Where does amplitude collide?

The greatest distance an oscillating quantity swings away from its rest value: for a vibrating string it is the peak displacement, for a sound wave the peak change in pressure, and it fixes how much energy the oscillation carries. French's 1971 Vibrations and Waves treats it as the constant in front of the sine that sets the height of the wave, a real, non-negative magnitude in physical units. The referent here is a measured peak of a real physical motion, not a complex bookkeeping number in quantum theory, a fitted parameter of a biological rhythm, or an angle read off the horizon.[1]

Unit

The maximum displacement or pressure of an oscillation away from its rest value, in physical units

Recovery means

Not applicable

Measured by

Read from the height of the waveform on an oscilloscope, a pressure meter, or a displacement sensor, in units such as metres or pascals

A complex number attached to each possible outcome of a quantum measurement, whose squared modulus gives the probability of that outcome, a rule first stated by Born in his 1926 Zur Quantenmechanik der Stoßvorgänge. Because these numbers are complex, they can add and cancel, so two paths to the same result can interfere in a way that ordinary probabilities cannot. The referent is a bookkeeping quantity of the theory that is never observed directly and can be negative or complex, unlike the strictly real, measurable peak of a classical wave, the estimated swing of a rhythm, or a navigator's angle.[2]

Unit

A complex number attached to an outcome, whose squared modulus is a probability

Recovery means

Not applicable

Measured by

Inferred, never seen directly: recovered up to a phase from measured probabilities and from interference patterns predicted by the Born rule

In cosinor analysis, a cosine curve of a chosen period is fitted by least squares to time-stamped measurements, and the amplitude is half the distance between the peak and the trough of that fitted curve. Cornelissen's 2014 Cosinor-based rhythmometry defines it as an estimated model parameter that comes with a confidence interval, so it can be tested for being different from zero. The referent is a number produced by fitting a model to noisy data, not a physical peak you can meter, a complex quantum quantity, or an angle at the horizon.[3]

Unit

Half the peak-to-trough range of a cosine curve fitted to rhythmic data, in the units of the measurement

Recovery means

Not applicable

Measured by

Estimated from a least-squares fit of a cosine of fixed period to timed data, and reported with a confidence interval

The angular distance of a celestial body from the east or west point of the horizon at the moment it rises or sets, measured north or south along the horizon. Bowditch's The American Practical Navigator gives it as an angle computed from the body's declination and the observer's latitude, chiefly to check a compass against a known bearing. The referent is a horizontal angle in degrees tied to sunrise and sunset geometry, sharing only the word with a wave's peak, a quantum probability quantity, or a rhythm's fitted swing.[4]

Unit

An angle on the horizon, north or south of the east or west point, at rising or setting, in degrees

Recovery means

Not applicable

Measured by

Computed from declination and latitude, or observed as the body's bearing at rising or setting, then compared with the compass to find its error