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Huygens' Principle In 1678 the great Dutch physicist Christian Huygens (1629-1695) wrote a treatise called Traite de la Lumiere on the wave theory of light, and in this work he stated that the wavefront of a propagating wave of light at any instant conforms to the envelope of spherical wavelets emanating from every point on the wavefront at the prior instant (with the understanding that the wavelets have the same speed as the overall wave). An illustration of this idea, now known as Huygens' Principle, is shown below. http://www.mathpages.com/home/kmath242/kmath242.htm This drawing depicts the propagation of the wave “front”, but Huygens’ Principle is understood to apply equally to any locus of constant phase (not just the leading edge of the disturbance), all propagating at the same characteristic wave speed. This implies that a wave doesn't get "thicker" as it propagates, i.e., there is no diffusion of waves. For example, if we turn on a light bulb for one second, someone viewing the bulb from a mile away will see it "on" for precisely one second, and no longer. Similarly, the fact that we see sharp images of distant stars and galaxies is due to Huygens’ Principle. However, it’s worth noting that this principle is valid only in spaces with an odd number of dimensions. (See below for a detailed explanation of why this is so.) If we drop a pebble in a calm pond, a circular wave on the twodimensional surface of the pond will emanate outward, and if Huygens' Principle was valid in two dimensions, we would expect the surface of the pond to be perfectly quiet both outside and inside the expanding spherical wave. But in fact the surface of the pond inside the expanding wave (in this two-dimensional space) is not perfectly calm, its state continues to differ slightly from its quiescent state even after the main wave has passed through. This excited state will persist indefinitely, although the magnitude rapidly becomes extremely small. The same occurs in a space with any even number of dimensions. Of course, the leading edge of a wave always propagates at the characteristic speed c, regardless of whether Huygens' Principle is true or not. In a sense, Huygens' Principle is more significant for what it says about what happens behind the leading edge of the disturbance. Essentially it just says that all the phases propagate at the same speed. From this simple principle Huygens was able to derive the laws of reflection and refraction, but the principle is deficient in that it fails to account for the directionality of the wave propagation in time, i.e., it doesn't explain why the wave front at time t + Dt in the above figure is the upper rather than the lower envelope of the secondary wavelets. Why does an expanding spherical wave continue to expand outward from its source, rather than re-converging inward back toward the source? Also, the principle originally stated by Huygens does not account for diffraction. Subsequently, Augustin Fresnel (1788-1827) elaborated on Huygens' Principle by stating that the amplitude of the wave at any given point equals the superposition of the amplitudes of all the secondary wavelets at that point (with the understanding that the wavelets have the same frequency as the original wave). The Huygens-Fresnel Principle is adequate to account for a wide range of optical phenomena, and it was later shown by Gustav Kirchoff (1824-1887) how this principle can be deduced from Maxwell's equations. Nevertheless (and despite statements to the contrary in the literature), it does not actually resolve the question about "backward" propagation of waves, because Maxwell's equations themselves theoretically allow for advanced as well as retarded potentials. It's customary to simply discount the advanced waves as "unrealistic", and to treat the retarded wave as if it was the unique solution, although there have occasionally been interesting proposals, such as the Feynman-Wheeler theory, that make use of both solutions. Incidentally, as an undergraduate, Feynman gave a seminar on this "new idea" at Princeton. Among the several "monster minds" (as Feynman called them) in attendance was Einstein, to whom the idea was not so new, because 30 years earlier Einstein had debated the significance of the advanced potentials with Walther Ritz. In any case, the Huygens-Fresnel Principle has been very useful and influential in the field of optics, although there is a wide range of opinion as to its scientific merit. Many people regard it as a truly inspired insight, and a fore-runner of modern quantum electro-dynamics, whereas others dismiss it as nothing more than a naive guess that sometimes happens to work. For example, Melvin Schwartz wrote that to consider each point on a wavefront as a new source of radiation, and to add the radiation from all the new sources together, “makes no sense at all”, since (he argues) “light does not emit light; only accelerating charges emit light”. He concludes that Huygens’ principle “actually does give the right answer” but “for the wrong reasons”. However, Schwartz was expressing the classical (i.e., late 19th century) view of electromagnetism. The propagation of light in quantum field theory actually is consistent with the very interpretation of Huygens’ principle that Schwartz regarded as nonsense. Whether we have now actually found the true "reason" for the behavior of light is debatable, and ultimately every theory is based on some fundamental principle(s), but it's interesting how widely the opinions on various principles differ. (I'm reminded of the history of Fermat's Principle, and of Planck's reverence for the Principle of Least Action.) It could be argued that the “path integral” approach to