question: Why can a particle not reach absolute zero?
comment: Temperature is a measure of the heat of a substance. Heat is the vibration of particles. For a particle to reach absolute zero, it must stop moving, utterly stop. To be able to reduce a particle's vibration, the vibrations have to be moved somewhere else, like to other particles (like how heat spreads through a metal, each particle knocking the one next to it and passing the energy along). However, each collision used to pass energy along cannot possibly take ALL the energy away, always some remains. To get as close to absolute zero as we have, techniques such as using lasers to reduce the vibration have been used, but lasers themselves inherently are made of energy, and will cause vibrations. Thus far, we do not have a way of removing the last residual vibrations.
passages: On 3 January 2013, physicists announced that they had created a quantum gas made up of potassium atoms with a negative temperature in motional degrees of freedom for the first time.
  
  Section::::History.
   Section::::Very low temperatures.
  
  The average temperature of the universe today is approximately , based on measurements of cosmic microwave background radiation.
  
  Absolute zero cannot be achieved, although it is possible to reach temperatures close to it through the use of cryocoolers, dilution refrigerators, and nuclear adiabatic demagnetization. The use of laser cooling has produced temperatures less than a billionth of a kelvin. At very low temperatures in the vicinity of absolute zero, matter exhibits many unusual properties, including superconductivity, superfluidity, and Bose–Einstein condensation. To study such phenomena, scientists have worked to obtain even lower temperatures.
   Section::::Relation with Bose–Einstein condensate.
  
  A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near absolute zero. Under such conditions, a large fraction of the bosons occupy the lowest quantum state of the external potential, at which point quantum effects become apparent on a macroscopic scale.
   Section::::Experimental observations.:Fine structure constant.
  
  Taking (Planck's constant divided by ), (the speed of light), and (the electromagnetic coupling constant i.e. a measure of the strength of the electromagnetic force (where is the absolute value of the electronic charge and formula_61 is the vacuum permittivity)) we can form a dimensionless quantity called the fine-structure constant:
   This state of matter was first predicted by Satyendra Nath Bose and Albert Einstein in 1924–25. Bose first sent a paper to Einstein on the quantum statistics of light quanta (now called photons). Einstein was impressed, translated the paper from English to German and submitted it for Bose to the "Zeitschrift für Physik", which published it. Einstein then extended Bose's ideas to material particles (or matter) in two other papers.
   Now, if the initial state is very localized in position, it will be very spread out in momentum, and thus we expect that the wave function will rapidly spread out, and the connection with the classical trajectories will be lost. When Planck's constant is small, however, it is possible to have a state that is well localized in "both" position and momentum. The small uncertainty in momentum ensures that the particle "remains" well localized in position for a long time, so that expected position and momentum continue to closely track the classical trajectories for a long time.
   Section::::History.:Limit to the "degree of cold".
   Section::::Quantum field theory.:The quantum electrodynamic vacuum.:Necessity of the vacuum field in QED.
  
  The vacuum state of the "free" electromagnetic field (that with no sources) is defined as the ground state in which for all modes . The vacuum state, like all stationary states of the field, is an eigenstate of the Hamiltonian but not the electric and magnetic field operators. In the vacuum state, therefore, the electric and magnetic fields do not have definite values. We can imagine them to be fluctuating about their mean value of zero.
   It is commonly thought of as the lowest temperature possible, but it is not the lowest "enthalpy" state possible, because all real substances begin to depart from the ideal gas when cooled as they approach the change of state to liquid, and then to solid; and the sum of the enthalpy of vaporization (gas to liquid) and enthalpy of fusion (liquid to solid) exceeds the ideal gas's change in enthalpy to absolute zero. In the quantum-mechanical description, matter (solid) at absolute zero is in its ground state, the point of lowest internal energy.
   Section::::Overview.
  
