Based on these two insights, Bohr argued that a quantum theory can never explain classical physics. Some physicists argue that we just haven't worked hard enough, and that we do fundamentally live in a quantum world , and that we can reproduce classical physics from purely quantum rules.
One of these phrases is obvious click-bait, the other is demonstrably false. The Higgs boson is the fundamental particle associated with the Higgs field , a field that gives mass to other fundamental particles such as electrons and quarks. Not all fundamental particles have mass.
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Your Privacy This site uses cookies to assist with navigation, analyse your use of our services, collect data for ads personalisation and provide content from third parties. Ok Cookie options. In the one dimensional model, the atoms were restricted to moving along the line, so all the phonons corresponded to longitudinal waves. In three dimensions, vibration is not restricted to the direction of propagation, and can also occur in the perpendicular plane, like transverse waves.
This gives rise to the additional normal coordinates, which, as the form of the Hamiltonian indicates, we may view as independent species of phonons. This is known as a dispersion relation. At low values of k i. As a result, packets of phonons with different but long wavelengths can propagate for large distances across the lattice without breaking apart.
This is the reason that sound propagates through solids without significant distortion. This behavior fails at large values of k , i. It should be noted that the physics of sound in air is different from the physics of sound in solids, although both are density waves. This is because sound waves in air propagate in a gas of randomly moving molecules rather than a regular crystal lattice.
In real solids, there are two types of phonons: "acoustic" phonons and "optical" phonons. Longitudinal and transverse acoustic phonons are often abbreviated as LA and TA phonons, respectively. They are called "optical" because in ionic crystals like sodium chloride they are excited very easily by light in fact, infrared radiation.
This is because they correspond to a mode of vibration where positive and negative ions at adjacent lattice sites swing against each other, creating a time-varying electrical dipole moment. Optical phonons that interact in this way with light are called infrared active. Optical phonons which are Raman active can also interact indirectly with light, through Raman scattering. Optical phonons are often abbreviated as LO and TO phonons, for the longitudinal and transverse varieties respectively.
This is because k is only determined up to multiples of constant vectors, known as reciprocal lattice vectors. Physically, the reciprocal lattice vectors act as additional "chunks" of momentum which the lattice can impart to the phonon. Bloch electrons obey a similar set of restrictions. It is usually convenient to consider phonon wave vectors k which have the smallest magnitude k in their "family".
The set of all such wave vectors defines the first Brillouin zone. Additional Brillouin zones may be defined as copies of the first zone, shifted by some reciprocal lattice vector. A crystal lattice at zero temperature lies in its ground state , and contains no phonons. According to thermodynamics, when the lattice is held at a non-zero temperature its energy is not constant, but fluctuates randomly about some mean value.
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