原天地之美 達萬物之理

1

高崇文 中原大學物理系

原天地之美 達萬物之理

2

莊子．知北遊：「天地有大美而不言，四時有明法而不議，萬物有成理而不說。聖人者，原天地之美而達萬物之理，是故至人無為，大聖不作，觀於天地之謂也。

Parmenides

3

Parmenides of Elea (early 5th century BCE) was an

ancient Greek philosopher born in Elea, a Greek city on

the southern coast of Italy. He was the founder of the

Eleatic school of philosophy. The single known work of

Parmenides is a poem, On Nature, which has survived

only in fragmentary form. In this poem, Parmenides

describes two views of reality. In "the way of truth" (a part

of the poem), he explains how reality (coined as "what-is")

is one, change is impossible, and existence is timeless,

uniform, necessary, and unchanging. In "the way of

opinion," he explains the world of appearances, in which

one's sensory faculties lead to conceptions which are false

and deceitful.

Nor was once, nor will be

4

He argued that movement was impossible because it requires moving into "the void",

and Parmenides identified "the void" with nothing, and therefore (by definition) it does

not exist. That which does exist is The Parmenidean One, which is timeless, uniform,

and unchanging:

How could what is perish? How could it have come to be? For if it came into being,

it is not; nor is it if ever it is going to be. Thus coming into being is extinguished,

and destruction unknown. (B 8.20-22)

Nor was [it] once, nor will [it] be, since [it] is, now, all together, / One, continuous;

for what coming-to-be of it will you seek? / In what way, whence, did [it] grow?

Neither from what-is-not shall I allow / You to say or think; for it is not to be said or

thought / That [it] is not. And what need could have impelled it to grow / Later or

sooner, if it began from nothing? Thus [it] must either be completely or not at all.

(B 8.5-11)

[What exists] is now, all at once, one and continuous... Nor is it divisible, since it is

all alike; nor is there any more or less of it in one place which might prevent it

from holding together, but all is full of what is. (B 8.5-6, 8.22-24)

And it is all one to me / Where I am to begin; for I shall return there again. (B 5)

Zeno‘s paradoxes

5

Zeno's paradoxes are a set of philosophical problems generally thought to have been

devised by Greek philosopher Zeno of Elea (ca. 490–430 BC) to support Parmenides's

doctrine that contrary to the evidence of one's senses, the belief in plurality and change

is mistaken, and in particular that motion is nothing but an illusion. It is usually

assumed, based on Plato's Parmenides (128a-d), that Zeno took on the project of

creating these paradoxes because other philosophers had created paradoxes against

Parmenides's view. Thus Plato has Zeno say the purpose of the paradoxes "is to show

that their hypothesis that existences are many, if properly followed up, leads to still

more absurd results than the hypothesis that they are one." (Parmenides 128d).

Achilles and Tortoise

6

In the paradox of Achilles and the Tortoise, Achilles is in a

footrace with the tortoise. Achilles allows the tortoise a

head start of 100 metres. If we suppose that each racer

starts running at some constant speed (one very fast and

one very slow), then after some finite time, Achilles will

have run 100 metres, bringing him to the tortoise's

starting point. During this time, the tortoise has run a

much shorter distance, say, 10 metres. It will then take

Achilles some further time to run that distance, by which

time the tortoise will have advanced farther; and then

more time still to reach this third point, while the tortoise

moves ahead. Thus, whenever Achilles reaches

somewhere the tortoise has been, he still has farther to

go. Therefore, because there are an infinite number of

points Achilles must reach where the tortoise has already

been, he can never overtake the tortoise.

Arrow paradox

7

In the arrow paradox , Zeno states that for

motion to occur, an object must change the

position which it occupies. He gives an

example of an arrow in flight. He states that in

any one (durationless) instant of time, the

arrow is neither moving to where it is, nor to

where it is not. It cannot move to where it is not,

because no time elapses for it to move there; it

cannot move to where it is, because it is

already there. In other words, at every instant

of time there is no motion occurring. If

everything is motionless at every instant, and

time is entirely composed of instants, then

motion is impossible.

Reply to Zeno

8

(A) Aristotle's objection to the arrow paradox was that "Time is not composed of

indivisible nows any more than any other magnitude is composed of indivisibles.

Saint Thomas Aquinas, commenting on Aristotle's objection, wrote "Instants are

not parts of time, for time is not made up of instants any more than a magnitude

is made of points, as we have already proved. Hence it does not follow that a

thing is not in motion in a given time, just because it is not in motion in any instant

of that time.

(B) Before 212 BC, Archimedes had developed a method to derive a finite answer for

the sum of infinitely many terms that get progressively smaller. Modern calculus

achieves the same result, using more rigorous methods. These methods allow

the construction of solutions based on the conditions stipulated by Zeno, i.e. the

amount of time taken at each step is geometrically decreasing. Infinite processes

remained theoretically troublesome in mathematics until the late 19th century.

The epsilon-delta version of Weierstrass and Cauchy developed a rigorous

formulation of the logic and calculus involved. These works resolved the

mathematics involving infinite processes

Road to atomism

9

Parmenides made the ontological argument against nothingness, essentially

denying the possible existence of a void. According to Aristotle, this led

Democritus and Leucippus, and many other physicists, to propose the atomic

theory, which supposes that everything in the universe is either atoms or voids,

specifically to contradict Parmenides' argument. Aristotle himself reasoned, in

opposition to atomism, that in a complete vacuum, motion would encounter no

resistance, and "no one could say why a thing once set in motion should stop

anywhere; for why should it stop here rather than here? So that a thing will either

be at rest or must be moved ad infinitum, unless something more powerful get in

its way. Popper wrote:

So what was really new in Parmenides was his axiomatic-deductive method,

which Leucippus and Democritus turned into a hypothetical-deductive method,

and thus made part of scientific methodology.

Democritus

10

Democritus ("chosen of the people") (c. 460 – c. 370

BC) was an Ancient Greek philosopher born in Abdera,

Thrace, Greece. A pupil of Leucippus, he was an

influential pre-Socratic philosopher who formulated an

atomic theory for the universe. The many anecdotes

about Democritus, especially in Diogenes Laërtius,

attest to his disinterest, modesty, and simplicity, and

show that he lived exclusively for his studies. He was

cheerful, and was always ready to see the comical side

of life, which later writers took to mean that he always

laughed at the foolishness of people. Popularly known

as the Laughing Philosopher (for laughing at human

follies).

Mechanical Explanation

11

Democritus followed in the tradition of Leucippus, who

seems to have come from Miletus, and he carried on the

scientific rationalist philosophy associated with that city.

They were both strict determinists and thorough

materialists, believing everything to be the result of natural

laws. Unlike Aristotle or Plato, the atomists attempted to

explain the world without reasoning to purpose, prime

mover, or final cause. For the atomists questions should

be answered with a mechanistic explanation, while their

opponents search for explanations which, in addition to the

material and mechanistic, also included the formal and

teleological. Modern science has focused on mechanistic

questions, which have led to scientific knowledge,

especially in physics, The atomists looked exclusively for

mechanistic questions, and only admitted mechanistic

answers.

Democritean atoms

12

The theory of Democritus and Leucippus held that

everything is composed of "atoms", which are physically,

but not geometrically, indivisible; that between atoms,

there lies empty space; that atoms are indestructible;

have always been, and always will be, in motion; that

there are an infinite number of atoms, and kinds of atoms,

which differ in shape, and size. Of the mass of atoms,

Democritus said "The more any indivisible exceeds, the

heavier it is." But his exact position on weight of atoms is

disputed. Leucippus is widely credited with being the first

to develop the theory of atomism, although Isaac Newton

preferred to credit the obscure Mochus the Phoenician

(whom he believed to be the biblical Moses) as the

inventor of the idea on the authority of Posidonius and

Strabo.

Void Hypothesis

13

The atomistic void hypothesis was a response to the paradoxes of

Parmenides and Zeno, the founders of metaphysical logic, who put forth

difficult to answer arguments in favor of the idea that there can be no

movement. They held that any movement would require a void—which is

nothing—but a nothing cannot exist. The Parmenidean position was "You say

there 'is' a void; therefore the void is not nothing; therefore there is not the

void." The position of Parmenides appeared validated by the observation that

where there seems to be nothing there is air, and indeed even where there is

not matter there is something, for instance light waves. The atomists agreed

that motion required a void, but simply ignored the argument of Parmenides

on the grounds that motion was an observable fact. Therefore, they asserted,

there must be a void. This idea survived in a refined version as Newton's

theory of absolute space, which met the logical requirements of attributing

reality to not-being.

Democritus‘ cosmology

14

Democritus held that the Earth was round, and stated that originally the

universe was composed of nothing but tiny atoms churning in chaos, until they

collided together to form larger units—including the earth and everything on it.

He surmised that there are many worlds, some growing, some decaying; some

with no sun or moon, some with several. He held that every world has a

beginning and an end, and that a world could be destroyed by collision with

another world. To epitomize Democritus's cosmology, Russell calls on Shelley:

"Worlds on worlds are rolling ever / From creation to decay, / Like the bubbles

on a river / Sparkling, bursting, borne away

Fifth element

15

Aristotle proposed a fifth element, aether, in

addition to the four proposed earlier by

Empedocles.

Earth, which is cold and dry; this corresponds to

the modern idea of a solid.

Water, which is cold and wet; this corresponds

to the modern idea of a liquid.

Air, which is hot and wet; this corresponds to the

modern idea of a gas.

Fire, which is hot and dry; this corresponds to

the modern ideas of plasma and heat.

Aether, which is the divine substance that makes

up the heavenly spheres and heavenly bodies

(stars and planets).

Mount Etna in Sicily, the

legendary location of

Empedocles' alleged

suicide

Fifth element

16

Each of the four earthly elements has its

natural place. All that is earthly tends toward

the center of the universe, i.e., the center of

the Earth. Water tends toward a sphere

surrounding the center. Air tends toward a

sphere surrounding the water sphere. Fire

tends toward the lunar sphere (in which the

Moon orbits). When elements are moved out of

their natural place, they naturally move back

towards it. This is "natural motion"—motion

requiring no extrinsic cause. So, for example,

in water, earthy bodies sink while air bubbles

rise up; in air, rain falls and flame rises.

Outside all the other spheres, the heavenly,

fifth element, manifested in the stars and

planets, moves in the perfection of circles.

Aristotle and his cosmology In his Metaphysics, Aristotle developed a physical cosmology

of spheres, based on the mathematical models of Eudoxus.

