Samenvatting
We present the SCOP-formalism, an operational approach to quantum mechanics.
If a State--COntext--Property--System (SCOP) satisfies a specific set of
`quantum axioms', it fits in a quantum mechanical representation in Hilbert
space. We present a model in which the maximal change of state of the system
due to interaction with the measurement context is controlled by a parameter
$N$. In the case $N=2$ the system reduces to a model for the spin
measurements on a quantum spin-1/2 particle. In the limit $N\rightarrow
\infty $ the system is classical. For the intermediate cases it is
impossible to define an orthocomplementation on the set of properties.
Another interesting feature is that the probability of a state transition
also depends on the context which induces it. This contrasts sharply with
standard quantum mechanics for which Gleason's theorem states the uniqueness
of the state transition probability and independent of measurement context.
We show that if a SCOP satisfies a Gleason-like condition, namely that all
state transition probabilities are independent of which measurement context
induces the change of state, then the lattice of properties is
orthocomplemented.
If a State--COntext--Property--System (SCOP) satisfies a specific set of
`quantum axioms', it fits in a quantum mechanical representation in Hilbert
space. We present a model in which the maximal change of state of the system
due to interaction with the measurement context is controlled by a parameter
$N$. In the case $N=2$ the system reduces to a model for the spin
measurements on a quantum spin-1/2 particle. In the limit $N\rightarrow
\infty $ the system is classical. For the intermediate cases it is
impossible to define an orthocomplementation on the set of properties.
Another interesting feature is that the probability of a state transition
also depends on the context which induces it. This contrasts sharply with
standard quantum mechanics for which Gleason's theorem states the uniqueness
of the state transition probability and independent of measurement context.
We show that if a SCOP satisfies a Gleason-like condition, namely that all
state transition probabilities are independent of which measurement context
induces the change of state, then the lattice of properties is
orthocomplemented.
| Originele taal-2 | English |
|---|---|
| Titel | QUANTUM THEORY: Reconsideration of Foundations-5. AIP Conference Proceedings |
| Uitgeverij | Springer |
| Pagina's | 33-44 |
| Aantal pagina's | 12 |
| Volume | 1232 |
| ISBN van geprinte versie | 978-0-7354-0777-0 |
| Status | Published - mei 2010 |