Absolute zero is a fundamental lower bound on the temperature of any macroscopic system. It is approximately -273.15 degrees Celsius. It is unachievable in practice but it exists as a limit for real physical phenomena, and it was inferred by extrapolation from kinetic theory, and from other considerations in theoretical physics. One would like to define it as the temperature at which all motion ceases, but even at absolute zero some motion remains due to the requirements of quantum mechanics. Alternate definitions are that absolute zero is the temperature at which no further energy can be extracted from a physical body, or the temperature at which the entropies of perfect crystals vanish, or the temperature at which the entropy change of an adiabatic process vanishes.
A state of absolute zero was first proposed by Guillaume Amontons in 1702 who was investigating the relationship between pressure and temperature in gases. He lacked accurate and precise thermometers so his results were only semi-quantitative, but he established that the pressure of a gas increases by roughly one-third between "cold" temperatures and the boiling point of water. His work led him to speculate that a sufficient reduction in temperature would lead to the disappearance of pressure. The problem is that all real gases liquefy during the approach to absolute zero.
In 1848, William Thomson, 1st Baron Kelvin proposed an absolute thermodynamic temperature scale in which equal reduction in measured temperature gave rise to equal reduction in the heat of a body. This freed the concept from the constraints of the gas laws and established absolute zero as the temperature at which no further heat could be removed from a body. Absolute zero has never been reached, and it appears it never will be. It may be asymptotically approached like the speed of light, but never attained.
Kinetic theory and motion
According to kinetic theory, there should be no movement of individual molecules at absolute zero, so any material at this temperature would be solid. In a monatomic gas, most of the energy is in the form of translational motion, and the temperature can be measured in terms of the distribution of this motion, with slower speeds corresponding to lower temperatures, perhaps even down to absolute zero. But this is contrary to experimental evidence, and it is predicted that helium will never solidify, no matter how much it is cooled or compressed.
Because of quantum-mechanical effects, the speed at absolute zero is larger than zero and depends, along with the energy, on the volume within which a particle is confined. At absolute zero, the molecules and atoms in a system are all in their ground state, the state of lowest possible energy, and a system has the least amount of kinetic energy allowed by the laws of physics. But the lowest possible zero-point energy for a confined particle in a box is not zero. Rather than being fixed and non-moving, the equation for the energy levels shows that no matter how low the temperature gets, even when the quantum number takes its minimum value of one, a particle still has some translational kinetic energy and motion. This is a reflection of Heisenberg's uncertainty principle, which states that the position and the momentum of a particle cannot both be known precisely at any given time.
Similarly, using the harmonic approximation for the vibrations of a diatomic molecule, the quantum harmonic oscillator yields a positive zero-point energy even when the vibrational quantum number takes its minimum value of zero. For polyatomic molecules, and for bodies such as crystals, whose normal mode motions can not be assigned to individual atoms or chemical bonds, the lowest-energy state is that of the system as a whole.
Classically, the absolute temperature T of a system of molecules at thermodynamic equilibrium assigns an average of 1/2 kT to each quadratic kinetic and/or potential energy.