9.26.2016 Quote of the Day

planets space saturn cosmosChapter 1 : THE COPERNICAN VIEW OF THE WORLD
THIS little book purports to serve as an introduction to the great problems of space, time and motion. The inquiries it is concerned with are very old. Men have been forming ideas concerning space and time since times immemorial, and curiously enough, have been writing and fighting about these things with the greatest interest, even fanaticism. This has been a strange strife, indeed, having little to do with economic necessities ; it has always dealt
with abstract things, far removed from our daily life and
with no direct influence upon our daily activities. Why
do we need to know whether the sun revolves around the
earth or vice versa? What business of ours is it, anyway?
Can this knowledge be of any use to us?

.

No sooner have we uttered these questions than we
become aware of their foolishness. It may not be of any
use to us, but we want to know something about these
problems. We do not want to go blindly through the
world. We desire more than a mere existence. We need
these cosmic perspectives in order to be able to experience a feeling for our place in the world. The ultimate
questions as to the meaning of our actions and as to the
meaning of life in general always tend to involve astronomical problems. Here lies the mystery surrounding

CC BY by NASA Goddard Photo and Video
CC BY by NASA Goddard Photo and Video

astronomy, here lies the wonder we experience at the
sight of the starry sky, the wonder growing in proportion
to our understanding of immense distances of space and
of the stars inner nature. Here is the source of scientific
as well as popular astronomy.

These two branches have diverged in the course of
their development. Astronomy, as a science, has come to
forget its primitive wonder: instead, it approaches the
realm of stars with sober research and calculation. This
disenchantment with its subject-matter, which scientific
study invariably entails, has permeated astronomy to a
greater degree than the layman realizes. In observing the
astronomers of today, how they measure, take notes, calculate, how little attention fiiey pay to mysterious speculations, one may be surprised to find the wonderful structure of learning so cut and dry at a close range. Yet nothing is more wrong and more objectionable than the feeling of a heartbreaking loss, with which some people regard the vanishing mysticism of the skies. Although science may have destroyed a few naive fantasies, what she has put in their place is so immensely greater that we
can well bear the loss.

It takes perseverance and energy, of course, to comprehend the discoveries of science; but whoever undertakes the study is bound to learn many more surprising things from it than a naive study of nature can disclose. Scientific astronomy has always exercised, in fact, a great influence upon everyday thinking and upon the popular conception of the universe. If it is difficult today to pronounce the name of Copernicus without thinking of a turning point of history, it is not only because the name
is connected with a profound transformation in the
science, but also because all our knowledge and thinking
have been deeply affected by his discovery. The statement
that the earth does not occupy the center of the world
means more than an astronomical fact; we interpret it as asserting that man is not the center of the world, that
everything which appears large and mighty to us is in
reality of the smallest significance, when measured by
cosmic standards. The statement has been made possible
as a result of scientific development in the course of
thousands of years, yet it definitely contradicts our immediate experience. It takes a great deal of training in
thinking to believe in it at all Nowadays we are no
longer conscious of these things, because we have been
brought up since childhood in the Copernican view of
the world. However, it cannot be denied that the view
belies the testimony of our senses, that every immediate
evidence shows the earth as standing still while the
heavens are moving. And who among us can declare in
all seriousness that he is able to imagine the tremendous
size of the sun or to comprehend the cosmic distances
defying all earthly ways of measurement? The significance of Copernicus lies precisely in the fact that he
broke with an old belief apparently supported by all
immediate sensory experiences. He could do it only be
cause he had at his disposal a considerable amount of
accumulated scientific thought and scientific data, only because he himself had followed the road of disillusionment in knowledge before he glimpsed new and broader
perspectives.

If we endeavor to trace, in the following pages, the
development of the problems of space and time, beginning with the discovery of Copernicus and closing with
the still less accessible theory of the Copernicus of our
day, we have no other alternative than to apply hard
scientific thought to every step of the way. We must add
that the discoveries of modern science have been made
possible only by the abundance of new scientific materials.
Einstein’s doctrines are by no means an outgrowth of
astronomical reflections alone; they are grounded in the
facts of the theory of electricity and light as well. We are
able to comprehend them only insofar as we get acquainted with all of their sources. This derivation from several sources is characteristic of the theory of relativity. While the modern source gave rise to the special theory of relativity, the older sources provided the material for the construction of the general theory of relativity, in which the old and new knowledge became blended in a magnificent unity.

