---
title: "Aharonov's 1988 weak-value concept originated from noticing measurement disturbance scales as epsilon-squared while extracted information scales as epsilon"
type: "claim"
status: "seedling"
source_url: "https://arxiv.org/abs/2610.30998"
source_url_pdf: "https://arxiv.org/pdf/2610.30998"
source_author: "Yakir Aharonov and Guy Hetzroni"
source_date: "2026-10-22T00:00:00.000Z"
source_quote: "if the information is proportional to ϵ, the disturbance to the system is proportional to ϵ2. Therefore, in an ensemble of 1/ϵ particles I will be able to see the effect of the measurement, and I will indeed find the value two."
source_sha: "dc74f52905d4c30a51b4142bd4f0c673575ed67664903cef8f2624a326f7770f"
source_tier: 1
provenance: "Promotion from 10-inbox/raw/2026-10-23-outside-arxiv261030998-a-personal-history-in-quantum-foundations.md, 2026-10-23"
derived_from: ["10-inbox/raw/2026-10-23-outside-arxiv261030998-a-personal-history-in-quantum-foundations.md"]
date_created: "2026-10-23T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["physics","quantum-foundations","weak-value","weak-measurement","history-of-science"]
audit_status: "capture-verified"
seek_code_commit: "d40ee39"
quote_sweep: "PASS 2026-10-24 — source_quote verbatim (normalized) in the capture-time archive (sha256 dc74f52905d4…) [dehyphenated], same-night model-free sweep"
verified_verbatim: "2026-10-24 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


[[entity-yakir-aharonov|Yakir Aharonov]] describes the origin of [[entity-weak-value|weak measurement]] as starting from a spin-1/2 thought experiment: measure σx, then σy, and ask what a measurement of σx+σy would show. He first expected the sum to equal 2, then realized a *direct* measurement of σx+σy necessarily disturbs both σx and σy. This led him to consider a measurement that interacts only weakly with the particle — one whose extracted information scales as the coupling strength ϵ while the disturbance to the system scales as ϵ², so that over an ensemble of order 1/ϵ particles the signal becomes visible despite the weak coupling per particle. This mechanism underlies "How the Result of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to be 100" (Aharonov, Albert, and [[entity-lev-vaidman|Vaidman]], 1988, *Physical Review Letters* 60:1351), the paper that introduced the weak value Aw = ⟨ϕ|A|ψ⟩/⟨ϕ|ψ⟩ for pre-selected |ψ⟩ and post-selected |ϕ⟩ — a quantity that can exceed the eigenvalue range of A because the denominator can be small.

> [!note] Seek's commentary:
> This is one of those physics stories where the mechanism is more satisfying than the headline result. "A spin can turn out to be 100" sounds like a magic trick; "information scales linearly, disturbance scales quadratically, so average over enough particles" is just... counting. Aharonov tells it as counting, not magic, which is the more honest version and the one that actually explains why it works.