Classical mechanics measuring vectors

As for classical systems, measurement of the properties of macroscopic quantum systems is subject to experimental error that exceeds the quantum-mechanical uncertainty. For two measurable quantities F and G the inequality is defined as AFAG >> (5F6G.The state vector of a completely closed system described by a time-independent Hamiltonian H, with eigenvalues En and eigenfunctions is represented by... 

A very remote analogy is conservation laws in classical and quantum physics. Description of quantum mechanics in terms of classical mechanics is not well defined, which happens because of commutativity of classical values and noncommutativity of their quantum analogs. We should regularize it and as a result part of classical symmetries may be realized in such a way that some conservation laws cannot be measured at all (e.g., conservation of the angular momentum as a vector). That example turns our attention to problem of observations. 

The static theory discussed in the previous section describes the equilibrium situation in chiral nematics very well - in general, theory and experiment are in good accord. The dynamic situation is less clear. On the molecular scale, the chiral nematic and nematic phases are identical the question then becomes, how does the macroscopic twist or helicity modify the vector stress tensor of the achiral nematic phase defined by the so-called [109] Leslie friction coefficients a -a T Experimentally, viscosity coefficients that are then related to the Leslie coefficients are measured in a way that depends specifically on the experiment being used to determine them. The starting point for discussion of dynamic properties is to use classical mechanics to describe the time dependencies of the director field n (r, t), the velocity field v (r, t), and their interdependency. Excellent reviews of this, for achiral nematics, are to be found in [59,109,... 

If the velocity U of an electron within the beam is constant outside the solenoid, the variation of the vector potential A as a function of time in the medium, and thus also in the solenoid, will induce a modification of the phase, as indicated by the equations written above. This will produce a modification of the boundary conditions on the boundary of the solenoid for the quantities a and b. We must also stress that the modification of the vector potential outside the solenoid is generated by either an external or an internal source feeding the solenoid. This can explain the existence of the Aharonov-Bohm effect for toroidal, permanent magnets. The interpretation of the Aharonov-Bohm effect is therefore classic, but the observation of this effect requires the principle of interference of quantum mechanics, which enables a phase effect to be measured. 

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