In Aristotle's fully developed celestial model, the spherical

Earth is at the centre of the universe and the planets are

moved by either 47 or 55 interconnected spheres that form a

unified planetary system, whereas in the models of Eudoxus

each planet's individual set of spheres were not connected to

those of the next planet. Aristotle added additional spheres to

those proposed by Eudoxus, to counteract the motion of the

outer spheres. Aristotle considers that these spheres are

made of an unchanging fifth element, the aether. Each of

these concentric spheres is moved by its own god — an

unchanging divine unmoved mover, and who moves its

sphere simply by virtue of being loved by it.

Aristotle

384 BC – 322 BC

Unmoved mover

Aristotle argues, in Book 8 of the Physics and Book 12

of the Metaphysics, "that there must be an immortal,

unchanging being, ultimately responsible for all

wholeness and orderliness in the sensible world". He

argued that the bare existence of change requires the

postulation of a first cause, an unmoved mover whose

necessary existence underpins the ceaseless activity

of the world of motion‖. Aristotle's Metaphysics (―after

the Physics‖), develops his peculiar stellar theology of

the prime mover, an independent divine eternal

unchanging immaterial substance. This Aristotelian

concept had its roots in cosmological speculations of

the earliest Greek "Pre-Socratic" philosophers and

became highly influential and widely drawn upon in

medieval philosophy and theology.

Almagest of Claudius Ptolemy

The Almagest is a 2nd-century mathematical and

astronomical treatise on the apparent motions of the stars

and planetary paths. Written in Greek by Claudius Ptolemy,

a Roman era scholar of Egypt, it is one of the most

influential scientific texts of all time, with its geocentric

model accepted for more than twelve hundred years from

its origin in Hellenistic Alexandria, in the medieval

Byzantine and Islamic worlds, and in Western Europe

through the Middle Ages and early Renaissance.

Claudius Ptolemy

AD 90 – c. AD 168

Prograde and retrograde motions

For superior planets the planet would typically move through in the night sky

slower than the stars. Each night the planet would "lag" a little behind the star.

This is prograde motion. Occasionally, near opposition, the planet would appear

to move through in the night sky faster than the stars. This is retrograde motion.

Ptolemy's model, in part, sought to explain this behavior. The inferior planets

were always observed to be near the sun, appearing only shortly before sunrise

or shortly after sunset. To accommodate this, Ptolemy's model fixed the motion

of Mercury and Venus so that the line from the equant point to the center of the

epicycle was always parallel to the earth-sun line.

A small circle whose center lies on a

larger one (the deferent ). The planet

swings around on the epicycle while the

center of the epicycle is carried around

the deferent. In this way the retrograde

motion could be explained.

Epicycle

A point offset from the center of

circular motion. By offsetting the

Earth from the center of the circular

motion it would appear that planets

moved faster at some times of the

year than others.

Eccentrics

A point displaced from the

center of the circular orbit

around which the motion of the

planet really was uniform. This

helped get the varying speed of

the planets better than just

using eccentrics.

Equant

Antikythera mechanism

24

The Antikythera mechanism is an ancient analog computer

designed to calculate astronomical positions. It was recovered

in 1900–1901 from the Antikythera wreck,but its significance

and complexity were not understood until a century later. The

construction has been dated to the early 1st century BCE.

Technological artifacts approaching its complexity and

workmanship did not appear again until the 14th century CE,

when mechanical astronomical clocks began to be built in

Western Europe.Professor Michael Edmunds of Cardiff

University, who led a 2006 study of the mechanism, said:

This device is just extraordinary, the only thing of its kind. The

design is beautiful, the astronomy is exactly right. The way the

mechanics are designed just makes your jaw drop. Whoever

has done this has done it extremely carefully ... in terms of

historic and scarcity value, I have to regard this mechanism as

being more valuable than the Mona Lisa.

—30 November 2006

The Antikythera

mechanism is

kept at the

National

Archaeological

Museum of

Athens

Antikythera mechanism

25

The mechanism was operated by turning a small hand crank

(now lost) which was linked via a crown gear to the largest

gear (the 4 spoked gear visible on the front of fragment A

(named b1)). This allowed setting of the date on the front dial.

The action of turning the hand crank would also cause all

interlocked gears within the mechanism to rotate, resulting in

the calculation of the position of the Sun and Moon and other

astronomical information, such as moon phases, eclipse

cycles, and theoretically the locations of planets.

They have changed the world forever!

Ferdinand Magellan

1480 – 1521

Portuguese explorer

His expedition

completed the first

circumnavigation

of the Earth.

Martin Luther

1483-1546

seminal figure

of a reform movement in

sixteenth century

Christianity,

Protestant Reformation.

Michelangelo

1475 –1564

was an Italian

Renaissance

sculptor, painter,

architect,

poet, and engineer.

Nicolaus Copernicus

1473-1543

mathematician and

Astronomer who

formulated a

heliocentric

model of the universe

Retrograde motion of planets

Less epicycles?

Although Copernicus' models reduced the magnitude

of the epicycles considerably, whether they were

simpler than Ptolemy's is moot. Copernicus eliminated

Ptolemy's somewhat-maligned equant but at a cost of

additional epicycles The idea that Copernicus used

only 34 circles in his system comes from his own

statement in Commentariolus. By the time he

published De revolutionibus orbium coelestium, he

had added more circles. Copernicus in his works

exaggerated the number of epicycles used in the

Ptolemic system; although original counts ranged to

80 circles, by Copernicus's time the Ptolemic system

had been updated by Peurbach towards the similar

number of 40; hence Copernicus effectively replaced

the problem of retrograde with further epicycles.

