Cultural History of Physics EXCERPT

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Károly Simonyi

A Cultural History of Physics

b Dv K



Originally published in Hungarian as A fizika kultûr története , Fourth Edition, Akadémiai Kiadó, Budapest, 1998, and published in German as Kulturgeschichte der Physik , Third Edition,Verlag Harri Deutsch, Frankfurt am Main, 2001. First Hungarian edition 1978.

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Library of Congress Cataloging‑in‑Publication Data

Simonyi, Károly.[Fizika kultúrtörténete. English]A cultural h istory of physics / Károly Simonyi ; translated by David Kramer.

p. cm.Includes bibliographical references and index.ISBN 978-1-56881-329-5 (alk. paper)1. Physics--History. I. Title.

QC7.S55313 2010530.09--dc22 2010009407

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xi

Foreword by

Charles Simonyi

An exceptional book such as this d v rd y dr - rm. My r w wrg y d vd vry r-r w g w gr Hgr r gr. H d r grg v rd my gg. Y, y rgd mr 1960 Hgry,

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xii

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w v u w gug g xpv pw, bu, xb, Eg, u p w b jb v ubj g v gug.

Sp k u A Ku P u- pj, pgp g upv -, g, pu. T b w b Dv K.T x w vw b Rb S Ax Fb DL. CH p g, ug -u. O vv pj w Cb Agu, S Cw, JuNzz, S Ru.

T pubg ’ wk wu v b pb wu upp : , Zuz, b, , w, L. Sp p Ikó Cug w u g-u kwg.

F, I u gu P. Ew W Iu Av Su bug pgu.



xiii

Preface

oday, the history of science p w g, w w ub- j g, w ju, w uv . A, u, w p p, gup u bk bg . H p g p p k g ubj, g w w . T k p bk w p g b u— x bk

b g u—w p ppbkgu b p ubjv , , pppb g, .

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, kwg w x qu, A, . Pp w wu bu w w ub v upu Px M Eu, g p, w u H , p Eup . I w wu uv ug A— w bv xp—w wu u qu, v u, gu g gv g u g. T k up pg gu pbu qu wk u.

T bk , , wk pub ug , v xbk g u. I b u’ w g u b , u w g pg k g u .T g b p p bu u w qu x. I p qu pb x up -, qu—p bkgu— p



xiv

x p, w bk.

Bgp u b g g x, w qu p , b u x gu p. Tu u u w bk b pu, , p.

T p u v— u —p v u, pv k bk — g— uu p.

T u bk u u— p pj-— bk. S bk bbgp vv p u, u , pv w-gg vw. T u

g gv pp gu qu, g w pb g u. T gu v b k—g, wvpb— , p b u Hug b.

F, u wu k k w pp bk. F , k u Ikó Cug, wpp ppg up pub vg ub pb.

T u’ k g wg Hug b p g wk p k pp b u p bk: Lb Uv, Bup; BupUv Lb; N Széé Lb; b B- Abb P; Székév b; M- Lb Uv Hv Iu, Mk; Lb Hug A S, Bup.

T u wu k k wg uu u, w uv vb wu g:CERN, Gv; Zw g u; Muu C P-; Muu V; Np Muu, Hzg Augu Lb, Wbü; B S Muu.

T u k U pubg p, Lpzg, pub Aké Kó, Bup, H Du pub, pu BMü, p p b. A b vub D. M Fk w D. O H, w w g u u x.

T p Cp 5 w b P A Pkó, wv p ugg, x. I uw p u k.

I b bv, I k , wvw Ab x p w wk. I k w C gu upp, b .

T u v gz w w k, p ugg, p pb. H w b ub z p. F, uk w, w ppg up, bb-gp wk, u pgg qu.

Károly Simonyi, 2000



1

introduction

0.1 T Hy Py I Rv O Lv y

In today’s industrialized societies, m p v- m v p . F vm my k v m p k vy v. Iv y vv v y my; , k k m. B p p— “ ”— m ? A vy, v m v

v v p v m ? O p m m, mpy m pp y y C. P. Snow (1905–1980), p p “ ,” , m ? (S F 0.1 Q 0.1.) A y’ zp mk y, v p y ? A , py v k vy m; mv, mk y p k p p , ’ k, mp

-m?I x, y py ? F py, mp y p , - m v mpm m, m m y , p py, -m— m, pp vy , mv— y v m - m v m , v v . I y , py: Human culture is a

single, unifed whole, and it is only or us, the consumers o culture, that the problemarises how its signifcant elements are to be selected, appropriated, and transmitted ( Q 0.2–0.4). Y m pxy, v p, , y p mv, m y mpy - v.

T m y py mk v, m my vy, , x: T m , , , v, p p m—

pp p . A y k pv v xp. Mv, y py xmp y v.

O , m k , xp, not xp m y py? T m k mpy p p, “,”k. I mp m v y p p

Figure 0.1 A scientist with the ecstasy of a saint or of an

artist. This image of a Greek scholar in a medieval cathedral

stands as a symbol of the unity of human culture (statue of

Ptolemy in the Ulm cathedral, sculpted in 1470 by Jörg Syrlin).

Quotation 0.1

I believe the intellectual life of the whole of westernsociety is increasingly being split into two polargroups. …

Literary intellectuals at one pole—at the otherscientists, and as the most representative, thephysical scientists. Between the two a gulf of mutual incomprehension—sometimes (particularly

among the young) hostility and dislike, but mostof all lack of understanding. They have a curiousdistorted image of each other. …

The non-scientists have a rooted impression thatthe scientists are shallowly optimistic, unawareof man’s condition. On the other hand, scientistsbelieve that the literary intellectuals are totallylacking in foresight, peculiarly unconcerned withtheir brother men, in a deep sense anti-intellectual,anxious to restrict both art and thought to theexistential moment. …

[There was a somewhat well-known scientist] who,when asked what books he read, replied rmly andcondently: “Books? I prefer to use my books astools.” It was very hard not to let the mind wander—what sort of tool would a book make? Perhaps ahammer? A primitive digging instrument? …

continued on next page



2

xp, y pv m xpm p y v

, p xpm, rediscover the

laws or themselves. Y y, mp qy y v

mpy mp y v

, y pp qy -

k. Oy pp v

p vy, q y , my

m .

A xmp, m m p, yp m y

v m , m

p p Galileo (1564–1642). B v

p m m p , we have removed the only

signifcant new element o discovery and originality. A m m k,

m p v xpm py m m y v y v mz.

Galileo's vm v xpm pp

m . I , the description o the experimen-

tal setup is the crucial step, y m y mp pm

x v mm.

, xpm p k p v pp,

y q p . T p m

m pp y Galileo, ,

xp pm v- k vy. I v p

y: Galileo m m y m m

v m m; my, y’

y, vy m v m m y y m

p.

C m k p v z m p-

py: W pp

y q k v p

m my. I pp

mpy xp m m, v-

mp vy.

O v m y py

p y y py— -

py m.

T y py v mv p py. I

m y m

, ppy, py Gk m

v v y. T Bertrand Russell (1872–1970),

Plato (. 427–. 347 bce) p m k y p m k y Gottlob Frege

(1848–1925), Alfred North Whitehead (1861–1947), m. T

Werner Heisenberg (1901–1975), Plato -

m y ( Q 1.20).

T y py v ,

m , y: Nmy, p m y

ypy pp. Opp y

Quotation 0.1, continued

It isn’t that they lack the interests. It is much more

that the whole literature of the traditional culturedoesn’t seem to them relevant to those interests.They are, of course, dead wrong. As a result, theirimaginative understanding is less than it could be.They are self-impoverished. But what about the otherside? They are impoverished too—perhaps moreseriously, because they are the vainer about it. …

As with the tone-deaf, they don’t know what theymiss. They give a pitying chuckle at the news of scientists who have never read a major work of English literature. They dismiss them as ignorantspecialists. Yet their own ignorance and their own

specialization is just as startling. A good manytimes I have been present at gatherings of peoplewho, by the standards of the traditional culture,are thought highly educated and who have withconsiderable gusto been expressing their incredulityat the illiteracy of scientists. Once or twice I havebeen provoked and have asked the company howmany of them could describe the Second Law of Thermodynamics. The response was cold: it wasalso negative. Yet I was asking something which isabout the scientic equivalent of: Have you read awork of Shakespeare’s? I now believe that if I had

asked an even simpler question—such as, Whatdo you mean by mass, or acceleration, which is thescientic equivalent of saying, Can you read?—notmore than one in ten of the highly educated wouldhave felt that I was speaking the same language.So the great edice of modern physics goes up, andthe majority of the cleverest people in the westernworld have about as much insight into it as theirNeolithic ancestors would have had. …

In our society (that is, advanced western society) wehave lost even the pretence of a common culture.Persons educated with the greatest intensity weknow can no longer communicate with each otheron the plane o f their major intellectual concern. Thisis serious for our creative, intellectual, and, aboveall, our normal life. It is leading us to interpret thepast wrongly, to misjudge the present, and to denyour hopes of the future. It is making it difcult orimpossible for us to take good action.

There is, of course, no complete solution … Butwe can do something. The chief means open tous is education—education mainly in primaryand secondary schools, but also in colleges and

universities. There is no excuse for letting anothergeneration be as vastly ignorant, or as devoid of understanding and sympathy, as we are ourselves.

—C. P. Snow, The Two Cultures and theScientifc Revolution, 1959 [pp. 4–16]



8

Fg 0.10 py g p g v -y py p Friedrich Hund (1896–1997); p w py w y .

L w py xmp w v vg q w py p w . W mg, xmp, gp y m p mp w w y x p. I p g y mvg, p p mp w p w m w w . T w g ( p ) k gy, k gy m mp g (Fg 0.11).

I gm m, qv pm w pp w:

A w , mg m w m w w , w w , w

, my w py. T v

m pv , w v w m v qy κ. T

v m g gm w v y xpm.

T v v m yg pv m g w, wv g y g mp pm p w m y

w v m mp py, w v p g ’ wkp.

0.2.4 Te Role of Modeling

I w k p w p py m qv, w

y w y. W my k wy , -

, mpy v py g w y

Figure 0.11 Molecular interpretation o the

adiabatic state equation.

Conservationof Energy

Conservationof Momentum

Principleof Statistical

Disorder (Entropy)

Excess Energy of a Collision

Excess Energy

of a Collision in theTime Interval dt

Excess Energy for N Particlesin the Time Interval dt

Constant

v x

2l

d t

Geometric Description

of the Motion of Heavenly Bodies

Laws Governing theMotion of the Planets

Analytical Mechanics

Classical Mechanics

1687

~1870

1820

1864

~1925

Terrestrial Motion (Qualitative)Law of

GravitationStatistical

Physics

Heat Caloricum Thermodynamics

Magnetism Polarity

Electricity Coulomb’s Law

Field Theory

Light Color Light Waves Quantum

Matter Chemistry

Theory

Figure 0.10 Junction points in the history o physics.

The dates indicate when the relationships between disparate

groups o phenomena were recognized:

1687: Publication o newton’S Principia

1820: ØrSted’S discovery o the magnetic properties o electric

current

1864: mAxwell’S electrodynamics

1870: Development o statistical mechanics

1925: Birth o quantum mechanics (ater [Hund 1972, p. 16]).

Figure 0.9 Simplifed schematic representation o the

scientifc method. A law encompasses a greater range o phe-

nomena than the individual observations on which it is based.

The limitation o the domain o validity is also indicated in thefgure.

Law (Generalization)

Induction

Deduction

Reality



9

G— w kg pmy pp v, y, km p m vy —w p- pm, m , j k mp mp xmp, w v v y.

I g mp y gv pm p-v y py y . A ppxm, w mg v y vpm gv kwg, p pp py v . B y vy gy . Spy, Gk, : y w mk p , y w g y k “g m.”

I w m xmp w v yg , m w p, w my z-

m y v mp. Txpm p y , w y y y p. B v x p, w v mk z: w m p py mv w . Dg mp pp rapidly . T g , w y - gy p y mp. A m , p kg m m

pm mpy p, mp w xpm v, , w

mm, m y. F xmp, k m - mp m m vwp, w w v m g mp y slow , w mp v m g w mp p vvg p mp-. H w m w k w w z— y w y p mp— g y k gm.

Ag y mp , k mp, w m g xp “vy py” “vy wy” py, m wypy in relation to what . Cy, w p mp, w g w w - m . T m m g vm,

m x p g . T m g w p m m m , g . A g vg p w w mp mp w f g.

Pm —w y m v—gy pp m. J g w v— m mpx m m w w m— mppm p p, vvg m .

F m qv, v , p m-p pm q, gg y -

g, my, y mv, py . T m w p- w w mk m p.I m y m f p , , mp pm m m w m m w qv vg.I m m, v w qy p px mpz w y yg y.

Figure 0.12 The balance and the harp as used in daily lie

are almost identical to the “abstract” balance and harp thatcan be treated mathematically. It is no coincidence that it was

precisely or these instruments that the frst quantitative natu-

ral laws were ormulated. (The Book of the Dead, twenty-frst

dynasty, Metropolitan Museum o Art, New York; Wall painting

rom the tomb o Rekhmire, eighteenth dynasty.)

Quotation 0.7

It is a most remarkable demand that is oftenmade, but never fullled, even by those whomake it: One should present one’s experience

without any theoretical apparatus, and let thereader, the student, form his own conclusions.For merely looking at a subject cannot advanceour understanding. Every look passes over into anobservation, every observation into a meditation,every meditation into a connection, and so one maysay that we theorize with every attentive glance atthe world. However, to do so with consciousness,with self-knowledge, with freedom, and to makeuse of a daring word, much skill is needed if theabstraction that we fear is to be harmless and theresult of our experience that we hope for is to comealive and be useful.

—goethe, On the Theory of Colors, Preface

Conclusive knowledge rests in every individual as ina seedcase. Through the observation of things wecome to wondering, from wondering to concluding,and from concluding, we come to true knowledge.

—albertuSMagnuS [Liertz 1932, p. 15]



10

C . I y mk m. T

g w wg v m , kg

w wg g p (Fg 0.12). T p-

, m m w k “ ”— ,

g g w-m v pp p w v

mv y w —w

p g g ppxm.

B w w m j m

pw pp m. I w w mv y pm,

mk m p, w v k -

vy m p ; mg y

y v m g p pm. F xmp, Aristotle

(384–322 bce) v w m m vyy v

w p wg . v pp—-—w m, Galileo wk w m p

m p yw , y pkg,

y v vg m p vm.

A v p p -

pvy gg mg g w p w

p py v mk

m g w p.

C m gv Gk—p xgg p—

g w m w -z. T xgg vwg p w

w v m m g; w m

y, y gv py m. T p vw, w y m

m p, py v y

y g mg m m

, my g pg w py mm.

0.3 Em Ppy S

0.3.1 Illusory Simplicity Fm y y wy w, m w k g -

y— v p wk. T y,

w mgy, y w

w y.

A w , g w g mg, y

g gg. N m w v w m

y, y w . B v w, w k m y

v p m, w m p g jm q

w w ppy y m-- y w.I Fg 0.13, mp gm Fg 0.9 p g .

T pm :

1. F vg, y m w m. Evy m-

m y v. By w qm-m-

w mw, mpy m v

mg m

y m mp . T

Quotation 0.8

Every age has scoffed at its predecessor, accusing

it of having generalized too boldly and too naively.deSCarteS used to commiserate with the Ionians.deSCarteS in his turn makes us smile, and no doubtsome day our children will laugh at us. Is there noway of getting at once to the gist of the matter,and thereby escaping the raillery which we foresee?Cannot we be content with experiment alone?No, that is impossible; that would be a completemisunderstanding of the true character of science.The man of science must work with method. Scienceis built up of facts, as a house is built of stones;but an accumulation of facts is no more a science

than a heap of stones is a house. Most importantof all, the man of science must exhibit foresight.Carlyle has written somewhere something after thisfashion. “Nothing but facts are of importance. John laCkland passed by here. Here is something that isadmirable. Here is a reality for which I would give allthe theories in the world.” Carlyle was a compatriotof baCon, and, like him, he wished to proclaim hisworship of the God of Things as they are.

But baCon would not have said that. That is thelanguage of the historian. The physicist would mostlikely have said: “John laCkland passed by here. It is all

the same to me, for he will not pass this way again.”

—henri PoinCaré, Science and Hypothesis, 1905

Quotation 0.9

[heiSenbergquotingbohr:] “Science is the observationof phenomena and the communication of theresults to others, who must check them. Only whenwe have agreed on what has happened objectively,or on what happens regularly, do we have a basisfor understanding. And this whole process of

observation and communication proceeds bymeans of the concepts of classical physics.… Itis one of the basic presuppositions of sciencethat we speak of measurements in a languagethat has basically the same structure as the onein which we speak of everyday experience. Wehave learned that this language is an inadequatemeans of communication and orientation, but it isnevertheless the presupposition of all science.”

[Later, while washing the dishes after a meal takenat a hikers’ hostel,bohr continues:] “Our washing upis just like our language,” Niels said. “We have dirty

water and dirty dishcloths, and yet we manage toget the plates and glasses clean. In language, too,we have to work with unclear concepts and a formof logic whose scope is restricted in an unknownway, and yet we use it to bring some clarity into ourunderstanding of nature.

—wernerheiSenberg, Physics and Beyond: Encountersand Conversations, 1971



11

means that reality appears to us to be already encoded into an “experimentallanguage” even when we wish to describe a concrete situation in its “unadul-terated reality” (Figure 0.14, Quotations 0.7 and 0.8). In other words, every experimental attempt already assumes a theory.

2. o interpret a phenomenon, we have assumed the existence o general physicallaws. O course, we have arrived at these laws based on perceived reality, using theinductive method. We thus extrapolate rom a fnite set o experiences collected inthe past and rom experiences to be observed in the uture, the number o whichis in principle infnite. What is to guarantee the validity o this extrapolation?

3. Beginning with a concrete situation and general laws, we arrive, via logi-cal procedures—mathematics and geometry—at new hypotheses, which we wish to check against reality. But what guarantees do we have that the laws o mathematics and geometry apply to reality?

4. Te results thus derived must o course again be checked against reality, which as we have already noted is just raw material to be observed and ana-lyzed. Hypotheses derived rom theory can be conronted only with hypoth-eses that in turn have been confrmed or reuted by yet other hypotheses.

5. In connection with all this, there arise the notions o subject and object, which are linked to the separation between the observer and the observed

phenomenon. Tis issue does not arise because physicists have doubts aboutthe objective existence o an external world independent o the observer, butrather because they view the experimental apparatus as an integral compo-nent o the external world. Furthermore, it also cannot be denied that thephysicists themselves and their system o concepts are also a part o reality.

Physicists believe in the objective nature o physics as a science, in that withinphysics, in relation to natural phenomena, assertions can be made that are“intersubjective,” that is, that can be understood by anyone o sound mindpossessing the requisite education. Moreover, these assertions are assumed toembody the possibility or persons o said sound mind and requisite education

to experimentally check, reveriy, or reproduce their contents. It is here thatsocial practices or judging objectivity and or establishing the criteria or truthmake their appearance (Quotation 0.9). Te social practice is a long process: itverifes in the present the assertions o the past. Te real problem arises when we want to make assertions or the uture with some expectation o certainty.

6. Still another point has to be considered: In order to construct a diagramlike that o Figure 0.13, we have to assume that the phenomena o reality can be subdivided into recognizable partial phenomena; that is, the identi-

Quotation 0.10

The ancients established the axiom that all ourideas come from our senses; and this great truth is,today, no longer a subject of controversy. …

However, all the sciences do not draw on the sameexperimental foundation. Pure mathematics requiresless than all the others; next come the physic-mathematical sciences; then the physical sciences. …

Certainly it would be satisfactory to be able toindicate exactly the point at which each scienceceased to be experimental and became entirelyrational [read: in order to develop rationally, startingfrom principles obtained from experiment]; that is,to be able to reduce to the smallest number thetruths that it is necessary to infer from experimentand which, once established, sufce to embrace all

the ramications of the science, being combined byreason alone. But this seems to be very difcult. Inthe desire to penetrate more deeply by reason alone,it is tempting to give obscure denitions, vague andinaccurate demonstrations. It is less inconvenientto take more information from experiment than


Law

Encoding Encoding

E n c o d i n g

ConcreteSituation

Logical Step

(Mathematical Derivation) Explanation,Prediction

Comparisonwith

Reality

Reality

Figure 0.13 The path o science “rom reality to reality” in greater detail.

Figure 0.14

Conrontation with

reality: We use this

apparatus to ask o

nature directly whatthe magnetic mo-

ment o a particular

particle is. Contact

with “unadulterated

reality” is possible

only i a well-

developed system o

concepts and laws

has been estab-

lished. (Brookhaven

National Labora-

tory , rom L’ère

atomique.)

The measurement method serves as the operational

defnition o those concepts that orm the elements o

the language o science, and as such, it does not meth-

odologically belong to the theory. But, in addition, the

measurement itsel is also a physical process, and in this

regard it is a part o the ull theory. In this manner the

very same process appears both as a premise and as

a result in the theory and with this, the language o

physics reaps a cyclic, sel-consistent structure that is

unheard o in other ormal languages.

—Mittelstaedt, Die Sprache der Physik [The Language of Physics], 1972 [p. 85]



23

0.4.4 Physics in a New Role

o a physicist, physics, with all its doubts and uncertainties and in spite o a poten-

tially ignoble role in the uture history o mankind, is nevertheless the most mar-

velous creation o the human imagination, a creation capable o lling an activelie with meaning. Physics is by itsel incapable o pointing the way to answering

the great questions o human existence. Physics is ethically neutral, although the

physicist is not. Yet the physicist is convinced that although no ethical categories

are applicable to theories about the physical universe, aesthetic ones certainly are.

It is still the case today that the utility o the sciences takes precedence over all

other arguments in their avor. Wherever one looks—on the ront pages o the daily

newspapers, in the proceedings o learned societies, or in long-range planning docu-

ments—everywhere one reads or hears about the implementation o scientic dis-

coveries. Troughout the world, even scientic institutions involved exclusively inbasic research justiy their existence with claims that the results o their work will

sooner or later nd practical application. All this is as it should be, and considering

the current state o the world economy, the useulness o a scientic result is indeed

o paramount importance. Nevertheless, especially in more highly developed societ-

ies, physics—and the other sciences as well—should gradually be given a new role—

something similar to the role o the arts. In addition to their useulness, we need to

bring to the oreront the aesthetic qualities o the sciences and thus recognize the

beauty o scientic results (Quotations 0.28 and 0.29). Saying it another way, we

should extend the idea o useulness: Science has been viewed as useul because it has

contributed to mankind’s material wellbeing by satisying immediate material needs.

However, beyond that, it should be recognized as being o crucial social signicance

in satisying cultural and spiritual needs. Te thirst or true knowledge about the

world, independent o the practical utility o the knowledge, is a real social phenom-

enon; the joy o understanding, o learning is or many people the same as the joy

and pleasure they derive rom works o art. I we ask ourselves whether the study

o semiconductors is o greater or lesser utility than theoretical speculation about

the curvature o the universe, the answer will assuredly be in avor o semiconduc-

tors. We can ofer as justication that with the use o semiconductors, cheap radio

receivers can be built. And what do we need radios or? We need them, among otherthings, to listen to broadcasts about all those interesting theories regarding the nature

o the cosmos, and in particular, about the curvature o the universe.

We do not need to urther analyze the joy that one experiences rom new

knowledge. Nonetheless, it is undeniable that in order to derive pleasure rom

the beauty o science, one has to study in preparation; in efect one has to de-

velop an “eye” or it. But the same holds or the aesthetic enjoyment o a work o

art. Figure 0.19 shows the undamental equations o general relativity, a modern-

ist sculpture, and a poem o our era. Most physicists see in Einstein’s equation

derivable laws that, building on the Newtonian worldview, provide a vision o thecosmos, joining geometry and physics in an intimate bond, not only a concrete

scientic and logical system, but also a work o art whose signicance lies in its

aesthetic value. Admittedly, it takes more efort to see the aesthetics behind the

symbols than in the sculpture or poem. But the appreciation o abstract works

o art also requires o the layman who is open to art a particular kind o education

and preparation as well as a certain efort. It thus becomes a question o individual

preerence what sort o intellectual investment brings about the greatest satisaction.

(a)

(b)

Figure 0.19 To appreciate the beauty o (a) the general

theory o relativity, (b) a sculpture, or (c) a poem, one requires,

in each case, a certain willingness to learn and a considerable

investment o intellectual eort. Einstein’s equation, which

brings together the ideas o mass and the geometry o space,

yields astounding new knowledge about our entire universe.

einStein introduced the idea that something which is

beautiul is very likely to be valuable in describing un-

damental physics. This is really a more undamental idea

than any previous idea. I think we owe it to einStein morethan to anyone else that one needs to have beauty in

mathematical equations which describe undamental

physical theories

—dirAc [Kragh 1980, p. 285]

Waiting for Godot , a statue by the Hungarian sculptor

Miklós Borsos, inspired by the play o Samuel Beckett.Duino Elegies by Rainer Maria Rilke, translated by A. S. Kline

(© 2001 All Rights Reserved).

Who, i I cried out, would hear me among the Angelic Orders?

And even i one were to suddenly

take me to its heart, I would vanish into its

stronger existence. For beauty is nothing butthe beginning o terror, that we are still able to bear,

and we revere it so, because it calmly disdains

to destroy us. Every Angel is terror.

…Early successes, Creation’s avourite ones,

mountain-chains, ridges reddened by dawns

o all origin – pollen o fowering godhead,

junctions o light, corridors, stairs, thrones,

spaces o being, shields o bliss, tempests

o storm-lled, delighted eeling and, suddenly, solitary

mirrors: gathering their own out-streamed beauty

back into their aces again…

—RaineR MaRia Rilke, Duino Elegies

(c)



49

gmy, h abac md makng pb a mahmaca amn gvn, pak, by nau. In cna, n h dcpn mn und a

cndn and pacuay n h qun h undamna cmpnn ma, much m abacn qud. I agan n cncdnc ha hGk w ab gv, wh h Pmac ym, a pc and quanavdcpn h mn h havny bd, h agan abacn ay bcau ud nunc a ngncan. W mgh ay ha h Pmacym a a description h mn h havny bd can b vwd vnday a cc, b u, wh cd vady—hugh a h am m h“cd vady” quacan cud b appd a mdn h a w.T Pmac ym wa dpacd n h xnh and vnnh cnu

ny bcau d n phyca xpanan h bvd phnmna and wa n uab h uh dvpmn dynamc.Fm h vwpn h hy cnc, upng wh wha bd-

n—qua a a h cuag n ba—h Gk ad wh h mdfcu qun a h u: wha h undamna nau hng, —ab mpd—wha a h undamna ma ma ha cmbn mh dvy h wd? Rgadng h qun, hy cud gv, cu, ny quaav pcu, and h quaav pcu a a gacy by Aristotle cudn b h uc cnnud dvpmn; ny cmp abandnmncud pn h way nw da abu h cmpn ma. In cna, h

ancn amc hy, vn hugh a ny quaav, had h pby anman n a quanav hy hddn whn .

In what follows, all the lines of development sketched here will be presented,even if we cannot go into every detail. In general, we shall content ourselves—as we did in the section on Egyptian and Babylonian science—to present the mostimportant results. All the while, however, we should not neglect to indicate how certain ideas were formed and perfected, because only in this way can we truly discover the process by which great ideas develop.

Figure 1.32

PYThagoras and music

(miniature, about

1210; Bayrische Staats-

bibliothek).

Quotation 1.9

Pythagoras is one of the most interesting and

puzzling men in history. Not only are the traditionsconcerning him an almost inextricable mixture of truth and falsehood, but even in their barest andleast disputable form they present us with a verycurious psychology. He may be described, briey, asa combination of einstein and Mrs. eDDy. He foundeda religion, of which the main tenets were thetransmigration of souls and the sinfulness of eatingbeans. His religion was embodied in a religiousorder, which, here and there, acquired control of theState and established a rule of the saints. But theunregenerate hankered after beans, and sooner orlater rebelled.

Some of the rules of the Pythagorean order were:To abstain from beans.Not to pick up what has fallen.Not to touch a white cock.Not to break bread …Not to stir the re with iron …Not to walk on highways.Not to let swallows share one’s roof.When the pot is taken off the re, not to leave the

mark of it in the ashes, but to stir them together.

—bertranD russell, A History of Western Philosophy ,1945 [pp. 31–32]

ANAXAGORAS

ARISTARCHUS

KEPLER

PHILOLAUS

E U D O X U S

ERATOSTHENES

HIPPARCHUS

PTOLEMY

COPERNICUS

HIPPOCRATES

ARCH YTAS

PLATO

APO LLONI US

BOLYAI

FIBONACCI

E U C L I D

ALH AZE N

ARC HIM EDE S

ARI STOTL E

PHILOPONUS

GALILEO

THALES

PARMENIDES

DEMOCRITUS

LUCRETIUS

BOYLE

P Y T H A G O R A S

Figure 1.31 Themes in Greek natural science. The arrows indicate the length o time or which an

idea was accepted as scientifc truth.



62

h W y h hy Gassendi(1592–1655)—v hh Lucretius’ , L,

h I — h ’ h

v, h A —v h v —j h hy.

Plato h h y h q

v. H j all k, h h -

, h . T Empedocles h hh —h, , , — h

h . T h h h

h y , h , , h

h z. T h h h , h h hx-h () h, h h , h h .

T h , h h, h h yh h (F 1.44). T h h

y Aristotle Empedocles h y v h y. F 1.44, x, k y Kepler. Plato

h v h . H z h h

v h : h h, h, h, ,

h , x h 30º, h , h 45º (F 1.45 1.46).

I h , h h v

. T h q , , hh h x y A = F2. F h y

q h, h ,

k , hy h W = A 2F.

A h y , hy , k Plato’ , k h, h. I h , y h k

h h y h k

hz . T h h h H

2O vy ,

y h h h h Plato. T h h

h h h

y hy. O h , y , h

yy. S hz y h yy -

, hy v h vy x. Heisenberg h h-

z h h h h hy h Plato (Q 1.20 1.21).

Aristotle h Empedocles. Wh h h -

h, , , , h h h

y– –. T, F 1.44, h y ; , y ; , ; , . A

Aristotle, h h

, h h

h. I h , h y .

I h , h x v , x

(mixtio, μϊξις). Aristotle h h -

Fire

Earth d r y

w a r m Air

c o l d Water w e t

Cosmos

Figure 1.44 Association o the our Platonic solids

with the our elements o Parmenides. The th Platonic solid

represents the idea o the cosmos (ater KePler).

New groups were appended to this group o our over

the course o time, with repercussions detectable to this

day. hiPPocraTes ounded, and galen rened, the idea o

“humoral pathology”: Health is determined by the proper

proportions (eukrasia) o the our humors. Sickness is

caused by a disturbance in these proportions (dyskrasia).The our humors are blood, phlegm, yellow bile, and black

bile. The dierences in human temperaments can be traced

to an excess o the humors: sanguine ( sanguis = blood),

choleric (chole = bile, anger, hate), melancholy (melancho-

lia = black bile), phlegmatic ( phlegma; re, infammation,

phlegm causing infammation).

We thus arrive at the ollowing groups o our:

octahedron air warm–wet

tetrahedron re warm–dry

hexahedron earth cold–dry

icosahedron water cold–wet

spring blood sanguine

summer yellow bile choleric

autumn black bile melancholic

winter phlegm phlegmatic




63

h x, h , h hq hh h h x h. A hy h y v h vy v hv h

h h h h v. T vy, h minima natura-lia, h h L Sh, hy h Ahy y hy, v h h .

1.3.1.1 Plato and the “Elementary Particles”

First of all, everyone knows, I’m sure, that re, earth, water and air are bod-

ies. Now everything that has bodily form also has depth. Depth, moreover,

is of necessity comprehended within surface, and any surface bounded by

straight lines is composed of triangles. Every triangle, moreover, derives from

two triangles, each of which has one right angle and two acute angles. Of these two triangles, one [the isosceles right-angled triangle] has at each of

the other two vertices an equal part of a right angle, determined by its divi-

sion by equal sides; while the other [the scalene triangle] has unequal parts

of a right angle at its other two vertices, determined by the division of the

right angle by unequal sides. This, then, we presume to be the originating

principle of re and of the other bodies, as we pursue our likely account in

terms of Necessity. Principles yet more ultimate than these are known only

to the god, and to any man he may hold dear.

We should now say which are the most excellent four bodies that can come

to be. They are quite unlike each other, though some of them are capable of breaking up and turning into others and vice-versa. If our account is on the

mark, we shall have the truth about how earth and re and their proportion-

ate intermediates [water and air] came to be. For we shall never concede to

anyone that there are any visible bodies more excellent than these, each con-

forming to a single kind. So we must wholeheartedly proceed to t together

the four kinds of bodies of surpassing excellence, and to declare that we have

come to grasp their natures well enough.

Of the two [right-angled] triangles, the isosceles has but one nature, while

the scalene has innitely many. Now we have to select the most excellent

one from among the innitely many, if we are to get a proper start. So if anyone can say that he has picked out another one that is more excellent for

the construction of these bodies, his victory will be that of a friend, not an

enemy. Of the many [scalene right-angled] triangles, then, we posit as the

one most excellent, surpassing the others, that one from [a pair of ] which the

equilateral triangle is constructed as a third gure. Why this is so is too long

a story to tell now. But if anyone puts this claim to the test and discovers that

it isn’t so, his be the prize, with our congratulations. So much, then, for the

selection of the two triangles out of which the bodies of re and the other

bodies are constructed—the [right-angled] isosceles, and [right-angled] sca-

lene whose longer side squared is always triple its shorter side squared [i.e.,the half-equilateral].

At this point, we need to formulate more precisely something that was not

stated clearly earlier. For then it appeared that all four kinds of bodies could

turn into one another by successive stages. But the appearance is wrong. While

there are indeed four kinds of bodies that come to be from the [right-angled]

triangles we have selected, three of them come from triangles that have un-

Figure 1.44 continued

Below, we quote rom the Labyrinthus medicorum (1538)

o Paracelsus to show the rst uncertain steps rom hu-

moral pathology to iatrochemistry (that is, to the idea that

lie processes and methods o cure have a chemical basis).

And such the physician should understand o the

cause that he not indicate the qualtates and hu-

mores: but the elements as mothers and their pro-

creationes as species, not [as] humores. Not that

one should say: Cuius humoris? Melancholici: yet

melancholia is nothing other than a mad, sense-

less phantastica illness, not a pillar o the our [ele-

ments]. Also do not say: Cuius Complexionis? Cho-

lericae, but Calidae Sectae. Now, Cholera is not

one o the our pillars, but a Morbus o all types o

expulsion. Thus also: Cuius Qualitatis? Sanguineae:

thus Sanguis is not one o the our pillars, but the

Corpus Venarum, like the wine in a barrel. Thus

also not: Cuius Naturae? Phlegmaticae: now, is

not Phlegma snot rom the nose, what has it to

do with the stomach? But Cuius Elementi? Aquae,

Terrae, Ignis, Aeris: now the answer arises: rom

what element does sickness arise? From re, not

Cholera: rom earth, not Melancholia: rom water,

not Phlegmate: rom air, not Sanguine. So it would

appear. And do not say: that is Melancholicum,

because neither heaven nor earth knows about

melancholy. Do not say: that is Cholera, Phlegma,

Sanguis, etc. So it is that nature knows nothing o

its process and order. So as the physician becomes

acquainted with the element, so will he nd in theGeneratis all illnesses o which mankind suers.

We can also mention the ollowing noteworthy parallel.

h. J. eYsencK (1916–1997) nds the precursors o his

model o personality in hiPPocraTes. Based on his statistical

investigations,eYsencK maintained that individuals can be

grouped in the categories stable/unstable and introvert/

extrovert. Thus he arrives at the ollowing our groups,

where we have added the corresponding Hippocratic

types:

stable–extrovert → sanguine

unstable–extrovert → choleric

unstable–introvert → melancholicstable–introvert → phlegmatic

Quotation 1.21

This attempt to assign geometrical gures to thesimple bodies is on all counts irrational. In therst place, the whole of space will not be lled up.Among surfaces it is agreed that there are threegures which ll the place that contains them—thetriangle, the square, and the hexagon: among solidsonly two, the pyramid and the cube. But they need

more than these, since they hold that the elementsare more. Secondly, the shape of all the simplebodies is observed to be determined by the place inwhich they are contained, particularly in the case of water and air. The shape of the element thereforecannot survive, or it would not be everywhere incontact with that which contains the whole mass.But if its shape is modied, it will no longer be




64

equal sides, whereas the fourth alone is fashioned out of isosceles triangles.

Thus not all of them have the capacity of breaking up and turning into one an-

other, with a large number of small bodies turning into a small number of large

ones and vice-versa. There are three that can do this. For all three are made up

of a single type of triangle, so that when once the larger bodies are broken up,

the same triangles can go to make up a large number of small bodies, assum-

ing shapes appropriate to them. And likewise, when numerous small bodies

are fragmented into their triangles, these triangles may well combine to make

up some single massive body belonging to another kind.

So much, then, for our account of how these bodies turn into one another. Let

us next discuss the form that each of them has come to have, and the vari-

ous numbers that have combined to make them up. Leading the way will be

the primary form [the tetrahedron], the tiniest structure, whose elementary

triangle is the one whose hypotenuse is twice the length of its shorter side.

Now when a pair of such triangles are juxtaposed along the diagonal [i.e., their

hypotenuses] and this is done three times, and their diagonals and short sides

converge upon a single point as center, the result is a single equilateral trian-

gle, composed of six such triangles. When four of these equilateral triangles

are combined, a single solid angle is produced at the junction of these plane

angles. This, it turns out, is the angle which comes right after the most obtuse

of the plane angles. And once four such solid angles have been completed, we

get the primary solid form, which is one that divides the entire circumference

[sc. of the sphere in which it is inscribed] into equal and similar parts.

The second solid form [the octahedron] is constructed out of the same tri-angles which, however, are now arranged in eight equilateral triangles and

produce a single solid angle out of four plane angles. And when six such solid

angles have been produced, the second body has reached its completion.

Now the third body [the icosahedron] is made up of a combination of one

hundred and twenty of the elementary triangles, and of twelve solid angles,

each enclosed by ve plane equilateral triangles. This body turns out to have

twenty equilateral triangular faces. And let us take our leave of this one of

the elementary triangles, the one that has begotten the above three kinds

of bodies and turn to the other one, the isosceles [right-angled] triangle,

which has begotten the fourth [the cube]. Arranged in sets of four whoseright angles come together at the center, the isosceles triangle produced a

single equilateral quadrangle [i.e., a square]. And when six of these quad-

rangles were combined together, they produced eight solid angles, each of

which was constituted by three plane right angles. The shape of the resulting

body so constructed is a cube, and it has six quadralinear equilateral faces.…

Let us now assign to re, earth, water and air the structures which have just

been given their formations in our speech. To earth let us give the cube, be-

cause of the four kinds of bodies earth is the most immobile and the most

pliable—which is what the solid whose faces are the most secure must of

necessity turn out to be, more so than the others. Now of the [right-angled]triangles we originally postulated, the face belonging to those that have

equal sides has a greater natural stability than that belonging to triangles

that have unequal sides, and the surface that is composed of the two trian-

gles, the equilateral quadrangle [the square], holds its position with greater

stability than does the equilateral triangle, both in their parts and as wholes.

Hence, if we assign this solid gure to earth, we are preserving our “likely

account.” And of the solid gures that are left, we shall next assign the least

Figure 1.45 The our Platonic solids associated with

the our elements together with the “elementary particles”

that constitute them. PlaTo considered the possibility o

imagining the regular solids, that is, the elements, as built

up rom two types o triangles, that is, rom still simplerelements. The triangles o the rst kind are isosceles right

triangles, whereas those o the second type are right tri-

angles whose hypotenuse is twice the length o the shorter

leg, that is, triangles obtained by halving an equilateral tri-

angle. The regular solids correspond in a way to our chemi-

cal elements; the triangles, to the elementary particles.



water, since its shape was the determining factor.

Clearly therefore the shapes of the elements arenot dened. Indeed it seems as if nature itself here shows us the truth of a conclusion to whichmore abstract reasoning also points. Here, as ineverything else, the underlying matter must bedevoid of form and shape, for so, as is said in theTimaeus, the “receiver of all” will be best able tosubmit to modication. It is like this that we mustconceive of the elements, as the matter of theircompounds, and this is why they can change intoeach other, and lose their qualitative differences.

—aristotle, On the Heavens [Guthrie, p. 319]



65

mobile of them to water, to re the most mobile, and to air the one in be-

tween. This means that the tiniest body belongs to re, the largest to water,

and the intermediate one to air—and also that the body with the sharpest

edges belongs to re, the next sharpest to air, and the third sharpest to water.

Now in all these cases the body that has the fewest faces is of necessity the

most mobile, in that it, more than any other, has edges that are the sharp-

est and best t for cutting in every direction. It is also the lightest, in that

it is made up of the least number of identical parts. The second body ranks

second in having these same properties, and the third ranks third. So let us

follow our account, which is not only likely but also correct, and take the solid

form of the pyramid that we saw constructed as the element or the seed of

re. And let us say that the second form in order of generation is that of air,

and the third that of water.

Now we must think of all these bodies as being so small that due to their smallsize none of them, whatever their kind, is visible to us individually. When, how-

ever, a large number of them are clustered together, we do see them in bulk.

And in particular, as to the proportions among their numbers, their motions

and their other properties, we must think that when the god had brought

them to complete and exact perfection (to the degree that Necessity was will-

ing to comply obediently), he arranged them together proportionately.

Given all we have said so far about the kinds of elemental bodies, the follow-

ing account [of their transformations] is the most likely: When earth encoun-

ters re and is broken up by re’s sharpness, it will drift about—whether the

breaking up occurred within re itself, or within a mass of air or water—untilits parts meet again somewhere, ret themselves together and become earth

again. The reason is that the parts of earth will never pass into another form.

But when water is broken up into parts by re or even by air, it could happen

that the parts recombine to form one corpuscle of re and two of air. And the

fragments of air could produce, from any single particle that is broken up, two

re corpuscles. And conversely, whenever a small amount of re is enveloped

by a large quantity of air or water or perhaps earth and is agitated inside them

as they move, and in spite of its resistance is beaten and shattered to bits, then

any two re corpuscles may combine to constitute a single form of air. And

when air is overpowered and broken down, then two and one half entire formsof air will be consolidated into a single, entire form of water.

Let us recapitulate and formulate our account of these transformations as

follows: Whenever one of the other kinds is caught inside re and gets cut

up by the sharpness of re’s angles and edges, then if it is reconstituted as

re, it will stop getting cut. The reason is that a thing of any kind that is alike

and uniform is incapable of effecting any change in, or being affected by, any-

thing that is similar to it.

—Plato, Timaeus [pp. 1256–1259]

1.3.2 Motion under Terrestrial Conditions: Peripatetic Dynamics

Dy h hy h h h - hh, h vyy , h hh h h y h.T zz h v h x, vh h v v hk. I, x hv

Figure 1.46 euclid mentions only convex regular solids.

In 1809, PoinsoT constructed our regular nonconvex solids.

Then in 1811, cauchY proved that there are exactly our such

solids. The gure shows one o these (rom the Great Soviet Encyclopedia).

archimedes considered semiregular solids, that is, solids

composed o regular polygons, but not all identical. Plate XII

shows one o these Archimedean solids, the rhombicuboc-

tahedron, composed o eight triangles and eighteen squares

(on the let in Pacioli’s painting).

In our time, the Archimedean solid composed o twelve

regular pentagons and twenty regular hexagons—the trun-

cated icosahedron—has acquired a particular signicance

(see also Figure 2.66). Sixty carbon atoms arranged at the

vertices o this solid yield a stable carbon molecule, called

buckminsterullerene or (C60

-Ih)[5,6]ullerene. It is named or

the architect bucKminsTer fuller. Its discoverers were awardedthe 1996 Nobel Prize in chemistry.

Buckminsterullerene is also called the “soccer-ball mol-

ecule,” since the stitching pattern on many o the world’s

soccer balls is that o this Archimedean solid.


As mentioned earlier, the Pythagoreans knew that there

were at least ve regular solids; the proo that there areexactly ve is due to PlaTo’s riend TheaeTeTus, who appears

as an interlocutor in the Dialogues. In his Elements, euclid

gives a proo that relies on a previously proved theorem,

that the sum o the dihedral angles at the vertex o a solid

must be less than 360º. I we now wish to obtain a regular

solid whose aces are equilateral triangles, we may have

three, our, or at most ve such triangles at each vertex.

Thus arise the tetrahedron, octahedron, and icosahedron.

With squares as aces, there must be three—neither more

nor less—and we obtain the cube. Finally, we may have

three regular pentagons at a vertex, giving us the dodeca-

hedron.

Today, one may obtain the proo rom a 1758 theorem o

euler: The numbers v o vertices, e o edges, and f o aces

in a convex solid are related by the ormula

v 2 e 1 f 5 2.



66

y h y h y , hv h x.I h h G, h . Ev Aristotle— h k vy v h

y v h v h y— y y x y h . Fh-, h k h h h Plato, Plato’ h v. Aristotle’ y h y vyy v h v y Aristotle h h y yz hy - v. Hv, y h h vy h A v h y v h . W h h .

A y, hh v h y h h , y y h entire A v.I , y y h h P hy , h h y h v h yy z h, vh k h, h h h h v hv y .

H, k h Aristotle h h- h y h y y -h , h h v y . Cvy, k y h v h Aris-

totle k, y hy h (P III).

L h hv vyh h Newton’ k v, vyy v, h h h x, y h h v h h h- , h vy, x, v . W hk h h h k, h v hv y y . I h h , y

h , fy h , h k . A h hv h : h - h h h v . A y h h , y. O ,

h . F h k h, k hky, hh k . A h , h y h h h y v - h. W h y ; h k h , h . Evy, h h y , y h h, h

v , h h, y h h y.I v; h S y k h hz, h -

v. T h h y, h h h y h v. C v Eh, h ky h ky: v h hh v y h h x Eh. I , y , hh h hv h Eh must be diferent .

Quotation 1.22

The Pythagoreans … did not accept, in things divineand eternal, such disorder as [the heavenly bodies]moving sometimes more quickly, sometimes moreslowly, and sometimes standing still. ... One wouldnot accept such anomaly of movement in the goingsof an orderly and well-mannered man. The businessof life is often the cause of slowness or of swiftnessfor men. But in the case of the incorruptible natureof the stars, it is not possible to adduce any causeof swiftness or slowness. For this reason, they putforward the question: how would the phenomenabe accounted for by means of uniform and circularmotions?

—geMinos of rhoDes, Introduction to the Phenomena [pp. 117–118]

Quotation 1.23

It is instructive to see how the ideas in Quotation 1.22are later echoed in the writings of the great Jewishphilosopher MaiMoniDes (1135–1204):

That the sphere is endowed with a soul is clear uponreection. However, he who hears this may deemthis a matter that is difcult to grasp or may regardit as impossible because of his imagining that whenwe say, “endowed with a soul,” the soul referred to islike the soul of a man, or an ass and a bull. Now thisis not the meaning of the dictum. This meaning israther that the local motion of the sphere is a proof of there indubitably being in it a principle in virtue of which it is moved. And this principle is undoubtedlyand incontestably a soul. This may be explained asfollows. It is absurd that the circular motion of thesphere should be similar to the rectilinear motionof the stone downwards or to the motion of the

re upwards, so that the principle of that motionwould be a nature and not a soul. For what is movedin natural motion is only moved by the principlesubsisting in it, when the object to be moved isnot in its place, and it is moved in order that it mayseek to come to its place. However, when the objectin question reaches its place, it comes to rest. Thesphere, on the other hand, is moved in its own placein a circular motion. … In consequence this circularmotion can only come about in virtue of a certainmental representation, which determines thesphere’s moving in that particular way. Now there

is no mental representation without intellect. Inconsequence the sphere must be endowed with anintellect. … [T]he soul, in virtue of which there is the




67

W hv h v h A :

1. E : h h (motus a se).2. :

. M v (motus a se ).. N : hvy ; h v (motus secundum naturam mo-tus naturalis ).

. V (motus violentus ).

T v h , hy hv , hy v— h h y v— , hy h y hh h h k. T , v , y h (Q 1.22 1.23).

F h v , v h H hv v h h P y-

: Fy h h ()h. A h , h h - .

T h P y h : S x h , hvy hv h , h - v, hvy h . T, h y h y h .

I vyy v, h h v k: hy v? T h q y A y, h h h v : Evy v , y y, (omne quod movetur ab alio movetur ). T, , hh h h h , h , .

P y h h v - y hh ; h , vy , k v (motor conjunctus ). I A y,h v h vy h y. O , hvy h y qvy. T y

h h hy y y A (Q 1.24). F v, y h y v h h vy vy h . W y h h Aristotle h h h y’ y h P y.

T vy y y h v h . V-y v y k, vy h , vy h . I y’ , y

velocity effective causeresistance

≈ ⇒ ≈v F

R .

W h, hh h h y- y, vh vyy v. I xh h, x, h v y h h , h k h y v h y .


motion, and the intellect, by which the objectis represented to oneself, are not both of themtogether sufcient to account for the coming-about of such a motion until desire for the notionrepresented is conjoined with them. Furthermore,it follows necessarily from this that the sphere hasa desire for that which it represents to itself andwhich is the beloved object: namely, the deity, mayHe be exalted.aristotle says that it is in this mannerthat the deity causes the sphere to move, I meanto say through the fact that the sphere desires tocome to be like that which it apprehends, whichis the notion represented—a notion that is mostexceedingly simple, in which there is no change

and no coming-about of a new state, and fromwhich good always overows. This is impossiblefor the sphere qua a body unless its activity be acircular motion and nothing else. For this is the nalperfection of what is possible for a body to have asits perpetual activity. …

As for the assertion that the spheres are living andrational, I mean to say endowed with apprehension,it is true and certain also from the point of viewof the Law; they are not dead bodies similar to reand earth—as is thought by the ignorant—but

they are—as the philosophers say—living beingswho obey their Lord and praise Him and extol Himgreatly. Thus Scripture says: The heavens tell of the

glory of God,and so on.

—MaiMoniDes, The Guide of the Perplexed ,Chapters 4 and 5 [pp. 255, 256, 259]

Quotation 1.24

We observe that the same weight or body travelsfaster for two reasons, either because there is adifference in the medium through which it travels,as through water or earth or air, or because, otherthings being the same, the traveling body has anexcess of density [or weight] or of lightness. Themedium through which the body travels is a causeby the fact that it obstructs the body, most of all if it[the medium] is travelling in the opposite direction,but even if it is resting; and it does so more if it is noteasily divisible, and such is a more viscous medium.




138

T A w g W w M Ag w Avicenna (ibn Sina, . 980–1037) Averroes (Ibn-Rushd, 1126–1198). Avicenna p . H p-p w A w P. H pp p pk

p Omar Khayyám, w w wg g (Q 2.9). Averroes w M Ag “T C.” H Dante’ Divine Comedy .F , Aristotle w pp p x (Q 2.10). W pk p Aristotle, w homas Aquinas k g g w Averroes’ pp.N, Averroes p A w w w p w ; , G P w .

2.3.3 Some Outstanding Contributions of Arab Science

A p p pk . A ,Ep w p p . H w z p-p A .

I 1459, P J amshid al-K ashi π 17 - p.

T w kw ( p n)

( ) ., , ,a b a C a b C a b C ab bn n

n

n

n

n

n n

n n+ − = + + + +

− −

−

−

1

1

2

2 2

1

1

T wg p w kw f ppg :

C C C n m n m n m, , ,

.= +− − −1 1 1

T p w Ep P’ g.F w xp w ,

,

a k k

a

n

=

∑ =1

1 2 3 4, , , , , .

T, xp, pw n w

a n a a

a

a

n

a

n

a

n

a

4

1

4 4 4 2

1

11 2 3

1

5= =

=∑ ∑∑

= + + + + = +

−

==∑

1

n

.

T al-K ashi, , w p z 1´ p p. , 3º 72º 60º g

(72º – 60º) = 12º = 72º · 60º – 72º · 60º

3º = (15º – 12º).

1°,

cos cos cosφ φ φ

= −43

33

3

Figure 2.36 Illustration o a balance rom al-KhazInI’sBook of the Balance of Wisdom, 1121.

Figure 2.37

The apparatus

o al-BI ˉ rI ˉ nI ˉ or

measuring

specic gravity

in al-KhazInI’s book

[Dorman 1974].

Figure 2.35

The relation-

ships in a

regulardecagon.



139

-g

x x 30 7850393433644006 45+ =. ,

w 17 p.

W , w p w p p. H -g w k p.

72°, g g g ( w g 36° g w w g 2 3 72° 5 144°) r

r

25 1−( )

(Fg 2.35).I p, A p Gk p wk-

g g p g (Fg 2.36 2.37). I g, a lhazen (ibn al h aytham, 965–. 1039) w g Ep . H

Ptolemy ’ w w g , g pp. Hw, w w.H p p , pp , p w . M, p p Fg 2.38, w g pp g , g a lhazen’ g .T k : G w p A B p x g , p M ’ OMM ́ g α MB MA. T p p g p p w g g g p A g pB . a lhazen p -g p , w w .

T A Ptolemy ’s wk , g ne plus ultra, kg , w p , p . Hw,

g wk w p , p . T, , UlUgh beg.H al-K ashi w w. H pp UlUgh beg. Tg pp gg j w : g x w 40 g 60º (Fg 2.39).

Figure 2.38 On the problem o alhazen. A ray o light

emitted rom point A should, ater refection in a sphericalmirror, arrive at point B. According to the law o refection,

the angles AMM ′ and M ′MB should be equal. (leonardo

also had a solution to this problem.)

(a) (b)

Figure 2.39

(a) The sextant o the observatory built by uluGh

BeG in Samarkand.

(b) uluGh BeG (portrait rom the 1690 book Prodromus Astronomiae by hevelIus).

Quotation 2.10

Nature created him [Aristotle] to place before oureyes an example of human perfection. Providencehas given him to us so that we might know whatcan be known. His teaching is the highest truth;

his reason, the highest form of human powers of comprehension that can exist.

—AVerroes

(a) (b)



154

Hw, Aquinas w y w M A, y: T w- p w p , w p , w pp y Aquinas’ Albertus Magnus.

T py y pp p ww y , py. I - p w w, y w y y y , wx w, w w y . D - S, Saint Augustine, py p C F, w p w w . H , w w S 1.5.1,

. B w , w, , y . Ey j , py . F , (Q 2.22), w y z psi enim allor sum (I , I ), w y Descartes : cogito ergo sum (I , I). Augustine y p (illuminatio Dei ).T w p Descartes A p w p G. Aquinas p Augustine’ p w. I p, w

w y pp, y . I p, Aqui-nas p Augustine’ illuminatio, w , w S, w y: T S’ y w, w y S, j w.

