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Zero point energy is an application in quantum mechanics that explains the energies for the strong, weak, and electromagnetic interactions as seen at zero temperature. It is almost always applied to electromagnetic interactions. This article will deal with those same electromagnetic energies. Albert Einstein and Otto Stern first offered this theory, based on the work of Max Planck, in 1913 to explain. Einstein first thought that this theory would explain his belief in a stationary universe(cosmological constant), but abandoned that idea after Hubble redshift was proven.
Zero point energy is often synonymous with the background energy in space even when there is a lack of matter(vacuum energy or quantum vacuum zero point energy). Often zero point energy relates to the phenomenon in quantum physics of an object having a ground state that is not zero. The energy of a system is relative, and is defined only in relation to some given state(reference state). Typically, you might associate a motionless system with zero energy, but that is purely arbitrary. In quantum physics, it is natural to associate the energy with the expectation value of a certain operator, thus becoming the Hamiltonian of the system. For almost all quantum-mechanical systems, the lowest possible expectation value of this operator, which would be the zero-point energy, is not zero. Adding any constant to the Hamiltonian will give an equivalent description of the physical system, but can alter the zero-point energy. Regardless of what constant is added to the Hamiltonian, the minimum momentum is always the same non-zero value.
One of the best known ways to demonstrate zero point energy is the use of a quantum harmonic oscillator. 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. Based on that, you can picture electromagnetic radiation 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 each wave has a specific direction, frequency and polarization state. Each wave represents a propagating mode of the electromagnetic field. Each wave is equivalent to a quantum harmonic oscillator.
Now, take all of those waves or modes and combine them. 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. Using this reference point, quantum physics predicts that all of space must be filled with electromagnetic zero-point fluctuations that are 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, it is argued that the zero point fluctuations must cease at a corresponding Planck frequency. This thinking has led to the belief that the zero point energy of space should be 110 times greater than the energy at the center of the Sun.
There are two good articles about zero point energy. One is here and the other is here. On Universe Today we have a great article about the relationship between dark energy and zero point energy. Astronomy Cast offers a good episode about the large scale structure of the Universe.