What is counterargument of Copernicus?

There have been two arguments against heliocentrism, the first one is about why we are not throw out by the rotation of the Earth. The second one is about the absence of the stellar parallax.

Copernicus answered the second question with a very simple answer. They are too small to be measured. Which is the correct answer.

Copernicus didn‘t answer the first question. However he asked the

following question: if we cannot believe the Earth is rotating, how can we believe the stars which are at the infinite distances and probably infinite heavy objects to move daily?

By asking this question Copernicus has abandoned the ancient concept of celestial sphere because those stars should not move but are attached at the celestial sphere according to the theory of celestial sphere.

Tycho Brahe

Tycho Brahe (1546 – 1601) was a Danish nobleman

known for his accurate and comprehensive

astronomical and planetary. In his De nova stella (On

the new star) of 1573, he refuted the Aristotelian belief

in an unchanging celestial realm. His precise

measurements indicated that "new stars," (stellae

novae, now known as supernovae) in particular that of

1572, lacked the parallax expected in sub-lunar

phenomena, and were therefore not "atmospheric"

tailless comets as previously believed, but were above

the atmosphere and moon. Using similar

measurements he showed that comets were also not

atmospheric phenomena as previously thought, and

must pass through the supposedly "immutable"

celestial spheres.

Johannes Kepler

31

Johannes Kepler ( 1571 – 1630)

was a German mathematician,

astronomer and astrologer. A key

figure in the 17th century scientific

revolution, he is best known for

his eponymous laws of planetary

motion, codified by later

astronomers, based on his works

Astronomia nova, Harmonices

Mundi, and Epitome of

Copernican Astronomy. These

works also provided one of the

foundations for Isaac Newton's

theory of universal gravitation.

Tycho and Kepler

32

Tycho began corresponding with Kepler,

starting with a harsh but legitimate

critique of Kepler's system; among a host

of objections, Tycho took issue with the

use of inaccurate numerical data taken

from Copernicus. Through their letters,

Tycho and Kepler discussed a broad

range of astronomical problems, dwelling

on lunar phenomena and Copernican

theory . But without the significantly more

accurate data of Tycho's observatory,

Kepler had no way to address many of

these issues

Kepler‘s idea

33

Adapted from his 1609

Astronomia nova, established the

position of Earth‘s orbit. In the

Copernican system, Mars returns

to the same position K on its orbit

every 687 days. Earth, starting at

Θ, makes a complete

counterclockwise revolution

every 365 days and continues

around to H after the remaining

322 days it takes Mars to

complete its revolution. Similar

times bring Earth to E and Z in

subsequent revolutions of Mars.

Kepler thus verified that Earth‘s

orbit needed to be shifted from

the solid outline to the dashed

one.

War on Mars!

34

Kepler found that the use of a circular orbit led to

an 8‘ error at the octants of its orbit. Because

God had given him such a great observer in

Tycho Brahe—whose typical observational errors

were 2‘ or less—Kepler wrote that he dared not

stop with a maximum error of 8‘. (When Mars

was observed from Earth at close approach, the

heliocentric error of 8‘ became nearly a half-

degree geocentric error.) Thus Kepler continued

waging war on Mars. Kepler tried a variety of

oval curves that could have fit the observations

equally as well as the ellipse. But he was

unsatisfied with the physical basis for choosing

any of them until he noticed that one focus of an

approximating ellipse coincided with the Sun.

That curve and focus made it easier for Kepler to

conjure up a physical explanation

Physics instead of Geometry

35

In Kepler‘s day, virtually all astronomers looked to mother

geometry for inspiration. Kepler was unique in seeking

physical causes for celestial motions. Even his astute

teacher, Michael Maestlin, urged him to forget about physical

causes and to attend to geometry alone for explanation. But

in Kepler‘s vision, Earth‘s constant speed in the Copernican

system made no physical sense. Surely it should actually

move faster in January when it was closer to the Sun. In both

Ptolemaic and Copernican systems, the Sun appeared to

move faster in January because of the eccentric positioning

of its, or Earth‘s, orbital circle. Kepler called the phenomenon

the optical effect. But he also wanted the total apparent

motion to be a combination of the optical effect and a

physical effect. If each effect played a comparable role, then

the Copernican eccentricity of Earth‘s orbit had to be halved,

or bisected, Kepler reasoned. In that case, the Sun‘s varying

distance from Earth would be half as great as previously

assumed.

Michael Maestlin (1550,– 1631)

was a German astronomer and

mathematician, known for being

the mentor of Johannes Kepler.

Elliptical orbit

36

Finding that an elliptical orbit fit

the Mars data, he immediately

concluded that all planets move

in ellipses, with the sun at one

focus—Kepler's first law of

planetary motion. Because he

employed no calculating

assistants, however, he did not

extend the mathematical analysis

beyond Mars. By the end of the

year, he completed the

manuscript for Astronomia nova,

though it would not be published

until 1609 due to legal disputes

over the use of Tycho's

observations, the property of his

heirs

Rene Descartes (1596-1650)

37

René Descartes (1596 – 1650) was a French

philosopher, mathematician, and writer who spent

most of his adult life in the Dutch Republic. He has

been dubbed the ‘Father of Modern Philosophy’,

and much subsequent Western philosophy is a

response to his writings. His Meditations on First

Philosophy continues to be a standard text at most

university philosophy departments. He is perhaps best

known for the philosophical statement "Cogito ergo

sum―.

Cartesian coordinate

38

Descartes' influence in mathematics is

equally apparent; the Cartesian coordinate

system — allowing reference to a point in

space as a set of numbers, and allowing

algebraic equations to be expressed as

geometric shapes in a two-dimensional

coordinate system (and conversely, shapes

to be described as equations) — was

named after him. He is credited as the

father of analytical geometry, the bridge

between algebra and geometry, crucial to

the discovery of infinitesimal calculus and

analysis. Descartes was also one of the

key figures in the Scientific Revolution and

has been described as an example of

genius.

Void and space (1644)

39

Because of his philosophical beliefs, René

Descartes proposed in 1644 that no empty

space can exist and that space must

consequently be filled with matter. The parts of

this matter tend to move in straight paths, but

because they lie close together, they can't move

freely, which according to Descartes implies that

every motion is circular, so the aether is filled

with vortices. Descartes also distinguishes

between different forms and sizes of matter in

which rough matter resists the circular

movement more strongly than fine matter. Due to

centrifugal force, matter tends towards the outer

edges of the vortex, which causes a

condensation of this matter there.

Theory of vortex

40

The rough matter cannot follow this

movement due to its greater inertia—so

due to the pressure of the condensed outer

matter those parts will be pushed into the

center of the vortex. According to

Descartes, this inward pressure is nothing

else than gravity. He compared this

mechanism with the fact that if a rotating,

liquid filled vessel is stopped, the liquid

goes on to rotate. Now, if one drops small

pieces of light matter (e.g. wood) into the

vessel, the pieces move to the middle of

the vessel

Blaise Pascal(1623-1662)

Blaise Pascal (1623 – 1662) was a French

mathematician, physicist, inventor, writer and Christian

philosopher. He was a child prodigy who was educated

by his father, a tax collector in Rouen. Pascal's earliest

work was in the natural and applied sciences where he

made important contributions to the study of fluids, and

clarified the concepts of pressure and vacuum by

generalizing the work of Evangelista Torricelli. Pascal

also wrote in defense of the scientific method. By 1646,

Pascal had learned of Evangelista Torricelli's

experimentation with barometers. Having replicated an

experiment that involved placing a tube filled with

mercury upside down in a bowl of mercury, Pascal

questioned what force kept some mercury in the tube

and what filled the space above the mercury in the

tube.

Vacuum or invisible matter?

At the time, most scientists contended that, rather than a vacuum, some invisible

matter was present. This was based on the Aristotelian notion that creation was a

thing of substance, whether visible or invisible; and that this substance was forever

in motion. Furthermore, "Everything that is in motion must be moved by something,"

Aristotle declared. Therefore, to the Aristotelian trained scientists of Pascal's time, a

vacuum was an impossibility.

How so? As proof it was pointed out: Light passed through the so-called "vacuum"

in the glass tube. Aristotle wrote how everything moved, and must be moved by

something. Therefore, since there had to be an invisible "something" to move the

light through the glass tube, there was no vacuum in the tube. Not in the glass tube

or anywhere else. Vacuums – the absence of any and everything – were simply an

impossibility.

Experiment of Pascal

Following more experimentation in this vein, in 1647

Pascal produced Experiences nouvelles touchant le vide

("New Experiments with the Vacuum"), which detailed

basic rules describing to what degree various liquids

could be supported by air pressure. It also provided

reasons why it was indeed a vacuum above the column

of liquid in a barometer tube.

On 19 September 1648, after many months of Pascal's

friendly but insistent prodding, Florin Périer, husband of

Pascal's elder sister Gilberte, was finally able to carry

out the fact-finding mission vital to Pascal's theory.

Pascal replicated the experiment in Paris by carrying a

barometer up to the top of the bell tower at the church of

Saint-Jacques-de-la-Boucherie, a height of about fifty

meters. The mercury dropped two lines.

Otto von Guericke, in 1656 to demonstrate the air pump

that he had invented, and the concept of atmospheric

pressure. The first artificial vacuum had been produced

a few years earlier by Evangelista Torricelli, and had

inspired Guericke to design the world's first vacuum

pump, which consisted of a piston and cylinder with one-

way flap valves. The hemispheres became popular in

physics lectures as an illustration of the strength of air

pressure, and are still used in education. A pair of the

original hemispheres are preserved in the Deutsches

Museum in Munich. In 1663 (or, according to some

sources, in 1661) the same demonstration was given in

Berlin before Frederick William, Elector of Brandenburg

with twenty-four horses.

Magdeburg hemispheres

Boyle and Hooke

After learning about Guericke's

pump through Schott's book,

Robert Boyle worked with

Robert Hooke to design and

build an improved air pump.

From this, through various

experiments, they formulated

what is called Boyle's law,

which states that the volume of

a body of an ideal gas is

inversely proportional to its

pressure.

Robert Boyle (1627-1691)

46

Robert Boyle, (1627 – 1691) was an Irish 17th-

century natural philosopher, chemist, physicist, and

inventor. Although his research clearly has its roots

in the alchemical tradition, Boyle is largely

regarded today as the first modern chemist, and

therefore one of the founders of modern chemistry,

and one of the pioneers of modern experimental

scientific method. He is best known for Boyle's law,

which describes the inversely proportional

relationship between the absolute pressure and

volume of a gas, if the temperature is kept constant

within a closed system. Among his works, The

Sceptical Chymist is seen as a cornerstone book

in the field of chemistry.

