Although the term ''zero-point energy''
applies to all three of these interactions in nature, customarily
(and hereafter in this article) it is used in reference only to the
The least possible uncertainty of position times momentum is specified by Planck's constant, h.
A parallel uncertainty exists between measurements involving time and energy (and other so-called conjugate variables in quantum mechanics). This minimum uncertainty is not due to any correctable flaws in measurement, but rather reflects an intrinsic quantum fuzziness in the very nature of energy and matter springing from the wave nature of the various quantum fields.
This leads to the concept of
As the temperature is lowered to absolute
zero, helium remains a liquid, rather than freezing to a solid,
owing to the irremovable zero-point energy of its atomic motions.
(Increasing the pressure to 25 atmospheres will cause helium to
A residual motion will always remain due to
the requirements of the Heisenberg uncertainty principle, resulting
in a zero-point energy, equal to 1/2 hf, where f is the oscillation
Each wave represents a,
Each mode is equivalent to a harmonic oscillator and is thus subject to the Heisenberg uncertainty principle.
From this analogy, every mode of the field must have 1/2 hf as its average minimum energy. That is a tiny amount of energy in each mode, but the number of modes is enormous, and indeed increases per unit frequency interval as the square of the frequency.
The spectral energy density is
determined by the density of modes times the energy per mode and
thus increases as the cube of the frequency per unit frequency per
unit volume. The product of the tiny energy per mode times the huge
spatial density of modes yields a very high theoretical zero-point
energy density per cubic centimeter.
The density of this energy depends critically on where in frequency the zero-point fluctuations cease.
Since space itself is thought to break
up into a kind of quantum foam at a tiny distance scale called the
Planck scale (10-33 cm), it is argued that the zero point
fluctuations must cease at a corresponding Planck frequency (1043
Hz). If that is the case, the zero-point energy density would be 110
orders of magnitude greater than the radiant energy at the center of
There is one major difference between zero-point electromagnetic radiation and ordinary electromagnetic radiation. Turning again to the Heisenberg uncertainty principle one finds that the lifetime of a given zero-point photon, viewed as a wave, corresponds to an average distance traveled of only a fraction of its wavelength.
Such a wave ''fragment'' is somewhat different
than an ordinary plane wave and it is difficult to know how to
That is the only kind of spectrum that has the property of being Lorentz invariant.
The effect of motion is
to Doppler shift detected electromagnetic radiation, but a
frequency-cubed spectrum has the property that up-and-down-shifting
of the radiation is exactly compensated, i.e. there is as much
radiation Doppler shifted into a given frequency interval as there
is shifted out by uniform motion.
The perceived ''temperature'' is
directly proportional to the acceleration.
They were analyzing the theory of van der Waals forces when Casimir had the opportunity to discuss ideas with Niels Bohr on a walk.
According to Casimir,
Bohr ''mumbled something about zero-point energy'' being relevant.
This led Casimir to an analysis of zero-point energy effects in the
related problem of forces between perfectly conducting parallel
This fact leads to the situation that there is a zero-point radiation overpressure outside the plates which acts to push the plates together. This can be considered analogous to radiation pressure (radiation pressure from the Sun pushes comet tails away from the comet nucleus), and the resulting effect is now called the Casimir force. It has the property of increasing in strength with the inverse fourth power of the plate separation.
The force ceases when elements of the plates come into contact, the surface smoothness of the plates being a limiting factor, or when the plates are so close that the corresponding zero-point radiation wavelengths no longer ''see'' a perfectly conducting surface.
The actual non-continuous nature of
the plates, as opposed to the true surface and molecular nature of
the materials, becomes an important factor for very short distances.
It has since been verified even more
precisely, by U. Mohideen at the University of California at
Riverside, again in agreement with Casimir's formula. Moreover the
Casimir force (also called
Casimir effect) has become relevant
to micro-electro-mechanical structures in which it is both a problem
(termed ''stiction'') and a possible mechanism for control.
It is perfectly possible to explain the
Casimir effect by taking into account the quantum-induced motions of
atoms in each plate and examining the retarded potential
interactions of atoms in one plate with those in the other.
In spite of the dubious nature of these claims (to date no such device has passed a rigorous, objective test), the concept of converting some amount of zero-point energy to usable energy cannot be ruled out in principle.
Zero-point energy is
not a thermal reservoir, and therefore does not suffer from the
thermodynamic injunction against extracting energy from a lower
Applying the same polarity charge to all
the plates would yield a repulsive force between plates, thereby
opposing the Casimir force which is acting to push the plates
together. Adjusting the electrostatic force so as to permit the
Casimir force to dominate will result in adding energy to the
electric field between the plates, thereby converting zero-point
energy to electric energy.
Nevertheless, this would demonstrate the
concept of conversion of zero-point energy in principle if the
Casimir effect attribution to zero-point energy is correct (which is
This led to the concept of dark energy, which is in effect a resurrection of Einstein's cosmological constant. (The universe now appears to consist of about 70 percent dark energy, 25 percent dark matter and five percent ordinary matter.)
Zero-point energy has the desired property of
driving an accelerated expansion, and thus having the requisite
properties of dark energy, but to an absurdly greater degree than
required, i.e. 120 orders of magnitude.
At first glance one might assume that if there is an enormous amount of zero-point energy underlying the universe, its effect would be to dramatically curve the universe to a minute size.
Indeed, if the spectrum of zero-point energy extends
to the Planck scale, its energy density would be the mass equivalent
of about 1093 grams per cubic centimeter which would reduce the
universe to a size smaller than an atomic nucleus.
