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In mathematics and physics, the plate trick, also known as Dirac's string trick (after Paul Dirac, who introduced and popularized it), [1] [2] the belt trick, or the Balinese cup trick (it appears in the Balinese candle dance), is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, while ...
As the coffee cup is rotated it carries the spinor, and its flag, along the strip. If the cup is rotated through 360°, the spinor returns to the initial position, but the flag is now underneath the strip, pointing outward. It takes another 360° rotation in order to return the flag to its original orientation.
In particular, if a beam of spin-oriented spin- 1 / 2 particles is split, and just one of the beams is rotated about the axis of its direction of motion and then recombined with the original beam, different interference effects are observed depending on the angle of rotation. In the case of rotation by 360°, cancellation effects are ...
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. [1] [2]: 183–184 Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
corresponds to a vector rotation through an angle θ about an axis defined by a unit vector v = a 1 σ 1 + a 2 σ 2 + a 3 σ 3. As a special case, it is easy to see that, if v = σ 3, this reproduces the σ 1 σ 2 rotation considered in the previous section; and that such rotation leaves the coefficients of vectors in the σ 3 direction ...
In three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which always exists by virtue of the Euler's rotation theorem; the magnitude specifies the rotation in radians about that axis (using the right-hand rule to determine direction).
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An interpretation that avoids this conflict is to say that the rotating spheres experiment does not really define rotation relative to anything in particular (for example, absolute space or fixed stars); rather the experiment is an operational definition of what is meant by the motion called absolute rotation. [2]