Will Pearson: "Scott Aaronson, is the spin of an electron a definite property? "
The fractional spin (1/2 spin) of QM is not. In nature there is (yes-arbitrarily) clock wise or counter clockwise. A ball or an electron can only spin in one direction in relation to a previously defined direction. Spin is dynamic, referring to direction of rotation or angular momentum - not orientation which is static.
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The law is referring to an isolated physical system. And if...
Then how can the law apply? Configuration space is not a physical system itself but a description and is represented by vectors defined by coordinates. The coordinates in this system are forward, back, and time.
Position and velocity are dynamic concepts-a movie. In order to exist, an object must be made of matter and must have location- as in a (static) photograph.
Vectors represent magnitude and direction along a number line, therefore I take it to mean that A and B are representing particles changing location along a one dimensional line in relation to time. Physical objects can not be represented by dynamic numbers (vectors...elevation, depth and breadth) but defined by the static dimensions of length, width and heighth and located by coordinates (longitude, latitude and altitude).
If we describe our configuration space as 2 particles in relation to each other and time (and with no set limits) then our space is unbounded (without borders, that is...open) and therefore not subject to the 2nd law of thermodynamics. Further, one dimensional particles that can only move forward and backward can not exist in a 3d world. Without relation to up/down and left/right, forward/back is meaningless.
From this it is pretty clear that 0d or 1d particles can not exist.