2.5.2 Faith and Experience

T y w p w - p p wy w wy w. I Albertus Magnus (. 1200–1280, F 2.54 2.55), doctor universalis Aquinas, w w D p y . W Albertus Magnus ’ p p Gy, D , w wy. T p w pp pp w . I Albertus’ w, y Fui et vidi experiri (I w w pp wy). H p (Q 2.23 2.24) ’ w p w

. H j -. H w y :T w .

T p xp xp w pz y OxS, y Grosseteste (. 1175–1253) Roger Ba-con (F 2.56 2.57). T w Ep , w w w y.Grosseteste p p. H w

Figure 2.55 alBertusmaGnus: Philosophia naturalis.

(Incunabula, 1487, Székesfehérvár Diocesan Library.)

Quotation 2.21

It is one thing to inquire which is the true historyof creation, another to ask what Moses, who was sogood a servant to the family of your faithful, meantthose who read or heard his words to understandby them.

As for the rst sort of disagreement, I wish to haveno dealing with any who think things which inreality are false; and as for the second, I wish to havenone with any who think that Moses wrote what

was not true.

—Augustine, Confessions XII.23 [p. 300]

Quotation 2.22

If I am mistaken, I exist. He who does not existclearly cannot be mistaken; and so, if I am mistaken,then, by the same token, I exist. And since, if I ammistaken, it is certain that I exist, how can I bemistaken in supposing that I exist? Since, therefore,I would have to exist even if I were mistaken, it isbeyond doubt that I am not mistaken in knowingthat I exist. And, consequently, neither am Imistaken in knowing that I know.

—Augustine, The City of God against the Pagans



155

w p y w wpy p w w p (Q 2.25).H w w p p-. T Francis Bacon -

y. Grosseteste’ p, Roger Bacon, y p w doctor mirabilis , y y ppy xp pp j (tota philosophiae in-tentio non est nisi verum naturas et proprietates evolvere ). w -w w, y , , y, xp ( per auctoritatem et rationem et experientiam). Bacon w . A w xp, , w y y , y xp: Ey p xp- (Oportet ergo omnia certifcari per viam experientiae ).

W p , p wy w p p y x. I pp p, y p w, p w w . Ny, x - . B, xp w Bacon y y j . Bacon w xp: x xp y -, xp, y, p (divina inspiratio). T - pp y p , w p

pp (divinae inspirationes non solum in spiritualibus sed et in corporalibus et scientiis philosophiae ). Bacon xp p, w p (raptus ), w -p y. S Bacon, p w xp.

I w y E p p. H y F Peter of Maricourt (Peter Peregrinus) pp - (Epistola de Magnete , 1269) p , , w w S 4.4.1, . Peter y xp, xpy p xp pppp ; , w y -y . A x pp p p y Nicholas

of Autrecourt (. 1299–. 1369). H y w — David Hume— ppy z w y , w y (Q 2.26).

Grosseteste y - pp : pp y , wy j p w wy ; pp y, wy , p p w w wp x .

H w pp Ockham’ z. William of Ock-ham ( Occam, . 1288–. 1348), , x F

Figure 2.56 roGer

BaCon (ca. 1214–1294).

Studied in Paris, where

he later held his rst lec-

tures onarIstotle

. Ater1247, he studied a wide

variety o subjects at

Oxord and built himsel

a laboratory. In 1257, he

entered the Franciscan

order. Between 1266

and 1268 he wrote

Opus majus, Opus mi-

nus, and Opus tertium.

From 1277, he was

imprisoned by his order

on charges o heresy.

In general, BaCon’s

modernity is exaggerated. But in any case, it is correct that he

recognized the importance of experimentation. He valued highly

the work o pIerre demarICourt, calling him dominus experimento-

rum. BaCon himsel experimented with lenses and mirrors. Above

all, he was interested in alchemy. He was the rst European

to provide a precise recipe or the manuacture o gunpowder

(1242). He seriously investigated the problem o fight, making

use o a balloon made o thin copper oil with movable wings.

He built a camera obscura and actually used it or observations o

a solar eclipse. BaCon appreciated the importance o mathematics

or the sciences, encouraged the study o languages, and even

sketched the outlines o a utopian society.

Having laid down undamental principles o the wisdomo the Latins so ar as they are ound in language, math-

ematics and optics, I now wish to unold the principles o

experimental science, since without experience nothing can

be suciently known. For there are two modes o acquiring

knowledge, namely, by reasoning and experience. Reason -

ing draws a conclusion and makes us grant the conclusion,

but does not make the conclusion certain, not does it re -

move doubt so that the mind may rest on the intuition o

truth, unless the mind discovers it be the path o experi-

ence; since many have the arguments relating to what can

be known, but because the lack experience they neglect the

arguments, and neither avoid what is harmul nor ollow

what is good. For i a man who has never seen a re shouldprove by adequate reasoning that re burns and injures

things and destroys them, his mind would not be satised

thereby, nor would he avoid re, until he placed his hand

or some combustible substance in the re, so that he might

prove by actual experience that which reasoning taught. But

when he has actual experience o combustion his mind is

made certain and rests in the ull light o truth. Thereore,

reasoning does not suce, but experience does.

—roGer BaCon [Newman 1956, p. 1758]

A th part o experimental science concerns the abrication

o instruments o wonderully excellent useulness, such as

machines or fying, or or moving in vehicles without ani-mals and yet with incomparable speed, or o navigating with-

out oarsmen more switly than would be thought possible

through the hands o men. For these things have been done

in our day, lest anyone should ridicule them or be astonished.

And this part teaches how to make instruments by which in-

credible weights can be raised or lowered without diculty

or labor. … Flying machines can be made, and a man sitting




174

b bj. A , b q , b - b x. H, b , b, b ,

, , . I, b j b . W, , b b

? A q b: A . W F .4 , : T q M A, , , , ( , S ), , b . , b E. F .4 . A Newton’ . A Newton, , , b z .

N b b b (b .1),

b . H, b , , , b -z b. I , b . T b b (F .5). We must not overlook the act that ideological arguments were in no way limited

to verbal exchanges, particularly in cases where economic and ideological issues were

COSMOS

COSMOS

Geostatic, Finite, Hierarchical

TERRESTRIAL PHYSICSUniform Circular MotionCELESTIAL PHYSICS

≈

A R I S T O T L E

Nicholas of Cusa

KINEMATICS DYNAMICS STATICS

COPERNICUS

COPERNICUS

De Soto

(Simplied)

Tycho Brahe(Complexied) Dead End

GALILEO

Heliostatic, Innite, Homogeneous

Dead End

Figure 3.4 The stages along the path to the unifcation

o celestial and terrestrial physics.

Figure 3.3 The distribution o scientifc

books published beore 1545 according toConrAd Gesner.

Dialectic, Rhetoric, Poetics

Mechanics, Arithmetic, Geometry,Music, Astronomy

Economics, Politics, Law

Metaphysics, Ethics

Magic, Astro logy

Theology

Medicine

Natural Philosophy

Grammar

History,Geography

Quotation 3.3I speak thus to my listeners: Look, this is taughtby aristotle, that is the opinion of plato; so speaksGalen, and thus hippoCrates. Who listens to me mustconcede: The works of Borrius command completetrust, for not one of them is his own; rather, themost illustrious minds speak through his mouth… If thoughts come to me that I don’t nd in theirworks, I discard them at once as suspicious or putthem aside until they become old and die out beforethey have seen the light of day.

—GirolaMoBorrio, Pisa, 1676, in lalande, Lectures sur la philosophie des sciences

Quotation 3.4

And albeit, it may be said by the learned in theMathematicalles, as hath beene already writtenby some, that this is no question or matter fora Mechanitian or Mariner to meddle with, nomore than is the nding of the Longitude, for thatit must bee handled exquisitely by Geometrical




175

closely connected. Among the events that fnally led to the vision o a homoge-neous universe—or, more concretely, to the replacement o the relation F ∝ v by F ∝ Δ v —belong also the burning o heretics at the stake and the horrors o thereligious wars (Figure 3.6).

1543 CoPerniCus De revolutionibus orbium coelestium

1585GiordAno

BrunoDel infnito, universe e mondi

1585 stevin Weeghconst 1600 GilBert De magnete

1609 KePler Astronomia nove aitiologethos seu Physica coelestis

1610 GAlileo Sidereus Nuncius

1619 KePler Harmonices mundi …

1620 BACon Novum Organum

1623 GAlileo Saggiatore

1632 GAlileo Dialogo sopra I due massimi sistemi del mondo

1638 GAlileo Siscorsi e dimonstrazioni matematiche intorno a due nuove scienze

1637 desCArtes Discours de la method

1644 desCArtes Principia philosophiae

1647 PAsCAl Expériences Nouvelles touchant le Vide

1660 Boyle Touching the Spring and Weight o Air

1672 GueriCKe Experimenta nova Magdeburgica

1673 HuyGens Horologium oscillatorium

1687 newton Philosophiae naturalis principia mathematica

1690 HuyGens Traité de la lumière

1690 loCKe An essay concerning human understanding

Table 3.1 Signifcant ideas in signifcant books o the time.

Figure 3.5 The book De re metallica, by AGriColA

(GeorG BAuer, 1494–1555), was an epoch-making event in

mining and metallurgy. O particular interest or us are the

methods o measurement described and, above all, the

construction o multistage pumps. The Scholastic problem

o horror vacui has here become a technical problem.


demonstration, and Arithmeticall Calculation: inwhich Artes, they would have all Mechanitians and

Sea-men to be ignorant, or at leaste insufcientliefurnished to performe such a matter. … But I doeverily thinke, that notwithstanding the learned inthose Sciences, being in their studies amongst theirbookes, can imagine greate matters, and set downetheir farre fetcht conceits, in faire showe, and withplawsible wordes, wishing that all Mechanicianswere such, as for want of uttereance, should beforced to deliver unto them their knowledge andconceites, that they might ourish upon them, andapplye them at their pleasures: yet there are inthis land divers Mechanicians, that in their severall

faculties and professions, have the use of those Artesat their ngers endes, and can apply them to theirseverall purposes, as effectually and more readily,then those that would most condemne them.

—roBert norMan, The Newe Attractive [p. ii]



176

3.2 Numerology and Reality 3.2.1 Back to Plato in a New Spirit

E, R, b . O - . F, b b , x b Aristotle Plato Pythagoras. I b j b -

(F .7). A b , b b .

T -. T x bj b ’ .H Leonardo, b b .

T bb ; , b b . I b Pythagoras Plato, b . A , q-, (S 1.2.). N, - b “” , b . A , P , , x-,

x .S- b,

b facts . A , Kepler, b b , b P .

T j A b G - b Aristotle b . A

Figure 3.6 Theoretical arguments were not the

decisive actor in the ormation o a new worldview. (HAns

HolBein tHe younGer: Bad War .)

Figure 3.7 Canon o proportions or the humanfgure by leonArdo (top) and dürer (bottom).

Quotation 3.5

Following plato and the Py thagoreans, the greatestmathematicians of that divine age, my teacherthought that in order to determine the causes of the phenomena circular motions must be ascribedto the spherical earth.

—rhetiCus, “Narratio Prima” [pp. 147–148]



177

, - , b , , b M A. T R b , b b - D A.

.2.2 Te Retrograde Revolutionary: Copernicus

T N-P b C . A Coper-nicus Regiomontanus, b b (S 2.6.5).

I x , I -, Copernicus (F .8, P XIV) b q Aristarchus o Samos, S

, — E— b S b. I , Copernicus, b , - equants P , b b P , , — , — with constant velocity , , b - b. A , Copernicus P , b (Q .5 .6).

T b Copernicus’ x. I 1514 Commentariolus , Copernicus b . T, 1540 b, Narratio prima, Rhe-ticus b Copernicus’ . Copernicus , De revolutionibus orbium coelestium (O ), b 154, q b ; F .9.

Figure

3.8 According toHevelius, the prede-

cessors o CoPerniCus

were Ptolemy, Al-

BAteGnius (Al-BAttAni),

and reGiomontAnus.PrinCewilliAm iv o

Hessen (1532–1592)became known or

his catalog o stars.

The picture is romHevelius’s book Ura-

nographia (1687).

niKolAus CoPerniCus

(miKołAj KoPerniK):

born 1473 in Toru ´

n, son o a merchant, raised ater his ather’s death by his

uncle, the bishop o Warmia. Studied in Kraków, then in Bo-

logna, Padua, Ferrara (where in 1503 he received a doctorate

in ecclesiastical law), and Rome. Also studied medicine and

served as his uncle’s personal physician. From 1512, withoutordination, was canon at the Frombork cathedral. Died in

Frombork, 1543. Published his ideas about astronomy frst

in 1512 in his Commentariolus, which was distributed in

manuscript as a pamphlet. An extensive description o his

cosmology is contained in the 1540 article by the Wittenberg

proessor rHetiCus: Narratio Prima. His magnum opus, De

revolutionibus orbium coelestium, was published in Nurem-

berg shortly beore his death.

First o all I wish you to be convinced … that this man

whose work I am now treating is in every feld o knowl-

edge and in mastery o astronomy not inerior to Re-

giomontanus. I rather compare him with Ptolemy, notbecause I consider Regiomontanus inerior to Ptolemy,

but because my teacher shares with Ptolemy the good

ortune o completing, with the aid o divine kindness,

the reconstruction o astronomy which he began, while

Regiomontanus—alas, cruel ate—departed this lie be-

ore he had time to erect his columns.

—rHetiCus, First Narration (Narratio Prima) [Boas Hall 1962]

Quotation 3.6

People give ear to an upstart astrologer who stroveto show that the earth revolves, not the heavens

or the rmament, the sun and the moon, as if someone moving by carriage or by ship thoughthimself to be stationary and the land and trees tobe moving. But the case is more like this: One whowants to appear clever cannot go along with whateveryone seems to observe; he must come up withsomething different. So this clever soul, who wantsto turn the whole of science of astronomy upsidedown. Yet even in those difcult matters I put myfaith in Sacred Scriptures, for Joshua commandedthe sun to stand still, and not the earth.

—Martin luther,

June 4, 1539 [Deely 2001, pp.495–496]



178

I , E b S Copernican revolution, - b b . T, x, Kant “C ” .

I , C x .

Copernicus b b (Q .7).F C P (F .10) S b. I b , b E

Figure 3.9 The

book De revolutionibus

orbium coelestium, one

o the most important

works in the historyo European culture,

was published in 1543

in Nuremberg. The

book contains a brie

oreword directed

to the reader that is

attributed not to CoPer-

niCus, but to osiAnder.

Following the oreword

is a letter rom Cardinal

sCHönBerG to CoPerniCus,

and fnally a dedication

to Pope PAul iii.

The entire work con-

sists o six books. The

frst book describes

a simple model o

a heliocentric solar

system and contains,

moreover, a sum-

mary o the necessary

mathematical theorems

o trigonometry, plane

and spherical. In the

ollowing fve books,

CoPerniCus oers a de-

scription o the orbitso Earth, the Moon,

and the planets using

tables, epicycles, and

deerents.

The pages reproduced

here rom the second

edition (Basel, 1566)

are taken rom the

exemplar at Charles

University, Prague,

whose unique eature

is that it contains tyCHo

BrAHe’s handwrittennotes. The Basel edi-

tion also contains the

book Narratio Prima byrHetiCus (acsimile edi-

tion, Prague, 1971).

I have no doubt that certain learned men, now that the

novelty o the hypotheses in this work has been widely

reported—or it establishes that the Earth moves, and

indeed that the Sun is motionless in the middle o the

universe—are extremely shocked, and think that the

scholarly disciplines, rightly established once and or all,

should not be upset. But i they are willing to judge thematter thoroughly, they will fnd that the author o this

work has committed nothing which deserves censure.

For it is proper or an astronomer to establish a record o

the motions o the heavens with diligent and skilul ob-

servations, and then to think out and construct laws or

them, or rather hypotheses, whatever their nature may

be, since the true laws cannot be reached by the use o




179

celestial spheres based on their relative positions with respect to the fxed stars. Tetwo systems, from this viewpoint, are equivalent when both the Copernican andPtolemaic observers see the same angular coordinates or the Sun and planets inrelation both to one another and to a selected fxed star, and thereore both observ-

ers can record the same trajectory on their star maps. We begin the proo o this equivalence with the observation that in the Ptol-

emaic system, only the ratio o the radius o the deerent and that o the epicyclehave any signifcance; the radius o the latter can thereore be chosen arbitrarily (Figure 3.11). For the convenience o the proo, let us choose it to be equal tothe radius o Earth’s orbit (Figure 3.12). Te ollowing illustrations demonstratethe equality o the relevant angles to a terrestrial observer in the cases o an inner(Figure 3.13) and an outer (Figure 3.14) planet.

Let us carry out the proo in somewhat more detail in the case o an outer planet. We begin with the Copernican system and draw in Figure 3.14, in black, the result-ing paths. At a given point in time, suppose that Earth is located at the point E anda planet at point P . Te directions are then shown in which an observer on Earthviews the Sun (S ) and the planet. Now we let Earth assume the role played by theSun and move the point E into the place previously occupied by S , resulting in thepoint S being mapped to S ́ , so that the Sun is again viewed rom Earth at the same


reason; and rom those assumptions the motions can

be correctly calculated, both or the uture and or the

past. Our author has shown himsel outstandingly skilul

in both these respects. Nor is it necessary that these hy-potheses should be true, nor indeed even probable, but

it is sufcient i they merely produce calculations which

agree with the observations. That is, unless anyone is

so ignorant o geometry and optics that the epicycle o

Venus seems to him probable, or he thinks that it is in

accordance with its law that it is sometimes ahead o the

Sun and sometimes lags behind it by orty degrees or

more. For who does not see that rom that assumption it

necessarily ollows that the star’s diameter appears more

than our times greater, and its area more than sixteen

times greater, at perigee than at apogee, to which all

the experience o the ages is opposed. There are other

things also in this discipline which are no less absurd,which it is quite unnecessary to examine or the present

purpose. For it is clear enough that this subject is com-

pletely and simply ignorant o the laws which produce

apparently irregular motions. And i it does work out any

laws—as certainly it does work out very many—it does

not do so in any way with the aim o persuading anyone

that they are valid, but only to provide a correct basis or

calculation. Since dierent hypotheses are sometimes

available to explain one and the same motion (or in-

stance eccentricity or an epicycle or the motion o the

Sun) an astronomer will preer to seize on the one which

is easiest to grasp; a philosopher will perhaps look more

or probability; but neither will grasp or convey anything

certain, unless it has been divinely revealed to him. Let

us thereore allow these new hypotheses also to become

known beside the older, which are no more probable,

especially since they are remarkable and easy; and let

them bring with them the vast treasury o highly learned

observations. And let no one expect rom astronomy, as

ar as hypotheses are concerned, anything certain, since

it cannot produce any such thing, in case i he seizes

on things constructed or any other purpose as true, he

departs rom this discipline more oolish than he came

to it. Farewell.

