Everything about Conservation Of Energy totally explained
In physics, the
law of conservation of energy states that the total amount of
energy in any isolated system remains constant but can't be recreated, although it may change forms, for example friction turns
kinetic energy into thermal energy. In
thermodynamics, the first law of thermodynamics is a statement of the conservation of energy for thermodynamic systems, and is the more encompassing version of the conservation of energy. In short, the law of conservation of energy states that energy can not be created or destroyed, it can only be changed from one form to another.
History
Ancient philosophers as far back as
Thales of Miletus had inklings of the conservation of some underlying substance of which everything is made. However, there's no particular reason to identify this with what we know today as "mass-energy" (for example, Thales thought it was water). In
1638,
Galileo published his analysis of several situations—including the celebrated "interrupted pendulum"—which can be described (in modern language) as conservatively converting potential energy to kinetic energy and back again. However, Galileo didn't state the process in modern terms and again can't be credited with the crucial insight. It was
Gottfried Wilhelm Leibniz during
1676-
1689 who first attempted a mathematical formulation of the kind of energy which is connected with
motion (kinetic energy). Leibniz noticed that in many mechanical systems (of several
masses,
mi each with
velocity vi ),
»
where
L is the Lagrangian function. For this particular form to be valid, the following must be true:
- The system is scleronomous (neither kinetic nor potential energy are explicit functions of time)
- The kinetic energy is a quadratic form with regard to velocities.
- The potential energy doesn't depend on velocities.
Noether's Theorem
The conservation of energy is a common feature in many physical theories. It is understood as a consequence of
Noether's theorem, which states every symmetry of a physical theory has an associated conserved quantity; if the theory's symmetry is time invariance then the conserved quantity is called "energy". In other words, if the theory is invariant under the
continuous symmetry of
time translation then its energy (which is
canonical conjugate quantity to time) is conserved. Conversely, theories which are not invariant under shifts in time (for example, systems with time dependent potential energy) don't exhibit conservation of energy -- unless we consider them to exchange energy with another, external system so that the theory of the enlarged system becomes time invariant again. Since any time-varying theory can be embedded within a time-invariant meta-theory energy conservation can always be recovered by a suitable re-definition of what energy is. Thus conservation of energy is valid in all modern physical theories, such as special and general relativity and quantum theory (including
QED).
Relativity
With the invention of
special relativity by
Albert Einstein, energy was proposed to be one component of an
energy-momentum 4-vector. Each of the four components (one of energy and three of momentum) of this vector is separately conserved in any given
inertial reference frame. Also conserved is the vector length (
Minkowski norm), which is the
rest mass. The relativistic energy of a single
massive particle contains a term related to its
rest mass in addition to its kinetic energy of motion. In the limit of zero kinetic energy (or equivalently in the
rest frame of the massive particle, or the
center-of-momentum frame for objects or systems), the total energy of particle or object (including internal kinetic energy in systems) is related to its
rest mass via the famous equation
. Thus, the rule of
conservation of energy in special relativity was shown to be a special case of a more general rule, alternatively called the
conservation of mass and energy,
the conservation of mass-energy,
the conservation of energy-momentum,
the conservation of invariant mass or now usually just referred to as
conservation of energy.
In
general relativity conservation of energy-momentum is expressed with the aids of a
stress-energy-momentum pseudotensor.
Quantum theory
In
quantum mechanics, energy is defined as proportional to the
time derivative of the
wave function. Lack of
commutation of the time derivative operator with the time operator itself mathematically results in an
uncertainty principle for time and energy: the longer the period of time, the more precisely energy can be defined (energy and time become a
conjugate Fourier pair). However, quantum theory in general, and the uncertainty principle specifically, don't violate energy conservation.
Mathematical viewpoint
From a mathematical point of view, the energy conservation law is a consequence of the shift
symmetry of
time; energy conservation is implied by the empirical fact that the
laws of physics don't change with time itself (see:
Noether's theorem). Philosophically this can be stated as "nothing depends on time per se".
Further Information
Get more info on 'Conservation Of Energy'.
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