In this chapter we shall deal with old material ; in the
next two chapters we shall present the special theory of
relativity and its origin; and the last three chapters will
be devoted to the blending of the material and, therefore,
to the general theory of relativity.

world space planet The_Earth_seen_from_Apollo_17The world-picture found by Copernicus goes back to
the ancient Greeks. It was systematized about 140 A.D. by Ptolemy Claudius of Alexandria and outlined in his
famous work Almagest. The most important feature of
the Ptolemaic scheme of the universe is the principle
that the earth is the center of the world. The heavenly
globe revolves around it; and Ptolemy knew full well
that it has the same spherical shape below the horizon,
which it assumes above the horizon. In fact, Ptolemy
knew even that the earth is a sphere. His proofs to this
effect reveal a great knowledge of astronomy. He shows,
first of all, the existence of curvature from north to south.
As the Polar Star stands higher in the north and lower
in the south, the surface of the earth must be correspond
ingly curved. The. proof of the existence of curvature
from west to east reveals even better observation. When
the clocks are set by the sun in two places located west
and east, and when an eclipse of the moon is thus observed, it will be seen at different times. However, the
eclipse is a single objective event and should be seen
everywhere at the same time. Hence we conclude that
the clocks at the two places are not in accord. This can
be accounted for by the curvature of the earth in the
west-east direction : the sun passes the line of the meridian
at different moments in different places.

In spite of the recognition of the spherical shape of
the earth, Ptolemy was far from admitting its movement
He contended, on the contrary, that it was impossible for
the earth to be moving at all, either in a rotating or in a
progressive manner. As far as the former is concerned,
he admitted the possibility of such an opinion, as long as the movement of the stars was considered. However,
when we take into consideration everything that happens
around us and in the air, this view so he argues be
comes obviously absurd. For the earth, during its rotation, would have to leave the air behind. Objects in the
atmosphere, such as flying birds, not being able to follow
the rotation, would have to be also left behind. A progressive motion of the earth is equally impossible for, in
that case, the earth would leave the center of the heavenly
sphere, and we would see by night a smaller part of the
sphere) and by day a larger one.

One can see from these arguments that the great
astronomer has devoted much serious thought to the
problem. In the light of his rather limited knowledge of
mechanics and of the heavenly spaces, his reasoning must
have seemed quite conclusive. As far as his last objection
was concerned, he could .not have suspected that the
interstellar distances were so great as to make the lateral
shift of the earth completely unnoticeable.

The planets are characterized, according to Ptolemy,
by common movements. Their path, as observed in the
sky, is determined by superimposed circular orbits. As
a result, there arise the so-called “epicycles.” One must
admit that Ptolemy has deeply understood the nature of
planetary movements. When one gets acquainted with the
Copernican conception, one discovers the facts revealed
behind Ptolemy’s epicycles: the loop of the planets
course mirrors their double motion as regards the earth.
In the first place, they move in a circle around the sun, and in the second place, this movement is observed from the earth which, in its turn, revolves around the sun.

The Ptolemaic conception of the universe dominated
the learned people’s minds for more than one thousand
years. The man who undermined this firm tradition
Nicholas Copernicus required great independence of
thought as well as great scientific knowledge, for only an
insight into the ultimate relations of nature could give
him the ability to discern new approaches to truth.

