Zeropoint energy
From Academic Kids

In a quantum mechanical system such as the particle in a box or the quantum harmonic oscillator, the lowest possible energy is called the zeropoint energy. According to classical physics, the kinetic energy of a particle in a box or the kinetic energy of the harmonic oscillator may be zero if the velocity is zero. Quantum mechanics with its uncertainty principle implies that if the velocity is measured with certainty to be exactly zero, the uncertainty of the position must be infinite. This either violates the condition that the particle remain in the box, or it brings a new potential energy in the case of the harmonic oscillator. To avoid this paradox, quantum mechanics dictates that the minimal velocity is never equal to zero, and hence the minimal energy is never equal to zero.
Contents 
A few formulae
A particle in a box is defined by the potential energy
 <math>V(x)=0<math> for <math>l/2 \leq x \leq l/2<math>
which is defined to be infinite for <math>\leftx\right > l/2<math>. The wave function with the minimal energy eigenvalue is then
 <math>\psi(x) = C \sin(\pi x/l)<math>
where <math>C<math> is an important normalization constant. The (zeropoint) energy of this wave function is pure kinetic and equal to
 <math>E_0 = \frac{\hbar^2\pi^2}{2ml^2}<math>
which is nonzero. Similarly, the zeropoint energy of the quantum harmonic oscillator with the frequency <math>\omega<math> is equal to
 <math>E_0 = \frac{1}{2} \hbar\omega.<math>
Both of these simplest cases have a useful generalization to the case of quantum field theory. Quantum field theory  such as Quantum Electrodynamics  may be regarded as a collection of infinitely many harmonic oscillators, and quantum mechanics therefore predicts a nonzero vacuum energy. Although the absolute value of the vacuum energy is partly a matter of convention, the difference between the vacuum energy of various configurations has a physical meaning.
Existence
Does electromagnetic zeropoint energy exist, and if so, are there any practical applications and does it have any connection with dark energy? The theoretical basis for electromagnetic zeropoint energy is clear. According to Sciama (1991):
 "Even in its ground state, a quantum system possesses fluctuations and an associated zeropoint energy, since otherwise the uncertainty principle would be violated. In particular the vacuum state of a quantum field has these properties. For example, the electric and magnetic fields in the electromagnetic vacuum are fluctuating quantities."
The Casimir effect is an example of a oneloop effect in quantum electrodynamics that can be simply explained by the zeropoint energy.
History
The concept of zeropoint energy originated with Max Planck in 1911. The average energy of a harmonic oscillator in this hypothesis is (where <math>h<math> is Planck's constant and <math>\nu<math> is frequency):
 <math>E=
\frac{h\nu}{2} + \frac{h\nu}{e^{h\nu/kT}1} <math>
At the same time Einstein and Hopf (1910) and Einstein and Stern (1913) were also studying the properties of zeropoint energy. Shortly thereafter Nernst (1916) proposed that empty space was filled with zeropoint electromagnetic radiation. Then in 1925 the existence of zeropoint energy was shown to be “required by quantum mechanics, as a direct consequence of Heisenberg's uncertainty principle” (Sciama 1991). As any textbook on quantum optics will show (e.g. Loudon 1983), the way to quantize the electromagnetic field is to associate each mode of the field with a harmonic oscillator with the result that the minimum energy per mode of the electromagnetic quantum vacuum is <math>h\nu/2<math> .
Problems and answers
Zeropoint energy shares a problem with the Dirac sea: both are potentially infinite. In the case of zeropoint energy, there are reasons for believing that a cutoff does exist in the zeropoint spectrum corresponding to the Planck scale. Even this results in an enormous amount of zeropoint energy whose existence is assumed to be negated (in spite of the unmistakable mandate of the Heisenberg uncertainty principle) by the claim that the mass equivalent of the energy should gravitate, resulting in an absurdly large cosmological constant, contrary to observations. Matters are not quite so straightforward.
In response to the question “Do ZeroPoint Fluctuations Produce a Gravitational Field?” Sciama (1991) writes:
 "We now wish to comment on the unsolved problem of the relation between zeropoint fluctuations and gravitation. If we ascribe an energy <math>h\nu/2<math> to each mode of the vacuum radiation field, then the total energy of the vacuum is infinite. It would clearly be inconsistent with the original assumption of a background Minkowski spacetime to suppose that this energy produces gravitation in a manner controlled by Einstein’s field equations of general relativity. It is also clear that the spacetime of the real world approximates closely to the Minkowski state, at least on macroscopic scales. It thus appears that we must regularize the zeropoint energy of the vacuum by subtracting it out according to some systematic prescription. At the same time, we would expect zeropoint energy differences to gravitate. For example, the (negative) Casimir energy between two planeparallel perfect conductors would be expected to gravitate; otherwise, the relativistic relation between a measured energy and gravitation would be lost."
It is precisely localizable differences in the zeropoint energy that may prove to be of some practical use and that may be the basis of dark energy phenomena. Moreover it has also been found that asymmetries in the zeropoint field that appear upon acceleration may be associated with certain properties of inertia, gravitation and the principle of equivalence (Haisch, Rueda and Puthoff 1994; Rueda and Haisch 1998; Rueda, Haisch and Tung 2001).
