Quantum mechanics predicts the existence of what are usually called .pdf

Quantum mechanics predicts the existence of what are usually called ''zero-point'' energies for
the strong, the weak and the electromagnetic interactions, where ''zero-point'' refers to the
energy of the system at temperature T=0, or the lowest quantized energy level of a quantum
mechanical system. 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
electromagnetic case.
In conventional quantum physics, the origin of zero-point energy is the Heisenberg uncertainty
principle, which states that, for a moving particle such as an electron, the more precisely one
measures the position, the less exact the best possible measurement of its momentum (mass
times velocity), and vice versa. 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 zero-point energy.
Zero-point energy is the energy that remains when all other energy is removed from a system.
This behaviour is demonstrated by, for example, liquid helium. 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 freeze.)
A harmonic oscillator is a useful conceptual tool in physics. Classically a harmonic oscillator,
such as a mass on a spring, can always be brought to rest. However a quantum harmonic
oscillator does not permit this. 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 frequency.
Electromagnetic radiation can be pictured as waves flowing through space at the speed of light.
The waves are not waves of anything substantive, but are ripples in a state of a theoretically
defined field. However these waves do carry energy (and momentum), and each wave has a
specific direction, frequency and polarization state. Each wave represents a ''propagating mode
of the electromagnetic field.''
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.
From this line of reasoning, quantum physics predicts that all of space must be filled with
electromagnetic zero-point fluctuations (also called the zero-point field) creating a universal sea
of zero-point energy. 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 the Sun.
How could such an enormous energy not be wildly evident? 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 interpret this.
On the other hand, zero-point energy appears to have been directly measured as current noise in
a resistively shunted Josephson junction by Koch, van Harlingen and Clarke up to a frequency of
about 0.6 Tz (see Abstract).
LORENTZ INVARIANCE OF THE SPECTRUM
That the spectrum of zero-point radiation has a frequency-cubed dependence is of great
significance. 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.
A remarkably different phenomenon occurs when accelerating through zero-point radiation. The
zero-point radiation acts upon an accelerating detector as if the detector were immersed in a
thermal spectrum, even though heat and temperature are not involved. The perceived
''temperature'' is directly proportional to the acceleration.
CASIMIR EFFECT
In 1947 Hendrik Casimir, once an assistant of Pauli, was working in applied industrial research
at the Philips Laboratory in the Netherlands along with physicist J. T. G. Overbeek. 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 plates.
The cavity between such plates cannot sustain all modes of the electromagnetic field. In
particular wavelengths comparable to the plate separation and longer are excluded from the
region between the plates. 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 noncontinuous nature
of the plates, as opposed to the true surface and molecular nature of the materials, becomes an
important factor for very short distances.
The Casimir force was not measured to high precision until the mid 1990s, when measurements
by S. Lamoreux at the University of Washington verified Casimir's predictions to within five
percent in the size range of a few microns. 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.
The Casimir force is widely cited as evidence that underlying the universe there must be a sea of
real zero-point energy. This argument follows from Casimir's analysis and prediction. It is not
necessarily true, however. 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.
FORWARD THOUGHT EXPERIMENT
There is growing interest concerning the possibility of tapping zero-point energy and many
claims exist of ''over unity devices'' (gadgets yielding a greater output than the required input
for operation) driven by zero-point energy. 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 temperature reservoir.
In 1993 Cole and Puthoff published a thermodynamic analysis, ''Extracting energy and heat
from the vacuum'' (see below), in which they concluded that ''extracting energy and heat from

