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 which is thought by many to produce dark energy. 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.
Here, is Planck's constant, is the frequency, k is Boltzmann's constant, and T is the absolute 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:
Thus, according to this expression, even at absolute zero the energy of an atomic system has the value ½hν.
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 non-zero, 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 simultaneously, with arbitrary accuracy. 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 thermodynamics, since temperature is defined as the average translational kinetic energy of a moving particle, the existence of non-zero minimal energy of the particle implies that it is impossible to achieve the temperature of absolute zero.
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.
A phenomenon that is commonly and erroneously presented as 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 (Philips Research), who considered the quantized electromagnetic field between a pair of grounded, neutral metal plates. A small force can be measured between the plates, which can be regarded as the change of the zero-point energy of the electromagnetic field between the plates. However, there is still some debate on this issue, since the Casimir effect can be shown to be equally well described by a different theory involving charge-current interactions (the radiation-reaction picture), as argued by Robert Jaffe of MIT . Other such vacuum-induced phenomena include the spontaneous emissions of light (photons) by atoms and nuclei, the observed Lamb shift of the energy levels of atoms, and the anomalous value of electron's gyromagnetic ratio, to name a few.
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; both produce 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.
The Casimir effect has established zero point energy as an uncontroversial and scientifically accepted phenomenon. The concept of zero point energy has also become associated with pseudoscience, particularly the design and invention of "free energy" devices, which are essentially perpetual motion machines.
Zero-point energy is in the Half-Life 2 Series, manifested in the Zero-Point Energy Field Manipulator, also known as the gravity gun. See link for more info.
Zero-point energy is also very common in the Stargate SG1 and Stargate Atlantis series in the form of Zero Point Modules (ZPM) used for generating massive amounts of power required to power certain objects in the universe. It said to work by extracting vacuum energy from an artificially generated region of subspace until it reaches maximum entropy.
In The Incredibles, Syndrome makes a casual reference to zero-point energy when using his personal arsenal against Mr. Incredible, implying that it powers them.
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 which is thought by many to produce dark energy. 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.
Here, is Planck's constant, is the frequency, k is Boltzmann's constant, and T is the absolute 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:
Thus, according to this expression, even at absolute zero the energy of an atomic system has the value ½hν.
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 non-zero, 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 simultaneously, with arbitrary accuracy. 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 thermodynamics, since temperature is defined as the average translational kinetic energy of a moving particle, the existence of non-zero minimal energy of the particle implies that it is impossible to achieve the temperature of absolute zero.
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.
A phenomenon that is commonly and erroneously presented as 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 (Philips Research), who considered the quantized electromagnetic field between a pair of grounded, neutral metal plates. A small force can be measured between the plates, which can be regarded as the change of the zero-point energy of the electromagnetic field between the plates. However, there is still some debate on this issue, since the Casimir effect can be shown to be equally well described by a different theory involving charge-current interactions (the radiation-reaction picture), as argued by Robert Jaffe of MIT . Other such vacuum-induced phenomena include the spontaneous emissions of light (photons) by atoms and nuclei, the observed Lamb shift of the energy levels of atoms, and the anomalous value of electron's gyromagnetic ratio, to name a few.
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; both produce 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.
The Casimir effect has established zero point energy as an uncontroversial and scientifically accepted phenomenon. The concept of zero point energy has also become associated with pseudoscience, particularly the design and invention of "free energy" devices, which are essentially perpetual motion machines.
Zero-point energy is in the Half-Life 2 Series, manifested in the Zero-Point Energy Field Manipulator, also known as the gravity gun. See link for more info.
Zero-point energy is also very common in the Stargate SG1 and Stargate Atlantis series in the form of Zero Point Modules (ZPM) used for generating massive amounts of power required to power certain objects in the universe. It said to work by extracting vacuum energy from an artificially generated region of subspace until it reaches maximum entropy.
In The Incredibles, Syndrome makes a casual reference to zero-point energy when using his personal arsenal against Mr. Incredible, implying that it powers them.
|
|
|
|
|
|
|
|
|
|
|