quantum field theory – according to which every trajectory through every point in space is treated equivalently as part of a possible path of the system – is an expression of Huygens’ Principle. It’s also worth reflecting on the fact that the quantum concept of a photon necessitates Huygens’ Principle, so evidently quantum mechanics can work only in space with an odd number of dimensions. http://en.wikipedia.org/wiki/Scientific_revolution The scientific revolution was not marked by any single change. The following new ideas contributed to what is called the scientific revolution: The replacement of the Earth by the Sun as the center of the solar system. The replacement of the Aristotelian theory that matter was continuous and made up of the elements Earth, Water, Air, Fire, and Aether by rival ideas that matter was atomistic or corpuscular or that its chemical composition was even more complex The replacement of the Aristotelian idea that heavy bodies, by their nature, moved straight down toward their natural places; that light bodies, by their nature, moved straight up toward their natural place; and that ethereal bodies, by their nature, moved in unchanging circular motions with the idea that all bodies are heavy and move according to the same physical laws The replacement of the Aristotelian concept that all motions require the continued action of a cause by the inertial concept that motion is a state that, once started, continues indefinitely without further cause The replacement of Galen's treatment of the venous and arterial systems as two separate systems with William Harvey's concept that blood circulated from the arteries to the veins "impelled in a circle, and is in a state of ceaseless motion" But the most innovative idea at the core of what is commonly called scientific method in modern physical sciences is the one stated by Galileo in his book Il Saggiatore in relation to the interpretation of experiments and empirical facts: "Philosophy [i.e., physics] is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth." http://en.wikipedia.org/wiki/Scientific_revolution Many of the important figures of the scientific revolution, however, shared in the Renaissance respect for ancient learning and cited ancient pedigrees for their innovations. Nicolaus Copernicus (1473– 1543), Kepler (1571–1630), Newton (1643–1727) and Galileo Galilei (1564–1642) all traced different ancient and medieval ancestries for the heliocentric system. In the Axioms Scholium of his Principia Newton said its axiomatic three laws of motion were already accepted by mathematicians such as Huygens (1629–1695), Wallace, Wren and others, and also in memos in his draft preparations of the second edition of the Principia he attributed its first law of motion and its law of gravity to a range of historical figures. According to Newton himself and other historians of science, his Principia's first law of motion was the same as Aristotle's counterfactual principle of interminable locomotion in a void stated in Physics 4.8.215a19—22 and was also endorsed by ancient Greek atomists and others. As Newton expressed himself: Many of the important figures of the scientific revolution, however, shared in the Renaissance respect for ancient learning and cited ancient pedigrees for their innovations. Nicolaus Copernicus (1473– 1543), Kepler (1571–1630), Newton (1643–1727) and Galileo Galilei (1564–1642) all traced different ancient and medieval ancestries for the heliocentric system. In the Axioms Scholium of his Principia Newton said its axiomatic three laws of motion were already accepted by mathematicians such as Huygens (1629–1695), Wallace, Wren and others, and also in memos in his draft preparations of the second edition of the Principia he attributed its first law of motion and its law of gravity to a range of historical figures. According to Newton himself and other historians of science, his Principia's first law of motion was the same as Aristotle's counterfactual principle of interminable locomotion in a void stated in Physics 4.8.215a19—22 and was also endorsed by ancient Greek atomists and others. As Newton expressed himself: All those ancients knew the first law [of motion] who attributed to atoms in an infinite vacuum a motion which was rectilinear, extremely swift and perpetual because of the lack of resistance... Aristotle was of the same mind, since he expresses his opinion thus...[in Physics 4.8.215a19-22], speaking of motion in the void [in which bodies have no gravity and] where there is no impediment he writes: 'Why a body once moved should come to rest anywhere no one can say. For why should it rest here rather than there ? Hence either it will not be moved, or it must be moved indefinitely, unless something stronger impedes it.' If correct, Newton's view that the Principia's first law of motion had been accepted at least since antiquity and by Aristotle refutes the traditional thesis of a scientific revolution in dynamics by Newton's because the law was denied by Aristotle. The geocentric model remained a widely accepted model until around 1543 when Nicolaus Copernicus published his book entitled De revolutionibus orbium coelestium. At around the same time, the findings of Vesalius corrected the previous anatomical teachings of Galen, which were based upon the dissection of animals even though they were supposed to be a guide to the human body. Antonie van Leeuwenhoek, the first person to use a microscope to view bacteria. Andreas Vesalius (1514–1564) was an author of one of the most influential books on human anatomy, De humani corporis fabrica. French surgeon Ambroise Paré (c.1510–1590) is considered as one of the fathers of surgery. He was leader in surgical techniques and battlefield medicine, especially the treatment of wounds. Partly based on the works by the Italian surgeon and anatomist Matteo Realdo Colombo (c. 1516 - 1559) the Anatomist William Harvey (1578–1657) described the circulatory system. Herman Boerhaave (1668–1738) is sometimes referred to as a "father of physiology" due to his exemplary teaching in Leiden and textbook 'Institutiones medicae' (1708). It was between 1650 and 1800 that the science of modern dentistry developed. It is said that the 17th century French physician Pierre Fauchard (1678–1761) started dentistry science as we know it today, and he has been named "the father of modern dentistry". Pierre Vernier (1580–1637) was inventor and eponym of the vernier scale used in measuring devices. Evangelista Torricelli (1607– 1647) was best known for his invention of the barometer. Although Franciscus Vieta(1540,1603) gave the first notation of modern algebra, John Napier (1550–1617) invented logarithms, and Edmund Gunter (1581–1626) created the logarithmic scales (lines, or rules) upon which slide rules are based, it was William Oughtred (1575– 1660) who first used two such scales sliding by one another to perform direct multiplication and division; and thus is credited as the inventor of the slide rule in 1622. Blaise Pascal (1623–1662) invented the mechanical calculator in 1642. The introduction of his Pascaline in 1645 launched the development of mechanical calculators first in Europe and then all over the world. He also made important contributions to the study of fluid and clarified the concepts of pressure and vacuum by generalizing the work of Evangelista Torricelli. He wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat (1601–1665) on probability theory, strongly influencing the development of modern economics and social science. Gottfried Leibniz (1646-1716), building on Pascal's work, became one of the most prolific inventors in the field of mechanical calculators ; he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, foundation of virtually all modern computer architectures. The chemical philosophy Newton in a 1702 portrait by Godfrey Kneller. Chemistry, and its antecedent alchemy, became an increasingly important aspect of scientific thought in the course of the sixteenth and 17th centuries. The importance of chemistry is indicated by the range of important scholars who actively engaged in chemical research. Among them were the astronomer Tycho Brahe, the chemical physician Paracelsus, and the English philosophers Robert Boyle and Isaac Newton. Unlike the mechanical philosophy, the chemical philosophy stressed the active powers of matter, which alchemists frequently expressed in terms of vital or active principles—of spirits operating in nature. Empiricism The Aristotelian scientific tradition's primary mode of interacting with the world was through observation and searching for "natural" circumstances through reasoning. It viewed experiments to be contrivances that at best revealed only contingent and non-universal facts about nature in an artificial state. Coupled with this approach was the belief that rare events which seemed to contradict theoretical models were "monsters", telling nothing about nature as it "naturally" was. During the scientific revolution, changing perceptions about the role of the scientist in respect to nature, the value of evidence, experimental or observed, led towards a scientific methodology in which empiricism played a large, but not absolute, role. Under the influence of scientists and philosophers like Francis Bacon, an empirical tradition was developed by the 16th century. The Aristotelian belief of natural and artificial circumstances was abandoned, and a research tradition of systematic experimentation was slowly accepted throughout the scientific community. Bacon's philosophy of using an inductive approach to nature—to abandon assumption and to attempt to simply observe with an open mind—was in strict contrast with the earlier, Aristotelian approach of deduction, by which analysis of known facts produced further understanding. In practice, of course, many scientists (and philosophers) believed that a healthy mix of both was needed—the willingness to question assumptions, yet also to interpret observations assumed to have some degree of validity. At the end of the scientific revolution the organic, qualitative world of book-reading philosophers had been changed into a mechanical, mathematical world to be known through experimental research. Though it is certainly not true that Newtonian science was like modern science in all respects, it conceptually resembled ours in many ways— much more so than the Aristotelian science of a century earlier. Many of the hallmarks of modern science, especially in respect to the institution and profession of science, would not become standard until the mid-19th century Mathematization Scientific knowledge, according to the Aristotelians, was concerned with establishing true and necessary causes of things. To the extent that medieval natural philosophers used mathematical problems, they limited social studies to theoretical analyses of local speed and other aspects of life. The actual measurement of a physical quantity, and the comparison of that measurement to a value computed on the basis of theory, was largely limited to the mathematical disciplines of astronomy and optics in Europe. In the 16th and 17th centuries, European scientists began increasingly applying quantitative measurements to the measurement of physical phenomena on the Earth. Galileo maintained strongly that mathematics provided a kind of necessary certainty that could be compared to God's: "With regard to those few mathematical propositions which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty."