[[File:Weber-Fechner law demo - dots.svg|thumb|An illustration of the Weber–Fechner law.
On each side, the lower square contains 10 more dots than the upper one. However the perception is different:
On the left side, the difference between upper and lower square is clearly visible. On the right side, the two squares look almost the same.]]
The Weber–Fechner laws are two related scientific laws in the field of psychophysics, known as Weber's law and Fechner's law. Both 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.
Ernst Heinrich Weber states that "the minimum increase of stimulus which will produce a perceptible increase of sensation is proportional to the pre-existent stimulus," while Gustav Fechner's law is an inference from Weber's law (with additional assumptions) which states that the intensity of our sensation increases as the logarithm of an increase in energy rather than as rapidly as the increase.
History and formulation of the laws
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. He made the claim that "...psycho-physics is an exact doctrine of the relation of function or dependence between body and soul."
Weber's law
Ernst Heinrich Weber (1795–1878) was one of the first persons 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.
In sensation and contrast, change is defined as "contrast over time". The senses detect the change; in Weber's law, specifically, it is relative change, not absolute change, which is detected. In Weber's law, to notice a change in stimulus (e.g. brightness or weight), the change must be constant proportion of the original stimulus. Weber's law states that just noticeable difference is proportional to the magnitude of the initial stimulus. The brain is a percentage of change detector. The differential threshold is the smallest difference needed to differentiate two stimuli for each sense has been studied by using similarly methods to signal detection. For instance, holding an object that weighs 1,2,10, and 11lbs. If one were to hold the lightest object (1lb), and then swap out that object for the 2lb object, one could easily tell that the second object is heavier than the first. There is a 100 % weight increase from the first object to the second. However, it becomes more difficult when the difference is a smaller percentage of the initial object's weight. For example, if one were to hold the 10lb object, and then swap it out and hold the 11lb object, it would be difficult for one to tell which of the two is heavier, because there is only a 10 % increase from the first to the second object. This demonstrates that bigger stimuli require a larger difference in order to be noticed. This is Weber's Law.
Fechner formulated several versions of the law, all communicating the same idea. One formulation states: