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. It can be thought of as the rough intrinsic quantum mechanical size of a particle. 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 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 iz 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. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ...

For fermions, the Compton wavelength sets the cross-section of interactions. For example, the cross-section for Thomson scattering of a photon from an electron is equal to , where α is the fine-structure constant and λ_e is the Compton wavelength of the electron divided by 2 pi, which is equal to meters. For gauge bosons, the Compton wavelength sets the effective range of the Yukawa interaction: since the photon is massless, electromagnetism has infinite range. Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. ... Thomson scattering is the scattering of electromagnetic radiation by a charged particle. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Bosons, named after Satyendra Nath Bose, are particles which form totally-symmetric composite quantum states. ... In particle physics, Yukawa interaction, named after Hideki Yukawa, is an interaction between a scalar field and a Dirac field of the type . The Yukawa interaction can be used to describe the strong nuclear force between nucleons (which are fermions), mediated by pions (which are scalar mesons). ... For the Science Fiction weapon, as seen in Star Trek, see Photon torpedo. ...

It can be contrasted with the de Broglie wavelength, which depends on the momentum of a particle and determines the cutoff between particle and wave behavior in quantum mechanics. The wavelength is the distance between repeating units of a wave pattern. ... Fig. ...

The Compton wavelength 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: in Planck units the Schwarzschild radius is equal to the mass, whereas the Compton wavelength is equal to the inverse of the mass. The Planck mass is the natural unit of mass, denoted by mP. mP = ≈ 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. ... 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. ... In physics, Planck units are physical units of measurement originally proposed by Max Planck. ...

References

1. The Planck Length
2. The Planck Length at Physlink.com