# Zero-Point Energy

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## zero-point energy

[′zir·ō ¦pȯint ′en·ər·jē]
(statistical mechanics)
The kinetic energy retained by the molecules of a substance at a temperature of absolute zero.

## Zero-Point Energy

in a quantum-mechanical system, the difference between the ground-state energy and the energy that corresponds to the minimum potential energy. Zero-point energy is a consequence of the uncertainty principle (seeUNCERTAINTY PRINCIPLE).

In classical mechanics it was assumed that a particle can exist in a state of minimum potential energy and have zero kinetic energy. In this case the particle is at stable equilibrium and has a minimum energy equal to the potential energy at the equilibrium point. In quantum mechanics the uncertainty principle states that the range of values Δx for the coordinate x of a particle is related to the range of values ΔP for the particle’s momentum P by the expression ΔPΔx ∼ ħ, where ħ is Planck’s constant. As Δ x → 0, the localization of the particle near the potential energy minimum gives a large value for the particle’s mean kinetic energy, since the range of values of the momentum is large, as implied by the expression ΔP∼ħΔx. On the other hand, when Δx ≠ 0, that is, when the degree of the particle’s localization is reduced, the mean potential energy increases because the particle spends considerable time in an area in which the potential energy exceeds the minimum value the ground-state energy of a quantum-mechanical system corresponds to the lowest energy that is permitted by the uncertainty principle.

Zero-point energy is a general property of all coupled systems of microparticles. It is not possible to convert a system into a state that has an energy lower than zero-point energy without changing the system’s structure.

S. S. GERSHTEIN

References in periodicals archive ?
0] is the infinite zero point energy contribution, and the finite contribution [u.
To obtain a finite total zero point energy, it has sometimes been suggested that the integral (6) should be truncated at a cut-off frequency corresponding either to the Planck length or to a high energy of 100 GeV.
This force is due to the low-frequency part of the zero point energy pressure, because only the small high-frequency modes are allowed to squeeze in between the plates.
In this factor, however, the zero point energy cancels and disappears when expression (1) is substituted into the deductions [15];
For the zero point energy part k = 0, however, conventional theory yields [[bar.
However, for the zero point energy part of the same equation, the analogous situation is not fully determined because there is no corresponding and independent parameter which determines the average photon energy;
In the limiting case T = 0 of a pure zero point energy photon gas, one would thus have to study an ensemble of continuous states, to search for the most probable distribution of frequency among the oscillators at a given total and finite energy per unit volume.
With these points in mind, it is here concluded that the zero point energy requires a separate statistical treatment.
With this proposal the revised form of the density (4) of the zero point energy becomes
In a gas cloud of photons of zero point energy, there is an antigravity force due to the photon gas pressure gradient, and a gravitation force due to the intrinsic mass of the same photons as determined by the total energy according to Einstein's mass-energy relation.

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