Zero-point energy

In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess; it is the energy of the ground state of the system. The term arises commonly in reference to the ground state of the quantum harmonic oscillator. In quantum field theory, it is a synonym for the vacuum energy, an amount of energy associated with the vacuum of empty space. In physical cosmology, the vacuum energy is taken to be the origin of the cosmological constant. Experimentally, the zero-point energy of the vacuum leads directly to the Casimir effect, and is directly observable in nanoscale devices. Also, 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.

Because zero point energy is the lowest possible energy a system can have, this energy cannot be removed from the system.

Despite the definition, the concept of zero-point energy, and the hint of a possibility of extracting "free energy" from the vacuum, has attracted the attention of amateur inventors. Numerous perpetual motion and other pseudoscientific devices, often called free energy devices, exploiting the idea, have been proposed. As a result of this activity, and its intriguing theoretical explanation, it has taken on a life of its own in popular culture, appearing in science fiction books, games and movies.

Foundational physics

In classical physics, the energy of a system is relative, and is defined only in relation to some given state (often called reference state). Typically, one might associate a motionless system with zero energy, although doing so is purely arbitrary.

In quantum physics, it is natural to associate the energy with the expectation value of a certain operator, the Hamiltonian of the system. For almost all quantum-mechanical systems, the lowest possible expectation value that this operator can obtain is not zero; this lowest possible value is called the zero-point energy.

The origin of a minimal energy that isn't zero can be intuitively understood in terms of the Heisenberg uncertainty principle. This principle states that the position and the momentum of a quantum mechanical particle cannot both be known arbitrarily accurately. If the particle is confined to a potential well, then its position is at least partly known: it must be within the well. Thus, one may deduce that within the well, the particle cannot have zero momentum, as otherwise the uncertainty principle would be violated. Because the kinetic energy of a moving particle is proportional to the square of its velocity, it cannot be zero either. This example, however, is not applicable to a free particle—the kinetic energy of which can be zero.

Zero-point energy is also associated with the phenomenon dubbed Zitterbewegung by Schroedinger.

Varieties of zero-point energy

The idea of zero-point energy occurs in a number of situations, and it is important to distinguish these, and note that there are many closely related concepts.

In ordinary quantum mechanics, the zero-point energy is the energy associated with the ground state of the system. The most famous such example is the energy $E={\hbar\omega\over 2}$ associated with the ground state of the quantum harmonic oscillator. More precisely, the zero-point energy is the expectation value of the Hamiltonian of the system.

In quantum field theory, the fabric of space is visualized as consisting of fields, with the field at every point in space and time being a quantized simple harmonic oscillator, with neighboring oscillators interacting. In this case, one has a contribution of $E={\hbar\omega\over 2}$ from every point in space, resulting in a technically infinite zero-point energy. The zero-point energy is again the expectation value of the Hamiltonian; here, however, the phrase vacuum expectation value is more commonly used, and the energy is called the vacuum energy.

In quantum perturbation theory, it is sometimes said that the contribution of one-loop and multi-loop Feynman diagrams to elementary particle propagators are the contribution of vacuum fluctuations or the zero-point energy to the particle masses.

Some have drawn comparisons between the zero-point field and other universal energy field theories such as the akashic field, the aether and other less popular variants.

Other potentials of zero-point energy aside from the "free energy theories" are the idea that interaction with the zero-point field of the vacuum may produce propulsive effects, that would not be free energy just a new and perhaps more efficient form of propulsion. Groups such as NASA [1] and British Aerospace have been looking into this idea. As of yet, there is no known way to interact with the vacuum in this way, but they do have a few theories that may warrant investigation in the future. They entitle these theories "Hypothetical space drives".[2]

 Lorentz Invariance of the Zero-Point Radiation 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 Δf as there is shifted out by uniform motion.

 Unruh-Davies Effect

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 T=ha/4π2ck, where a is the acceleration, c the speed of light, and k is the Boltzmann constant.

