Editing Energy (section)

=== Relativity ===
When calculating kinetic energy ([[Mechanical work|work]] to accelerate a [[mass|massive body]] from zero [[speed]] to some finite speed) relativistically – using [[Lorentz transformations]] instead of [[Newtonian mechanics]] – Einstein discovered an unexpected by-product of these calculations to be an energy term which does not vanish at zero speed. He called it [[rest energy]]: energy which every massive body must possess even when being at rest. The amount of energy is directly proportional to the mass of the body:
<math display="block"> E_0 = m_0 c^2 ,</math>
where
* ''m''<sub>0</sub> is the [[Rest Mass|rest mass]] of the body,
* ''c'' is the [[speed of light]] in vacuum,
* <math>E_0</math> is the rest energy.

For example, consider [[electron]]–[[positron]] annihilation, in which the rest energy of these two individual particles (equivalent to their rest mass) is converted to the radiant energy of the photons produced in the process. In this system the [[matter]] and [[antimatter]] (electrons and positrons) are destroyed and changed to non-matter (the photons). However, the total mass and total energy do not change during this interaction. The photons each have no rest mass but nonetheless have radiant energy which exhibits the same inertia as did the two original particles. This is a reversible process – the inverse process is called [[pair creation]] – in which the rest mass of particles is created from the radiant energy of two (or more) annihilating photons.

In general relativity, the [[stress–energy tensor]] serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation.<ref name="MTW"/>

Energy and mass are manifestations of one and the same underlying physical property of a system. This property is responsible for the inertia and strength of gravitational interaction of the system ("mass manifestations"), and is also responsible for the potential ability of the system to perform work or heating ("energy manifestations"), subject to the limitations of other physical laws.

In [[classical physics]], energy is a scalar quantity, the [[canonical conjugate]] to time. In [[special relativity]] energy is also a scalar (although not a [[Lorentz scalar]] but a time component of the [[energy–momentum 4-vector]]).<ref name="MTW">{{Cite book |author=Misner |first1=Charles W. |title=Gravitation |last2=Thorne |first2=Kip S. |last3=Wheeler |first3=John Archibald |publisher=W.H. Freeman |year=1973 |isbn=978-0-7167-0344-0 |location=San Francisco}}</ref> In other words, energy is invariant with respect to rotations of [[space]], but not invariant with respect to rotations of [[spacetime]] (= [[Lorentz boost|boosts]]).