CC BY by jimmiehomeschoolmom

The canon of Frauenburg was long known as a
learned astronomer before his new ideas were presented;
he had studied in Italy all branches of science, he had
acted as doctor and church administrator in his home
town, and his astronomic knowledge was so well recog
nized that in 1514 he was asked by the Lateran Coun
cil for his opinion on questions of calendar reform. His
new ideas concerning the system of the universe were
formed, in their essence, at the age of 33, However, he
did not promulgate them at that time, but devoted the
following years to a thorough elaboration and demon
stration of his theories. Only excerpts of his doctrine
were published during his lifetime. His main work en
titled “Of the Rotation of Celestial Bodies” appeared
only after his death in 1546. He read the proofs only on
his death-bed and thus failed to notice that his friend
Osiander supplied the work with a foreword which con
tained a cautious compromise with the opinions of the
Church.

If we examine the proofs given by Copernicus of his new theory, we find them quite insufficient from the point
of view of present-day knowledge. He was able, in fact,
to cite as a distinct advantage only the greater simplicity
of his system. He regards it as improbable that the stars
move with great speed in their large orbits and finds it
mo)re likely that the earth rotates on its axis, so that the
speed of motion in each particular point is considerably
smaller. Against Ptolemy s objection to this he urges that
Ptolemy considered the rotating movement of the earth
as implying force, whereas it is simply natural ; its laws
differ completely from those of a sudden jerky movement
All of this is certainly inconclusive. We know today that
Newton’s theory contains the first real proof of the
Copernican conception of the universe. But it seems that
new ideas are able to gain foothold by the sheer power of
their inherent truth long before their objective verifica
tion has been obtained.

On the other hand, it is very important to acknowledge that the Copernican theory offers a very exact calculation of the apparent movements of the planets and that
the tabulations (the so-called “Ephemerides”) accompanying it are far superior to the older ones. Here lies one
of the reasons which led the scientists to accept the
Coperpican system, even though it must be conceded that,
from the modern standpoint, practically identical results
could be obtained by means of a somewhat revised Ptolemaic system. Furthermore, Copernicus calculated quite
accurately the radii of the planetary orbits (within less
than \%). In fact, he knew already that the sun must be slightly off the center of the solar system, for an assumption to the contrary led to estimable discrepancies.

The progression of a solar eclipse on August 1, 2008, viewed from Novosibirsk, Russia. The time between shots is three minutes. by User:Kalan
The progression of a solar eclipse on August 1, 2008, viewed from Novosibirsk, Russia. The time between shots is three minutes. by User:Kalan

Yet there was still a long way from this discovery to
the recognition of the elliptic shape of the orbits; any
conclusive evidence to this effect required above all
better astronomic instruments. In this important connection, we must consider Tycho Brahe who is less prominent as a theoretician than as a builder of outstanding
instruments. Brahe was able to work for many decades
under the protection of the Danish king. He built the
castle Uranienburg on an island, to which was attached
a large settlement where precise instruments were prepared for him in special plants. It is amazing how the  precision of instruments was increased in this manner. For instance, Copernicus had to be satisfied with measurements within 10 of the arc. This corresponds approximately to an angle covered by a five-pence piece at a distance of six meters. Tycho increased the precision to within half a minute of the arc. This angle would be enclosed by the same coin at a distance of 120 meters.
With the instruments of today, of course, angles can be
measured within one hundredth of a second of the arc.
The coin would have to be placed at a distance of 360
kilometers to enclose such a small angle.

This precision we owe mainly to the use of the telescope. Tycho had to work without a telescope. One of his
sextants with which he conducted his observations of
Mars still stands in the Prague observatory, where Tycho,  exiled from Denmark, spent the last years of his life
(c. 1600).

Figure 1 shows the picture of this historic instrument.
The pointed leg is set in a stand. The whole instrument
is movable at the hinge in the upper end of the leg. It
measures IVfc meter at the shank. The shank may be
turned and has a sight-hole at the bottom to the left, an
ironplate with a slit, through which a sharp edge on the

Figure I. A Tycko Brake s Sextant

upper end of the shank (to the right) is adjusted. This
endpiece slides along an angle-scale. The sight-plate itself measuring several centimeters is reproduced in an
enlarged form at the upper left corner. By means of such
a crude-looking apparatus, Tycho found the data on
which modern astronomy is historically resting.

