<A>
motion problem:
Aristotle believed motion occurred due to the nature (or form) & not because of ‘unnatural’ forces; heavy bodies (earth, water) move down, and ‘light’ things (air, fire) moved up. He failed to address the issue of relative versus absolute motion..
Descartes (1644 Principles of Philosophy) argued the essence of matter was extension (size and shape) & extension constitutes the nature of space, hence space & matter were one & the same. He claimed that all motion was motion of bodies relative to one another, not a literal change of space.
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Newton challenged Descartes’s theories(1687, Mathematical Principles of Natural Philosophy). He founded classical mechanics on the premise that space is distinct from body & time passes uniformly without regard to whether anything happens in the world. He spoke of absolute space & time, to distinguish these from the various ways by which we measure them (which he called relative spaces and relative times).
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Leibniz posited monads, simple but "ultimate units of existence in nature" (The Monadology, 1714); they change continuously over time, each monad is unique. They are un-affected by time, subject to only creation & annihilation. Monads are centres of force; substance is force, while space, matter & motion are merely phenomenal & are completely relative.
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<B>
gravitation (Newton’s hypothesis limited): *
Newton’s theory of gravity posited that all objects, from apples to the Sun, planets and stars, exert a force that attracts other objects. That universal law of gravitation worked well in predicting the motion of planets & objects on Earth. However this theory on gravity didn't work for some things, like Mercury which has a peculiar orbit around the sun. The orbits of planets shift over time, but Mercury’s orbit shifted faster than Newton predicted. How could this be explained?
In Einstein’s general relativity theory, the effects of gravitation are ascribed to spacetime curvature instead of a force, a very different view of gravity. Instead of exerting an attractive force, each object curves the fabric of space and time around them, forming a sort of well that other objects (even beams of light) fall into. The sun is like a bowling ball on a mattress (SEE IMAGE BELOW), it creates a depression that draws the planets close. This new model solved the Mercury problem. It showed that the sun so curves space that it distorts the orbits of nearby bodies, including Mercury. Mercury is like a marble forever circling the bottom of a drain. Einstein’s theory has been confirmed by more than a century of experiments, starting with a 1919 solar eclipse in which the path of light from distant stars was shifted by the sun’s intense gravitation, just as Einstein had predicted & by just the amount he had predicted.
<C>
Conservation of Energy (validity): *
The image below is a diagrammatic representation of an isolated, closed and open system. An infinite universe is neither closed or isolated.
<D>
an infinite space:*
size of the universe
Early in the 20th century astronomers believed that the visible universe & Milky Way were co-equal. Few bought the island universes theory, that spiral nebulae were enormous star systems, comparable to the Milky Way, scattered through space with vast empty distances between them. Astronomers did not believe observation support this. However in 1917 H Curtis observed nova Messier (object M31) within the Andromeda Galaxy. Searching the photographic record, he found 11 more novae & noticed that on average, they were10 magnitudes fainter than those within our galaxy. Their faintness implied that they were at great distances from the Milky Way, which he estimated to be 150,000 parsecs. He became a proponent of the island universes theory.
expansion of the universe.
The static character of the universe was also challenged. In 1912, American astronomer VM Slipher made spectrographic studies of the brightest spiral nebulae to determine their composition. Spectroscopy is the study of the interaction between matter & electromagnetic radiation as a function of the wavelength. It is the precise study of colour as generalized from visible light to all bands of the electromagnetic spectrum. Slipher discovered that many spiral nebulae had high Doppler shifts, indicating movement away from the Milky Way & at a high rate of speed.
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<E>
Fresnel (experiments with light-waves): *
In 1690 Huygens hypothesized light was a wave, not a particle or corpuscle as Newton hypothesised. There were several problems. Waves were longitudinal; they have only 1 form of propagation direction, rather than 2 polarizations like transverse waves. As such they could not explain birefringence (where 2 polarizations of light are refracted differently by a crystal). It was also assumed light waves (like sound or other mechanical waves in fluids) required a medium for propagation. Huygens supplied this medium with his Luminiferous aether, a substance which permeated all space. Newton dismissed this & his corpuscle theory of light dominated.
In 1810, Arago posited that variations in the refractive index of a substance predicted by Newton’s corpuscular theory would provide a useful method for measuring the velocity of light. Yet he found that there was no difference in refraction between stars, regardless of time, day or season. In 1818 Fresnel examined Arago's results but used a wave theory of light. He believed if light were transmitted as waves the refractive index of the glass-air interface should vary as the glass moved through the aether to strike the incoming waves at different velocities when the earth rotated & seasons changed. He proposed the glass prism carried some of the aether along with it making the prism denser. He created the Fresnel drag coefficient to adjust for this increased density & this successful explained Arago's null result. Fresnel introduced the stationary aether concept that is dragged by substances such as glass but not by air. Even more importantly his proposals reanimated the wave theory of light over Newton’s corpuscular theory. Fresnel pointed out that light could be a transverse wave rather than a longitudinal wave; the polarization of a transverse wave (like Newton's "sides" of light) could then explain birefringence (double refraction). Following a series of experiments on diffraction, Newton’s theory was abandoned. However transversal waves also had a problem. A transverse wave apparently required the propagating medium to behave as a solid, as opposed to a fluid. A solid that did not interact with other matter was strange. Many alternatives were suggested, and Maxwell even paied lip service! However the door began to close on the aether when the Michelson–Morley experiment (1887) produced a null result.
<F>
transversal (light waves):*
examples include waves created on a horizontal length of string or the membrane of a drum; light is a transverse wave where the oscillations are the electric and magnetic fields point at right angles to the rays that describe the direction of propagation.
see image
<G>
longitudinal (light waves): *
Sound travels through longitudinal waves.
see image
LEFT: At the same time, we see the use of atmospheric perspective in the background, employing effective sfumato, showing us a vista in distant space.
RIGHT: Each episode has an autonomous existence. The gesture of the Madonna, as she sits framed by the jutting wing of the building, coincides with the reflection made by the falling light upon the stone, while the close-knit perspective network of the bosom, the controlled movement of the interposed suspended gesture, and the withdrawal of the head, become fleeting signals of emotion.
<D>
theory of functions of several complex variables: *
A differentiable function of a complex variable is equal to its Taylor series. As such, complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions).
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BELOW:
a 3-dimensional plot of the absolute value of the complex gamma function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is, at every point of its domain, complex differentiable in a neighborhood of the point.