Properties
Lastly, insights may be offered on certain quantum properties (Compton wavelength, de Broglie wavelength, spin) and on massenergy equivalence (E=mc^{2}) if it proves to be the case that zeropoint fluctuations interact with matter in a phenomenon identified by Erwin Schrödinger known as zitterbewegung (Haisch and Rueda 2000; Haisch, Rueda and Dobyns 2001; Nickisch and Mollere 2002).
As intriguing as these latter possibilities are, the first order of business is to unambiguously detect and measure zeropoint energy. While a Casimir experiment such as that of Forward (1984) can in principle measure energy that may be attributed to the existence of real zeropoint energy, there are alternative explanations involving sourcesource quantum interactions in place of real zeropoint energy (see Milonni 1994). To move beyond this ambiguity of interpretation experiments that will test for the reality of measurable zeropoint energy will need to be devised.
See Also
Pop Culture References
In the Justice League Episode, 'Hereafter', Vandal Savage had taken over the world and invented a Zero Point Generator in the boredom of immortality which was used to power a time machine to transport Superman back to the present.
In the movie The Incredibles, the villain Syndrome uses a ray that can immobilize an opponent, suspending him in midair. Director Brad Bird, speaking in a DVD commentary, says that in searching for a name for the device (or at least a better one than "the Immobiray"), he came across and used a reference to "zeropoint energy", which Syndrome himself uses to describe his weapon. (Of course, this is simply a cool name rather than a practical application at this time!)
In HalfLife 2, one of the weapons at your disposal is the "Zero Point Energy Field Manipulator", better known by its nickname the "Gravity Gun". It allows you to pick up and launch any mediumsized objects, and was used to market the game's detailed physics engine.
The television show Stargate Atlantis also makes references to zeropoint energy in the form of ZeroPoint Modules or ZPMs. These ZPMs are used to power the technology of The Ancients, such as the Galactic Stargate which allows the exploration team to travel to the Pegasus Galaxy and the energy shield which protects the city of Atlantis.
Another television series called ZERO.POINT is in development that centers around the machinations of a quantum physicist searching for zeropoint energy technology and a drifter who wanders in perfect synchronicity.
ZPE is also a potential energy source of interest to independent researchers outside of mainstream research entitities, such as the late Eugene Mallove, and figures into discussions on radio programs such as Coast to Coast AM.
In Marvel Comic's "Ultimate Nightmare" issue one, the disguised Captain Mahrvell has helped humans develop a star drive based on ZPE. He offhandedly tosses off that quantum wave fluctuations were discovered to cause inertia, which is the SED Hypothesis (covered here (http://www.calphysics.org/inertia.html)).
In season 2 of Alias (TV series), Sydney Bristow is tasked to retrieve a music box that supposedly contains a formula for zeropoint energy.
References
 Einstein, A. and Hopf, L., Ann. Phys., 33, 1096 (1910a); Ann. Phys., 33, 1105 (1910b).
 Einstein, A. and Stern, O., Ann. Phys., 40, 551 (1913).
 Forward, R., Phys. Rev. Phys. Rev. B, 30, 1700 (1984). http://www.calphysics.org/articles/Forward1984.pdf
 Haisch, B. and Rueda, A., Phys. Lett. A, 268, 224 (2000). http://xxx.arxiv.org/abs/grqc/9906084
 Haisch, B., Rueda, A., and Dobyns, Y., Ann. Phys., 10, No. 5, 393 (2001). http://xxx.arxiv.org/abs/grqc/0002069
 Haisch, B., Rueda, A. and Puthoff, H.E. 1994, Phys. Rev. A., 69, 678. http://www.calphysics.org/articles/PRA94.pdf
 Loudon, R., The Quantum Theory of Light, (Oxford: Clarendon Press) (1983).
 Milonni, P., The Quantum Vacuum: an Introduction to Quantum Electrodynamics (New York: Academic) (1994).
 Nernst, W., Verh. Dtsch. Phys. Ges., 18, 83 (1916).
 Nickisch, L. J. and Mollere, J., physics/0205086 (2002). http://www.arxiv.org/abs/physics/0205086
 Rueda, A. and Haisch, B., Found. Phys., 28, No. 7, 1057 (1998a) http://xxx.arxiv.org/abs/physics/9802030; Phys. Lett. A, 240, 115 (1998b). http://xxx.arxiv.org/abs/physics/9802031
 Rueda, A., Haisch, B. and Tung, R., preprint, grqc/0108026 (2001). http://xxx.arxiv.org/abs/grqc/0108026
 Sciama, D. W. in “The Philosophy of Vacuum” (S. Saunders and H. R. Brown, eds.), (Oxford: Clarendon Press) (1991).
External links
 ZERO.POINT (http://www.zeropoint.tv), scifi television series in development about the search for zeropoint energy.
 Calphysics (http://www.calphysics.org/zpe.html)
 Institute for Advanced Studies at Austin (http://www.earthtech.org/index.html), dedicated primarily to the study of ZPE.
 Zero Point Energy (http://freeenergynews.com/Directory/ZPE/)  Claims to working energy technologies that tap the theoretical zero point, theory, resources. (FreeEnergyNews.com directory page)
General subfields within physics  
Classical mechanics  Condensed matter physics  Continuum mechanics  Electromagnetism  General relativity  Particle physics  Quantum field theory  Quantum mechanics  Solid state physics  Special relativity  Statistical mechanics  Thermodynamics 