1543 – The transition in cosmology from a Ptolemaic cosmology to a Copernican one.
Two observations seemed to support the idea that Earth was the center of the Universe: First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. While the Moon and the planets have their own motions, they also appear to revolve around Earth about once per day. Second, Earth seems to be unmoving from the perspective of an earthbound observer; it feels solid, stable, and stationary.
1543 – The acceptance of the work of Andreas Vesalius, whose work De humani corporis fabrica corrected the numerous errors in the previously-held system created by Galen.
1687 – The transition in mechanics from Aristotelian mechanics to classical mechanics.
According to Aristotle there are four elements that make up everything in the terrestrial spheres: earth, air, fire and water (Aristotle borrows this from Empedocles proving there's already a consensus on this matter. Aristotle held that the heavens are made of a special weightless and incorruptible, unchangeable fifth element called "aether". For your information, "aether."
1718-present. – The transition from the luminiferous "aether" present in space to electromagnetic radiation in spacetime.
Go to this Wikipedia article. I want to contrast the following statements by leading scientists:
Newton: "Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them?"
Einstein: We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an aether. According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time.
One more: Most physicists in the 20th century concluded that this early modern notion of a luminiferous aether was not a useful concept (Einstein however stated that this consideration was too radical and too anticipatory and that his theory of relativity still needed the presence of a medium with certain properties). There is simultaneously consensus and disensus. So is there an "aether" after all? We could call this an unsettled case in scientific endeavor.
1780s – The acceptance of Lavoisier's theory of chemical reactions and combustion in place of phlogiston theory, known as the chemical revolution.
As crazy as it seems the phlogiston theory stated that phlogisticated substances are substances that contain phlogiston and dephlogisticate when burned. The theory springs from Empedocles and Aristotle. At the time, fire was thought of as a substance and burning was seen as a process of decomposition which applied only to compounds. Empirical evidence shows that burning is not always accompanied by a loss of material and a better theory was needed to account for this. Thus, the phlogiston theory. Dephlogisticating is the process of releasing stored phlogiston, which is absorbed by the air. Growing plants then absorb this phlogiston, which is why air does not spontaneously combust and also why plant matter burns as well as it does. Thus phlogiston accounted for combustion via a process that was opposite to that of the oxygen theory. In general, substances that burned in air were said to be rich in phlogiston; the fact that combustion soon ceased in an enclosed space was taken as clear-cut evidence that air had the capacity to absorb only a finite amount of phlogiston.
1826 – The discovery of hyperbolic geometry.
In the 19th century, hyperbolic geometry was explored extensively by Nikolai Ivanovich Lobachevsky, János Bolyai, Carl Friedrich Gauss and Franz Taurinus. Unlike their predecessors, who just wanted to eliminate the parallel postulate from the axioms of Euclidean geometry, these authors realized they had discovered a new geometry.[10][11] Gauss wrote in an 1824 letter to Franz Taurinus that he had constructed it, but Gauss did not publish his work. Gauss called it "non-Euclidean geometry"[12] causing several modern authors to continue to consider "non-Euclidean geometry" and "hyperbolic geometry" to be synonyms. Taurinus published results on hyperbolic trigonometry in 1826, argued that hyperbolic geometry is self consistent, but still believed in the special role of Euclidean geometry. The complete system of hyperbolic geometry was published by Lobachevsky in 1829/1830, while Bolyai discovered it independently and published in 1832.
1880 – The germ theory of disease vs. Galen's miasma theory.
The miasma theory (also called the miasmatic theory) is an obsolete medical theory that held that diseases—such as cholera, chlamydia, or the Black Death—were caused by a miasma (μίασμα, Ancient Greek for "pollution"), a noxious form of "bad air", also known as night air.
Empirical evidence: The miasma theory was consistent with the observation that disease was associated with poor sanitation, and hence foul odors, and that sanitary improvements reduced disease. However, it was inconsistent with the findings arising from microbiology and bacteriology in the later 19th century, which eventually led to the adoption of the germ theory of disease, although consensus was not reached immediately. Concerns over sewer gas, which was a major component of the miasma theory developed by Galen, and brought to prominence by the "Great Stink" in London in the summer of 1858, led proponents of the theory to observe that sewers enclosed the refuse of the human bowel, which medical science had discovered could teem with typhoid, cholera, and other microbes.
It was not until 1876 that Robert Koch proved that the bacterium Bacillus anthracis caused anthrax, which brought a definitive end to miasma theory.
1919 – The transition between the worldview of Newtonian gravity and general relativity.
1964 - The discovery of cosmic microwave background radiation leads to the big bang theory being accepted over the steady state theory in cosmology.
1965 - The acceptance of plate tectonics as the explanation for large-scale geologic changes.
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