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Zero-point energy
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Zero-point energy

This article is in multiple sections that need to be merged.

In a quantum mechanical system such as the particle in a box, the lowest possible energy is called the zero-point energy.

Does electromagnetic zero-point energy exist, and if so, are there any practical applications and does it have any connection with dark energy? The theoretical basis for electromagnetic zero-point energy is clear. According to Sciama (1991):

"Even in its ground state, a quantum system possesses fluctuations and an associated zero-point 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 concept of zero-point energy originated with Max Planck in 1911. The average energy of a harmonic oscillator in this hypothesis is (where is Planck's constant and is frequency):

At the same time Einstein and Hopf (1910) and Einstein and Stern (1913) were also studying the properties of zero-point energy. Shortly thereafter Nernst (1916) proposed that empty space was filled with zero-point electromagnetic radiation. Then in 1925 the existence of zero-point 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 .

Zero-point energy shares a problem with the Dirac sea: both are potentially infinite. In the case of zero-point energy, there are reasons for believing that a cutoff does exist in the zero-point spectrum corresponding to the Planck scale. Even this results in an enormous amount of zero-point 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 Zero-Point Fluctuations Produce a Gravitational Field?” Sciama (1991) writes:

"We now wish to comment on the unsolved problem of the relation between zero-point fluctuations and gravitation. If we ascribe an energy 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 space-time 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 space-time of the real world approximates closely to the Minkowski state, at least on macroscopic scales. It thus appears that we must regularize the zero-point energy of the vacuum by subtracting it out according to some systematic prescription. At the same time, we would expect zero-point energy differences to gravitate. For example, the (negative) Casimir energy between two plane-parallel 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 zero-point 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 zero-point 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). Lastly, insights may be offered on certain quantum properties (Compton wavelength, de Broglie wavelength, spin) and on mass-energy equivalence (E=mc2) if it proves to be the case that zero-point fluctuations interact with matter in a phenomenon identified by Schrödinger known as zitterbewegung (Haisch and Rueda 2000; Haisch, Rueda and Dobyns 2001; Nickisch and Mollere 2004).

As intriguing as these latter possibilites are, the first order of business is to unambiguously detect and measure zero-point 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 zero-point energy, there are alternative explanations involving source-source quantum interactions in place of real zero-point energy (see Milonni 1994). To move beyond this ambiguity of interpretation experiments that will test for the reality of measureable zero-point energy will need to be devised.


  1. Einstein, A. and Hopf, L., Ann. Phys., 33, 1096 (1910a); Ann. Phys., 33, 1105 (1910b).
  2. Einstein, A. and Stern, O., Ann. Phys., 40, 551 (1913).
  3. Forward, R., Phys. Rev. Phys. Rev. B, 30, 1700 (1984). http://www.calphysics.org/articles/Forward1984.pdf
  4. Haisch, B. and Rueda, A., Phys. Lett. A, 268, 224 (2000). http://xxx.arxiv.org/abs/gr-qc/9906084
  5. Haisch, B., Rueda, A., and Dobyns, Y., Ann. Phys., 10, No. 5, 393 (2001). http://xxx.arxiv.org/abs/gr-qc/0002069
  6. Haisch, B., Rueda, A. and Puthoff, H.E. 1994, Phys. Rev. A., 69, 678. http://www.calphysics.org/articles/PRA94.pdf
  7. Loudon, R., The Quantum Theory of Light, (Oxford: Clarendon Press) (1983).
  8. Milonni, P., The Quantum Vacuum: an Introduction to Quantum Electrodynamics (New York: Academic) (1994).
  9. Nernst, W., Verh. Dtsch. Phys. Ges., 18, 83 (1916).
  10. Nickisch, L. J. and Mollere, J., physics/0205086 (2002). http://www.arxiv.org/abs/physics/0205086
  11. 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
  12. Rueda, A., Haisch, B. and Tung, R., preprint, gr-qc/0108026 (2001). http://xxx.arxiv.org/abs/gr-qc/0108026
  13. Sciama, D. W. in “The Philosophy of Vacuum” (S. Saunders and H. R. Brown, eds.), (Oxford: Clarendon Press) (1991).