electromagnetic zero-point radiation via the use of the Casimir force'' is in principle possible
without violating the laws of thermodynamics.
A thought experiment for a device that readily demonstrates how the Casimir force could be put
to use in principle was proposed by physicist Robert Forward in 1984 (see below). A ''vacuum
fluctuation battery'' could be constructed consisting of stacked conducting plates. 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.
One can imagine an even simpler microdevice in which the Casimir force pushes two plates
together thereby engaging some kind of lever which does work.
There is no practical application in these examples since ideally it would take just as much
energy, and in practice somewhat more energy owing to frictional and other losses, to separate
the plates for a second cycle. 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 debatable).
DARK ENERGY
A major discovery in astrophysics in the late 1990s was the finding from type Ia supernovae
redshift-luminosity observations that the expansion of the universe is accelerating. 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.
According to relativity theory, energy is equivalent to mass as a source of gravity, thus zero-
point energy should gravitate, which according to general relativity means producing a positive
curvature in space-time. 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.
Zero-point energy behaves differently. 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.
A further peculiarity is that a ratio of w=-1 implies that the zero-point energy exerts a negative
pressure which, counter-intuitively, leads to an expansion of space-time.
Thus zero-point energy would appear to be identical with the mysterious dark energy, but
unfortunately if the energy spectrum does continue up to the Planck frequency, there may be 120
orders of magnitude more energy per cubic centimeter than the observations of cosmic
acceleration permit. Indeed, this amount of zero-point energy, interpreted this way, would have
accelerated the universe into oblivion in microseconds.
Recent work by Christian Beck at the University of London and Michael Mackey at McGill
University may have resolved the 120 order of magnitude problem. In that case dark energy is
nothing other than zero-point energy. In Measureability 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.
STOCHASTIC ELECTRODYNAMICS THEORY
Although zero-point energy is usually regarded as a quantum phenomenon and a consequence of
the Heisenberg uncertainty relationship, the existence of zero-point energy was inferred by
Einstein, Planck, Nernst and others in the context of blackbody radiation prior to the discovery of
quantum mechanics. Einstein and Otto Stern came close to deriving the blackbody function
without assuming quantization but with the presence of zero-point energy. Nernst in 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.
In the 1960s British physicist Trevor Marshall and, separately, American Timothy Boyer were
two of the principal investigators who essentially took up the abandoned approach and pushed it
much farther by asking the question: which quantum phenomena might be explained using solely
classical physics plus an assumed classical representation of a zero-point field with zero-point
energy? For the contribution of other researchers, see the book "The Quantum Dice" by de la
Pena and Cetto (below). 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 physics involved.
This theory has had some success, although it is far from explaining most quantum effects. Apart
from its ontological aspirations of possibly doing away with quantum physics in favor of solely
classical physics, SED is useful as a computational tool since it involves well-known classical
electrodynamics in place of more esoteric quantum laws and processes.
Two noteworthy successes of SED are its derivation of the Planck blackbody function without
assuming quantization and its suggestion that the Bohr orbit of hydrogen could arise without a
quantum law. 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.
Recent simulations by Cole have successfully modeled the electron motion in the Coulomb
potential of a hydrogen atom and have thereby replicated the electron probability density
predicted by the Schroedinger wave function. 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 autoionization, i.e. a
single very high frequency, hence very energetic, zero-point fluctuation could free the electron.
The representation of the zero-point field as an ensemble of plane waves each with an energy of
precisely 1/2 hf in all possible directions and random phases was modified in 1995 by Ibison and
Haisch. 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 behaviour.
ZITTERBEWEGUNG
Schroedinger was apparently the first to note that solving the Dirac equation for the motion of
the electron resulted in a necessary component that could be interpreted as random, speed-of-
light fluctuations of a point-like particle. He dubbed this motion ''zitterbewegung'' (German
for ''jitter motion''). In SED theory, the phenomenon of zitterbewegung is caused by the
electromagnetic zero-point fluctuations.
Several things are interesting about zitterbewegung. First, since the fluctuations occur at the
speed of light, then at this level the electron would have to be massless, mass arising at some
higher level of motion. Secondly, the fluctuations smear out the average position over a volume

the Compton radius in size, which suggests a physical interpretation of the wave function and the
associated probability density. (Scattering experiments indicate that the electron is far smaller
than its Compton size, indeed point-like for all we know.) Thirdly, simulations that have recently
been done show that if such a massless, fluctuating point particle is accelerated in an electric
field, the zitterbewegung acquires a helical motion suggestive of spin. The possible association
of zitterbewegung with spin has been made by a number of authors over the years such as Barut
and Zanghi, Hestenes, Huang, Weisskopf, etc.
Zitterbewegung thus suggests possibly deep connections between zero-point energy and the
mass-energy relationship of matter and with the quantum properties of particles.
SPECULATIVE CONNECTION TO INERTIAL AND GRAVITATIONAL MASS
Click here for a new popular-level overview on this topic by Marcus Chown.
The connection in SED theory between zitterbewegung and the zero-point fluctuations have led
to speculative investigations of a possible mass-generating role as an alternative to the Higgs
field. 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 forthcoming Large Hadron Collider at CERN
scheduled to go on line in May 2008.
Even if the Higgs field is experimentally discovered, however, that will still not explain the
origin of inertial mass of ordinary matter. The Higgs field applies only to the electro-weak sector
of the Standard Model. 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.
SED studies published in the 1990s showed that a massless point-charge oscillator accelerating
through the zero-point field will experience a Lorentz force (from the magnetic components of
the zero-point fluctuations) that turns out to be directly proportional to acceleration, allowing the
derivation of the fundamental F=ma relationship of mechanics from electrodynamics. 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 focussed on superstring- and M-theory.
Solution
Quantum mechanics predicts the existence of what are usually called ''zero-point'' energies for
the strong, the weak and the electromagnetic interactions, where ''zero-point'' refers to the
energy of the system at temperature T=0, or the lowest quantized energy level of a quantum
mechanical system. 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
electromagnetic case.
In conventional quantum physics, the origin of zero-point energy is the Heisenberg uncertainty
principle, which states that, for a moving particle such as an electron, the more precisely one
measures the position, the less exact the best possible measurement of its momentum (mass
times velocity), and vice versa. 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 zero-point energy.
Zero-point energy is the energy that remains when all other energy is removed from a system.
This behaviour is demonstrated by, for example, liquid helium. 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 freeze.)
A harmonic oscillator is a useful conceptual tool in physics. Classically a harmonic oscillator,
such as a mass on a spring, can always be brought to rest. However a quantum harmonic
oscillator does not permit this. 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 frequency.
Electromagnetic radiation can be pictured as waves flowing through space at the speed of light.