Robert Boyle (1627-1691)

47

Material bodies are, according to Boyle, composed of

extremely small particles, which combine to form clusters of

various sizes and configurations. The configurations, motions,

and collisions of these clusters produce secondary qualities,

including the chemical properties of matter. Boyle conducted

many observations and experiments aiming to demonstrate

that various chemical properties can be explained

mechanically. He performed an extensive series of

experiments with the newly fabricated air pump to prove that

the properties of air—most notably its "spring"—could be

explained in mechanical terms. In his work, The Sceptical

Chymist (1661) Boyle abandoned the Aristotelian ideas of the

classical elements—earth, water, air, and fire in favor of

corpuscularianism. His later work, The Origin of Forms and

Qualities (1666), Boyle to used corpuscularianism to explain

all of the major Aristotelian concepts, marking a departure

from traditional Aristotelianism.

Natural Philosophy

48

Gassendi and Descartes set the agenda for the next generation of natural

philosophers, who accepted mechanical principles in general, believing

that they had to choose between Gassendi's atomism and Descartes's

plenism. Robert Boyle (1627–1691), Christiaan Huygens (1629–1695),

and Isaac Newton (1642–1727)

Christiaan Huygens(1629-1695)

49

Huygens followed Descartes in attempting to

mathematize physics and the mechanical philosophy. He

applied this approach to create a wave theory of light, a

mathematical analysis of centrifugal force, and an

improved theory of impact. He applied mathematics to

physical problems far more successfully than had

Descartes. Huygens adhered to the tenets of the

mechanical philosophy of his time. In particular he sought

explanations of the force of gravity that avoided action at

a distance. Huygens adhered to what has been called,

more explicitly, "experimentally-oriented corpuscular-

mechanical" natural philosophy. In the analysis of the

Scientific Revolution this appears as a mainstream

position, at least from the founding of the Royal Society

to the emergence of Newton.

Wave theory of Light

50

Huygens is remembered especially for his wave theory

of light. It was published in 1690 in his Traité de la

lumière (Treatise on light). A basic principle of Huygens

is that the speed of light is finite, a point which had been

the subject of an experimental demonstration by Olaus

Roemer (1679 at the Paris Observatory), but which

Huygens is presumed to have believed already. It deals

with wave fronts and their normal rays, with propagation

conceived by means of spherical waves emitted along

the wave front .It was justified as an ether theory,

involving transmission via perfectly elastic particles, a

revision of the view of Descartes. The nature of light was

therefore a longitudinal wave.

Ole Rømer

1644 – 1710,,

Wave theory of Light

51

Huygens had experimented in 1672 with double

refraction (birefringence) in Icelandic spar

(calcite), a phenomenon discovered in 1669 by

Rasmus Bartholin. At first he could not elucidate

what he found. He later explained it with his

wave front theory and concept of evolutes. He

also developed ideas on caustics. Newton in his

Opticks of 1704 proposed instead a corpuscular

theory of light. The theory of Huygens was not

accepted, by some, because longitudinal waves

cannot show birefringence. The interference

experiments of Thomas Young vindicated a

wave theory in 1801: the results could not be

explained with light particles. The solution to the

problem Huygens had faced was then resolved

by a transverse wave theory.

Christiaan Huygens(1629-1695)

52

After his first visit to England in 1661, when he

attended a meeting of the Gresham College

group in April and learned directly about Boyle's

air pump experiments, Huygens spent time in

late 1661 and early 1662 replicating the work. It

proved a long process, brought to the surface an

experimental issue ("anomalous suspension")

and the theoretical issue of horror vacui, and

ended in July 1663 as Huygens became a

Fellow of the Royal Society. It has been said that

Huygens finally accepted Boyle's view of the

void, as against the Cartesian denial of it.

Luminiferous aether

To Robert Boyle in the 17th century, shortly before Isaac Newton, the aether

was a probable hypothesis and consisted of subtle particles, one sort of which

explained the absence of vacuum and the mechanical interactions between

bodies, and the other sort of which explained phenomena such as magnetism

(and possibly gravity) that were inexplicable on the basis of the purely

mechanical interactions of macroscopic bodies:

...though in the ether of the ancients there was nothing taken notice of but a

diffused and very subtle substance; yet we are at present content to allow that

there is always in the air a swarm of steams moving in a determinate course

between the north pole and the south.

Robert Boyle, The Works of the Honourable Robert Boyle, ed. Thomas Birch,

2nd edn., 6 vols. (London, 1772), III, 316;

Luminiferous aether: Newton

Isaac Newton contended that light was made up of

numerous small particles. This could explain such

features as light's ability to travel in straight lines

and reflect off surfaces. This theory was known to

have its problems: although it explained reflection

well, its explanation of refraction and diffraction

was less satisfactory. In order to explain refraction,

Newton's Opticks (1704) postulated an "Aethereal

Medium" transmitting vibrations faster than light,

by which light, when overtaken, is put into "Fits of

easy Reflexion and easy Transmission", which

caused refraction and diffraction.

Luminiferous aether: Newton

He wrote, "I do not know what this Aether is", but that if it consists of particles then they must be "exceedingly smaller than those of Air, or even than those of Light: The exceeding smallness of its Particles may contribute to the greatness of the force by which those Particles may recede from one another, and thereby make that Medium exceedingly more rare and elastic than Air, and by consequence exceedingly less able to resist the motions of Projectiles, and exceedingly more able to press upon gross Bodies, by endeavoring to expand itself."

