Weber–Fechner law

The Weber–Fechner law refers to two related laws in the field of psychophysics, known as Weber's law and Fechner's law. Both laws relate to human perception; more specifically the relation between the actual change in a physical stimulus and the perceived change. This includes stimuli to all senses; vision, hearing, taste, touch and smell.

Both Weber's law and Fechner's law were formulated by Gustav Theodor Fechner (1801–1887). They were first published in 1860 in the work Elemente der Psychophysik(Elements of psychophysics). This publication was the first work ever in this field, and where Fechner coined the term psychophysics to describe the interdisciplinary study of how humans perceive physical magnitudes.

Ernst Heinrich Weber (1795–1878) was one of the first people to approach the study of the human response to a physical stimulus in a quantitative fashion. Fechner was a student of Weber and named his first law in honor of his mentor, since it was Weber who had conducted the experiments needed to formulate the law.

Fechner formulated several versions of the law, all stating the same thing. One formulation states:

"Simple differential sensitivity is inversely proportional to the size of the components of the difference; relative differential sensitivity remains the same regardless of size."

What this means is that the perceived change in stimuli is proportional to the initial stimuli.

Weber's law also incorporates the Just Noticeable Difference (JND). This is the smallest change in stimuli that can be perceived. As stated above, the JND is proportional to the initial stimuli. Fechner found that the JND is constant for any sense.

Although Weber's law includes a statement of the proportionality of a perceived change to initial stimuli, Fechner never formulated this statement as a mathematical expression. Instead, he only refers to this as a rule of thumb regarding human perception.

This rule of thumb has been expressed mathematically, as Weber contrast.

Weber contrast is not part of Weber's law.

Fechner noticed in his own studies that different individuals have different sensitivity to certain stimuli. For example, the ability to perceive differences in light intensity could be related to how good that individual's vision is. He also noted that the human sensitivity to stimuli changes depends on which sense is affected. He used this to formulate another version of Weber's law that he named the Massformel, the "measurement formula". Fechner's law states that the subjective sensation is proportional to the logarithm of the stimulus intensity. According to this law, human perceptions of sight and sound work as follows: Perceived loudness/brightness is proportional to logarithm of the actual intensity measured with an accurate nonhuman instrument.

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