The waves are not waves of anything substantive, but are ripples in a state of a theoretically
defined field. However these waves do carry energy (and momentum), and each wave has a
specific direction, frequency and polarization state. Each wave represents a ''propagating mode
of the electromagnetic field.''
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.
From this line of reasoning, quantum physics predicts that all of space must be filled with
electromagnetic zero-point fluctuations (also called the zero-point field) creating a universal sea
of zero-point energy. 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 the Sun.
How could such an enormous energy not be wildly evident? 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 interpret this.
On the other hand, zero-point energy appears to have been directly measured as current noise in
a resistively shunted Josephson junction by Koch, van Harlingen and Clarke up to a frequency of
about 0.6 Tz (see Abstract).
LORENTZ INVARIANCE OF THE SPECTRUM
That the spectrum of zero-point radiation has a frequency-cubed dependence is of great
significance. 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.

A remarkably different phenomenon occurs when accelerating through zero-point radiation. The
zero-point radiation acts upon an accelerating detector as if the detector were immersed in a
thermal spectrum, even though heat and temperature are not involved. The perceived
''temperature'' is directly proportional to the acceleration.
CASIMIR EFFECT
In 1947 Hendrik Casimir, once an assistant of Pauli, was working in applied industrial research
at the Philips Laboratory in the Netherlands along with physicist J. T. G. Overbeek. 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 plates.
The cavity between such plates cannot sustain all modes of the electromagnetic field. In
particular wavelengths comparable to the plate separation and longer are excluded from the
region between the plates. 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 noncontinuous nature
of the plates, as opposed to the true surface and molecular nature of the materials, becomes an
important factor for very short distances.
The Casimir force was not measured to high precision until the mid 1990s, when measurements
by S. Lamoreux at the University of Washington verified Casimir's predictions to within five
percent in the size range of a few microns. 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.
The Casimir force is widely cited as evidence that underlying the universe there must be a sea of
real zero-point energy. This argument follows from Casimir's analysis and prediction. It is not
necessarily true, however. 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.
FORWARD THOUGHT EXPERIMENT

