Zero-point energy
Information about Zero-point energy
In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system. The concept was first proposed by Albert Einstein and Otto Stern in 1913. The term "zero-point energy" is a translation of the German Nullpunktsenergie. All quantum mechanical systems have a zero point energy. The term arises commonly in reference to the ground state of the quantum harmonic oscillator and its null oscillations. In quantum field theory, it is a synonym for the vacuum energy, an amount of energy associated with the vacuum of empty space. In 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.
Because zero point energy is the lowest possible energy a system can have, this energy cannot be removed from the system. A related term is zero-point field, which is the lowest energy state of a field, i.e. its ground state, which is non-zero.[1]
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.
In 1913, using this formula as a basis, Albert Einstein and Otto Stern published a paper of great significance in which they suggested for the first time the existence of a residual energy that all oscillators have at absolute zero. They called this "residual energy" and then Nullpunktsenergie (in German), which later became translated as zero-point energy. They carried out an analysis of the specific heat of hydrogen gas at low temperature, and concluded that the data are best represented if the vibrational energy is taken to have the form:[2]
Thus, according to this expression, even at absolute zero the energy of an atomic system has the value ½hν.[3]
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. (Caveat: If we add an arbitrary constant to the Hamiltonian, we get another theory which is physically equivalent to the previous Hamiltonian. Because of this, only relative energy is observable, not the absolute energy. This does not change the fact that the minimum momentum is nonzero, however.)
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.
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
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 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.
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. 
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.
Professor Ulf Leonhardt and Dr Thomas Philbin, from the University of St Andrews in Scotland, have worked out a way of reversing this pheneomenon, known as the Casimir force, so that it repels instead of attracts. Their discovery could ultimately lead to frictionless micro-machines with moving parts that levitate.[4]
Rueda, Haisch and Puthoff[5][6][7] have proposed that an accelerated massive object interacts with the zero point field to produce an electromagnetic drag force which gives rise to the phenomenon of inertia; see stochastic electrodynamics.
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Because zero point energy is the lowest possible energy a system can have, this energy cannot be removed from the system. A related term is zero-point field, which is the lowest energy state of a field, i.e. its ground state, which is non-zero.[1]
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.
History
In 1900, Max Planck derived the formula for the energy of a single "energy radiator", i.e. a vibrating atomic unit, as:
- Here,
is Planck's constant, 
is the frequency, k is Boltzmann's constant, and T is the temperature.
In 1913, using this formula as a basis, Albert Einstein and Otto Stern published a paper of great significance in which they suggested for the first time the existence of a residual energy that all oscillators have at absolute zero. They called this "residual energy" and then Nullpunktsenergie (in German), which later became translated as zero-point energy. They carried out an analysis of the specific heat of hydrogen gas at low temperature, and concluded that the data are best represented if the vibrational energy is taken to have the form:[2]
Thus, according to this expression, even at absolute zero the energy of an atomic system has the value ½hν.[3]
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. (Caveat: If we add an arbitrary constant to the Hamiltonian, we get another theory which is physically equivalent to the previous Hamiltonian. Because of this, only relative energy is observable, not the absolute energy. This does not change the fact that the minimum momentum is nonzero, however.)
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.
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
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
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.
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
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Unsolved problems in physics: Why doesn't the zero-point energy of vacuum cause a large cosmological constant? What cancels it out?
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.
Use in propulsion and levitation
Another area of research in the field of zero point energy is how it could be used for propulsion. NASA and British Aerospace both have programs running to this end though practical technology is still a long way off. For any success in this area, it would have to be possible to create repulsive effects in the quantum vacuum, which according to theory should be possible and experiments to produce and measure these effects are planned for the future.Professor Ulf Leonhardt and Dr Thomas Philbin, from the University of St Andrews in Scotland, have worked out a way of reversing this pheneomenon, known as the Casimir force, so that it repels instead of attracts. Their discovery could ultimately lead to frictionless micro-machines with moving parts that levitate.[4]
Rueda, Haisch and Puthoff[5][6][7] have proposed that an accelerated massive object interacts with the zero point field to produce an electromagnetic drag force which gives rise to the phenomenon of inertia; see stochastic electrodynamics.
"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 endeavor — the design and invention of so-called "free energy" devices, similar to perpetual motion machines in the past, and with a similar level of success.Related patents
- U.S. Patent 5590031; System for converting electromagnetic radiation energy to electrical energy.
See also
References
1. ^ Gribbin, John (1998). Q is for Quantum - An Encyclopedia of Particle Physics. Touchstone Books. ISBN 0-684-86315-4.
2. ^ Laidler, Keith, J. (2001). The World of Physical Chemistry. Oxford University Press. ISBN 0198559194.
3. ^ Introduction to Zero-Point Energy - Calphysics Institute
4. ^ Telegraph article Physicists have 'solved' mystery of levitation published July 8, 2007 See also physicsworld and st-andrews.ac.uk.
5. ^ Haisch, Bernard; Alphonso Rueda, H.E. Puthoff (February 1994). "Inertia as a zero-point-field Lorentz force". Physical Review A 49 (2): 678-694.
6. ^ Rueda, Alfonso; Bernhard Haisch (1998). "Contribution to inertial mass by reaction of the vacuum to accelerated motion". Found.Phys. 28: 1057-1108.
7. ^ Rueda, Alfonso; Bernhard Haisch (1998). "Inertia as reaction of the vacuum to accelerated motion". Phys.Lett. A240: 115-126.
2. ^ Laidler, Keith, J. (2001). The World of Physical Chemistry. Oxford University Press. ISBN 0198559194.
