ising model political preference
This
reality,
which
is
described
jointly
by
the
dynamical
variables
and
the
state
vector,
is
not
the
reality
we
customarily
think
of,
but
is
a
reality
composed
of
many
worlds27
as
a
source
of
potential
splitting
to
come
in
the
development
of
time.
In order to understand what Everett was worried about, one must first understand how the standard collapse formulation of quantum mechanics works. The theory involves the following principles (von Neumann, 1955):
- Representation of States: The state of a physical system S is represented by an element of unit length in a Hilbert space (a vector space with an inner product).
- Representation of Observables: Every physical observable O is represented by a Hermitian operator O on the Hilbert space representing states, and every Hermitian operator on the Hilbert space corresponds to some observable.
- Eigenvalue-Eigenstate Link: A system S has a determinate value for observable O if and only if the state of S is an eigenstate of O. If it is, then one would with certainty get the corresponding eigenvalue as the result of measuring O of S.
- Dynamics: (a) If no measurement is made, then a system S evolves continuously according to the linear, deterministic dynamics, which depends only on the energy properties of the system. (b) If a measurement is made, then the system S instantaneously and randomly jumps to a state where it either determinately has or determinately does not have the property being measured. The probability of each possible post-measurement state is determined by the system's initial state. More specifically, the probability of ending up in a particular final state is equal to the norm squared of the projection of the initial state on the final state.
COSMOLOGICAL PARALLELS
http://people.biology.ufl.edu/ulan/pubs/Emergnce.pdf
The drive toward more definitive structures, if allowed to proceed uninterrupted,
would, as Popper (1990) intuited, lead to an evolutionary dead
end. No further changes would be possible. Physicists will recognize in
this dynamic their developing narrative for the evolution of physical matter
and laws (Chaisson 2001). After the Big Bang, subtle asymmetries led
to the self-selection of various enduring forms out of an initial homogeneous
substrate, and with them appeared certain regularities in their interactions.
Through progressive feedback, the forms and their interactions
grew quite precise and stable, culminating in matter with its accompanying
laws.
Phase Transition and Pattern
http://www.santafe.edu/media/workingpapers/04-09-028.pdf
Formation in a Model of
Collective Choice Dynamics
Sitabhra Sinha
S. Raghavendra
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