Zero-point energy From Wikipedia, the free encyclopedia Zero-point energy, also called quantum vacuum zero-point energy, is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential well. This results in motion even at absolute zero. For example, liquid helium does not freeze under atmospheric pressure at any temperature because of its zero-point energy. The concept of zero-point energy was developed in Germany by Albert Einstein and Otto Stern in 1913, as a corrective term added to a zero-grounded formula developed by Max Planck in 1900.[1][2] The term zero-point energy originates from the German Nullpunktsenergie.[1][2] An alternative form of the German term is Nullpunktenergie (without the s). Vacuum energy is the zero-point energy of all the fields in space, which in the Standard Model includes the electromagnetic field, other gauge fields, fermionic fields, and the Higgs field. It is the energy of the vacuum, which in quantum field theory is defined not as empty space but as the ground state of the fields. In cosmology, the vacuum energy is one possible explanation for the cosmological constant.[3] A related term is zero-point field, which is the lowest energy state of a particular field.[4] Contents [hide] 1 History 2 Relation to the uncertainty principle 3 Varieties 4 Experimental observations 5 Gravitation and cosmology 6 Utilization controversy 7 In popular culture 8 See also 9 Notes 10 Bibliography 11 External links History[edit] In 1900, Max Planck derived the formula for the energy of a single energy radiator, e.g., a vibrating atomic unit:[5] \epsilon = \frac{h\nu}{ e^{\frac{h\nu}{kT}}-1} where h is Planck's constant, \nu is the frequency, k is Boltzmann's constant, and T is the absolute temperature. Then in 1913, using this formula as a basis, Albert Einstein and Otto Stern published a paper 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 Nullpunktsenergie (German), later 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[1][2] \epsilon = \frac{h\nu}{ e^{\frac{h\nu}{kT}}-1} + \frac{h\nu}{2} According to this expression, an atomic system at absolute zero retains an energy of ½hν. Relation to the uncertainty principle[edit] Zero-point energy is fundamentally related to the Heisenberg uncertainty principle.[6] Roughly speaking, the uncertainty principle states that complementary variables (such as a particle's position and momentum, or a field's value and derivative at a point in space) cannot simultaneously be defined precisely by any given quantum state. In particular, there cannot be a state in which the system sits motionless at the bottom of its potential well, for then its position and momentum would both be completely determined to arbitrarily great precision. Therefore, the lowest-energy state (the ground state) of the system must have a distribution in position and momentum that satisfies the uncertainty principle, which implies its energy must be greater than the minimum of the potential well.