Editing Energy (section)

== Conservation of energy ==
{{Main|Conservation of energy}}
The fact that energy can be neither created nor destroyed is called the law of [[conservation of energy]]. In the form of the [[first law of thermodynamics]], this states that a [[closed system]]'s energy is constant unless energy is transferred in or out as [[Work (thermodynamics)|work]] or [[heat]], and that no energy is lost in transfer. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. Whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.<ref>Charles Kittel, Walter D. Knight and Malvin A. Ruderman. Berkeley Physics Course, Vol. 1.</ref>

While heat can always be fully converted into work in a reversible isothermal expansion of an ideal gas, for cyclic processes of practical interest in [[heat engine]]s the [[second law of thermodynamics]] states that the system doing work always loses some energy as [[waste heat]]. This creates a limit to the amount of heat energy that can do work in a cyclic process, a limit called the [[available energy]]. Mechanical and other forms of energy can be transformed in the other direction into [[thermal energy]] without such limitations.<ref name="thermo-laws"/> The total energy of a system can be calculated by adding up all forms of energy in the system.

[[Richard Feynman]] said during a 1961 lecture:<ref name="RPF1"/>
{{Blockquote|There is a fact, or if you wish, a ''law'', governing all natural phenomena that are known to date. There is no known exception to this law – it is exact so far as we know. The law is called the ''[[conservation of energy]]''. It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.|''[[The Feynman Lectures on Physics]]''}}

Most kinds of energy (with gravitational energy being a notable exception)<ref>{{cite web|url=http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html |title=E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws |publisher=UCLA Physics & Astronomy |date=December 1996 |first1=Nina |last1=Byers  |access-date=2010-12-12 |url-status=dead |archive-url=https://web.archive.org/web/20110514080739/http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html |archive-date=2011-05-14 }}</ref> are subject to strict local conservation laws as well. In this case, energy can only be exchanged between adjacent regions of space, and all observers agree as to the volumetric density of energy in any given space. There is also a global law of conservation of energy, stating that the total energy of the universe cannot change; this is a corollary of the local law, but not vice versa.<ref name="thermo-laws">[http://www.av8n.com/physics/thermo-laws.htm ''The Laws of Thermodynamics'']. {{webarchive|url=https://web.archive.org/web/20061215201900/http://www.av8n.com/physics/thermo-laws.htm|date=2006-12-15}} including careful definitions of energy, free energy, et cetera.</ref><ref name="RPF1">{{Cite book|first=Richard|last=Feynman|title=The Feynman Lectures on Physics; Volume 1 |chapter=Ch. 4: Conservation of Energy |chapter-url=https://feynmanlectures.caltech.edu/I_04.html#Ch4-S1-p2|year=1964|publisher=Addison Wesley|location=US|isbn=978-0-201-02115-8|access-date=2022-05-04|archive-date=2022-07-30|archive-url=https://web.archive.org/web/20220730093042/https://www.feynmanlectures.caltech.edu/I_04.html#Ch4-S1-p2|url-status=live}}</ref>

This law is a fundamental principle of physics. As shown rigorously by [[Noether's theorem]], the conservation of energy is a mathematical consequence of [[translational symmetry]] of time,<ref>{{cite web |url=http://ptolemy.eecs.berkeley.edu/eecs20/week9/timeinvariance.html |title=Time Invariance |publisher=Ptolemy Project |work=EECS20N |access-date=2010-12-12 |url-status=live |archive-url=https://web.archive.org/web/20110717210455/http://ptolemy.eecs.berkeley.edu/eecs20/week9/timeinvariance.html |archive-date=2011-07-17 }}</ref> a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. This is because energy is the quantity which is [[canonical conjugate]] to time. This mathematical entanglement of energy and time also results in the uncertainty principle – it is impossible to define the exact amount of energy during any definite time interval (though this is practically significant only for very short time intervals). The uncertainty principle should not be confused with [[energy conservation]] – rather it provides mathematical limits to which energy can in principle be defined and measured.

Each of the basic forces of nature is associated with a different type of potential energy, and all types of potential energy (like all other types of energy) appear as system [[mass]], whenever present. For example, a compressed spring will be slightly more massive than before it was compressed. Likewise, whenever energy is transferred between systems by any mechanism, an associated mass is transferred with it.

In [[quantum mechanics]] energy is expressed using the [[Hamiltonian operator]]. On any time scales, the uncertainty in the energy is by
: <math>\Delta E \Delta t \ge \frac { \hbar } {2 } </math>
which is similar in form to the [[Heisenberg Uncertainty Principle]] (but not really mathematically equivalent thereto, since ''H'' and ''t'' are not dynamically conjugate variables, neither in classical nor in quantum mechanics).

In [[particle physics]], this inequality permits a qualitative understanding of [[virtual particles]], which carry [[momentum]]. The exchange of virtual particles with real particles is responsible for the creation of all known [[fundamental forces]] (more accurately known as [[fundamental interactions]]). [[Virtual photons]] are also responsible for the electrostatic interaction between [[electric charge]]s (which results in [[Coulomb's law]]), for [[Spontaneous fission|spontaneous]] radiative decay of excited atomic and nuclear states, for the [[Casimir force]], for the [[Van der Waals force]] and some other observable phenomena.