Quantum machine Quantum machine A quantum machine is a human-made device whose collective motion follows the laws of quantum mechanics. The idea that macroscopic objects may follow the laws of quantum mechanics dates back to the advent of quantum mechanics in the early 20th century. However, as highlighted by the Schrödinger's cat thought experiment, quantum effects are not readily observable in large-scale objects. Consequently, quantum states of motion have only been observed in special circumstances at extremely low temperatures. The fragility of quantum effects in macroscopic objects may arise from rapid quantum decoherence. Researchers created the first quantum machine in 2009, and
Symmetry in quantum mechanics There are rotational matrices for each spin quantum number. Evaluating the exponential for a given "z"-projection spin quantum number "s" gives a (2"s" + 1)-dimensional spin matrix. This can be used to define a spinor as a column vector of 2"s" + 1 components which transforms to a rotated coordinate system according to the spin matrix at a fixed point in space. For the simplest non-trivial case of "s" = 1/2, the spin operator is given by where the Pauli matrices in the standard representation are: The total angular momentum operator is the sum of the orbital and spin and