going below absolute zero
The coldest temperature that can conceivably be reached is absolute zero, or zero degrees on the Kelvin scale. Negative temperatures on the Kelvin scale are said to be impossible, however nature seems to have a way to reach down below absolute zero. Once it gets there though is when the really interesting stuff happens.....temperature
Temperature is understood by most people to be a way of measuring hotness or coldness. There are three scales to determine temperature: Fahrenheit, Celsius, and Kelvin. Fahrenheit and Celsius are relative scales which means they define temperatures based on reference points. These reference points just happen to be the boiling and freezing points of water. The Kelvin scale, however, is based on Charles's law for gases. Charles's law for gases states that the volume of gases is proportional to temperature. When a graph is plotted of volumes of gases versus temperature, no volume is ever negative. This implies that no temperature (on the Kelvin scale) is ever negative. This can be said due to the proportionality of the temperature-volume relationship and that no volume of gas in reality can ever be negative.The kinetic molecular theory states that the kinetic energy of gases depends on their temperature. With lower temperatures, gases have less energies, therefore, having slower motion. However, all energy can never be removed from a system which is another reason why it is thought that temperatures can never be zero on the Kelvin scale.
molecular energy distribution
Every molecule possesses some amount of energy. Imagine a system where the molecules have only two choices for energy states: excited or ground. An example that we will also use later is a magnetic field. In a magnetic field the molecules align with the field so that they are in the ground state, or the molecules align opposite the field in an excited state. Those molecules that align in opposition of the magnetic field require more energy to exist in this higher energy state. The Boltzmann distribution law is a law that is used to determine the energy levels of molecules. It also determines the number of molecules in each energy state. The equation derived from this law says that as temperature increases there is more energy available which, in turn, increases the ratio of excited state molecules to ground state molecules. According to this equation, as the temperature gets closer to absolute zero, the ratio also approaches zero. This is because, at absolute zero, there is no energy to distribute to the molecules. This results in all of the molecules going to the ground state. Alternatively, as the temperature goes to infinity, the ratio approaches one. The molecules are distributed equally to the excited and ground states.population inversions
However, there are conditions when there is enough energy absorption that the excited state molecules outnumber the ground state molecules. This is where we recall our example of the magnetic field. Suppose there existed ten molecules in a system. Eight of them existed at the ground state and two were in the excited state. If the magnetic field was suddenly switched, for an instant, the eight ground state molecules were in the excited state and the two excited state molecules were in the ground state. This is called a population inversion.A formula derived from the formula that earlier determined the ratio of ground to excited state molecules can calculate the temperature of a system based on the populations of the energy levels. It says that if the ratio exceeds one (equilibrium of excited state molecules and ground state molecules), then the absolute temperature is negative. A temperature below absolute zero!
Manipulation of an equation that determines total energy for a molecular system reveals that the molecules below absolute zero have much more energy the those above absolute zero. This means, if you recall the laws from above, that the molecules below absolute zero are actually hotter than those above absolute zero!
reality of negative kelvin
Upon first guess, most people would think that to get below absolute zero, you would need to go from positive to zero then down to negative. However, paradoxically, negative absolute temperatures can only be obtained through infinite temperatures (as the temperature goes to infinity, the ratio gets closer to one, and by inverting the population, the ratio goes above one). Population inversions really do happen in everyday life. They are the basis for lasers, in which the numbers of excited molecules outway those in the ground state. Therefore, lasers share properties with molecules below absolute zero. The concept of negative absolute temperatures has been verified using the magnetic field example.Ordinary means will not measure negative absolute temperatures. It takes something abstract to measure something abstract. That abstract measuring tool is mathematics. Mathematics takes the world from these abstract viewpoints and uncovers all the hidden mysteries and meanings the universe has to offer.