Download Huygens` Principle

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[7] or that its chemical composition was
even more complex[8]
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[9] 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[10]
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"[11]
But the most innovative idea[citation needed] 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."[12]
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),[13] Kepler (1571–1630),[14] Newton (1643–1727)[15] and
Galileo Galilei (1564–1642)[16][17][18][19] 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.[20] According to Newton himself and other historians of
science,[21] 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),[13] Kepler (1571–1630),[14] Newton (1643–1727)[15] and
Galileo Galilei (1564–1642)[16][17][18][19] 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.[20] According to Newton himself and other historians of
science,[21] 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.'[22]
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.[citation
needed]
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.[23] 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.[24] 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".[25]
Pierre Vernier (1580–1637) was inventor and eponym of the vernier
scale used in measuring devices.[26] 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.[27] 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.[28]
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[29] 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,[55] 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.[56]
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.[57] 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.[58] 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.[59][60]
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."[61]