GAP Measures and Wave Function Collapse
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918350989295616 |
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| author | Tumulka, Roderich |
| author_facet | Tumulka, Roderich |
| contents | GAP measures (also known as Scrooge measures) are a natural class of probability distributions on the unit sphere of a Hilbert space that come up in quantum statistical mechanics; for each density matrix $ρ$ there is a unique measure GAP$_ρ$. We describe and prove a property of these measures that was not recognized so far: If a wave function $Ψ$ is GAP$_ρ$ distributed and a collapse occurs, then the collapsed wave function $Ψ'$ is again GAP distributed (relative to the appropriate $ρ'$). This fact applies to collapses due to a quantum measurement carried out by an observer, as well as to spontaneous collapse theories such as CSL or GRW. More precisely, it is the conditional distribution of $Ψ'$, given the measurement outcome (respectively, the noise in CSL or the collapse history in GRW), that is GAP$_{ρ'}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19993 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | GAP Measures and Wave Function Collapse Tumulka, Roderich Quantum Physics Mathematical Physics GAP measures (also known as Scrooge measures) are a natural class of probability distributions on the unit sphere of a Hilbert space that come up in quantum statistical mechanics; for each density matrix $ρ$ there is a unique measure GAP$_ρ$. We describe and prove a property of these measures that was not recognized so far: If a wave function $Ψ$ is GAP$_ρ$ distributed and a collapse occurs, then the collapsed wave function $Ψ'$ is again GAP distributed (relative to the appropriate $ρ'$). This fact applies to collapses due to a quantum measurement carried out by an observer, as well as to spontaneous collapse theories such as CSL or GRW. More precisely, it is the conditional distribution of $Ψ'$, given the measurement outcome (respectively, the noise in CSL or the collapse history in GRW), that is GAP$_{ρ'}$. |
| title | GAP Measures and Wave Function Collapse |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2602.19993 |