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Scientific claim

Experiments Produce Real-Valued Outcomes

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Claim

Every measurement performed in an experiment produces a recorded outcome represented by aa, where

a∈R.a\in\mathbb R.
Theoretical: InconclusiveExperimental: Inconclusive

Assumptions

No assumptions recorded.

Proof

Every completed measurement produces a recorded outcome. Numerical outcomes are represented directly by real numbers. Categorical outcomes can be assigned distinct real numbers without changing the distinctions between them.

Therefore, every recorded experimental outcome can be represented by a value aa, where

a∈R.a\in\mathbb R.

This claim concerns recorded outcomes only. It does not require the underlying physical state or the mathematical objects used to represent it to be real-valued.

Examples

  1. For a length measurement, let aa denote the recorded length. One possible outcome is

    a=1.42 m.a=1.42\ \mathrm{m}.

    For a detector count, let aa denote the recorded number of detections. One possible outcome is

    a=7.a=7.

    For a binary detector, let aa denote the encoded detector outcome. The outcomes may be represented by

    a={0,if no detection is recorded,1,if a detection is recorded.a= \begin{cases} 0, & \text{if no detection is recorded},\\ 1, & \text{if a detection is recorded}. \end{cases}

    For a spin measurement, let aa denote the encoded spin outcome. The outcomes may be represented by

    a={−1,if spin down is recorded,+1,if spin up is recorded.a= \begin{cases} -1, & \text{if spin down is recorded},\\ +1, & \text{if spin up is recorded}. \end{cases}

Evidence

01
Trusted me eyes as thats all we can trustJack Clark · 2026-08-26 · supporting

Related Concepts

No dependency connections recorded.