The spin observables for an elementary particle can be studied without any reference to the particle\u2019s position. They are then modeled as operators on a finite dimensional Hilbert space of spin states that is essentially independent of the infinite dimensional Hilbert space of \u201cwave\u201d functions on position space (which identify those aspects of the particle\u2019s state that are related to its position observables). And in this context for example the eigenstates for any spin component of a spin 1\/2 particle are superpositions of eigenstates for other components.<\/p>\n
Now you might (correctly) think that this talk of spin components means that we must still be thinking about directions in physical position space. But in fact the study of\u00a0any\u00a0two-valued observable (with values \u201cYes\u201d and \u201cNo\u201d or \u201cTrue\u201d and \u201cFalse\u201d) forces us to also consider other observables whose eigenstates are superpositions of the Yes and No eigenstates and whose relationship to the original observable are mathematically equivalent to those between spin components in different directions despite not actually having any connection with directions in physical space. And in quantum computing, although spin directions for a single particle are often used as a conceptual model, the choice of Yes\/No observable might in practice be something different.<\/p>\n
Of course, to study the progress of a quantum calculation, while disregarding space we still need to consider the\u00a0time\u00a0evolution of the system; but some aspects of the relationships between possible outcomes can be studied\u00a0without\u00a0reference to time in a similar way to how the time-independent Schrodinger equation can be used to study stationary states and energy levels of an atom or molecule. And in these types of analysis the question of whether and how some states are superpositions of other states is still relevant even though there is no reference to either space or time involved.<\/p>\n
Source: (1001) Alan Cooper’s answer to Would quantum superpositions function in the absence of time and space? – Quora<\/a><\/em><\/p>\n","protected":false},"excerpt":{"rendered":" The spin observables for an elementary particle can be studied without any reference to the particle\u2019s position. They are then modeled as operators on a finite dimensional Hilbert space of spin states that is essentially independent of the infinite dimensional Hilbert space of \u201cwave\u201d functions on position space (which identify those aspects of the particle\u2019s … Continue reading Superposition Independent of Space and Time<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,4],"tags":[28,94],"topics":[],"class_list":["post-1637","post","type-post","status-publish","format-standard","hentry","category-all","category-quora-answers","tag-quantum","tag-superposition"],"_links":{"self":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts\/1637","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/comments?post=1637"}],"version-history":[{"count":1,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts\/1637\/revisions"}],"predecessor-version":[{"id":1639,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/posts\/1637\/revisions\/1639"}],"wp:attachment":[{"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/media?parent=1637"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/categories?post=1637"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/tags?post=1637"},{"taxonomy":"topics","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/physics\/wp-json\/wp\/v2\/topics?post=1637"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}