Classical mechanics

In physics, classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the motions of bodies, and the forces that cause them. The other sub-field is quantum mechanics. Roughly speaking, classical mechanics was developed in the 400 years since the groundbreaking works of Brahe, Kepler, and Galileo, while quantum mechanics developed within the last 100 years, starting with similarly decisive discoveries by Planck, Einstein, and Bohr.

Limits of validity

The classical approximation to special relativity

Non-relativistic classical mechanics approximates the relativistic momentum rac{m_0 v}{ sqrt{1-v^2/c^2}} with m_0 v, so it is only valid when the velocity is much less than the speed of light.

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For example, the relativistic cyclotron frequency of a cyclotron, gyrotron, or high voltage magnetron is given by f=f_crac{m_0}{m_0+T/c^2}, where

Related Topics:
Cyclotron - Gyrotron - Magnetron

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f_c is the classical frequency of an electron (or other charged particle) with kinetic energy T and (rest) mass m_0 circling in a magnetic field.

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The (rest) mass of an electron is 511 KeV.

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So the frequency correction is 1% for a magnetic vacuum tube with a 5.11 KV. direct current accelerating voltage.

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The classical approximation to quantum mechanics

The ray approximation of classical mechanics breaks down when the de Broglie wave length is not much smaller than other dimensions of the system. For non-relativistic particles, this wave length is

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:lambda=rac{2pihbar}{p}

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where hbar is Plank's constant divided by 2pi and p is the momentum.

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Again, this happens with electrons before it happens with heavier particles. For example, the electrons used by Clinton Davisson and Lester Germer in 1927, accelerated by 54 volts, had a wave length of 0.167 nm, which was long enough to exhibit a single diffraction side lobe when reflecting from the face of a nickel crystal with atomic spacing of 0.215 nm.

Related Topics:
Electrons - Clinton Davisson - Lester Germer - Diffraction - Side lobe - Crystal

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With a larger vacuum chamber, it would seem relatively easy to increase the angular resolution from around a radian to a milliradian and see quantum diffraction from the periodic patterns of integrated circuit computer memory.

Related Topics:
Vacuum chamber - Angular resolution - Integrated circuit

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More practical examples of the failure of classical mechanics on an engineering scale are conduction by quantum_tunneling in tunnel diodes and very narrow transister gates in integrated circuits.

Related Topics:
Quantum_tunneling - Tunnel diode - Transister - Gate - Integrated circuit

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Classical mechanics is the same extreme high frequency approximation as geometric optics. It is more often accurate because it describes particles and bodies with rest mass. These have more momentum and therefore shorter De Broglie wave lengths than massless particles, such as light, with the same kinetic energies.

Related Topics:
High frequency approximation - Geometric optics - Rest mass

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