# Zero Point Energy

Quantum mechanics predicts the existence of what are usually called ''zero-point'' energies for the strong, the weak and the electromagnetic interactions, where ''zero-point'' refers to the energy of the system at temperature T=0, or the lowest quantized energy level of a quantum mechanical system. Although the term ''zero-point energy'' applies to all three of these interactions in nature, customarily (and hereafter in this article) it is used in reference only to the electromagnetic case.

In conventional quantum physics, the origin of zero-point energy is the Heisenberg uncertainty principle, which states that, for a moving particle such as an electron, the more precisely one measures the position, the less exact the best possible measurement of its momentum (mass times velocity), and vice versa. The least possible uncertainty of position times momentum is specified by Planck's constant, h. A parallel uncertainty exists between measurements involving time and energy (and other so-called conjugate variables in quantum mechanics). This minimum uncertainty is not due to any correctable flaws in measurement, but rather reflects an intrinsic quantum fuzziness in the very nature of energy and matter springing from the wave nature of the various quantum fields. This leads to the concept of zero-point energy.

Zero-point energy is the energy that remains when all other energy is removed from a system. This behaviour is demonstrated by, for example, liquid helium. As the temperature is lowered to absolute zero, helium remains a liquid, rather than freezing to a solid, owing to the irremovable zero-point energy of its atomic motions. (Increasing the pressure to 25 atmospheres will cause helium to freeze.)

A harmonic oscillator is a useful conceptual tool in physics. Classically a harmonic oscillator, such as a mass on a spring, can always be brought to rest. However a quantum harmonic oscillator does not permit this. A residual motion will always remain due to the requirements of the Heisenberg uncertainty principle, resulting in a zero-point energy, equal to 1/2 hf, where f is the oscillation frequency.

Electromagnetic radiation can be pictured as waves flowing through space at the speed of light. The waves are not waves of anything substantive, but are ripples in a state of a theoretically defined field. However these waves do carry energy (and momentum), and each wave has a specific direction, frequency and polarization state. Each wave represents a ''propagating mode of the electromagnetic field.''

Each mode is equivalent to a harmonic oscillator and is thus subject to the Heisenberg uncertainty principle. From this analogy, every mode of the field must have 1/2 hf as its average minimum energy. That is a tiny amount of energy in each mode, but the number of modes is enormous, and indeed increases per unit frequency interval as the square of the frequency. The spectral energy density is determined by the density of modes times the energy per mode and thus increases as the cube of the frequency per unit frequency per unit volume. The product of the tiny energy per mode times the huge spatial density of modes yields a very high theoretical zero-point energy density per cubic centimeter.

From this line of reasoning, quantum physics predicts that all of space must be filled with electromagnetic zero-point fluctuations (also called the zero-point field) creating a universal sea of zero-point energy. The density of this energy depends critically on where in frequency the zero-point fluctuations cease. Since space itself is thought to break up into a kind of quantum foam at a tiny distance scale called the Planck scale (10^{-33} cm), it is argued that the zero point fluctuations must cease at a corresponding Planck frequency (10^{43} Hz). If that is the case, the zero-point energy density would be 110 orders of magnitude greater than the radiant energy at the center of the Sun.

How could such an enormous energy not be wildly evident? There is one major difference between zero-point electromagnetic radiation and ordinary electromagnetic radiation. Turning again to the Heisenberg uncertainty principle one finds that the lifetime of a given zero-point photon, viewed as a wave, corresponds to an average distance traveled of only a fraction of its wavelength. Such a wave ''fragment'' is somewhat different than an ordinary plane wave and it is difficult to know how to interpret this.

On the other hand, zero-point energy appears to have been directly measured as current noise in a resistively shunted Josephson junction by Koch, van Harlingen and Clarke up to a frequency of about 0.6 Tz (see Phys. Rev. B Abstract).