a conversion takes place in elementary particle interactions, where the rest energy is transformed into kinetic energy. Such conversions between types of energy happen in nuclear weapons, in which the protons and neutrons in atomic nuclei lose a small fraction of their original mass, though the mass lost is not due to the destruction of any smaller constituents. Nuclear fission allows a tiny fraction of the energy associated with the mass to be converted into usable energy such as radiation, in the decay of the uranium, for instance, about 0.1% of the mass of the original atom is lost. In theory, it should be possible to destroy matter and convert all of the rest-energy associated with matter into heat and light, but none of the theoretically known methods are practical. One way to harness all the energy assoc...
Read more

Mass–energy equivalence

Image
In physics, mass–energy equivalence defines the relationship between mass and energy in a system’s rest frame, where the two values differ only by a constant and the units of measurement. The principle is described by Albert Einstein's famous formula: E = m c 2 {\displaystyle E=m\,c^{2}} The formula defines the energy E of a particle in its rest frame as the product of mass m with the speed of light squared ( c 2 ). Equivalently, the mass of a particle at rest is equal to its energy E divided by the speed of light squared ( c 2 ). Because the speed of light is a large number in everyday units (approximately 3 × 108 meters per second), the formula implies that a small amount of rest mass corresponds to an enormous amount of energy, which is independent of the composition of the matter. Rest mass, also called invariant mass, is the mass that is measured when the system is at rest. The rest mass is a fundamental physical property that remains independent of mome...
Read more

Mass in special relativity

Image
An object moves with different speeds in different frames of reference, depending on the motion of the observer. This implies the kinetic energy, in both Newtonian mechanics and relativity, is frame dependent , so that the amount of relativistic energy that an object is measured to have depends on the observer. The relativistic mass of an object is given by the relativistic energy divided by c2 . Because the relativistic mass is exactly proportional to the relativistic energy, relativistic mass and relativistic energy are nearly synonyms; the only difference between them is the units. The rest mass or invariant mass of an object is defined as the mass an object has when its rest frame, when it is not moving. The rest mass is typically denoted as just mass by physicists, though experiments have shown that the gravitational mass of an object depends on its total energy and not just its rest mass. The rest mass is the same for all inertial frames, as it is independent of the motion of ...
Read more