## Table of Contents

- DONE [B] Deutch Quantum theory as universal physical theory.pdf physicsreadquantum
- physicsreadquantum
- page 7, kinematically independent subsystems physicsreadquantum
- so, state is constant, and only changed during measurements?? collapse interpretation physicsreadquantum
- TODO but MW is not without its own problems namely the problem of prefered basis and the problem of probability. physicsreadquantum
- Everet formalism physicsreadquantum
- Right; I guess I have to read more on many world problematic. Maybe I shouldn't care at all and study something more practical like visualizing, simulations and solving? physicsreadquantum

## ¶DONE [B] Deutch Quantum theory as universal physical theory.pdf physicsreadquantum

### ¶ physicsreadquantum

When the quantum system has aninfinite number of degrees of freedom (i.e., in field theory) the operators ~bg may have to be distributions (see Gel'fand and Shilov, 1968), the Hilbert space ~ may have to be "rigged" (Bohm, 1980), the action may have to be renormalized, and so forth. We shall avoid all these issues by assuming not merely that the world has a finite number of degrees of freedom, but that its state space is finite dimensional.

### ¶page 7, kinematically independent subsystems physicsreadquantum

sufficient condition is that the Hamiltonian H is a sum of H_{1} + H_{2}, confined to the subsystems

#### ¶weaker condition, 'dynamical independence' , necessary and sufficient to ensure that a kinematically independent state remains so: physicsquantumread

(H - (H1 + H2)) psi = 0 for some H1 and H2

errr ????? wtf H1 and H2 are confined to subsystems?

Stated in words, kinematically independent subsystems are also dynamically independent if the state is an eigenstate of the Hamiltonian modulo terms confined to the subsystems.

### ¶so, state is constant, and only changed during measurements?? collapse interpretation physicsreadquantum

One widespread solution to this problem involves a fundamental change

in the quantum formalism presented in Section 2. The idea is that the state

10), which according to the formalism of Section 2 never changes, is in fact

subject to an intermittent, discontinuous motion. At certain instants ti, at

which measurements are said to have been "completed," 10) changes into

a randomly chosen simultaneous eigenstate of the observable being

measured and the observable doing the measuring. The probability of the

eigenstate lal, t~; a2, t~) being chosen is

I(O~-,la,, t~; a2, t~)l 2

where we have denoted by 10i) the state of the world between the ith and

( i + 1)th completion of a measurement.

no complete formulation has been achieved; difficult to find a criterion for specifying the instants at which measurement is complete

### ¶TODO but MW is not without its own problems namely the problem of prefered basis and the problem of probability. physicsreadquantum

### ¶Everet formalism physicsreadquantum

#### ¶x physicsquantumread

Instead, he proposes that the system and

apparatus observables are in general multivalued, possessing all the eigen-

values whose eigenstates appear in the representation (27).

#### ¶x physicsquantumread

It gives a picture of a world (i.e., everything that exists) consisting of many

coexisting universes (i.e., maximal sets observables with values) evolving

approximately independently on large scales, but in intimate interaction,

through interference effects, on small scales.

eh?