The Compton wavelength λ of a particle X is given by λ_X = h / m_Xc, where h is the Planck constant, m_X is the particle's mass and c is the speed of light. A particle generally behaves quantum mechanically when observed at distances shorter than its Compton wavelength. In particular, in the uncertainty relation for position and momentum, , when the position uncertainty Δx is less than the Compton wavelength, the momentum uncertainty Δp is greater than m_Xc. Since momentum carries energy, the uncertainty in energy is greater than m_Xc², which is enough energy to create another particle of type X. The Compton wavelength is therefore generally viewed as the cutoff below which quantum field theory, which can describe particle creation and annihilation, becomes important. Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ... Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ... Cherenkov effect in a swimming pool nuclear reactor. ... Fig. ... In quantum physics, the Heisenberg uncertainty principle, sometimes called the Heisenberg indeterminacy principle, expresses a limitation on accuracy of (nearly) simultaneous measurement of observables such as the position and the momentum of a particle. ... In physics, momentum is a physical quantity related to the velocity and mass of an object. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ...

The Compton length for one Planck mass is equal to the Planck length and is also equal to the Schwarzschild radius of one Planck mass. This is a simple case of dimensional analysis. The Planck mass is the natural unit of mass, denoted by mP. mP = (c / G)1/2 ≈ 2. ... The Planck length is the natural unit of length, denoted by . ... The Schwarzschild radius or gravitational radius is a characteristic radius associated with every mass. ... The Planck mass is the natural unit of mass, denoted by mP. mP = (c / G)1/2 ≈ 2. ... Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ...

Sources

• The Planck Length -- http://math.ucr.edu/home/baez/planck/node2.html
• http://www.physlink.com/Education/AskExperts/ae635.cfm