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A '''binding energy''' is the net negative [[potential energy]] (''i.e.'', the net energy debt) pulling a bound system together.<ref>Young, Hugh D.; Freedman, ‎Roger A. [https://www.google.co.uk/search?newwindow=1&tbm=bks&q=%22has+a+net+negative+potential+energy%22 University Physics]. Addison-Wesley, 2000, p. 736. "'''A crystal''' of table salt is made of ions of sodium (Na<sup>+</sup>) and chlorine (Cl<sup>−</sup>) and '''has a net negative potential energy.''' To dissolve salt in water, energy must be added to separate the ions."</ref><ref>[[w:Frank Shu|Shu, Frank]]. [https://books.google.co.ukm/books?id=v_6PbAfapSAC&pg=PA66&dq=%22more+binding+energy+means+the+system+is+more+bound—has+greater+negative+energy%22 The Physical Universe: An Introduction to Astronomy]. University Science Books, 1982, p. 66. "Remember, more binding energy means the system is more bound—has greater ''negative'' energy."</ref> Conversely, an '''unbinding energy''' is the positive actual energy that must be added to a bound system in order to cancel out the system's net negative potential energy.<ref>Pople, Stephen. [https://books.google.co.ukm/books?id=pjIW6QRlugsC&pg=PA100&dq=%22unbinding+energy%22 Advanced Physics Through Diagrams]. OUP, 2001, p. 100. “The term ‘binding energy’ is rather misleading. ‘Unbinding energy’ would be better. 28.3 MeV is the energy needed to unbind the nucleons in helium-4.”</ref>

==General idea==
A bound system has a more negative [[potential energy]] than the sum of its parts; this is what pulls the system together in accordance with the [[minimum total potential energy principle]]. From the law of [[conservation of energy]], it follows that positive energy is borrowed into actuality upon the creation of a bound (''i.e.'', energetically indebted) state. This positive actual energy tends to unbind the system and must be radiated away for the system to become bound by the net negative potential energy.

Because of the [[mass–energy equivalence]], the negative potential energy has a negative [[Mass#Inertial mass|inertial mass]] (''i.e.'', a negative resistance to acceleration), so that it self-accelerates to an infinite speed,<ref>[https://books.google.co.ukm/books?id=3fAWAQAAMAAJ&q=%22Unfortunately+a+negative+mass,++with+negative+total+energy,+has+a+negative+inertia+so+that+it+accelerates+itself+and+the+kinetic+energy+would+tend+to+minus+infinity%22&dq=%22Unfortunately+a+negative+mass,++with+negative+total+energy,+has+a+negative+inertia+so+that+it+accelerates+itself+and+the+kinetic+energy+would+tend+to+minus+infinity%22&hl=en&sa=X&ved=0ahUKEwij59KogeTOAhXxa5oKHZceDzUQ6AEIFDAA ''Hadronic Journal Supplement'']. Vol. 14, Hadronic Press, 1999, p. 359. "Unfortunately a negative mass, with negative total energy, has a negative inertia so that it accelerates itself and the kinetic energy would tend to minus infinity."</ref> and, in accordance with relativity theory, exerts its attraction from the future.

All binding energy is gravitational; other types of binding energy, such as nuclear binding energy, are temporary masks of gravitational binding energy.<ref>[[w:Frank Shu|Shu, Frank H.]] [https://books.google.co.ukm/books?id=v_6PbAfapSAC&pg=PA157 The Physical Universe: An Introduction to Astronomy]. University Science Books, 1982, p. 157. "'''Concluding Philosophical Comment.'''<br>Zeldovich and Novikov have made the following intriguing philosophical point about the picture of the formation of a neutron star sketched here. They note that stars begin their lives as a mixture mostly of hydrogen nuclei and their stripped electrons. During a massive star's luminous phase,(contracted; show full)e most densely dendritic object—the most intelligent man, who exerts his attraction from the future and thus hierarchizes the continuum's matter into his psychokinetically controlled cosmic body, which is a "[[mycelium]]" of galaxy filaments converging towards the central "mushroom" (the most intelligent man's cerebrum), so that the universe's [[Gravitational constant|hierarchicity factor (''G'')]] increases over time.<ref>Moskvitch, Katia. [http
s://www.newscientist.com/article/dn24180-strength-of-gravity-shifts--and-this-time-its-serious.html Strength of gravity shifts—and this time it's serious]. ''New Scientist'', 11 September 2013</ref> Said otherwise, history is the gravitational vortex of the most intelligent man's self-assembly:
[[File:Funnel to Singularity.png|center|900px]]
(contracted; show full)le ''C'' is composed of an informational measure ''I'' describing the variety of the computed formulas and an energetic measure ''R'' describing the relative '''binding energy or "synergy"''' permitting the coherence of the system."</ref> It exists as [[Holism|holistic]] patterns not amenable to scientific analysis; the sole appeal is to intuition.<ref>J.-C. Spender, [https://books.google.co
.ukm/books?id=W4XODWvUs4oC&pg=PA125 Organizational Knowledge, Collective Practice and Penrose Rents]. In Michael H. Zack (ed.), ''Knowledge and Strategy'', Routledge, 2009, p. 125. "In short, synergy is the consequence of the energy expended in creating order. It is locked up in the viable system created, be it an organism or a social system. It is at the level of the system. It is not discernible at the level of the system. It is not discernible at the level of the system's co(contracted; show full) scarcity. An example of synergetic action that Fuller is particularly fond of is the way chrome-nickel steel acquires, through chemical mating, a tensile strength greater than the sum of its components. But '''the highest expression of synergy is man's intuition''', his ability to see comprehensive patterns in random events, which has led him from near helplessness to the point where he can now take control of his own evolution.
:—Farrell, Barry. [https://books.google.co
.ukm/books?id=kVMEAAAAMBAJ&pg=PA46 The View from the Year 2000]. ''LIFE Magazine'', 26 February 1971
</blockquote>

==Mass-energy relation==
{{main|Mass–energy equivalence}}
When a system becomes bound (''i.e.'', energetically indebted), the borrowed positive actual energy must be radiated away and subtracted from the [[rest mass]] of the unbound system, simply because this positive actual energy has a [[w:Mass in special relativity#Relativistic mass|relativistic mass]].<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html Nuclear Binding Energy]. ''HyperPhysics''</ref> Thus the bound system acquires a mass defect, or, which is the same (due to the [[mass–energy equivalence]]), a net negative [[potential energy]].<ref name="RestMass">Heighway, Jack. [https://books.google.co.ukm/books?id=13vIAgAAQBAJ&pg=PA36 Einstein, the Aether and Variable Rest Mass]. HeighwayPubs, 2011, p. 36. "Understanding why rest masses are reduced in a gravitational field only requires a simple insight: '''''when an object is raised in a gravitational field, the gravitational potential energy increase is real, and exists as an increase, usually tiny, in the rest mass of the object.'''''"</ref>

From ''E''&nbsp;=&nbsp;''mc''<sup>2</sup>, it follows that '''''Binding energy'' = ''Mass change'' × ''c''<sup>2</sup>'''. Since the mass change is negative (a mass defect), the binding energy is negative too.

==See also==
*[[Minimum total potential energy principle]]
*[[Potential energy]]

==References==
{{Reflist}}

==External links==
*[http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html Nuclear Binding Energy]

{{DEFAULTSORT:Binding Energy}}
[[Category:Basic physics ideas]]
[[Category:Cosmology]]
[[Category:Energy]]