WIKI postulates, followed (in later posts on FB timeline) by introductory exploration to real-shared-intrasensorial-world Mequanizations (aka my take): 1) STATE VECTOR: In quantum physics, quantum state refers to the state of a quantum system. A quantum state is given as a VECTOR in a Hilbert space, called the state vector. 2) UNCERTAINTY PRINCIPLE: 1927, Heisenberg : Quantum mechanics shows that certain pairs of physical properties, like position and speed(aka position and momentum), cannot both be known to arbitrary precision: the more precisely one property is known, the less precisely the other can be known. WAVE FUNCTION COLLAPSE A wave function or WAVEFUNCTION (aka STATE FUNCTION) in quantum mechanics describes the quantum STATE of a system of one or more particles, and contains *all the information about the system considered in isolation*. Quantities associated with measurements, such as the average momentum of a particle, are *derived from the wavefunction by mathematical operations that describe* its *interaction with observational devices*. EIGEN- PREFIX refers to a ghostly concept known as INHERENCE (see below) In quantum mechanics, wave function COLLAPSE is the phenomenon in which a wave function(containing *all the information about the system considered in isolation*)—INITIALLY in a superposition of *several eigenstates*—*appears* to REDUCE to a *single* eigenstate (by observation). EIGENSTATE: The word eigenstate is derived from the German/Dutch word eigen, meaning inherent or characteristic. An eigenstate is the measured state of some object possessing quantifiable characteristics such as position, momentum, etc. The state being measured and described must be observable (i.e. something such as position or momentum that can be experimentally measured either directly or indirectly), and must have a *definite value*, called an EIGENVALUE(intuitive). EIGENVALUE : the result through observational device compromise ( measured either directly or indirectly) of ideal accuracy, of *a* set-valued , observationally-biased MEASUREMENT of a theoretically non-biased, yet observable EIGENSTATE.(my take) . EIGENVALUE(LINEAR ALGEBRA): (Eigenvalue also refers to a mathematical property of square matrices, a usage pioneered by the mathematician David Hilbert in 1904. Such matrices are called self-adjoint operators, and *represent observables in quantum mechanics*) EIGENVECTOR: An eigenvector of a square matrix A is a non-zero vector v that, when the matrix multiplies v, yields a constant multiple of v, the latter multiplier being commonly denoted by lambda (aka EIGENVALUE ) . In most treatments of quantum mechanics, the WAVEFUNCTION is complex-valued. In one important interpretation of quantum mechanics called the Copenhagen interpretation, the modulus squared of the wavefunction, |ψ|2, is a real number interpreted as the probability density of finding a particle in a given place at a given time, if the particles position is to be measured. Since the wavefunction is complex valued, only its *relative* phase and *relative* magnitude can be measured. It does not *directly tell anything* about the magnitudes or directions of *measurable observables*, one *has* to apply quantum operators to the wave function ψ and *find the EIGENVALUES which correspond to SETS OF POSSIBLE RESULTS of measurement*. 4) The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse
Posted on: Mon, 06 Oct 2014 23:57:00 +0000
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