## Etymologies

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## Examples

• There remains to recover, e.g., the representation of “observables” by self-adjoint operators, and the dynamics (unitary evolution).

Puppet X: 1

• Each bounded simple random variable f gives rise to a bounded self-adjoint operator A =

Puppet X: 1

• It is not difficult to show that a self-adjoint operator P with spectrum contained in the two-point set {0,1} must be a projection; i.e.,

Puppet X: 1

• Studying the properties off these observations one sees that they satisfy the necessary axioms to be linear operators, and, in fact, self-adjoint operators.

Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask

• Pauli pointed out that a (self-adjoint) time operator is incompatible with a Hamiltonian spectrum bounded below.

String Theory is Losing the Public Debate

• The observable quantities are represented by self-adjoint operators B on the Hilbert space.

Collapse Theories

• If the non-intrinsic, state-dependent properties are identified with all the monadic or relational properties which can be expressed in terms of physical magnitudes associated with self-adjoint operators that can be defined for the particles, then it can be shown that two bosons or two fermions in a joint symmetric or anti-symmetric state respectively have the same monadic properties and the same relational properties one to another (French and Redhead 1988; see also Butterfield 1993).

Identity and Individuality in Quantum Theory

• This amounts to rejecting that for every self-adjoint operator, there is a well-defined observable.

The Kochen-Specker Theorem

• If we further assume that to every self-adjoint operator there corresponds a QM observable, then the principle can be formulated thus:

The Kochen-Specker Theorem

• The principle trades on the mathematical fact that for a self-adjoint operator A operating on a Hilbert space, and an arbitrary function f:

The Kochen-Specker Theorem