Aberration of light

The aberration of light (also referred to as

astronomical aberration or stellar aberration) is an

astronomical phenomenon which produces an

apparent motion of celestial objects about their real

locations. It was discovered and later explained by

the third Astronomer Royal, James Bradley, in 1725,

who attributed it to the finite speed of light and the

motion of Earth in its orbit around the Sun.

56

What is stellar aberration?

Light from location 1 will appear to be

coming from location 2 for a moving

telescope due to the finite speed of

light, a phenomenon known as the

aberration of light.

Stellar aberration is independent of the

distance of a celestial object from the observer,

and depends only on the observer's

instantaneous transverse velocity with respect

to the incoming light beam, at the moment of

observation.

57

Annual aberration is due to the revolution of the Earth around the Sun.

Diagram illustrating

aberration of a star at

the north ecliptic pole

Diagram illustrating the effect of annual

aberration on the apparent position of

three stars at ecliptic longitude 270

degrees, and ecliptic latitude 90, 45 and

0 degrees, respectively 58

Aberration of γ Draconis

Bradley's data on the north-south

component of the aberration of γ

Draconis in 1727 establishing

stellar aberration.

As the Earth revolves around the Sun, it is

moving at a velocity of approximately

30 km/s. The speed of light is

approximately 300,000 km/s. In the special

case where the Earth is moving

perpendicularly to the direction of the star

( if angle θ is 90 degrees), the angle of

displacement, θ − φ, would therefore be the

ratio of the two velocities, or 1/10000, or

about 20.5 arc seconds.

To explain stellar aberration in the context of an aether-based theory of

light requires that there is relative motion between the aether and the

Earth, in other words, the aether be stationary even as the Earth moves through.

59

Airy Experiment (1871)

By means of a water-filled telescope, Airy

in 1871 looked for a change in stellar

aberration through the refracting water

because the light speed becomes slow in

the water. But the result is exactly same

with an empty telescope!

Remarkably this null result can be explained by

The drag coefficient introduced by Fresnel in 1818!

Sir George Biddell Airy

(B1801 – D1892) was an English

mathematician and astronomer,

Astronomer Royal from 1835 to

1881.

60

Fresnel drag coefficient Fresnel proposed that the medium would carry some of the aether along

with it. He realized that the velocity of propagation of waves depends on the

density of the medium so proposed that the velocity of light in the medium

would need to be adjusted by an amount of 'drag'. The velocity of light vn in

the glass without any adjustment is given by:

The drag adjustment vd is given by:

Where ρe is the aether density in the environment, ρg is the aether density in the medium

and v is the velocity of the medium with respect to the aether.

The factor can be written as because the refractive index, n, would be

dependent on the density of the aether.

This is known as the Fresnel drag coefficient.

The velocity of light in the medium is then given by:

Hence V/v keeps the same as the original situation!

61

Experiment of Fizeau (1851)

The experiment sent two beams of light through a

pair of tubes filled with flowing water, so that one

beam was always travelling in the same direction

as the flowing water, and the other was travelling

against the flow. The time lag between the two

beams was then measured with an interferometer.

)/(4 2 cfvLn

Fizeau registered during his experiment a shift of 0.23

interference lines; which implicates a drag; the empirical

value. The theoretical value of the drag factor f=0.48

The factor is calculated to be f=0.43. So within an error of

approx. 10%, the experiment of Fizeau confirmed Fresnel‘s

drag factor.

62

Maxwell and Aether

63

Later, Maxwell's equations showed that light is an

electromagnetic wave. Maxwell's equations required that all

electromagnetic waves in vacuum propagate at a fixed speed,

c. As this can only occur in one reference frame in Newtonian

physics , the aether was hypothesized as the absolute and

unique frame of reference in which Maxwell's equations hold.

That is, the aether must be "still" universally, otherwise c would

vary along with any variations that might occur in its supportive

medium. Maxwell noted in the late 1870s that detecting motion

relative to this aether should be easy enough. Light travels

along with the motion of the Earth would have a different speed

than light traveling backward, as they would both be moving

against the unmoving aether. Even if the aether had an overall

universal flow, changes in position during the day/night cycle,

or over the span of seasons, should allow the drift to be

detected.

Structure of aether [J.C.

Maxwell, 1861

Michelson-Morley Experiment (1887)

Since the Earth is in motion, it was

expected that the flow of aether

across the Earth should produce a

detectable "aether wind". Although

it would be possible, in theory, for

the Earth's motion to match that of

the aether at one moment in time, it

was not possible for the Earth to

remain at rest with respect to the

aether at all times, because of the

variation in both the direction and

the speed of the motion. But they

found no trace of such aether wind

at all! Interference pattern produced

with a Michelson Interferometer

using a red laser.

64

Michelson and Morley

Albert Abraham Michelson

(B 1852 – D1931) was an American physicist known for his

work on the measurement of the speed of light and

especially for the Michelson-Morley experiment. In 1907 he

received the Nobel Prize in Physics. He became the first

American to receive the Nobel Prize in sciences.

Edward Williams Morley (B.1838 - D 1923) was an American

scientist famous for the Michelson-Morley experiment. His best

remembered work, which he did together with Albert Abraham

Michelson in 1887, was the Michelson–Morley experiment.