There is growing interest concerning the possibility of tapping zero-point energy and many
claims exist of ''over unity devices'' (gadgets yielding a greater output than the required input
for operation) driven by zero-point energy. 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 temperature reservoir.
In 1993 Cole and Puthoff published a thermodynamic analysis, ''Extracting energy and heat
from the vacuum'' (see below), in which they concluded that ''extracting energy and heat from
electromagnetic zero-point radiation via the use of the Casimir force'' is in principle possible
without violating the laws of thermodynamics.
A thought experiment for a device that readily demonstrates how the Casimir force could be put
to use in principle was proposed by physicist Robert Forward in 1984 (see below). A ''vacuum
fluctuation battery'' could be constructed consisting of stacked conducting plates. 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.
One can imagine an even simpler microdevice in which the Casimir force pushes two plates
together thereby engaging some kind of lever which does work.
There is no practical application in these examples since ideally it would take just as much
energy, and in practice somewhat more energy owing to frictional and other losses, to separate
the plates for a second cycle. 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 debatable).
DARK ENERGY
A major discovery in astrophysics in the late 1990s was the finding from type Ia supernovae
redshift-luminosity observations that the expansion of the universe is accelerating. 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.
According to relativity theory, energy is equivalent to mass as a source of gravity, thus zero-
point energy should gravitate, which according to general relativity means producing a positive
curvature in space-time. 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.
Zero-point energy behaves differently. 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.
A further peculiarity is that a ratio of w=-1 implies that the zero-point energy exerts a negative
pressure which, counter-intuitively, leads to an expansion of space-time.
Thus zero-point energy would appear to be identical with the mysterious dark energy, but
unfortunately if the energy spectrum does continue up to the Planck frequency, there may be 120
orders of magnitude more energy per cubic centimeter than the observations of cosmic
acceleration permit. Indeed, this amount of zero-point energy, interpreted this way, would have
accelerated the universe into oblivion in microseconds.
Recent work by Christian Beck at the University of London and Michael Mackey at McGill
University may have resolved the 120 order of magnitude problem. In that case dark energy is
nothing other than zero-point energy. In Measureability 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.
STOCHASTIC ELECTRODYNAMICS THEORY
Although zero-point energy is usually regarded as a quantum phenomenon and a consequence of
the Heisenberg uncertainty relationship, the existence of zero-point energy was inferred by
Einstein, Planck, Nernst and others in the context of blackbody radiation prior to the discovery of
quantum mechanics. Einstein and Otto Stern came close to deriving the blackbody function
without assuming quantization but with the presence of zero-point energy. Nernst in 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.
In the 1960s British physicist Trevor Marshall and, separately, American Timothy Boyer were
two of the principal investigators who essentially took up the abandoned approach and pushed it
much farther by asking the question: which quantum phenomena might be explained using solely
classical physics plus an assumed classical representation of a zero-point field with zero-point
energy? For the contribution of other researchers, see the book "The Quantum Dice" by de la
Pena and Cetto (below). 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 physics involved.
This theory has had some success, although it is far from explaining most quantum effects. Apart
from its ontological aspirations of possibly doing away with quantum physics in favor of solely
classical physics, SED is useful as a computational tool since it involves well-known classical
electrodynamics in place of more esoteric quantum laws and processes.
Two noteworthy successes of SED are its derivation of the Planck blackbody function without
assuming quantization and its suggestion that the Bohr orbit of hydrogen could arise without a
quantum law. 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.
Recent simulations by Cole have successfully modeled the electron motion in the Coulomb
potential of a hydrogen atom and have thereby replicated the electron probability density
predicted by the Schroedinger wave function. 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 autoionization, i.e. a
single very high frequency, hence very energetic, zero-point fluctuation could free the electron.
The representation of the zero-point field as an ensemble of plane waves each with an energy of
precisely 1/2 hf in all possible directions and random phases was modified in 1995 by Ibison and
Haisch. 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 behaviour.

ZITTERBEWEGUNG
Schroedinger was apparently the first to note that solving the Dirac equation for the motion of
the electron resulted in a necessary component that could be interpreted as random, speed-of-
light fluctuations of a point-like particle. He dubbed this motion ''zitterbewegung'' (German
for ''jitter motion''). In SED theory, the phenomenon of zitterbewegung is caused by the
electromagnetic zero-point fluctuations.
Several things are interesting about zitterbewegung. First, since the fluctuations occur at the
speed of light, then at this level the electron would have to be massless, mass arising at some
higher level of motion. Secondly, the fluctuations smear out the average position over a volume
the Compton radius in size, which suggests a physical interpretation of the wave function and the
associated probability density. (Scattering experiments indicate that the electron is far smaller
than its Compton size, indeed point-like for all we know.) Thirdly, simulations that have recently
been done show that if such a massless, fluctuating point particle is accelerated in an electric
field, the zitterbewegung acquires a helical motion suggestive of spin. The possible association
of zitterbewegung with spin has been made by a number of authors over the years such as Barut
and Zanghi, Hestenes, Huang, Weisskopf, etc.
Zitterbewegung thus suggests possibly deep connections between zero-point energy and the
mass-energy relationship of matter and with the quantum properties of particles.
SPECULATIVE CONNECTION TO INERTIAL AND GRAVITATIONAL MASS
Click here for a new popular-level overview on this topic by Marcus Chown.
The connection in SED theory between zitterbewegung and the zero-point fluctuations have led
to speculative investigations of a possible mass-generating role as an alternative to the Higgs
field. 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 forthcoming Large Hadron Collider at CERN
scheduled to go on line in May 2008.
Even if the Higgs field is experimentally discovered, however, that will still not explain the
origin of inertial mass of ordinary matter. The Higgs field applies only to the electro-weak sector
of the Standard Model. 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.
SED studies published in the 1990s showed that a massless point-charge oscillator accelerating
through the zero-point field will experience a Lorentz force (from the magnetic components of
the zero-point fluctuations) that turns out to be directly proportional to acceleration, allowing the
derivation of the fundamental F=ma relationship of mechanics from electrodynamics. 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 focussed on superstring- and M-theory.

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