In physicsW, the zero-point energyW is the lowest possible energyW that a quantum mechanicalW physical system may possess and is the energy of the ground stateW of the system. The concept was first proposed by Albert EinsteinW and Otto SternW in 1913. All quantum mechanical systems have a zero point energy.

In quantum field theoryW, it is a synonym for the vacuum energyW, an amount of energy associated with the vacuumW of empty spaceW.

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,W which is the lowest energy state of a field;W i.e. its ground stateW, which is non-zero.

The purpose of this article is to explain the basic concept, and why it is considered by scientists to be impossible to extract the zero-point energy. In spite of this being widely accepted, and the reasons widely known, the concept is widely promoted - both for commercial gain, and from genuine belief.

For more details of the science, and for links for further study, see Wikipedia:Zero-point energy.

## 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 (physics)|operator, the Hamiltonian (quantum mechanics)|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.

## "Free energy" devices

As a scientific concept, the existence of zero point energy is not controversial although it may be debated. But perpetual motion machinesW and other power generating devices based on zero point energy are highly controversial, and rejected by mainstream scientists. Descriptions of practical zero point energy devices (or free energy devices) have thus far lacked cogency. Experimental demonstrations of zero point energy devices have thus far lacked credibility. For reasons such as these, claims to zero point energy devices and great prospects for zero point energy are deemed pseudoscienceW.

When a proposal breaks scientific laws, these are not laws that have to be "enforced" - it's a matter between the designer and reality (nature). The laws in question were not predefined by humans, but simply discovered long ago, and never found to be broken.

The discovery of zero point energy does not improve the world's prospects for perpetual motion machinesW. Much attention has been given to reputable science suggesting that zero point energy is infinite. But zero point energy is a minimum energy below which a thermodynamicW reaction can never take place, thus none of this energy can be withdrawn without altering the system to a different form in which the system has a lower zero point energy. The calculation that underlies the Casimir experiment, a calculation based on the formula predicting infinite vacuum energy, shows the zero point energy of a system consisting of a vacuum between two plates will decrease at a finite rate as the two plates are drawn together. The vacuum energies are predicted to be infinite, but the changes are predicted to be finite. Casimir combined the projected rate of change in zero point energy with the principle of conservation of energy to predict a force on the plates. The predicted force, which is very small and was experimentally measured to be within 5% of its predicted value, is finite. Even though the zero point energy might be infinite, there is no theoretical basis or practical evidence to suggest that infinite amounts of zero point energy are available for use, that zero point energy can be withdrawn for free, or that zero point energy can be used in violation of conservation of energy.

In principle, there remains the prospect of finding something that can be irreversibly altered or consumed to draw a net positive amount of energy through a zero point energy effect. Enthusiasm should be tempered by the realization that the Casimir effect produces tiny amounts of energy and those only in a non-renewable fashion.

# Discussion

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