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I don't really know what quantum decoherence is, but I have heard that it is used to explain why macroscopic objects do not seemingly follow quantum dynamics. Could someone please give a simple explanation of what decoherence is and why it follows from it that macroscopic objects do not seemingly follow quantum dynamics.

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If you have some familiarity with quantum physics, read this: – SMeznaric Sep 10 '12 at 11:45
For a nice toy model, see – jjcale Sep 10 '12 at 22:04

In quantum dimensions, i.e. order of hbar, matter has a dual nature, particle and probability wave.I.e depending on the experiment one will find particle attributes or wave attributes.

An example of particle behavior is the photoelectric effect: a photon hits an electron which is ejected and leaves an ionisation track .

An example of the wave nature is the two slit experiment, where there is an interference pattern even if individual electrons go through one at a time.

Waves are characterized by an amplitude ( in the qm case a probability when squared) and a phase. The phase is the angle that a particle's wave function has as it is oscillating, phi in the paragraph of the link "amplitude and modulation". When one particle interacts with the wave function of another particle the phases between the two wave forms will define their interference and beats, both classically and quantum mechanically.

Phases are important for classical waves too. Coherence between waves means that the angles between them remain constant in time and space and thus coherent beats can appear and interference patterns. If the phases between waves are random no interference patterns can appear. That is what the term "decoherence" means, classically and quantum mechanically: the correlation of the angles/phases is lost.

When one has more than two particles, each with its wave description, it is easier to lose the coherence between waves than to keep it. Avogadro's number says that there are 6.02214X×10^23 molecules in a mole. Even though each molecule in the mole has its QM wave function and QM phase, statistically the number is so huge that unless special conditions are carefully imposed the QM phases between the particles are lost and the quantum mechanical behavior is obscured.

Under special conditions, superconductivity for example, or superfluidity, the quantum behavior of the phases is maintained and the QM phases kept so that there is coherence and one observes macroscopic quantum mechanical effects.

Crystals also fall under the special conditions where coherence is maintained and we macroscopically see the effects in the symmetries of the crystal.

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Fragments of the environment continually interact with quantum systems. Initially uncorrelated, they become entangled. This entanglement washes out interference of the quantum system.

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I wrote a paper (review) on arxiv on decoherence and decoherence in complex systems for those "Can we advance macroscopic quantum systems outside the framework of complex decoherence theory?" `

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