—Osiander, “To the Reader Concerning the Hypotheses

o This Work” in COperniCus, On the Revolutions of theHeavenly Spheres [pp. 22–23]

Eart h Earth

Figure 3.10 The Ptolemaic and Copernican systems in

their simplest representations.

Figure 3.11 In the Ptolemaic system, the radii o the epicycles and deerent circles can be chosen

arbitrarily, as long as their ratio is kept fxed. The line joining the center o an epicycle to its planet (or

the outer planets) is, however, always parallel to the line connecting Earth and the Sun.

Figure 3.12 We have here chosen the deerent circle o the Ptolemaic system in such a way that the

epicycle’s radius is the same as that o the orbit o Earth. It is clear that the observable angles are equal.



180

b. I q b E , , E, b . W b

b : P . W

C , , P , b . W , S b , : P , S b E b E,

Figure 3.13 Equivalence in the case o the inner planets: The midpoint o the epicycle always lies

on the line connecting Earth and the Sun. The radius o the epicycle is equal to that o the orbit o the

planet, and the deerent coincides with the orbit o Earth.

Figure 3.14 For an outer planet, we show here the agreement o the two world systems when the

planet moves.

Quotation 3.7

The universe is globe-shaped, either because thatis the most perfect shape of all, needing no joint,

an integral whole; or because that is the mostcapacious of shapes, which is most tting becauseit is to contain and preserve all things; or becausethe most nished parts of the universe, I mean theSun, Moon and stars, are observed to have thatshape, or because everything tends to take onthis shape, which is evident in drops of water andother liquid bodies, when they take on their naturalshape. There should therefore be no doubt that thisshape is assigned to the heavenly bodies. …

The rst and highest of all is the sphere of the

xed stars, which contains itself and all things, andis therefore motionless. It is the location of theuniverse, to which the motion and position of allthe remaining stars is referred. For though someconsider that it also changes in some respect, weshall assign another cause for its appearing to doso in our deduction of the Earth’s motion. Therefollows Saturn, the rst of the wandering stars,which completes its circuit in thirty years. After itcomes Jupiter, which moves in a twelve-year-longrevolution. Next is Mars, which goes round biennially.An annual revolution holds the fourth place, in whichas we have said is contained the Earth along with thelunar sphere which is like an epicycle. In fth placeVenus returns every nine months. Lastly, Mercuryholds the sixth place, making a circuit in the space of eighty days. In the middle of all is the seat of the Sun.For who in this most beautiful of temples would putthis lamp in any other or better place than the onefrom which it can illuminate everything at the sametime? Aptly indeed is he named by some the lanternof the universe, by others the mind, by others theruler.trisMeGistus called him the visible God, sophoCles’ Electra, the watcher over all things. Thus indeedthe Sun as if seated on a royal throne governs hishousehold of Stars as they circle round him.

—CoperniCus, On the Revolutions of the Heavenly Spheres [pp. 36, 49–50]



181

C b,

b E S. F

, ’

S E. W S 1.4 (F 1.72),

b , S .

A F .10 C

. F, , q

, b

S. W (S 1.4) P

,

b , . E

b , ,

, b- x .

T b C

b F .15. W x

S, E. F -

E-S ES ,

S b

PS ES = sin .α

I C , ’ b b S. W F .16, b

b . W ,

x b ,

b x S. L

b E, . W

b P ́ . W E b

b S . L x E b b ω

E

b ωP , t

0

b. T E

ωE t 0, ω

P t 0. A b ,

b

ω ω α α π E Pt t

0 02= − + − .

L b E b E

b P

,

:

ω

π

ω

π

E

E

P

P

= =

2 2

, .

W b -

N , q

Figure 3.15 Determination o the orbital radius o

an inner planet in terms o the unit distance rom Earth

to the Sun.

Figure 3.16 Determination o the orbital period o an

inner planet according to CoPerniCus.



182

b b :

2 22

0 0

π π

π

T t N

T t N N

E P

( ) = ( )− .

I — , E’ b , b E b 1—

T t N T E (in years),= =1 0,

b

T T

T N = −

P

,

,T

T

T N

P=

+

.

T b x E . W F .17, , , -

b .T

C . H, q P q C . T C q P . B

P , q b , b C b, , b b .

I b Copernicus. A -, b, b , - j q b x q. T b — — Aristarchusj . ,

Copernicus , b b . TCopernicus , b q, b E S, P . I , b b, Coper-nicus 0 b.

F .18 — — C P-

b . W , . I b , - . I F .19, E S . W E b b S, , , S b , , , S. T C b x b . F , S

Figure 3.17 Determination o the orbital period o

an outer planet.

Figure 3.18 The dierence between the Ptolemaic

(top) and Copernican (bottom) systems largely disappears

when, in order to obtain agreement with observations, epi-

cycles and deerents are brought in [Cohen 1960, p. 58].

Sun

Sun

Earth

Earth



183

. T, , C heliocentric — , S —b heliostatic , S , , E .

T, b C , . T S ,

b P , b b x ; x, f , - . I C , ,

S , b f - S. B C b, S b b?

I b q, Copernicus’ b— , , Copernicus b Osiander— b . I

b , , b . B b , , , b C, fully elaborated C b only , b .

A, Copernicus , x C - x, , , — x — x (F .20). T

; , b P .

, F .21 E De Revolutionibus 1576 C P-

. A , J Clavius, P , C .M C , x, j b b — — .

I, Copernicus q . H

b, b x ,

. H x b . A b E b, , b . T

b .I , Copernicus

E - . I , A . A x

Figure 3.19 Copernicus did not use equants.

However, to “rescue the phenomena,” he had to

introduce complex double epicycles. Earth’s motionis also represented by such a complicated system

[Hall 1965, p. 62].

Then Mercury runs on seven circles in all; Venus on

fve; the earth on three, and round it the moon on

our; fnally Mars, Jupiter, and Saturn on fve each.

Altogether, thereore, thirty-our circles sufce to

explain the entire structure o the universe and the

entire ballet o the planets.

—CoPerniCus, Commentariolus [p. 90]

Figure

3.20 In his

1589 book,

pictured here,

mAGinus made

use o CoPerni-

Cus’s astro-

nomical data

but rejected

the Coperni-

can hypoth-

eses regarding

the motion o

Earth as ab-

surd. (Central

library o the

Benedictine

order, Pannon-

halma.)



184

q b E. R A bj , bb b, b b . B E , , “b” “b” b . Copernicus x bj

b. H, x— — bj , , .

bj x , b E -b S, f f , — — x b (F .22), Copernicusf : T E’b b . F ’ , , b , b z b . M,

b , , (x) ( b x ). W z Copernicus’

possibilities :

1. H - b P P . I

Figure 3.21 A representation o the Copernican

system in diGGes’s book. diGGes accepted the Copernican

system and even goes a step urther: The stars are no longer

arranged on crystalline spheres, but distributed in space.

The text in the outer ring o the picture, in modern English,

reads thus:

This orb o stars fxed infnitely up extends itsel in alti-

tude spherically, and thereore, immovable the palace

o elicity garnished with perpetual shining glorious

lights innumerable, ar excelling our sun both in quan-

tity and quality the very court o celestial angels, devoid

o grie and replenished with perect endless love the

dwelling place or the elect.

—tHomAs diGGes, Perft Description o the Caelestiall

Orbes according to the most ancienne doctrine o the

Pythagoreans lately revived by Copernicus and by Geo-

metricall Demonstrations approued, 1576

Figure 3.22 I Earth orbits the Sun, then the stars

must appear at dierent angles rom dierent points on

the orbit o Earth—or the stars must be very ar away.



185

, , b - b b P .

2. B E b ( -) b, Copernicus -

b A- , - - .

3. Copernicus’ S, b- , b b . I C z , , De revolutionibus , b

b C .

W , , x—, b— x

. I Copernicus’ , . F .2 ycho Brahe’ De revolutionibus , x Aristarchus. H, Copernicus Aris-tarchus’ b -b , x, -

x . T C b A b b (Q .8).

A Copernicus : O b C . W , (Giordano Bruno), (Campanella), b -

, (Galileo). I f, .C , , b,

(ycho Brahe) C, b (Kepler), , , b (Newton).T b b S ., C .

.2. A Compromise: ycho Brahe

Frederick II, D, b f , ychoBrahe (1546–1601), q (F .24)— E. I Ax E—x, S Ulugh Beg— b q .

Figure 3.23 A marginal note by tyCHo BrAHe in the

exemplar o the book De revolutionibus depicted in Figure 3.9.

Quotation 3.8

Salviati : … Nor can I ever sufciently admire theoutstanding acumen of those who have taken holdof this opinion and accepted it as true; they havethrough sheer force of intellect done such violenceto their own senses as to prefer what reason toldthem over that which sensible experience plainlyshowed them to the contrary. For the argumentsagainst the whirling of the earth which wehave already examined are very plausible, as we

have seen; and the fact that the Ptolemaics andAristotelians and all their disciples took them tobe conclusive is indeed a strong argument of theireffectiveness. But the experiences which overtlycontradict the annual movement are indeed somuch greater in their apparent force that, I repeat,there is no limit to my astonishment when I reectthat aristarChus and CoperniCus were able to makereason so conquer sense that, in deance of thelatter, the former became mistress of their belief.

—Galileo, Dialogue Concerning the Two Chief World Systems—Ptolemaic & Copernican [p. 328]



255

Newton dvd h hp d dppd h Huy-gens hd d pbhd h m .

Huygens’ hh mp h h b- h bhd—d h Pp d v Galileo—

h m m, qd (hh, b h , Descartes d k), b h m v d b d h . I h , Huygens mhd h p dm m vd ph. As we have already mentioned, Huygens was no philosopher; his strength lay—

as we have seen—in the establishment of simple, reasonable, but very productivefundamental physical principles. Nonetheless, Quotation 3.45, taken from the foreword to his book dedicated to problems of optics (Traité de la lumière ), representsone of the most cogent formulations of the basic principles of natural philosophy.

3.7 Newton and the Principia: The Newtonian Worldview

3.7.1 The Tasks Awaiting the Advent of Newton

I h pv , hv khd h ph d d h d d dm. L —b mmz h h v h dd h vh —h h Newton bd d h k hm. W hv pk h d b hh h d dvpd: ,

, d m.

• Freefall. T pbm mp h km bd mv h - , h pp h d vd h q h m, d h p h v bj— d dd— h h m . T mp hkm dp, b mp dm p.Huygens’ d- v h pbm dd b h , v hh d v b hd h h h h p—

h Huygens’ pp h v h dd d— d bd md .

• Collision. T mmm—h , h pd h m h bd d v— h v m p k .

• Circularmotion. T mp z h d m hm, , h Pp b h m m x b , v, m.M , p h m, h mp m v m, h h v v d h h v- h m vd d qv b.

Bhd h , zd d vb, -d hh m state d process d fv dd m b h .

F, Descartes p h mp h dv ph b q d xp d phm, d h qh h xp b md, m h pb b mmd vb d ppb .

Figure 3.117 Important events and creative periods

in newton’s lie. See also Plate XVII.

isAAC newton (1642–1727): According to the Julian calen-

dar then in use, born Christmas day in 1642; however, onthe Continent, the new year had already begun. newton’s

ather had died several months beore his son’s birth.

From 1661, newton, with the support o his uncle, studied

mathematics at Trinity College, Cambridge. During the

plague epidemic in 1665, he withdrew to his estate in

Woolsthorpe; this and the ollowing year are known as

Newton’s “anni mirabiles” (Plate XVII). At only 24 years

o age, newton conceived the undamental ideas or the

binomial theorem, dierential calculus, theory o color,

centripetal orce, laws o motion, and theory o gravita-

tion. On his return to Cambridge, he dealt with problems

o optics; in 1668, he completed a refecting telescope. In

1669, he was appointed to the Lucasian Chair o Math-

ematics at the University o Cambridge, to succeed isAAC

BArrow. In 1672, he presented his Theory of Light and

Colors to the Royal Society; this book precipitated such

dispute that he decided not to publish anything urther. A

summary o his work on optics was not published until


Year Age

Trinity College (Theology,Descartes, Gali leo)

P R I N C I P I A

Determination of theCelestial Orbits

Theory of SpectraTheory of Fluxions

Appointed LucasianProfessor of Mathematics

Warden of the Mint

Publicationof Opticks

President of the Royal Society

ANN US MI RAB IL IS



275

My theory—which in large measure I have taken fromothers—shows clearly whether I prefer truth or fame. Ihave namely built my entire astronomy on the basis of theCopernican cosmological hypothesis, the observations of Tycho Brahe, and the magnetic philosophy of the English-man William Gilbert.

He also seems to me particularly praiseworthy

for his many new andreasonable observations and

conclusions with which he puts toshame a great number of idiotic and

mendacious writers who write notonly what they know, but also

generally every crazy idea that theyhappen to hear without testing its

accuracy with experimentation. Perhapsthey operate in that way so that their books

will not be too thin. What I would still wishof Gilbert is a bit more of a mathematical, in

particular a solid geometric, basis… His proofs are, to put it frankly, not rigorous

enough, and they lack the force of beingconvincing, which we expect when conclusions

are presented as necessary and final.

Copernicus1473-1543

Kepler 1571-1630

Gilbert1544-1603

Galileo1564

-

1642

Mersenne1588-1648

Descartes1596-1650

Huygens1629-1695

Newton1643-1727

Leibniz1646-1716

All that has up to now been assumed about the ebb and flow of thetides seems to me to be completely mistaken. But of all the great menwho have expressed their ideas about this phenomenon, it is Kepler at whom I am the most surprised. Despite his inquiring mind andkeen understanding, and despite the fact that he has an excellentfeeling for the motions of the Earth, nevertheless, he has lent his ear to occult properties and other such childishness, such as the

dominance of the Moon over the oceans, and expressed hisapproval of them.

This is also oneof those to whomevery fiction suffices if it

happens to confirm hiscalculations

Bacon1561-1626

Verulamius [Bacon]has not only taken note

of the shortcomings of Scholastic philosophy, butalso offered reasonablemethods that can lead toimprovements: one shouldcarry out experiments andmake use of their results.He has given as asuccessful instance how heconcluded that heatconsists in the motion of particles that make up bodies. Otherwise, heunderstood nothing of mathematics and he lackeda deeper understanding of physics; he could not even

imagine the motion of the Earth and madelight of it as sheer nonsense.

I raise the question whether Galileo ever carried out anyexperiments on objects falling

along an inclined plane, for he has nowhere assertedthis and the proportionsthat he gives frequentlycontradict experiment.

All in all, I maintain, he philosophizes

better than what one usually sees: namely, in the sense that heavoids, as much as possible, the errors of the Scholastics and investigates physical phenomena based on mathematical ideas. In this connection we are

entirely of one opinion, since I am convinced that there is no other methodfor discovering truth. Concerning his geometric proofs, of which his

book contains a large number, I make no judgment, since I didnot have the patience to read through them; however, they

appear to me to be in order. As regards his assertions, oneneed not be, as I have noted, a great geometer to work

them out, and a brief glance at some of them led me toconclude that he does not take the shortest

route.

I hopethat posterity will judge

me kindly, not only withrespect to the things that I have

explained, but also to those that Ihave intentionally leftunmentioned, so as togive others the pleasure of their

discovery.

Good sir, I pray to God to

make you theApollonius and

Archimedes of our time, or even more thenext century, since your youth allows you toexpect an entirecentury.

But M. Descartes, who, it seems to me, envied Galileo his fame,longed to become the founder of a new philosophy. If things had gone

according to his hopes and efforts, one would have taught him in theacademies instead of Aristotle; therefore, he would gladly have counted on the

support of the Jesuits. But in pursuing this goal, he persisted stubbornly in manyof his earlier positions, even though they were frequently mistaken…

He assumed certain laws, even unproven ones, to be absolutely certain,for example, the laws of motion in collisions, and wished to have them

accepted with the argument that all of physics would be false if these laws were false. That is almost as if he had wished to

prove them by taking an oath on them. However, onlyone of his laws is correct, and it would not be

difficult for me to prove this.

Hewillaccom- plish greatthings in

this science,of which, I

see, almostno one

understands athing.

Whatthis truly great

man, Huygens, has saidabout my work suggests a

keen understanding.But…since all phenomena

of the heavens and oceans—atleast so far as I know—arise

most precisely as consequences,namely of gravitation, which actsaccording to the law that I havedescribed, and since natureoperates in as simple a wayas possible, I see myself obliged to ignore allother causes.

As for whatconcerns the causeof the tides, as given by Mr. Newton, I amin no way satisfied, just

as little as by all other theories that rest onattraction, which seemsto me absurd, … And I

have often wonderedhow he could make the

effort to carry out so manyexperiments and

calculations that have no basis other than the given

principle.

Right at the beginning of this

philosophy [of Descartes], it turned out

that one could understand whatM. Descartes was saying, in contrast to other philosophers, who used words

that did not promote understanding, such as qualities, substantial forms,intentional species, and so on. He rejected this shameless nonsense

more completely than anyone before him. However, what particularly recommends his philosophy is not only that he

speaks with repugnance of the old [philosophy], but thathe has dared, for all that occurs in nature, instead of

the old reasons, to give causes that can beunderstood.

It is not only the absurd conclusions from thistheory [that is, the theory of the definition of true and

absolute motion that Descartes gives in his Principia Philoso- phiae] that prove how muddled and unreasonable it is, but Descarteshimself appears to admit this, since he contradicts himself.

But toogreat a belief in

his own abilities led himastray, and others were led

astray by too great a belief in him.Descartes was—like manygreat men—too sure of himself, and I fear that not afew of his adherents willimitate the Peripatetics

—whom they neverthelessmock—by contentingthemselves with consultingthe books of their master instead of orienting

themselves by plaincommon sense and the

true nature of things.

He [Leibniz] useshypotheses rather than arguments resulting from experimenta-

tion, accuses me of opinions that I do not hold, and instead of askingquestions that should be answered by experiment before they are granted

entrance into philosophy, proposes hypotheses that should be accepted and believed before they are examined.

Ido not knowwhat I may appear to the world, but to

myself I seem to have been only like a boy playing on the seashore, and

diverting myself in now and thenfinding a smoother pebble or a prettier shell than ordinary,

whilst the great ocean of truth lay all undiscov-

ered before me.