For ordinary radiation, the ratio of
pressure to energy density is w=1/3c2, which is
customarily expressed in units whereby c=1, and thus the ratio is
expressed as w=+1/3. But for zero-point energy the ratio is w=-1.
This is owing to the circumstance that the zero-point energy density
is assumed to be constant: no matter how much the universe expands
it does not become diluted, but instead more zero-point energy is
assumed to be created out of nothing.
Indeed, this amount of zero-point
energy, interpreted this way, would have accelerated the universe
into oblivion in microseconds.
In that case dark energy is nothing other than zero-point energy.
In Measurability of vacuum fluctuations and dark energy and Electromagnetic dark energy they propose that a phase transition occurs so that zero-point photons below a frequency of about 1.7 THz are gravitationally active whereas above that they are not.
If this is the case, then the dark energy problem is solved: dark energy is the low frequency gravitationally active component of zero-point energy. Zero-point photons continue to exist above the 1.7 THz phase transition, consistent with measurable QED effects such as the Casimir effect, the Lamb shift, etc.
The proposed phase transition should be
testable in the near future when the Koch et al. experiment is
extended from 0.6 Tz to the proposed cutoff.
Einstein and Otto Stern came close to deriving the blackbody function without assuming quantization but with the presence of zero-point energy.
particular claimed in 1916 that the universe was filled with
zero-point energy. This line of investigation was abandoned with the
advent of quantum mechanics, but the concept of zero-point energy
soon reemerged with a quantum interpretation.
For the contribution of other researchers, see the book "The Quantum Dice" by de la Pena and Cetto.
This became the discipline known as stochastic electrodynamics (SED, earlier sometimes referred to as random electrodynamics). In the SED representation the zero-point field is taken to be a given, and is treated as an ensemble of ordinary electromagnetic plane waves having an energy 1/2 hf in each and every mode.
There is no quantum
In the latter case, the ground state electron is assumed to emit Larmor radiation which causes it to spiral inward, but this does not lead to collapse of the orbit because the electron also absorbs zero-point energy.
The calculation of the absorption was done by Boyer and later by Puthoff by treating the electron as undergoing harmonic oscillation rather than true motion in a Coulomb potential.
This is a weakness in the analysis but nonetheless it is striking that the Larmor emission and harmonic-oscillator-type absorption prove to be in balance exactly at the Bohr radius.
The fact that the orbital angular
momentum is zero in the quantum ground state is mirrored in the SED
orbiting-electron interpretation by random changes in the orbital
plane (due to the zero-point fluctuations) yielding a time averaged
zero net angular momentum.
In the SED case, the electron in a
Coulomb field is jostled by its emission and absorption to a range
of radial distances which reproduce the Schroedinger probability.
This is an intriguing extension of the earlier result, but problems
still remain such as the need to cut off the particle-field
interactions to avoid auto-ionization, i.e. a single very high
frequency, hence very energetic, zero-point fluctuation could free
They added a parameter having a random
distribution of energies with 1/2 hf as the mean, thereby yielding a
closer formal correspondence with the quantum behavior.
He dubbed this motion ''zitterbewegung''
(German for ''jitter motion''). In
SED theory, the phenomenon of
zitterbewegung is caused by the electromagnetic zero-point
Zitterbewegung thus suggests
possibly deep connections between zero-point energy and the
mass-energy relationship of matter and with the quantum properties
here for a new popular-level
overview on this topic by Marcus Chown
The Higgs field was first proposed in 1964 and is still a key element of the Standard Model of particle physics; it is needed to confer the property of mass on the fundamental particles. In the theory, all particles are intrinsically massless until acted upon by the Higgs field.
The quantum of the Higgs field is the Higgs boson. Attempts to detect the Higgs boson, and therefore to verify the Higgs field as the mass-generating mechanism of the Standard Model, have been unsuccessful.
The current best hope is on the
Large Hadron Collider at CERN
scheduled to go on line in May 2008.
The mass of ordinary matter is overwhelmingly due to the protons and neutrons in the nuclei of atoms. Protons and neutrons are comprised of the two lightest quarks: the up and down quarks.
The masses of their constituent quarks (approx. 0.005 and 0.010 GeV/c2 for the up and down quarks respectively) comprise only about one percent of the masses of the protons and neutrons (0.938 and 0.940 GeV/c2 respectively).
The remainder of the mass would have to
be due to the gluon fields and strong interaction energies. The
quark masses, the gluon fields and other strong interaction energies
would not be affected by a Higgs field. The origin of inertial mass
of ordinary matter is thus a wide open question.
This points to the electromagnetic quantum vacuum as the origin of forces which appear as inertial mass.
The same result can be derived by considering the transformation properties of the electromagnetic field when experienced in an accelerating coordinate system, and in that case the proper four-vector relativistic equation of motion can be derived.
A recent study showed that such a zero-point field based mass-generating approach would explain the origin of Einstein's principle of equivalence.
These as yet still speculative concepts suggest that zero-point energy may be involved in some of the most fundamental properties of matter.
It should be noted that this unorthodox
approach to mass based upon electrodynamics is not taken very
seriously by the mainstream physics community, whose efforts remain
focused on superstring - and
Nevertheless, SED interpretation of the Bohr orbit (above) does suggest a way whereby energy might be extracted.
Based upon this, a patent has been issued
and experiments have been underway at the University of Colorado (U.S.