Neither he nor Michelson ever considered that it disproved the

aether hypothesis. 65

Length contraction(1889) Michelson himself thought that the result

confirmed the aether drag hypothesis, in which

the aether is fully dragged by matter. However,

other experiments like the Fizeau experiment

and the effect of aberration disproved that

model. A possible solution came proposed by

George Francis FitzGerald and independently

proposed and extended by Hendrik Lorentz,

when a body moves through space its

dimension parallel to the line of motion would, it

become less by an amount that depended on its

speed. If the speed of the body is v and the

speed of light is c, then the contraction factor is

66

Hendrik Lorentz

Hendrik Antoon Lorentz (B. 1853 –D.1928) was a Dutch

physicist who shared the 1902 Nobel Prize in Physics with

Pieter Zeeman for the discovery and theoretical explanation of

the Zeeman effect. He also derived the transformation equations

subsequently used by Albert Einstein to describe space and time.

Lorentz theorized that the atoms might consist of charged

particles and suggested that the oscillations of these charged

particles were the source of light. When a colleague and former

student of Lorentz, Pieter Zeeman, discovered the Zeeman

effect in 1896, Lorentz supplied its theoretical interpretation. The

experimental and theoretical work was honored with the Nobel

prize in physics in 1902. Lorentz' name is now associated with

the Lorentz-Lorenz formula, the Lorentz force, the Lorentzian

distribution, and the Lorentz transformation.

67

After M-M experiment

68

As the publication of the result of Michelson-Morley

experiment in 1887, the null result, was the first clear

demonstration that something was seriously wrong

with the aether concept of that time. A series of

experiments using similar but increasingly

sophisticated apparatus all returned the null result as

well. Conceptually different experiments that also

attempted to detect the motion of the aether were the

1903 Trouton-Noble experiment in 1903 and the

experiments to detect double refraction by Lord

Rayleigh in 1902 and DeWitt Bristol Brace in 1904,

which like Michelson-Morley obtained a null result.

DeWitt Bristol Brace

(B.1859 – D. 1905) was an

American physicist Brace

was mainly concerned with

researches on optics.

Tourton-Noble experiment

69

In the experiment, a suspended parallel-plate capacitor is held by a fine

torsion fiber and is charged. If the aether theory were correct, the change in

Maxwell's equations due to the Earth's motion through the aether would lead

to a torque causing the plates to align perpendicular to the motion. Thus,

unless the aether were somehow fixed relative to the Earth, the experiment is

a test of relative motion between the aether and the earth. The result is null.

Double refraction

70

A calcite crystal seen

through a polarizing filter

Double refraction, is the

decomposition of a ray of

light into two rays (the

ordinary ray and the

extraordinary ray) when it

passes through certain

types of material, such as

calcite crystals, depending

on the polarization of the

light. This effect can occur

only if the structure of the

material is anisotropic . Displacement of light rays

with perpendicular

polarization through a

birefringent material.

double diffraction and length contraction

71

If polarized light is passed through a birefringent material, the direction of

polarization is rotated. Rayleigh realized that length contraction would by its

nature make a material birefringent. Light traveling perpendicular to the

direction of motion will ‗see‘ two different spacings of the atoms in the

material; light x-polarized will see a smaller atomic spacing than light which

is y-polarized.

Null result for length contraction

72

To make any changes easier to observe, Rayleigh placed a piece of strained

glass between the first polarizer and the liquid chamber. The strained glass has

its own natural birefringence, which results in an interference pattern at the

output of the experiment. Changes in birefringence (presumably due to length

contraction) could be easily seen as shifts in the position of the interference

pattern.

Rayleigh searched for length

contraction-induced

birefringence in bisulphide of

carbon and in water. He found

no such contraction

Abolition of Aether (1905)

In September 1905 (received June 30), Albert Einstein

published his annuls mirabilis paper on what is now

called Special Relativity. Einstein's paper includes a

fundamental new definition of space and time (all time

and space coordinates in all reference frames are equal,

so there is no "true" or "apparent" time) and the abolition

of the aether. It contains no references to other literature.

It does mention Lorentz, but only in §9, part II, in

connection with the treatment of the electromagnetic field.

Poincaré is not mentioned. Einstein derived everything

from two postulates!

73

Derivation of Fresnel formula

Max von Laue derived Fresnel formula

using special relativity in 1907. If V is the

velocity of light relative to the Fizeau

apparatus and U is the velocity of light

relative to the water and v is the velocity of

the water:

Using the velocity addition law:

74

Hail for the hero!

75

The profound change of the concept of space

and time has been achieved by the effort of

many Scientists. Nevertheless, the true hero is

still of no doubt the young Einstein. With

abolishing the concept of aether, our

understanding on the nature of light and the

field, the propagation of information

have also been changed for ever.

Hail for the hero!

Because of him we now can see and think

much deeper than our precedents.

Left: Berne‘s clock tower

Great Unifier- Einstein

76

Space Time

4-D Space-Time

Matter Energy

E=MC2

Space-

Time

Matter-

Energy

General Relativity

General

Relativity

Maxwell

Equation

Unified Theory

Unification of Forces

77

?

天法道 道法自然

78

有物混成，先天地生。寂兮寥兮，獨立而不改，周行而不殆，可以為天下母。吾不知其名，字之曰道，強為之名，曰大。大曰逝，逝曰遠，遠曰反。故道大，天大，地大，王亦大。域中有四大，而王居其一焉。人法地，地法天，天法道，道法自然。