After I was told that Newton had said somethingunusual about God in the Latin version of his Opticks, I had alook at it and had to laugh over the idea that space is thesensorium of God—as though God, the source of all things,

had need of a sensorium. … In metaphysics, this man, itwould seem, is not very successful.

Table 3.4 How the great

fgures o the seventeenth century

judged one another.



344

I w, Ohm w w . homas Johann Seebeck (1770–1831) 1821, Ohm w w . O ,Fourier’ 1822 w Ohm

w . T Ohm w : x, w w w “ ” , w w w w , w -, q w w -w . I w w w fw .

Ohm’ w w x Gustav Kirchho . I 1845, Ohm w w K w .Kirchho x j ;

x, P q “ ” O’ w.

K’ w, w, q . I , fw , fw - .

K’ w : w , “ ” ( ) q . A,

.T 1894 x , , - w A Charles Stein-metz (1865–1923). F q w w w x , , , w Oliver Heaviside (1850–1925), w j w L .

Figure 4.81 The construction o the voltaic pile

(rom one o voLta’s notebooks).

Figure 4.82 geoRg siMon oHM (1789–1854): Was

senior teacher o mathematics and physics at the gym-nasium in Cologne (1817–1828); rom 1833 directed

the polytechnic school in Nuremburg, and was ap-

pointed proessor at the University o Munich in 1849.

In addition to his well-known discoveries in basic

electrical circuits, oHM did signifcant work in acoustics.

He investigated the role o overtones in human hearing

(1843). HeLMHoLtz seized on oHM’s work on hearing in

working out his resonance theory.

Figure 4.83 Ohm’s law in its original orm.

Quotation 4.28

You certainly have a right to ask why it is incon-ceivable that no one tried the action o the voltaicpile on a magnet or twenty years. However, I believethat a cause o this is easily discovered: it simplyexisted in couLomB’s hypothesis on the nature o magnetic action; everyone believed this hypothesisas though it were a act; it simply discarded everypossibility o the action between electricity andso-called magnetic wires; the restriction was suchthat when M.arago spoke o these new phenomena

[o electromagnetism] at the Institute his remarkswere rejected just as the ideas o stones allingrom the heavens were rejected when M. Pictet reada memoir to the Institute on these stones. Everyonehad decided that all this was impossible. … Everyoneresists changing ideas to which he is accustomed.

—amPère,Letter to a riend, 1820 [Williams 1966, p. 60]



345

4.4.6 Te Magnetic Field o Electric Currents: Cross-Fertilization rom

Natural Philosophy

T w , x w q . T, w 1820.

A , w , w , fw fuidum . F, w w , j—, x— w .

E ( 100,000 ) (F 4.84). A , w, w w w . Coulomb’ w-, Ampère (Q 4.28), x -. S, : Tx w R , , .T . I Schelling’ , - , w , q.

Ørsted ; w . I , x f , w f w w Faraday w . A Ørsted’ (Q 4.29), - - w w. Ørsted

w . F , w w. H w w . I , w w w, w x.

Ørsted’ w q (F 4.85), x x. N, w - x E. Ørsted -, w w w L, E. I Ampère (Q 4.28) w . Hw, w w x w - . B x q q w , w w , w w .

Lightning Rod

Ferro-magnetic

Ring

Figure 4.84 Even today, the magnitude o the current in a

lightning strike (up to hundreds o thousands amperes) is deter-mined rom the magnetization o a ring made o errous material

slipped onto the grounding stake.

Quotation 4.29

Electromagnetism itsel was discovered in the year 1820, by Proessor HanS cHriStian oerSteD, o the University o Copenhagen. Throughout hisliterary career, he adhered to the opinion, that themagnetic eects are produced by the same powersas electrical. He was not so much led to this, by the

reason commonly alleged or this opinion, as bythe philosophical principle, that all phenomena areproduced by the same original power. …

In the month o July 1820, he again resumed the ex-periment, making use o a much more considerablegalvanical apparatus. The success was now evident,

yet e ects were still eeble in the frst repetitionso the experiment, because he employed only verythin wires, supposing that the magnetical eectwould not take place, when heat and light werenot produced by the galvanical current; but he soonound that conductors o a greater diameter give

much more eect; and he then discovered, by con-tinued experiments during a ew days, the unda-mental law o electromagnetism, viz. that the mag-netical effect of the electrical current has a circular motion round it.

—ØrSteD,Article about his own discovery in TheEdinburgh Encyclopaedia [Williams 1966, pp. 56, 58]

l



368

caloricum wg, g c wg bjc cg . T w ccg wc g wg w b g caloricum. T wg bc—b —w c c-

c; c bc cc c g w cc fuidum.

4.5.3 Rumord: But Heat Is Still a Form o Motion!

Dcg , C Rumord (Benamin hompson,1753–1814) k g g bc . I c , Rumord wk w bcb cc b .I 1800, x, Eg R I, w -

c w Davy wc bc g wk Faraday.Rumord’ cc wk w Mc, w B kg c . H c gc; , R R c.

Rumord k g cg - g wg bc. H c w b bjc bc, x, g q g c, q b w w z w cg . T

w c g c . W c xc x, wc g fc b c bc, Rumord w b bg bc, - x, g wg. Accg Rumord, c c g c wgg w b b c wg bjc. Rumord’c c b Q 4.42, g w c - c

bc, b .T wk bc w b b

x c g c. W wk bc , w c c b cc c, w cg q bc c . B xg g b c bg c b g , Rumord -bw . H w b cc g b cg. T w b b g b k w b c w c xc q - ; w, w c xc c w w.F b, Rumord w c cc: Hc b bc, bc w, w b b q b. H c b g cb c c b cc c, c w b g c b cc wk (Q 4.43). Q- 4.44, Rumord’ c, w c q c cgz-

Quotation 4.39

Any person who reects on the ideas which weannex to the word heat will perceive that this word

is used or two meanings, or to express two dierentthings. It either means a sensation excited in ourorgans, or a certain quality, aection, or conditiono the bodies around us, by which they excite in usthat sensation. The word is used in the frst sensewhen we say, we eel heat; in the second when wesay, there is heat in the fre, or in a hot stove. …

We must thereore adopt, as one o the most generallaws o heat, that “all bodies communicating reelywith each other, and exposed to no inequality o external action, acquire the same temperature,as indicated by a thermometer.” All acquire the

temperature o the surrounding medium. …

This is what has been commonly called an equalheat, or the equality o heat among dierentbodies; I call it the equilibrium of heat . The natureo this equilibrium was not well understood, untilI pointed out a method o investigating it. Dr.BoerHaave imagined, that when it obtains, there isan equal quantity o heat in every equal measureo space, however flled up with dierent bodies,and proessor muScHenBroek expresses his opinionto the same purpose: “Est enim ignis aequaliter per

omnia, non admodum magna, distributus, ita ut in pede cubico auri et aeris ut plumarum, par ignis sit quantitas.” The reason they give or this opinion is,that to whichever o these bodies the thermometerbe applied, it points to the same degree.

But this is taking a very hasty view o the subject.It is conounding the quantity o heat in dierentbodies with its general strength or intensity, thoughit is plain that these are two dierent things, andshould always be distinguished, when we arethinking o the distribution o heat.

—JoSePH BLack, Lectures on the Elements of Chemistry [pp. 21–22, 74, 75]

Quotation 4.40

It was ormerly a common supposition, that thequantities o heat required to increase the heat o dierent bodies by the same number o degrees,were directly in proportion to the quantity o matterin each; and thereore, when the bodies were o equal size, the quantities o heat were in proportionto their density. But very soon ater I began to think

on this subject (anno 1760), I perceived that thisopinion was a mistake, and that the quantities o heat which dierent kinds o matter must receive,to reduce them to an equilibrium with one another,or to raise their temperature by an equal numbero degrees, are not in proportion to the quantity o


F



369

g qc cc g g. F , w g, w c qc, wc w .

I g w Rumord, w w g

bc c w cc c xc- . H w -jc c b x g w, b w .

F ’ g c kc , w w b c Rumord’ cc . Hw, c w c bgg c. Rumord’ x w cc, b , b w b bc. T c, x, c x-b q b w c c b c; , bc fw b

, wc c cc xb . b , kc c q—

q—x c .T wg b z w c-

wc w —-bc kc -—c ccg x .

Heat

conduction

Thermal

radiation

Latent

heat

Frictional

heat

Quantitative

conclusion

possible?

Heat

substance

theory

yes yes yes no yes

Kinetic

theoryyes no no yes no

b b fw bc ( cc)c b g f fw, w w kc

, cc w c cb bc kwg c c c w b . N, b w kc w b b cc k. Tcaloricum c x , , g c, fw b bc g c. Tkc c . w , , b cgc , , .

Lkg b b, c w g - j c c c cc

bc — w cc, b wkg .

4.5.4 Fourier’s Teory o Heat Conduction

O cc bc w c b Fourier w c cc. Jean Baptiste Joseph Fourier (Fg 4.121) c . I w

k Fc R—, wg , Napoleon—


matter in each, but in proportions widely dierentrom this, and or which no general principle or

reason can yet be assigned. …Quicksilver, thereore, has less capacity or thematter o heat than water (i I may be allowedto use this expression) has; it requires a smallerquantity o it to raise its temperature by the samenumber o degrees. … We must, thereore, concludethat dierent bodies, although they be o thesame size, or even o the same weight, when theyare reduced to the same temperature or degree o heat, whatever that be, may contain very dierentquantities o the matter o heat; which dierentquantities are necessary to bring them to this level,

or equilibrium, with one another.

It may have been remarked that the discoverieswhich have been made in this way are veryunavorable to one o the opinions which havebeen ormed o the nature o heat. Many havesupposed that heat is a tremulous, or other, motiono the particles o matter, which tremendousmotion they imagined to be communicated romone body to another. But, i this were true, wemust admit that the communication would bein conormity with our general experience o the

communication o tremulous motion. We are notat liberty to eign laws o motion dierent romthose already admitted, otherwise we can makeany supposition account or any phenomena thatwe please. The denser substances ought surely tobe the most powerul in communicating heat toothers, or exciting it in them. The act, however, ina great many examples, and yet not in all, is justthe reverse. Such an opinion is thereore totallyinconsistent with the phenomena. I do not see howthis objection can be evaded.

—JoSePHBLack, Lectures on the Elements of Chemistry

[pp. 76, 77, 80]

Quotation 4.41

Fluidity was universally considered as produced by asmall addition to the quantity o heat which a bodycontains, when it is once heated up to its meltingpoint; and the return o such a body to a solid stateas depending on a very small diminution o thequantity o heat ater it is cooled to the same degree;that a solid body, when it is changed into a uid,receives no greater addition to the heat within it thanwhat is measured by the elevation o temperatureindicated ater usion by the thermometer; and that,when the melted body is again made to congeal, bya diminution o its heat, it suers no greater losso heat than what is indicated also by the simpleapplication to it o the same instrument.


The Physics of the



405

The Physics of the

Twentieth Century

5.1 “Clouds on the Horizon of Nineteenth-Century Physics”

5.1.1 A Conclusion or a New Start?

The TwenTieTh cenTury will usher in The physics o h h dm p,pomd h opm h u o h uy, d o phy’ -omphm. By h hy m h h m mpy o —bd o h oudo—h mum d uo uh

od o mo p um u (Quoo 5.1, 5.2).Ho, h phy o h m oud h o h hozo.

T o h o ud o u by Lod Kelvin 1900, hhh d:

The beauty and clearness of the dynamical theory, which asserts heat and

light to be modes of [mechanical] motion, is at present obscured by two

clouds. The rst came into existence with the undulatory theory of light…

How could the Earth move through an elastic solid, such as essentially is the

luminiferous ether? The second is the Maxwell–Boltzmann doctrine regard-

ing the partition of energy.

W mh oud h boh h opmm d h pmm pompdby ho o phom opp up h qu o h h uy h dd o o h mo. I , h oo Fu 5.1, umb o quo m, h y uh phomo:h o p, h dpd o oy o h m o h o, -yd doy, o mo oy . A phy ud by m o o phom,

h po o hm h o y b oud. T pobm

h d d po bd o h u hoy—d “-po” phy uy o m h h hoy o h h- um u o h phomo quo o oh dy pdu—bu h pdo md by h hoy do o h h pm-y mud u.

o pu py, p o phy hoy h p o ud o, umb o pm obo o b od hh hoy.

I Fu 5.1 h ho h do o h dp o phy y pd h d o h h uy. A h dy m-od, h phy opo h phy o ody m d h phy o h h. o b u, h d o uo uy o : My mdh h up m h houd o h h pop o od m-, od o o b b o pop om . To d o popod, h h h ouou mdum h hh h p o ody m omd b o h mo b mo .

Quotation 5.1 The more important fundamental laws and factsof physical science have all been discovered,

and these are now so rmly established thatthe possibility of their ever being supplanted inconsequence of new discoveries is exceedinglyremote. … Our future discoveries must be lookedfor in the 6th place of decimals.

—a. a. micHelson, Light Waves and Their Uses, 1903[Holton 1988, p.88]

Quotation 5.2

Now to the eld of physics as it presented itself at

that time. In spite of all the fruitfulness in particulars,dogmatic rigidity prevailed in matters of principles: Inthe beginning (if there was such a thing) God createdNewton’s laws of motion together with the necessarymasses and forces. This is all; everything beyondthis follows from the development of appropriatemathematical methods by means of deduction. Whatthe nineteenth century achieved on the strength of this basis, especially through the application of thepartial differential equations, was bound to arousethe admiration of every responsive person.

—albert einstein, “Autobiographical Notes” [p. 19]

Quotation 5.3

I am never content until I have constructed amechanical model of the object that I am studying.If I succeed in making one, I understand; otherwiseI do not. Hence I cannot grasp the electromagnetictheory of light. I wish to understand light as fullyas possible, without introducing things that Iunderstand still less. Therefore I hold fast to simpledynamics for there, but not in the electromagnetictheory, can I nd a model.

—Lord Kelvin, 1884 [Mason 1953, pp. 391–392]

Quotation 5.4

However, after the rst brilliant results of the kinetictheory of gases, its recent progress seems not tohave fullled expectations; at every attempt to placethis theory on a rmer footing, the difculties haveincreased at an alarming rate. Everyone who hasstudied the work of the two researchers who havedelved most deeply into the analysis of molecularmotion, maxwell and boltzmann, cannot avoid theimpression that in overcoming these problems,the admirable effort of acumen in physics andmathematical facility expended to date does notstand in the desired relationship to the fruitfulnessof the results obtained.

—PlancK [1958, Vol. 1, pp. 372–373]



406

Tmodym d p dp bu o podd b-

h o d oup o phom.Fy, h h , o , hoy o m h o o hh

o du phy phom o mophy po y h o mh. T mh po o h u, popod pom by Descartes, md u d qum h d o h h uy (Quoo 5.2).

E dbd h mp o udd h o om

d d opy h h hp o mh mod. E o Kelvin, hudd o phy phomo omp oy h mhmod o oud b podd (Quoo 5.3).

I Fu 5.1, h hoy o m dpyd h dhd bod o

d h o uy pd. Dp pd u, -, hh oud u ou o b o d mpo, dy d h po o, my, u o p p h oy. Yh hoy o p h bd o y pp—h qupohom. Maxwell omud h hom 1878 omp y, u- Lagrange’ zd ood h by o b h p-

, um oy h oo o y: I hm qubum, y pod quy mo h d o dom o p. I py d-py b uh hoy d pu pm oboh u h mo dfu, o o m h php oopzd umpo o h hoy pob o h odo. Tu, my udd hy Planck hm (Quoo 5.4), d oh (Quo-

o 5.5), ood upo h o h h d o pm.

Quotation 5.5

For a long time, physicists have assumed that allproperties of bodies ultimately can be reduced

to combinations of geometric gures and localmotions; the general principles to which all physicalproperties are subject should thus be none otherthan the principles that govern local motion,principles that underlie efcient mechanics. Thegeneral principles of physics would then be e ncodedin efcient mechanics.

The reduction of all physical properties of combinations of geometric gures and localmotions—what is usually called the mechanical explanation of the universe—seems today to havebeen refuted. And indeed, it is not to be refuted for a

priori or metaphysical or mathematical reasons butbecause it was up to now only a project, a dream,and not a reality. Despite great efforts, physicistshave not been able to devise such an arrangementof geometric gures and local motions that couldprovide, according to the rules of theoreticalmechanics, a satisfactory representation of an onlyslightly expanded circle of the physical laws.

Will the attempt to reduce all of physics totheoretical mechanics, an attempt that alwaysfailed in the past, perhaps succeed in the future?Only a prophet could answer this question in apositive or negative sense.

Without giving preference to one or other of theseanswers, it seems much more reasonable to avoidefforts, at least provisionally, that have thus farbeen fruitless, such as the mechanical explanationof the universe.

We therefore attempt to formulate a system of general laws—laws that all physical propertiesmust obey—without the a priori assumption thatall these properties are reducible to geometricgures and local motions. The system of thesegeneral laws will in what follows not be reduced tothe laws of efcient mechanics.

—P. DuHem, Traité d´énergétique ou dethermodynamique générale, 1911 [pp. 2, 3]

Physics of Matter Statistical

Theory

Radio Activi ty Spectra

m = m(v)

Thermodynamics

Physicsof the Ether

Specic Heat

Blackbody Radiation

Periodic Table

Quantum Mechanics(Atomic Shell, Nuclear Physics,

Particle Physics)

Relativity,Gravitation

X-Rays

c = const.

Figure 5.1 The structure o physics toward the end o the nineteenth century. Open problems are

indicated with a question mark, and the phenomena that could not be explained within the confnes o

classical physics appear in color.