3. ^ Introduction to Zero-Point Energy - Calphysics Institute
4. ^ Telegraph article Physicists have 'solved' mystery of levitation published July 8, 2007 See also physicsworld and st-andrews.ac.uk.
5. ^ Haisch, Bernard; Alphonso Rueda, H.E. Puthoff (February 1994). "Inertia as a zero-point-field Lorentz force". Physical Review A 49 (2): 678-694.
6. ^ Rueda, Alfonso; Bernhard Haisch (1998). "Contribution to inertial mass by reaction of the vacuum to accelerated motion". Found.Phys. 28: 1057-1108.
7. ^ Rueda, Alfonso; Bernhard Haisch (1998). "Inertia as reaction of the vacuum to accelerated motion". Phys.Lett. A240: 115-126.
Further reading
- Beiser, Arthur (1967). Concepts of Modern Physics. McGraw-Hill.
- Albert Einstein and L. Hopf (1910). "On a theorem of the probability calculus and its application to the theory of radiation". Ann. Phys. 33: 1096–1104.
- 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.
- Forward, R. (1984). "Extracting electrical energy from the vacuum by cohesion of charged foliated conductors". Phys. Rev. B 30: 1700.
- Forward, R. (February 1996). "Mass Modification Experiment Definition". Forward Unlimited. PL-TR-96-3004
- Bernard Haisch, Alfonso Rueda and York Dobyns (2001). "Inertial mass and the quantum vacuum fields". Annalen der Physik 10: 393-414.
- 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.
- Nernst, W. (1916). "?". Verh. Deutsch Phys. Ges. 18: 83.
- Alfonso Rueda and Bernard Haisch (2005). "Gravity and the Quantum Vacuum Inertia Hypothesis". Annalen der Physik 14: 479-498.
- Sciama, D. W. (1991). in Simon Saunders and Henry R. Brown, eds: The Philosophy of Vacuum. Oxford: Clarendon Press. ISBN 0-19-824449-5
- Wegerif, Boudewijn (February 11, 2002). Zero Point Energy - Fact or Fiction. Indybay. Retrieved on 2007-04-03..
External links
- Zero-point energy? "Ask the Van" popular science FAQ at University of Illinois.
- Philip Yam, "Exploiting Zero-point Energy", Scientific American Magazine, December 1997, pp. 82-85.
- Alokik Kanwal, Zero-point energy (Power Point presentation; rutgers.edu)
Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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energy (from the Greek ενεργός, energos, "active, working")[1] is a scalar physical quantity that is a property of objects and systems of objects which is conserved by nature.
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quantum mechanics is the study of the relationship between energy quanta (radiation) and matter, in particular that between valence shell electrons and photons. Quantum mechanics is a fundamental branch of physics with wide applications in both experimental and theoretical physics.
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Otto Stern
Born 17 January 1888
Sohrau, Kingdom of Prussia
Died July 17 1969 (aged 81)
Berkeley, California,
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Born 17 January 1888
Sohrau, Kingdom of Prussia
Died July 17 1969 (aged 81)
Berkeley, California,
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The quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator. It is one of the most important model systems in quantum mechanics because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable
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Quantum field theory (QFT) is a theoretical framework for constructing quantum mechanical models of field-like systems, or, equivalently, of many-body systems. It is widely used in particle physics and condensed matter physics.
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Vacuum energy is an underlying background energy that exists in space even when devoid of matter (known as free space). The vacuum energy results in the existence of most (if not all) of the fundamental forces - and thus in all effects involving these forces, too.
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A vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than standard atmospheric pressure. The Latin term in vacuo is used to describe an object as being in what would otherwise be a vacuum.
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Physical cosmology, as a branch of astronomy, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. Cosmology involves itself with studying the motions of the celestial bodies and the first cause.
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In physical cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe.
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In physics, the Casimir effect or Casimir-Polder force is a physical force exerted between separate objects due to resonance of all-pervasive energy fields in the intervening space between the objects.
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Nanotechnology refers broadly to a field of applied science and technology whose unifying theme is the control of matter on the atomic and molecular scale, normally 1 to 100 nanometers, and the fabrication of devices within that size range.
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In quantum field theory, the zero-point field is the lowest energy state of a field, i.e. its ground state, which is non zero.[1] This phenomenon gives the quantum vacuum a complex structure, which can be probed experimentally; see, for example, the Casimir effect.
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field is an assignment of a physical quantity to every point in space (or, more generally, spacetime). A field is thus viewed as extending throughout a large region of space so that its influence is all-pervading. The strength of a field usually varies over a region.
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stationary state is an eigenstate of a Hamiltonian, or in other words, a state of definite energy. It is called stationary because the corresponding probability density has no time dependence.
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perpetual motion, taken literally, refers to movement that goes on forever. This is possible in the current theoretical understanding of physics as in Newton's First Law of Motion.
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Max Planck
Max Karl Ernst Ludwig Planck
Born March 23 1858
Kiel, Germany
Died September 4 1947 (aged 89)
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Max Karl Ernst Ludwig Planck
Born March 23 1858
Kiel, Germany
Died September 4 1947 (aged 89)
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Planck constant (denoted ) is a physical constant that is used to describe the sizes of quanta. It plays a central role in the theory of quantum mechanics, and is named after Max Planck, one of the founders of quantum theory.
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The Boltzmann constant (k or kB) is the physical constant relating temperature to energy.
It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this
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It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this
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trillion fold).]]
Temperature is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics.
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Temperature is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics.
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Otto Stern
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Berkeley, California,
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Born 17 January 1888
Sohrau, Kingdom of Prussia
Died July 17 1969 (aged 81)
Berkeley, California,
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