Only Observables can be in Superposition?

[Varon]

Hi, is it true that only Observables can be in Superposition? Meaning superposition of dead and live cats is invalid by some unknown mathematical reasoning? Jambaugh stated thus in the other forum that only observables can be in superposition. What's the mathematical or quantum logical proof?

"Note my qualification about the temperature is not me merely being pedantic. There is a critical thermodynamic aspect of the measurement process. Note also temperature is a critical aspect of the "cat" when we speak of "alive" vs "dead". These are not properly quantum observables any more than is temperature and so it is not proper to speak of them being in superposition. This aspect is part of what makes the "cat" necessary as a "macroscopic system" for the purpose of the thought experiment. Recall also that the original purpose was to distance the meanings of classical states of reality and the quantum "state vectors" (which in CI do not represent states but rather classes of systems)."

 

[SpectraCat]

Hi, is it true that only Observables can be in Superposition? Meaning superposition of dead and live cats is invalid by some unknown mathematical reasoning? Jambaugh stated thus in the other forum that only observables can be in superposition. What's the mathematical or quantum logical proof?

"Note my qualification about the temperature is not me merely being pedantic. There is a critical thermodynamic aspect of the measurement process. Note also temperature is a critical aspect of the "cat" when we speak of "alive" vs "dead". These are not properly quantum observables any more than is temperature and so it is not proper to speak of them being in superposition. This aspect is part of what makes the "cat" necessary as a "macroscopic system" for the purpose of the thought experiment. Recall also that the original purpose was to distance the meanings of classical states of reality and the quantum "state vectors" (which in CI do not represent states but rather classes of systems)."

Yes, that seems correct. Remember a superposition is *coherent* ... it necessarily involves a well-defined phase relation between the components. You can add states together without the phase relationship to create mixed states ... that is actually what happens to superpositions when they decohere .. they become mixed states. You can mixed states from two pure quantum eigenstates with a 50-50 weighting, so that as for superpositions, half of the measurements on an ensemble of such systems give either value for the observable. However, mixed states do not exhibit quantum phenomena like coherence, interference, or entanglement.

Since classical objects do not have phase, they cannot be superposed. Thus a mixed state is a more appropriate designation for logic constructions like the (dead + alive) cat.

 

[Varon]

Yes, that seems correct. Remember a superposition is *coherent* ... it necessarily involves a well-defined phase relation between the components. You can add states together without the phase relationship to create mixed states ... that is actually what happens to superpositions when they decohere .. they become mixed states. Since classical objects do not have phase, they cannot be superposed. Thus a mixed state is a more appropriate designation for logic constructions like the (dead + alive) cat.

Uhm... how come in Many Worlds Interpretation, cat can be in superposition of dead and alive. I thought MWI just follow the same mathematics as QM. ?

 

[SpectraCat]

Uhm... how come in Many Worlds Interpretation, cat can be in superposition of dead and alive. I thought MWI just follow the same mathematics as QM. ?

I don't know much about MWI ... my guess is that it can't be in such a superposition in MWI either ... I doubt you will find that statement in texts by experts, but I could be wrong. Or perhaps they are using "superposition" loosely to include mixed states as well ... I don't know enough about MWI to say for sure. Do measurements on mixed states cause the same kind of branching as measurements on quantum superpositions in MWI?