420


The concepts o conventionalism are illustrated by the ollow-

ing quotes:

Can we maintain that certain phenomena which arepossible in Euclidean space would be impossible in non-

Euclidean space, so that experiment in establishing these

phenomena would directly contradict the non-Euclidean

hypothesis? I think that such a question cannot be seri-

ously asked. To me it is exactly equivalent to the ollow-

ing, the absurdity o which is obvious: There are lengths

which can be expressed in metres and centimetres, but

cannot be measured in toises, eet, and inches …

—Poincaré, Science and Hypothesis [p. 73]

Suppose, or example, a world enclosed in a large sphere

and subject to the ollowing laws: The temperature isnot uniorm; it is greatest at the centre, and gradually

decreases as we move towards the circumerence o the

sphere, where it is absolute zero. The law o this tem-

perature is as ollows: I R be the radius o the sphere,

and r the distance o the point considered rom the

centre, the absolute temperature will be proportional

to R2 – r 2. Further, I shall suppose that in this world all

bodies have the same co-efcient o dilatation, so that

the linear dilatation o any body is proportional to its

absolute temperature. Finally, I shall assume that a body

transported rom one point to another o dierent tem-

perature is instantaneously in thermal equilibrium with

its new environment. There is nothing in these hypoth-eses either contradictory or unimaginable. A moving

object will become smaller and smaller as it approaches

the circumerence o the sphere. Let us observe, in the

frst place, that although rom the point o view o our

ordinary geometry this world is fnite, to its inhabitants

it will appear infnite. As they approach the surace o

the sphere they become colder, and at the same time

smaller and smaller. The steps they take are thereore

also smaller and smaller, so that they can never reach

the boundary o the sphere. I to us geometry is only the

study o the laws according to which invariable solids

move, to these imaginary beings it will be the study o

the laws o motion o solids deformed by the differences

of temperature alluded to. …

Let me make another hypothesis: suppose that light

passes through media o dierent reractive indices, such

that the index o reraction is inversely proportional toR2 – r 2. Under these conditions it is clear that the rays o

light will no longer be rectilinear but circular.

—Poincaré, Science and Hypothesis [pp. 65–66]

Figure 5.17 Some acsimile pages rom EinstEin’s frst ar-

ticle on the theory o relativity. The titles o all three protago-nists’ articles indicate that the theory o relativity arose rom

problems in the feld o electrodynamics o moving bodies.lorEntz wrote his article in English (Figure 4.115): “Electro-

magnetic Phenomena in a System Moving with Any Velocity

Smaller than That o Light”; Poincaré’s was, o course, written

in French: Sur la dynamique de l´électron; and fnally, EinstEin’s

work bore the title Zur Elektrodynamik bewegter Körper .


mphd .” Idd, Einstein mu h h bhg h p-



421


As his starting point, lorEntz chooses the negative result

o the MichElson experiment and emphasizes the ad hoc

character o the solutions given thus ar by himsel andFitzGErald. He cites the experiment by trouton and noBlE rom

the previous year (1903) and reers to an opinion expressedby Poincaré already in 1900:

It would be more satisactory i it were possible to show

by means o certain undamental assumptions and

without neglecting terms o one order o magnitude or

another, that many electromagnetic actions are entirely

independent o the motion o the system. Some years

ago, I already sought to rame a theory o this kind. I

believe it is now possible to treat the subject with a bet-

ter result. The only restriction as regards the velocity will

be that it be less than that o light.

I shall start rom the undamental equations o the the-

ory o electrons. [pp. 12–13]

As is typical or him, EinstEin begins by emphasizing the

asymmetry o the MaxwEll equations or the case o moving

bodies. It is clear that only the relative motion o a magnet

and a conductor determines the observable phenomena, but

we still interpret dierently what happens when the magnet

moves and the conductor is stationary (here there will be

an electric feld and the current is induced) versus when

the magnet is stationary and the conductor moves (there is

no electric feld but a orce will act on the electrons in the

conductor and the current will be the same as in the frst

case). Then EinstEin mentions generally—without reerenceto concrete cases—the unsuccessul experimental eorts

to determine the motion o Earth relative to the absolutely

stationary “light medium.” Then comes the critical insight;

the conjecture that there is no distinguished inertial system

is raised to the level o an axiom together with a second

underlying assumption: The velocity o light is independent

o the state o motion o the light source and has the same

value or all inertial systems. The article continues in a radi-

cally new path: the defnition o simultaneity ollowed by a

derivation o the lorEntz transormation by interpreting what

it means to measure time and length.

This is perhaps what excited physicists more than anything

else. Even among the leading physicists, there were only aew who were truly comortable with the electrodynamics

o MaxwEll and lorEntz, and even ewer were capable o

recognizing the epoch-making signifcance o a transorma-

tion that leaves the MaxwEll equations invariant. And now,

with EinstEin, all one had to do was pay careul attention to

how clocks are synchronized, and one could not escape the

conclusion that all o physics had to be reconsidered. Ater

all, even a high school physics book starts with the discussion

o how to measure time, distance, and mass.

The article urther discusses the addition theorem o ve-

locities, the transormation rules or electromagnetic feld

quantities, the doPPlEr eect, the theory o aberration, and

the transormation rules or the energy o light rays; this isespecially important because the later article on the equiva-

lence o energy and mass continues rom this point.


hy vy mg b pd d mp, puy h Lorentz d Poincaré. I g u h d d h uh dvp-

m h hy, Planck d Minkowski md mp bu.

5.2.4 Te Measurement of Distance and ime

Nx h xm bfy h qu h vy pp y ud by bh Poincaré d Einstein.

T uv pp h hy p vy d h -g pu: Phy v h p h L -m h m ym h by ym.Fm h, dy h h pd gh ( vuum) h

vu dpd h d ym.

H h vby d h vh h mu-y h y h g hugh xpm, dvd by Einstein:

Img , h Fgu 5.20, mvg h pd p

bv dg by h . A d bv d h p mdp h pg . A xy h m hh h bv h p hbv dg by h , bh bv dpdy h muufh gh pu m h d b h . Wh u-

d h bv d h gd h m hh h gh pum h d b h ? T bv h —g u h by h mum h h u, h dg hmdd h , d h h vy gh dpd h

m— ud m h h h pu vd muuy hhy mu hv d h m m, h d, h h fh mu hvb h m m m h d b h .

T bv dg gd h h h pd gh d h gh g qu mu m v

d. Fm h muy h v h g h ud hh g m h b d h mu hv b bu hh g , h b d h h m hm h h

. T gh pu vg h h d ppgg h pd v h m m h pu vg h b h y h m md m. T y bv hu ud hh fh mu hv b d m.

I h hy vy, mg h vy p bh d ym

p pdg , hh mp h h h mm-y dg p h h d ym. Bu yh h y gv d ym h hy u gh. H dh? T mp y xp h y h pd gh d d gh

g m h g h d ym m t = 0. O vg h g, bv dg d r m h d g h m r /c ,d umg d phy u, h u yhuy.T mu h L m dvd m h hh h

h d ym K d K ́ yhd h gh pu h md h h g h d ym dd.

A hv , h m upg qu h L m h muy v . Dy d h h

Figure 5 17 continued



422


What is not to be ound in the article: Even though the

dynamics o the electron are discussed, the establishment

o the equations o motion had to wait or Planck. EinstEin

still speaks o longitudinal and transversal mass, like lorEntz.

However, the ormula

m c v c 0

2 2 21 2

1 1−( ) −

− /

/

or the kinetic energy is derived here.

The derivation o the ormula or the change o mass,

m m v c = −( )−

0

2 21 2

1 / , /

on the basis o mechanical considerations, that is, rom the

example o collision processes—observed in two inertial sys-

tems and on the assumption o conservation o energy and

momentum, just as it was done by huyGEns in the classicalcase—is the contribution o lEwis and tolMan (1908).

We have mentioned in the main text a characteristic eature

o EinstEin’s article: Not a single name, not a single earlier

publication, is mentioned, other than the name M. BEsso, a

riend and colleague who is thanked or his assistance.

Figure 5.18 Some acsimile pages rom Poincaré’s

article. It was submitted on July 28, 1905 and appeared in

1906 (Rendiconti del Circolo Matematico di Palermo 23,

p. 129). In his monograph, Pauli writes:

The ormal gaps let by Lorentz’s work were flled by

Poincaré. He stated the relativity principle to be gener-

ally and rigorously valid. [1981, p. 3]

In addition to results already mentioned in the main text,

we would emphasize the ollowing conclusions o the

article: The Lorentz transormation can be interpreted as

a rotation in our-dimensional space x , y , z , ict ; other qua-

druples o numbers could be ormed that obey the same

transormation rules as x , y , z , t . This yields a simple method

or fnding Lorentz-invariant quantities. ivanEnko reers

emphatically to a act that had essentially been orgotten:Poincaré was the frst to apply the theory o relativity to the

problem o gravitation; it was the frst realistic and correct

step in the direction o the modifcation o Newton’s lawo gravitation. Poincaré recognized the fnite speed o the

gravitational eect and attempted to fnd a relativistic cor-

rection to Newton’s law.

The question is still raised rom time to time as to why the

discovery o the theory o relativity is ascribed solely to EinstEin.

We have oered some explanations in the main text but here

is another: EinstEin published in one o the leading journals o

physics, while Poincaré, in contrast, wrote or mathematicians,

so to speak, in a relatively obscure Italian journal. Poincaré’s

abstract style and especially the act that he tended to under-

value his own work may also have played a role:

The importance o this question induced me to inves-tigate it recently; the results that I obtained agree on

all major points with those o Lorentz; only in some

isolated questions I eel compelled to modiy or supple-

ment them; in the uture, their dierences will come to

light; they are o only secondary signifcance.

Figure 5 39 continuedSpectrum

Rydberg Ritz



439

xprim h wou h ow rom oor bo o wrmr bo, i vio-

io o h so w o hrmomis.I is hr h h uiqu sigi o bbois boms r. B b-

bo w m bo h bsorbs h riio sriig i, hror is

bsorpivi is a = 1. Tus, h rioship giv bov is

e

a

e

a

e

e 1

1

2

2

= = = =

black

black 1

,

whih ms h h rio o missivi o bsorpivi o rbirr bo is

qu o h missivi o bbo. From wh w hv jus si, h quois

e /a r independent of any material constant o h bo ur ivsigio, so hisw is universal law of nature. Tis uivrs hrr givs h riio w orbbois is um sigi. Planck hims ws irigu b his

uivrs hrr (Quoio 5.20). I ws soo rogiz h bbo ri-io b riz i vi wih mi ws (o pium–iriium). I h

ws o h osur r p x mprur, h wihi h vi, h

riio rhs s o quiibrium, whih is h bbo riio. I ow opig is m so sm h h hrm quiibrium is o isurb, h

h riio mi hrough his opig b s qu o h bbo riio o vr goo pproximio (Figur 5.42). A vr simp go-

mri r ursb rioship xiss bw h rg si o h riio i h vi h isi o h riio mi rom h

opig i h w o h osur. T r proporio o h ohr, i iss o s h h os o proporioi ois h voi c wih whih

h rg propgs. W hror hv

B c

uv v =

4π

,

whr h or 1/4 p oms rom gomri osirios. I his ormu, uv

=

uv (v ,T ) is h rg wihi ui voum o h vi i ui rqu rg, B

v (v ,T ) is h ri powr mi prpiur pr ui r o h v-

i opig pr ui im io ui soi g.

T x sigi sp orwr i h ursig o h ws o bbo riio m wih h S–Bozm w. I 1879, whi zig msur-

ms b yndall, Stefan h h oowig isigh: Aorig o hos

msurms, priur s bo mprur o 1473 K ri 11.7


The year 1911 was also a signal year or kaMErlinGh-onnEs,

or in that year, he discovered the phenomenon o supercon-

ductivity (Plate XXII) in his already world-renowned low-tem-

perature laboratory. Today, we have unjustiably orgottensuch experimental physicists as knudsEn (1871–1948) andEMilwarBurG (1846–1931).knudsEn invented the manometer

now named or him and investigated gas fow at very low

pressures. warBurG discovered the phenomena o hysteresis

in erromagnetic materials and established the relationship

between hysteresis loss and the area o the hysteresis loop.

Finally, we have Paul lanGEvin (1872–1946), whose contri-

butions to the development o French and even European

physics went ar beyond his concrete results (properties o

ionized gases; relationship between mobility and recombi-

nation, the theory o paramagnets). For example, the twin

paradox is due to him. His role is comparable to that o Paul

EhrEnFEst, who also ailed to achieve the kinds o outstandingindividual results that might have brought him the greatest

international recognition: the Nobel Prize.

Blackbody Radiation

Light Quanta

Quantum Mechanics

Quantum Field Theory

Wien Einstein

AtomRutherford

Planck Sommerfeld

Bohr Heisenberg

de BroglieSchrödinger

Lenard Thomson

Figure 5.40 The main steps on the path to understanding the quantum world (ater[Hund 1974]).

Quotation 5.20

My original decision to devote myself to sciencewas a direct result of the discovery which has neverceased to ll me with enthusiasm since my early

youth—the comprehension of the far from obviousfact that the laws of human reasoning coincidewith the laws governing the sequences of theimpressions we receive from the world about us;that, therefore, pure reasoning can enable man togain an insight into the mechanism of the latter. Inthis connection, it is of paramount importance thatthe outside world is something independent fromman, something absolute, and the quest for thelaws which apply to this absolute appeared to meas the most sublime scientic pursuit of life.

—max PlancK, Scientifc Autobiography… [p. 13]

Born pak u wk Nl lu:



465

It appeared to me that it was not possible to arrive at a clear interpretation

of the Ψ-function by considering bound electrons. I had therefore been at

pains, as early as the end of 1925, to extend the matrix method, which obvi-

ously covered only oscillatory processes, in such a way as to be applicable toaperiodic processes. I was at that time the guest of the Massachusetts Insti-

tute of Technology in the U.S.A., and there I found in Norbert Wiener a distin-

guished collaborator. In our joint paper we replaced the matrix by the general

concept of the operator and, in this way, made possible the description of

aperiodic processes. Yet we missed the true approach, which was reserved

for Schrödinger; and I immediately took up his method, since it promised to

lead to an interpretation of the ψ-function. Once more an idea of Einstein’s

gave the lead. He had sought to make the duality of particles (light quanta

or photons) and waves comprehensible by interpreting the square of the op-

tical wave amplitudes as probability density for the occurrence of photons.This idea could at once be extended to the Ψ -function:Ψ 2 must represent the

probability density for electrons (or other particles). To assert this was easy;

but how was it to be proved? …

But the factor that contributed more than these successes to the speedy ac-

ceptance of the statistical interpretation of the Ψ -function was a paper by

Heisenberg that contained his celebrated uncertainty relationship, through

which the revolutionary character of the new conception was rst made clear.

—maxborn, “Statistical Interpretation of Quantum Mechanics,”

Nobel Lecture

Ev u malm Heisenberg’ a Schrödinger’ w uamally f, Schrödinger ml p u a y a ma-

maally quval, p al av w a a’ a. Heisenberg’ p:

The more I work with the physical parts of the Schrödinger theory, the more

disgusting I nd it.

Schrödinger, u, w u:

I found the complicated methods of transcendental algebra, which make any

visualization impossible, annoying, almost repulsive.

I plpal lu y f a wll: Schrödinger—lk Ein-stein (Qua 5.30, 5.31)— wa ap a a a u a

p aual pma a aual pa-m la ualv a a vual uu p. Hwv, majy py ap

“Cpa pa” (Fu 5.64) wk u y Heisenberg a Bohr.S al Fu 5.65 u 5.70 u llua m a u.

5.3.10 Heisenberg: Te Copenhagen Interpretation of Quantum Teory

The Copenhagen interpretation of quantum theory starts from a paradox.

Any experiment in physics, whether it refers to the phenomena of daily life

or to atomic events, is to be described in the terms of classical physics. The

concepts of classical physics form the language by which we describe the ar-

rangements of our experiments and state the results. We cannot and should

Quotation 5.30

The generation to which einstein, boHr and I belong,was taught that there exists an objective physicalworld, which unfolds itself according to immutablelaws independent of us; we are watching this

process as the audience watches a play in a theatre.einstein still believes that this should be the relationbetween the scientic observer and his subject.Quantum mechanics, however, interprets theexperience gained in atomic physics in a differentway. We may compare the observer of a physicalphenomenon not with the audience of a theatricalperformance, but with that of a football game wherethe act of watching, accompanied by applauding orhissing, has a marked inuence on the speed andconcentration of the players, and thus on what iswatched. In fact, a better simile is life itself, where

audience and actors are the same persons.

—born,“Physics and Relativity” [pp. 104–105]


the number of degrees of freedom of the system,there can be only one single quantum equation for

each system. In course of time the congurationpoint of classical theory describes a denite curve;on the other hand, the conguration point of thematerial wave lls at any given time the whole of innite space, including those parts of space wherepotential energy is greater than the total energy, sothat according to the classical theory, kinetic energywould become negative in these parts of space, andthe momentum imaginary. …

From the discrete characteristic energy values,discrete characteristic values of the period of oscillation may be derived. The latter are determined

according to the quantum postulate, in a similarmanner to that of a stretched cord with xed ends;with this distinction that the latter quantization isdetermined by an external condition, viz. the lengthof the cord, whereas in the present instance itdepends upon the quantum of action, which in turndepends directly upon the differential equation.

To each characteristic vibration there correspondsa particular wave function (ψ); this is the solutionof the wave equation; and all these differentcharacteristic functions form the componentelements for the description of any movement interms of wave mechanics.

—PlancK, The Universe in the Light of ModernPhysics [pp. 28–30]

Figure 5.64 The symbol o Copenhagen is the mermaid, a gure rom one o andErsEn’s airy tales;

the physicist, however, associates Copenhagen primarily with Bohr and his school, to which we may also



467

with high accuracy we cannot know the other with high accuracy; still we must

know both for determining the behavior of the system. The space-time distri-

bution of the atomic events is complementary to their deterministic descrip-tion. The probability function obeys an equation of motion as the co-ordinates

did in Newtonian mechanics; its change in the course of time is completely

determined by the quantum mechanical equation, but it does not allow a

description in space and time. The observation, on the other hand, enforces

the description in space and time but breaks the determined continuity of the

probability function by changing our knowledge of the system. …

*

A real difculty in the understanding of this interpretation arises, however,

when one asks the famous question: But what happens “really” in an atomic

event? It has been said before that the mechanism and the results of an ob-servation can always be stated in terms of the classical concepts. But what

one deduces from an observation is a probability function, a mathematical

expression that combines statements about possibilities or tendencies with

statements about our knowledge of facts. So we cannot completely objectify

the result of an observation, we cannot describe what “happens” between

this observation and the next. This looks as if we had introduced an element

of subjectivism into the theory, as if we meant to say: what happens depends

count hEisEnBErG, Pauli, dirac, EhrEnFEst, GaMow, landau, kraMErs, and klEin. The atmosphere was amiliar,

but opponents were not spared. hEisEnBErG reports on a visit by schrödinGEr in Physics and Beyond

[pp. 73–76]:

[A]lthough Bohr was normally most considerate and riendly in his dealings with people, he now

struck me as an almost remorseless anatic, one who was not prepared to make the least concession

or grant that he could ever be mistaken.