The man who continued Tycho Brahe s work was his
assistant Johann Kepler whose name surpasses by far that
of his master. Kepler carried on his observations with the
sextants of Tycho. He determined the course of the motion of Mars by means of so many individual observations that he was able to pronounce it with certainty as elliptical in shape. He discovered through mere measurement also other laws of planetary motion, called after him “the Kepler s laws.” One must admire the strength of character of this man, which manifests itself in his zeal for factual accuracy. Kepler was at first a mystic
and speculative dreamer, disinclined to sober observations. He concentrated in his early works on searching
for strange mathematical harmonies of nature, and such
a goal inclines one to distort facts rather than to establish
them. It remains true, however, that Kepler has accomplished much more for his own aim by his zeal for factual
accuracy than by his speculations. He himself expresses
this thought In his work entitled “Harmony of the
World,” which appeared in 1619, he writes concerning
the discovery of his laws:

“At last I have found it, and my hopes and expectations are proven to be true that natural harmonies are present in the heavenly movements, both in their totality and in detail though not in a manner which I previously imagined, but in another, more perfect, manner. . . If you forgive me, I shall be glad ; if you are angry, I shall endure it. Here I cast my
dice and write a book to be read by my contemporaries or
by the future generations. It may wait long centuries for
its readeif< But even God himself had to wait for six
thousand years for those who contemplate his work.”

We must not forget, however, that, though the astronomic picture of the universe was considerably advanced,
in regard to precision, by Kepler’s discoveries, neverthe
less, that world-view, though basically Copernican, differed very considerably from our Copernican idea of the
world. Copernicus as well as Kepler was of the opinion
that the solar system virtually exhausted the space of the
universe. The stars, according to them, were tiny dots in
the sphere of heavenly matter, which circumscribed the
whole of space. When Giordano Bruno expressed his
thoughts on the infinity of the firmament and maintained
that fixed stars were independent solar systems, Kepler
proceeded immediately to combat the idea. How difficult
it must have been to climb the stairs leading to our
present-day knowledge !

Astronomy made its decisive advance over Kepler’s
knowledge again through an improvement in the means
of observation through the invention of the telescope.
The great merit of having made the first serviceable
telescope and of having used it for the observation of the
sky belongs to Galileo ; though not the original inventor
of the telescope, he constructed it after hearing of such
instruments. He directed his telescope toward the moon
and recognized the spots on the moon, on account of their jagged outline and shifting illumination, as tremendous
mountains (1610). He pointed it towards Venus and saw
its sickle-like shape, similar to that of the moon, which
it periodically assumes as a result of receiving light from
the sun. He directed the telescope towards Saturn and
saw its triple figure the details of which he could not
yet discern. He directed it towards Jupiter and saw its
satellites (the four brighter ones) designated by him as
“medizeic planets.”

Parthenon Fredric Edwin Church
Parthenon Fredric Edwin Church

All these facts, with their enlargement and enrichment of the Copernican world, must have greatly astonished his contemporaries. It also provoked, to be sure,
the opposition of the old school of scientists who saw their tenets grounded in Aristotle seriously endangered. Galileo’s most precarious position can be best envisaged from
a letter written by him to Kepler:

“I am very grateful that you have taken interest in my investigations from the very first glance at them and thus have become the first and almost the only person who gives full credence to my contentions; nothing else could be really expected from a man with your keenness and frankness. But what will you say to the noted philosophers of our University who, despite repeated invitations, still refuse to take a look either at the moon or the telescope and so close
their eyes to the light of truth? This type of people
regard philosophy as a book like Aeneid or Odyssey and
believe that truth will be discovered, as they themselves
assert, through the comparison of texts rather than
through the study of the world or nature. You would laugh if you could hear some of our most respectable
university philosophers trying to argue the new planets
out of existence by mere logical arguments as if these
were magical charms.”

Galileo relates how another scientist refused to take a look through the telescope “because it would only confuse him.” The tragic fate of Galileo, caused by such antagonism, is well known. He had to pay with many years of incarceration and imprisonment for his sponsorship of the Copernican theory.

