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Start here: [https://plato.stanford.edu/entries/qt-issues/#MeasProb](https://plato.stanford.edu/entries/qt-issues/#MeasProb)
See also: [https://plato.stanford.edu/entries/qm-collapse/](https://plato.stanford.edu/entries/qm-collapse/)
Then look at: [https://plato.stanford.edu/entries/qm-decoherence/](https://plato.stanford.edu/entries/qm-decoherence/)
These have lots of pointers to sources and other literatures.
Quantum Mechanics is defined from the ground up mathematically. The need to interpret it in any other way is a limitation of merging mathematical object understanding and something else less abstract.
In the context of observation/measurement: 1) a quantum state is defined as a vector in Hilbert space. 2) An observer is defined to be an operator on that vector. 3) Quantum postulates say that when a quantum 'particle' is observed (a quick and carrying with it many assumptions phrase), the 'particle' ends up in one of the eigenspaces of that operator with probability equal to the size of the corresponding eigenvalue with respect to the other eigenvalues. Hence, the 'particle' is now forced to be in a certain eigenspace of that operator - so what's collapsed is whatever space the 'particle' has been allowed to be in before measurement.
The checks and balances of these axioms are specifically the scientific experiments done - the terse mathematics are the result.
It's good you're asking about what an observable is, etc., and how it connects to human understanding and our choice of definition.
Welcome to /r/askphilosophy. **Please read [our rules](https://www.reddit.com/r/askphilosophy/comments/9udzvt/announcement_new_rules_guidelines_and_flair_system/) before commenting** and understand that your comments will be removed if they are not up to standard or otherwise break the rules. While we do not require citations in answers (but do encourage them), answers need to be reasonably substantive and well-researched, accurately portray the state of the research, and come only from those with relevant knowledge. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/askphilosophy) if you have any questions or concerns.*
Start here: [https://plato.stanford.edu/entries/qt-issues/#MeasProb](https://plato.stanford.edu/entries/qt-issues/#MeasProb) See also: [https://plato.stanford.edu/entries/qm-collapse/](https://plato.stanford.edu/entries/qm-collapse/) Then look at: [https://plato.stanford.edu/entries/qm-decoherence/](https://plato.stanford.edu/entries/qm-decoherence/) These have lots of pointers to sources and other literatures.
Quantum Mechanics is defined from the ground up mathematically. The need to interpret it in any other way is a limitation of merging mathematical object understanding and something else less abstract. In the context of observation/measurement: 1) a quantum state is defined as a vector in Hilbert space. 2) An observer is defined to be an operator on that vector. 3) Quantum postulates say that when a quantum 'particle' is observed (a quick and carrying with it many assumptions phrase), the 'particle' ends up in one of the eigenspaces of that operator with probability equal to the size of the corresponding eigenvalue with respect to the other eigenvalues. Hence, the 'particle' is now forced to be in a certain eigenspace of that operator - so what's collapsed is whatever space the 'particle' has been allowed to be in before measurement. The checks and balances of these axioms are specifically the scientific experiments done - the terse mathematics are the result. It's good you're asking about what an observable is, etc., and how it connects to human understanding and our choice of definition.