## Copenhagen (notes on others)

If one considers quantum theory as a theory of information flow, then viewing it as a theory of background independent information flow of bits relative to two or more systems is consistent.

Principles of Copenhagen interpretation with interpretation consistent with information theory:

1. A system is completely described by a wave function ψ, which represents an observer’s knowledge of the system. (Heisenberg)

(number in phase space is a co-ordinate relative to the observing system.)

2. The description of nature is essentially probabilistic. The probability of an event is related to the square of the amplitude of the wave function. (Max Born)

(the larger the wave function the more likely that the background noise will affect it)

3. Heisenberg’s uncertainty principle ensures that it is not possible to know the values of all of the properties of the system at the same time; those properties that are not known with precision must be described by probabilities.

(this is the same thing as saying that a measurement is relative not absolute)

4. (Complementary Principle) Matter exhibits a wave-particle duality. An experiment can show the particle-like properties of matter, or wave-like properties, but not both at the same time.(Niels Bohr)

(very diff to explain, for sure, without a better model of phase space - perhaps this is analogous to whether one is looking at nodes or connections between them).

5. Measuring devices are essentially classical devices, and measure classical properties such as position and momentum.

(huh? this seems meaningless)

6. The Correspondence Principle of Bohr and Heisenberg, saying that the quantum mechanical description of large systems should closely approximate to the classical description.

In wave function collapse unobserved eigenvalues are removed from further consideration.

“An adherent of the subjective view, that the wave function represents nothing but knowledge, would take an equally subjective view of “collapse”, as nothing more than an observer becoming informed about something that was previously ambiguous.”

“Wigner’s Friend - Wigner puts his friend in with the cat. The external observer believes the system is in the state (|dead\rangle + |alive\rangle)/\sqrt 2. His friend however is convinced that cat is alive. I.e. for him, the cat is in the state | alive > . How can Wigner and his friend see different wave functions?”

A. If no system can be truly isolated then there is some point where Wigner and Wigner’s friend have to agree the overall state for them to communicate with each other.