Another achievement of Galileo had apparently no
direct connection with astronomy; but this connection
was discerned soon enough. Galileo was the first man to
investigate the laws of falling bodies. He has thereby
established the basic laws on which the science of mechanics was destined to grow. The apparatus he built was
quite primitive. For instance, he had no watch in the
modern sense of the word, but had to measure time by
means of water running out of a vessel. In spite of every
thing, he was able to determine the relationship between
the distance and the time of the fall, and also the law
of acceleration. He also discovered the fact a most surprising fact for his day that all bodies fall equally fast. Finally, he formulated the basic law of motion, named after him : that every body unaffected by external forces moves in a straight line at a uniform speed, and that this motion can never stop by itself.

Although these laws seem to be merely bits of factual
information, nevertheless they signify an extraordinary
progress as compared to the preceding era. There was no inclination at that time to collect data. It was believed
that all one wanted to learn could be disclosed by speculative thinking. Galileo s great achievement was that he
resorted to direct investigation of nature. Moreover, the
facts he discovered were destined to attain a significance
far beyond their own realm, namely, when Newton constructed the mechanics of heavens on them.

Fate allotted to the English physicist Isaac Newton
(1643-1727) an outstanding role in the history of the
natural sciences of the described period. He was the great
unifier who combined the individual discoveries of Copernicus, Kepler and Galileo into one magnificent system.
His intellectual achievement cannot be estimated too
highly. With the vision of a genius he realized that the
power of gravitation perceived by Galileo in his doctrines
concerning falling bodies had a significance far transcending the region of the earth, that this power of attraction constituted a property of all mass, and that it determined the planets behavior across cosmic distances. This far-reaching insight into the nature of things was accompanied by Newton s great caution in scientific investigation. He started with the correct premise that the power of attraction must diminish with distance. He then calculated what the magnitude of this power, already estimated

Sun and Moon, Hartmann Schedel's Nuremberg Chronicle, 1493
Sun and Moon, Hartmann Schedel’s Nuremberg Chronicle, 1493 

by Galileo on the surface of the earth, could be
at the distance of the moon. Next he computed the length of time required for the revolution of the moon around the earth, if this gravitational power was indeed respon
sible for the motion of the moon. All this was a magnificent elaboration of the original idea. Unfortunately, luck was against Newton, and his investigations resulted in anything but agreement with facts. Yet nothing shows better the greatness of the scholar s character than his conduct in the face of failure: he put his calculations away in a closet without publishing a single word concerning his profound meditations (1666). Only twenty
years later could the mistake be explained. The length
of the earth s radius, taken by Newton as the basis of his
calculations, had been inexact; new estimates on the astronomers part gave a new measurement with which Newton’s reflections about the moon proved to be in full
accord.

The mechanics of Newton has thus received confirmation, and it must have seemed like a magic key to his
contemporaries. His theory transformed the fundamental
facts of the preceding centuries into a uniform system,
including the Copernican theory of the heliocentric
motion of the planets, Kepler s laws concerning their
orbits, and Galileo s laws of falling bodies in a gravitational field. Kepler did not live to greet this triumph of thought; no doubt, he would have rejoiced over this proof of the harmony of cosmic motions.

The Copernican conception of the universe was at
last scientifically established, insofar as the laws under
lying it stood revealed. Up to that time the Copernican
conception of the universe, as compared to the Ptolemaic
conception, could justify itself only by its claim of re
presenting the world-picture in simpler terms. But now, with the addition of Newtonian mechanics, it became the
only acceptable one. Its real merit was made explicit: the
Copernican conception of the world provided an explanation of natural phenomena, a cosmic order governed by
laws. It was the destiny of the Western mind to absorb
this worldview which so much corresponded to its innate
tendencies of thought.

Thus ends the first period of new physics; and with
it has come a new method of inquiry to dominate the
natural sciences ever since. The collection of facts is the
starting point of investigation; but it does not mark its
end. Only when an explanation comes like a bolt of lightning and melts separate ideas together in the fire of
thoughtful synthesis, is that stage reached which we call
understanding and which satisfies the seeking spirit.

The following chapters will show how widely and
how consciously new physics has carried through this
method of inquiry.”