Relativistic mechanics
Further information: Mass in special relativity The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The invariant mass is another name for the rest mass of single particles. However, the more general invariant mass may also be applied to systems of particles in relative motion, and Conservation of energy The law of conservation of energy states that the total amount of energy in an isolated system remains constant. A consequence of this law is that energy cannot be created nor destroyed. The only thing that can happen with energy in an isolated system is that it can change form, for instance kinetic energy can become thermal energyIn addition to modifying notions of space and time, special relativity forces one to reconsider the concepts of mass Mass is a concept used in the physical sciences to explain a number of observable behaviors, and in everyday usage, it is common to identify mass with those resulting behaviors. In particular, mass is commonly identified with weight. But according to our modern scientific understanding, the weight of an object results from the interaction of its, momentum In classical mechanics, momentum is the product of the mass and velocity of an object (p = mv). For more accurate measures of momentum, see the section "modern definitions of momentum" on this page. It is sometimes referred to as linear momentum to distinguish it from the related subject of angular momentum. Linear momentum is a vector, and energy In physics, energy is a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law. Different forms of energy include kinetic, potential, thermal, gravitational, sound, light, elastic, and electromagnetic energy. The forms of energy are, all of which are important constructs in Newtonian mechanics In the fields of physics, classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies geometrically distributed within a certain boundary under the action of a system of forces. Special relativity shows, in fact, that these concepts are all different aspects of the same physical quantity in much the same way that it shows space and time to be interrelated.
There are a couple of (equivalent) ways to define momentum and energy in SR. One method uses conservation laws In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. Any particular conservation law is a mathematical identity to certain symmetry of a physical system. A partial listing of conservation laws that are said to be exact laws, or more precisely have never. If these laws are to remain valid in SR they must be true in every possible reference frame. However, if one does some simple thought experiments A thought experiment , sometimes called a Gedanken experiment, is a proposal for an experiment that would test or illuminate a hypothesis or theory using the Newtonian definitions of momentum and energy, one sees that these quantities are not conserved in SR. One can rescue the idea of conservation by making some small modifications to the definitions to account for relativistic velocities. It is these new definitions which are taken as the correct ones for momentum and energy in SR.
The energy and momentum of an object with invariant mass The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c2, which is equal to the mass of the m (also called rest mass in the case of a single particle), moving with velocity In physics, velocity is defined as the rate of change of position. It is a vector physical quantity; both speed and direction are required to define it. In the SI system, it is measured in meters per second: (m/s) or ms-1. The scalar absolute value (magnitude) of velocity is speed. For example, "5 meters per second" is a scalar and not a v with respect to a given frame of reference, are given by
respectively, where γ (the Lorentz factor The Lorentz factor or Lorentz term appears in several equations in special relativity, including time dilation, length contraction, and the relativistic mass formula. Because of its ubiquity, physicists generally represent it with the shorthand symbol γ. It gets its name from its earlier appearance in Lorentzian electrodynamics. The Lorentz) is given by
The quantity γm is often called the relativistic mass of the object in the given frame of reference,[27] although recently this concept is falling in disuse, and Lev B. Okun suggested that "this terminology [...] has no rational justification today", and should no longer be taught.[28] Other physicists, including Wolfgang Rindler Wolfgang Rindler is a leading physicist working in the field of General Relativity where he is well known for introducing the term "event horizon", Rindler coordinates, and for popularizing the use of spinors in general relativity. He is also a prolific textbook author and T. R. Sandin, have argued that relativistic mass is a useful concept and there is little reason to stop using it.[29] See Mass in special relativity The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The invariant mass is another name for the rest mass of single particles. However, the more general invariant mass may also be applied to systems of particles in relative motion, for more information on this debate. Some authors use the symbol m to refer to relativistic mass, and the symbol m0 to refer to rest mass.[30]
The energy and momentum of an object with invariant mass m are related by the formulas
The first is referred to as the relativistic energy-momentum equation. While the energy E and the momentum p depend on the frame of reference in which they are measured, the quantity E2 − (pc)2 is invariant, being equal to the squared invariant mass of the object (up to In mathematics, the phrase "up to xxxx" indicates that members of an equivalence class are to be regarded as a single entity for some purpose. "xxxx" describes a property or process which transforms an element into one from the same equivalence class, i.e. one to which it is considered equivalent. In group theory, for example, the multiplicative constant c4).
It should be noted that the invariant mass of a system
is greater than the sum of the rest masses of the particles it is composed of (unless they are all stationary with respect to the center of mass of the system, and hence to each other). The sum of rest masses is not even always conserved in closed systems, since rest mass may be converted to particles which individually have no mass, such as photons. Invariant mass, however, is conserved and invariant for all observers, so long as the system remains closed. This is due to the fact that even massless particles contribute invariant mass to systems, as also does the kinetic energy of particles. Thus, even under transformations of rest mass to photons or kinetic energy, the invariant mass of a system which contains these energies still reflects the invariant mass associated with them.
<<Table of Contents Special relativity (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies" | Next>> | Show All>>