  In classical mechanics all particles can be thought of as having some energy made up of their potential energy and kinetic energy. Temperature, for example, arises from the intensity of random particle motion caused by kinetic energy (known as brownian motion). As temperature is reduced to absolute zero, it might be thought that all motion ceases and particles come completely to rest. In fact, however, kinetic energy is retained by particles even at the lowest possible temperature. The random motion corresponding to this zero-point energy never vanishes as a consequence of the uncertainty principle of quantum mechanics.
   Section::::The uncertainty principle.
   At a quantum critical point, the critical fluctuations are quantum mechanical in nature, exhibiting scale invariance in both space and in time. Unlike classical critical points, where the critical fluctuations are limited to a narrow region around the phase transition, the influence of a quantum critical point is felt over a wide range of temperatures above the quantum critical point, so the effect of quantum criticality is felt without ever reaching absolute zero. Quantum criticality was first observed in ferroelectrics, in which the ferroelectric transition temperature is suppressed to zero.
   Section::::History.:Quantum field theory and beyond.
   Note that whereas absolute zero is the point of zero thermodynamic temperature and is also the point at which the particle constituents of matter have minimal motion, absolute zero is not necessarily the point at which a substance contains zero thermal energy; one must be very precise with what one means by "internal energy". Often, all the phase changes that "can" occur in a substance, "will" have occurred by the time it reaches absolute zero. However, this is not always the case. Notably, "T"=0 helium remains liquid at room pressure and must be under a pressure of at least to crystallize. This is because helium's heat of fusion (the energy required to melt helium ice) is so low (only 21 joules per mole) that the motion-inducing effect of zero-point energy is sufficient to prevent it from freezing at lower pressures. Only if under at least of pressure will this latent thermal energy be liberated as helium freezes while approaching absolute zero. A further complication is that many solids change their crystal structure to more compact arrangements at extremely high pressures (up to millions of bars, or hundreds of gigapascals). These are known as "solid-solid phase transitions" wherein latent heat is liberated as a crystal lattice changes to a more thermodynamically favorable, compact one.
   Perfect crystals never occur in practice; imperfections, and even entire amorphous material inclusions, can and do get "frozen in" at low temperatures, so transitions to more stable states do not occur.
   Consider now a gas of particles, which can be in different momentum states labeled formula_23. If the number of particles is less than the number of thermally accessible states, for high temperatures and low densities, the particles will all be in different states. In this limit, the gas is classical. As the density increases or the temperature decreases, the number of accessible states per particle becomes smaller, and at some point, more particles will be forced into a single state than the maximum allowed for that state by statistical weighting. From this point on, any extra particle added will go into the ground state.
   quantum mechanical phenomenon. Some systems, however (see the examples below), have a maximum amount of energy that they can hold, and as they approach that maximum energy their entropy actually begins to decrease.
  
  Section::::Definition of temperature.
  
  The definition of thermodynamic temperature as a function of the change in the system's entropy under reversible heat transfer :
  
  Entropy being a state function, the integral of over any cyclical process is zero. For a system in which the entropy is purely a function of the system's energy , the temperature can be defined as:
   Section::::"Absolute Zero".
   On the other hand, in quantizing gravity there are, in perturbation theory, "infinitely many independent parameters" (counterterm coefficients) needed to define the theory. For a given choice of those parameters, one could make sense of the theory, but since it is impossible to conduct infinite experiments to fix the values of every parameter, it has been argued that one does not, in perturbation theory, have a meaningful physical theory. At low energies, the logic of the renormalization group tells us that, despite the unknown choices of these infinitely many parameters, quantum gravity will reduce to the usual Einstein theory of general relativity. On the other hand, if we could probe very high energies where quantum effects take over, then "every one" of the infinitely many unknown parameters would begin to matter, and we could make no predictions at all.
   Section::::History.:The race to absolute zero.
   The problem with this continuum approximation for a Bose gas is that the ground state has been effectively ignored, giving a degeneracy of zero for zero energy. This inaccuracy becomes serious when dealing with the Bose–Einstein condensate and will be dealt with in the next section.
  
  Section::::Inclusion of the ground state.
  
  The total number of particles is found from the grand potential by
   Values of this order for the absolute zero were not, however, universally accepted about this period. Pierre-Simon Laplace and Antoine Lavoisier, in their 1780 treatise on heat, arrived at values ranging from 1,500 to 3,000 below the freezing-point of water, and thought that in any case it must be at least 600 below. John Dalton in his "Chemical Philosophy" gave ten calculations of this value, and finally adopted −3000 °C as the natural zero of temperature.
  
  Section::::History.:Lord Kelvin's work.
   Considering only certain degrees of freedom in matter, such as nuclear spins, systems with a negative temperature can be produced. They occur because equipartitioning is too slow to allow communication between the degrees of freedom where thermal energy is stored, such as the vibrational, rotational, and nuclear spin states of molecules. These systems are familiar from lasers. For these, theory predicts a mathematical singularity in temperature. When a spin system is excited with electromagnetic radiation and undergoes population inversion into an excited state, quantum physics formally assumes that its temperature function goes through a singularity. The spin temperature tends to positive infinity, before discontinuously switching to negative infinity. However, this applies only to specific degrees of freedom (the spin temperature in this case) in the system, while others would have normal temperature dependency. Thus, this singularity cannot be observed as ordinary sensible heat. If equipartitioning is possible, the system undergoes relaxation into a thermally uniform state with release of a finite quantity of heat. Before a physical infinite temperature could be reached, realistic ordinary matter would undergo phase transitions, such as evaporation, and never actually reach the infinite temperature.
   This means that at very cold temperatures, the change in energy with respect to beta, or equivalently the change in energy with respect to temperature, is also exponentially small. The change in energy with respect to temperature is the specific heat, so the specific heat is exponentially small at low temperatures, going to zero like
   A more thorough treatment, showing that the energy of the ground state actually saturates this bound and is exactly , requires solving for the ground state of the system.
  
  Section::::Atomic physics.
  