 Experimental evidence

The simplest experimental evidence for the existence of zero-point energy in quantum field theory is the Casimir effect. This effect was proposed in 1948 by Dutch physicist Hendrik B. G. Casimir, who considered the quantized electromagnetic field between a pair of grounded, neutral metal plates. A small force can be measured between the plates, which is directly ascribable to a change of the zero-point energy of the electromagnetic field between the plates.

Although the Casimir effect at first proved hard to measure, because its effects can be seen only at very small distances, the effect is taking on increasing importance in nanotechnology. Not only is the Casimir effect easily and accurately measured in specially designed nanoscale devices, but it increasingly needs to be taken into account in the design and manufacturing processes of small devices. It can exert significant forces and stress on nanoscale devices, causing them to bend, twist, stick and break.

Other experimental evidence includes spontaneous emissions of light (photons) by atoms and nuclei, observed Lamb shift of positions of energy levels of atoms, anomalous value of electron's gyromagnetic ratio, etc.

Gravitation and cosmology

In cosmology, the zero-point energy offers an intriguing possibility for explaining the speculative positive values of the proposed cosmological constant. In brief, if the energy is "really there", then it should exert a gravitational force. In general relativity, mass and energy are equivalent; either produces a gravitational field.

One obvious difficulty with this association is that the zero-point energy of the vacuum is absurdly large. Naively, it is infinite, but one must argue that new physics takes over at the Planck scale, and so its growth is cut off at that point. Even so, what remains is so large that it would visibly bend space, and thus, there seems to be a contradiction. There is no easy way out, and reconciling the seemingly huge zero-point energy of space with the observed zero or small cosmological constant has become one of the important problems in theoretical physics, and has become a criterion by which to judge a candidate Theory of Everything.

A uniformly accelerating observer will observe zero-point energy of the electromagnetic field as a thermal bath of real photons, in an effect known as the Unruh effect.

Rueda, Haisch and Puthoff (1994, [3] 1998a,[4] 1998b[5]) have proposed that an accelerated massive object interacts with the zero point field to produced an electromagnetic drag force which gives rise to the phenomenon of inertia; see stochastic electrodynamics.

 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.

 "Free energy" devices

The Casimir effect has established zero point energy as an uncontroversial and scientifically accepted phenomenon. However, the term zero point energy has also become associated with a highly controversial area of human endeavour—the design and invention of so-called free energy devices, similar to perpetual motion machines in the past. These devices purport to "tap" the zero-point field and somehow "extract energy" from it, thus providing an "inexhaustible", cheap, and non-polluting energy source.

Controversy arises when such devices are promoted without scientifically acceptable proof that they tap the energy sources claimed. Promoters of a device demonstrate no understanding of how the device might do so; they demonstrate misunderstanding of widely accepted scientific facts and methods, in development or communication of a theory concerning a device; they make no attempt to include simpler explanations for the claimed performance of a device.

Any of these behaviours are liable to taint the reputations of those involved with such devices, and qualified researchers are therefore likely to be reluctant to make any attempt to verify or even seriously dismiss such a device until its promoters demonstrate enough competence to be taken seriously.

 Forward Thought Experiment

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).

Notes

1. [1] Warp Drive, When?
2. [2] Warp drive, When?
3. 1994
4. 1998a
5. 1998b

References

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• Albert Einstein and L. Hopf (1910). "Statistical investigation of a resonator’ s motion in a radiation field". Ann. Phys. 33: 1105–1115.
• Albert Einstein and Otto Stern, (1913). "—". Ann. Phys. 40: 551.
• Loudon, R. (September 2000). The Quantum Theory of Light, Third Edition. Oxford: Clarendon Press. ISBN 0-19-850176-5.
• Milonni, Peter W. (1994). The Quantum Vacuum: an Introduction to Quantum Electrodynamics. New York: Academic. ISBN 0-12-498080-5.
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