On this occasion, schrödinGEr oered the ollowing bitter, and requently quoted, opinion:

I all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with

quantum theory.

hEisEnBErG recalls that the discussion became more and more violent:

And so discussions continued day and night. Ater a ew days Schrödinger ell ill, perhaps as a result

o his enormous eort; in any case, he was orced to keep to his bed with a everish cold. While Mrs.

Bohr nursed him and brought in tea and cake, Niels Bohr kept sitting on the edge o the bed talking

to Schrödinger: “But you must surely admit that…” No real understanding could be expected since,at the time, neither side was able to oer a complete and coherent interpretation o quantum me-

chanics. For all that, we in Copenhagen elt convinced toward the end o Schrödinger’s visit that we

were on the right track, though we ully realized how dicult it would be to convince even leading

physicists that they must abandon all attempts to construct perceptual models o atomic processes.

Some signicant elements o the Copenhagen interpretation may have come rom Bohr’s upbringing.JaMMEr (1974) in his analysis o Bohr’s philosophical background highlights kiErkEGaard, whose studenthøFFdinG was a university colleague o Bohr’s ather. According to kiErkEGaard, the creator o a philosophi-

cal system is himsel a part o that system that he wishes to explain:

One cannot view onesel, without sel-deception, as an indierent onlooker or impersonal observer;

one is necessarily always a participant. The determination o the boundary between the objective and

the subjective is an arbitrary act, and human lie consists in a series o decisions. Science is nothing

other than a well-determined action; and truth: a work o man, and indeed, not only because it isman who created knowledge, but because the signicant object o knowledge is not something that

has been standing complete since the beginning o time.

The psychology o williaM JaMEs also emphasizes the arbitrariness in demarcation and the uncontrollable

infuence o observation on the observed phenomenon. Finally, the philosophers o the Viennese School,

who were greatly infuenced by Mach, had similar ideas (“an assertion makes sense only i it can be em-

pirically veried”). The motto o wittGEnstEin, who came rom this circle, was this: “Whereo one cannot

speak thereo one must be silent.”

Figure 5.65

The collabora-

tors in Bohr’s

school could not

ree themselves

o science even

in their amuse-

ments. We show

here a acsimile

page o a parody

o Faust in which

the distribution

o roles is telling:

Faust is Paul Eh-

rEnFEst; Mephisto,wolFGanG Pauli;

and God, niEls

Bohr.

Paul EhrEnFEst

(1880–1933):

Student oBoltzMann in

Vienna; 1912:

successor to lo-

rEntz in the chair

o theoretical

physics in Leyden.

The adiabatic

principle estab-

lished by him in

1913 and worked out in detail in subsequent years bears hisname. EhrEnFEst showed in 1927 that the equations o motion

o classical mechanics ollow rom wave mechanics as a limiting

case. With his critical and pedagogically valuable contributions

to discussions, he contributed to the development o physics ar

beyond his concrete results. This contradiction between his im-

portant position and his creative capacity may have contributed

to his depression and suicide.


T q . B .



514

. B .B - — — q

y v y , y v - v . T v 1952y Bohr Mottelson v . W Aage Bohr, Niels Bohr’ , . I y y, v v N L: Marie andPierre Curie, --; Bragg; Bohrs, ; homsons, ; y, Siegbahns, . A , , 1954

y Feshbach, Porter, Weisskopf, y qv

. A y , - x , x y , y v, . T .

5.4.10 Nuclear Fission: Experimental Evidence, Teoretical Doubt

T vy 1930— — -. H v y vy . T x

vy, y y vv y , v y . W vy , Chadwick, Rutherford’ , , , -y x y, y z y y v x x y y -

(a) H Li He He MeV

(b) N n C p

C N e

1

1

3

7

2

4

2

4

14 14

14 14

17 5

0 1

+ = + +

+ = +

→ + +−

.

. 556

2

4

13

27

15

30

0

1

15

30

14

30

10

22

94

MeV

(c) He Al P n

P Si e

(d) Ne

+ = +

→ +

+

+

PPu Lr H n242

103

260

1

1

0

13= + +

Figure 5.115 (a) The frst nuclear reaction that was

accomplished with artifcially accelerated particles (cock-

croFt and walton, 1932).

(b) Due to cosmic radiation, some nitrogen atoms in the airare transormed into radioactive carbon, which decays with

a hal-lie o 5730 ± 40 years. The activity o radioactive

carbon incorporated into plant lie, and thereater into ani-

mals, decays ater the death o the organisms according to

the law o exponential decay. By comparing the amount o

radioactive carbon let with what is in the atmosphere, one

can determine the approximate date o the organism’s death

(willard Frank liBBy [1908–1980], radiocarbon dating, 1948).

(c) A current physics problem: Up to what atomic number

can transuranic elements be created? In laboratories under

the directorship o G. sEaBorG and a. Ghiorso, and o G. n.

Flyorov, the number 106 was achieved at the beginning o

the 1970s.Some transuranic elements can be ound in nature. Plu-

tonium-244, the one with the longest hal-lie (T 1/2

= 8 3

107 years), occurs in trace amounts in minerals. Neptu-

nium-237 (T 1/2

= 2.14 3 106 years) and plutonium-239 (T 1/2

= 2.4 3 104 years) can be ound in uranium ore.

Through neutron-capture reactions one can get as ar as

ermium ( Z = 100); by bombarding heavy elements with

light or medium-heavy ions, it has been possible to create

super-heavy atoms well above atomic number Z = 115, but

these are very short lived due to spontaneous alpha decay

and spontaneous fssion. Theoretically, there is still a pos-

sibility that an island o increased stability will be ound in

the neighborhood o certain higher “magic” numbers.

Figure 5.116 A historic document: The fssion cross

section o the U-235 nucleus as a unction o the energy

o the bombarding neutrons. The fgure plots the values

that were measured independently in three countries:

USSR, Great Britain (labeled Har in the fgure), and the USA

(labeled Col and KAPL). These results were top secret until

1955 because knowledge o this inormation is essential

or designing atomic bombs as well as or nuclear power

plants [United Nations 1955, p. 285].

The cross section o a reaction is defned in a way that rep-resents the measurement method: From the incident beam,

N particles per second all on a unit area o the target

material o density n atoms per cm3. While passing through

the distance d x , the beam encounters 1·n d x target atoms.

Due to nuclear (or other) reactions, the intensity o the

beam will decrease. The value o this decrease is −dN =


. Ev y y v y y. Hv, Bohr , , x, “O, Figure 5.116 continued



515

v ! O, ! T j !”

A vy , - y . Fermi’ y R qy q (F 5.121). T j y y P, Joliot-Curie’ . By vy , y , v , y x , -y , - . A x , x v y. B y ,

, 92 (), 93. I 1934, Fermi 92. A vy y, I j Fermi q y . T y v y y. I vy y, 1934, G , Ida Noddack, y Fermi’ Fermi v vy y . F , v, . T Noddack’

— y 1934:

One may just as well assume that in this new form of nuclear ssion by neu-trons, considerably more additional “nuclear reactions” take place than havethus far been observed from the action of proton and α rays on nuclei. With thelatter type of rays one nds only nuclear transformations giving off electrons,protons, and helium nuclei, which in the case of heavy elements changes themass of the bombarded nucleus only a little, since the elements that arise areclose neighbors. It is conceivable that in bombarding heavy nuclei with neu-trons, these nuclei would break up into several larger pieces, which would be

isotopes of known elements but not neighbors of the bombarded elements.

—iDanoDDacK, “Über das Element 93” (On the Element 93) [p. 654]

H , y y y. W y -vy, x y y y y . A v q

,

. I , v . T y y vy — , qv — . y y j v . T, Noddack’ y y.

N σ n d x , where the constant o proportionality σ is the cross

section o a single target atom with respect to the given

reaction (or the net total o other interactions). We can

interpret this equation as meaning that each target atom

appears as an area σ or each incident particle. Every 1 cm2

o the incident beam, sees the “eective” target area (n

d x )σ , and this is also the probability that one beam particle

will react with one target atom in the volume (1·d x ). There-

ore, the total number o reactions will be N (n·1·d x )σ . The

unit o the cross section: 1 barn = 10−24 cm2.

1

1

3

7

24

24

1 007825 7 016005

17 5

4 002604 4 0

H Li

He He MeV

+

= +

= + +

= +

. .

.

. . 002604 0 018622+ .

Figure 5.117 Energy balance o a nuclear

transormation.

E n e r g y

(c)

(b)

(a)

Figure 5.118

Models o the nucleus.

(a) Simple shell model.

(b) Liquid drop model.

(c) Optical model (ater

PEiErls).

nrgy rm th ytm. Tat t ndd bl t rla nrgy n hug quant-t vdncd by th xtnc th hydrgn bmb, n whch un ractn

Q t ti 6



523

ta lac whn th bmb t . T cntrlld rla un nrgy ha yt tb ralzd, but ucc wr vr achvd n th ara, mannd wuld b lbratdrm all th rv hrtag nrgy nw bng acd (Fgur 5.133).

5.4.13 Te Responsibility of Physicists

T act that rm a ractcal vwnt mt gncant dcvr th twntthcntury hav bn rmarly ut n th rvc ma dtructn ra th qu-tn th rnblt cnc, cally hyc, r mr t th nt, hyct. Cuntl artcl, tud, b, nvl, m, lay, and lm havbn dvtd t th tc (Qutatn 5.44, 5.45). W wuld mrly l t brvthat a hyct a mmbr human cty jut l any thr human bng, wthnthr gratr nr lr rnblt. Mt l d thr wr wth ddcatnand jy, cally n ca cratv wr, and rquntly gv n thught at all tutur cnqunc. It wll wrth radng th rcllctn Weisskopf abutth yar n whch th atmc bmb wa bng bult (Qutatn 5.46). W can that hyct wr wllng and wll mt lly cntnu t b wll-

ng t ma thmlv uul t gvrnmnt r th abrcatn vr mrdtructv wan (Fgur 5.134, Fgur 2.69), whl n actm artcatngn ac cnrnc. Anyn ntrtd n tudyng th atttud hyct rgardng th ctal

cnqunc thr cntc dcvr huld b awar th act that th rt

Quotation 5.46

It is very difcult to describe—let alone to judge—one’s feelings and one’s decisions after 30 years.

There are many now who say that a physicistshould devote his time to the search for truth andshould not devote his abilities to produce weaponsof destruction. It is easy to say, and it may even beright. There were very few who actually followed it.Pauli had to leave Europe at that time and was inPrinceton and he never even thought of joining anyof these war projects. But for a man in my position,and for so many others, not to join would havebeen a very difcult path to follow. I cannot tell

you why I went to Los Alamos. The fear that Hitler would make the bomb had much to do with it. If someone suggests I went just because everybodyelse did, he may be right. The signicance of physicsis a very difcult thing to describe. Physics is notonly the search for truth, it is also potential powerover nature; the two aspects cannot be separated.One may say that a physicist should search only fortruth and should leave the power over nature tosomebody else; but this attitude actually skirts thesubject and does not look at reality. The importantpoint about physics—and most of science—is notonly that it represents natural philosophy but thatit also is deeply involved in action—in life, in death,in tragedy, in abuse, in the human predicament.

Whether this is good or bad, who is to judge? Bothsides can be argued. Some terrible things havehappened since man made use of ssion. However,the rst bomb may have ended the war. At least,that is what we thought; we thought we had saveda million live; maybe we were right the second bombwas much harder to defend. We did participate in allthat and I don’t want to condemn or to justify it.

I cannot deny that those four years in Los Alamoswere a great experience, from a human as well asfrom a scientic point of view, in spite of the factthat they were devoted to the development of themost murderous device ever created by man. Suchare the contradictions of life. From the human pointof view, to live together, intellectually and otherwise,with the best physicists from the whole world(such as niels boHr, enrico fermi, J. cHaDwicK, r. Peierls,e. seGrè, and many more) was quite an experience.The discussions we had on philosophy, art, politics,physics, and on the future world under the shadowof a super-weapon remain unforgettable. Butalso from the purely professional level, we had toface tasks that never were faced before. It was aremarkable experience to deal with matter under

unusual conditions. We attempted to predict thebehavior of matter and make experiments about itunder conditions that were by factors of thousands


Figure 5.134 EinstEin’s letter to F. d. roosEvElt, president o the United States, in which he called the presi-

dent’s attention to the possibility o the creation o an atomic bomb. (See also Figure 2.69.)

My action concerning the atomic bomb and roosEvElt consisted merely in the act that, because o the

danger that hitlEr might be the frst to have the bomb, I signed a letter to the President which had been

drated by szilard. Had I known that that ear was not justifed, I, no more than szilard, would not have

participated in opening this Pandora’s box. For my distrust o governments was not limited to Germany.

Unortunately, I had no share in the warning made against using the bomb against Japan. Credit or this

must go to JaMEs Franck. I they had only listened to him!

—EinstEin, Letter to lauE, March 19, 1955 [Schweber 2008, p.61]

x . O d - W d -d



545

-, – , C- d, E , , d .

I CPT d, - CP - . Addd, x x d - d.

T d d . A , , d dd (SU

2d SU

3), d

, dd.

I 1960–1961, Murray Gell-Mann d Yuval Neeman d “-d ” d. Ad — Bdd—d, , d , , d : Sx d x, d dd d . F 5.167 -: E d . T q (S ), (Q ), (Y = B + S ), d j(I

3) dd.

T d d. F 5.168 10 3/2 d +1 ( 3/2+ d). B -, Gell-Mann d Nishiima dd x Ω− .C d, d x d d “” P - (F 1.35). T q x d Ω− d .

F , d I

3-Y d d

(F 5.169). T d xd—d x , — : Exd , ±⅓ d ±⅔.

T, 1964 Gell-Mann d George Zweig d — — d d , q. T -d Gell-Mann d — d— James Joyce’ Finnegans Wake . E d , d d, “T q M M.”

F 5.170 -

d q d . A , d d d. A d d: Bd q d, d,d dd . Boltzmann d Ld Kelvin d d dd d , d d. B j . I , d

Figure 5.166 An important symbol in the Orient, the

yin–yang symbol, is not mirror-symmetric, and perhaps it

is thereore not completely by chance that the violation omirror symmetry was discovered by Chinese scientists. In

the guest book o the Department o Atomic Physics at the

University o Budapest, we fnd hEisEnBErG quoting Plato, while

tunG-dao lEE, in contrast, wrote the ollowing ew lines o a

poem by lao Tzu (sixth century BcE):

The Tao that can be told

is not the universal Tao.

The name that can be named

is not the universal name.

In the inancy o the universe

there were no names.

Naming ragments the mysteries o lieinto ten thousand things

and their maniestations.

—Lao Tzu, The Tao Te Ching

Figure 5.167 With the help o the SU-3 symmetry, the

elementary particles can be organized into “multiplets.” The

fgure shows the octet o baryons with hal-integer spin.

I I

I

Boltzmann Kelvin Maxwell; , ck hu y, h u uch c h Pc (Q 5 53)



546

(Qu 5.53).

5.5.10 Back to the Apeiron?

I h h h p h pc phyc qu h : “Wh h cp ?” T h u hch h p y uccu h h ucu h h c ucu: O y h y h huh cp, h h, k up cp. p h p h c h, uc h h c p h y c . I h c h ucu, h pjc h h c y k h ucu uc u ck, h uc. F h y

pc, y c qu cu y h h-c- c pc u. Bu h h y hh ? W cuy h qu h p? Heisenberg’ py u :

If we speak of protons, pions, hyperons, and so on as consisting of smaller, as

yet unobserved, particles, of quarks, partons, then we are forgetting that the

sentence “they consist of…” has an acceptably clear sense only if we succeed

in decomposing these protons and so on into parts with a small expenditure

of energy, where the rest masses of the particles thus arising are much greater

than the expended energy.

Heisenberg hu h h h y pc , quu , h “p- uc.” T y pc, u , h y p- . Bcu y h p uchyph y Anaximander, Born c h uc apeiron.

T u y pc c c u h fuc hp uc . I cu h -c h u- qu Heisenberg pp h u hy h .

F h u h qu, h pp h y pc, -cu h , hu , h hy hu p h qu hy pcy h pc h h pp h .

The nal equation of motion for matter will probably be some quantized

nonlinear wave equation for a wave eld of operators that simply represents

matter, not any specied kind of waves or particles. This wave equation will

probably be equivalent to rather complicated sets of integral equations, which

have “eigenvalues” and “eigensolutions,” as physicists call it. These eigensolu-

tions will nally represent the elementary particles; they are the mathematical

forms which shall replace the regular solids of the Pythagoreans. We mightmention here that these “eigensolutions” will follow from the fundamental

equation for matter by much the same mathematical process by which the

harmonic vibrations of the Pythagorean string follow from the differential

equation of the string. But, as has been said, these problems are not yet solved.

If we follow the Pythagorean line of thought we may hope that the funda-

mental law of motion will turn out as a mathematically simple law, even if

Figure 5.168 The (3/2)+ decuplet (spin 3/2, parity +1).

This arrangement led to the prediction o the Ω− hyperon.

One hundred years earlier they would have said that a hole in

the periodic table would have to be flled.

Figure 5.169 I we place a triangle, the basic element

o the hexagon o the octet in Figure 5.167, in our coordinate

system (I 3, Y ), we represent the basic elements o physical

matter: the three quarks, u (up), d (down), and s (strange);

their quantum numbers are listed in Figure 5.170. The anti-

quarks could also be ound in an upward pointing triangle.

I I

I

Quotation 5.53

I too play with symbols, and have planned a littlework, Geometric Cabala, which is about the Ideas of natural things in geometry; but I play in such a waythat I do not forget that I am playing. For nothingis proved by symbols, nothing hidden is discoveredin natural philosophy through geometric symbols;things already known are merely tted [to them];unless by sure reasons it can be demonstrated that

they are not merely symbolic but are descriptions of the ways in which the two things are connected andof the causes of this connection.

—Kepler, Letter to JoAchimtAncKius, 1608 [Vickers1984, p. 155]


its evaluation with respect to the eigenstates may be very complicated. It

is difcult to give any good argument for this hope for simplicity—except

the fact that it has hitherto always been possible to write the fundamental Quotation 5.53, continued



547

the fact that it has hitherto always been possible to write the fundamental

equations in physics in simple mathematical forms. This fact ts in with the

Pythagorean religion, and many physicists share their belief in this respect,

but no convincing argument has yet been given to show that it must be so.—HeisenberG, Physics and Philosophy [pp. 72–73]

d q ,

d x, x:

γ γ γ γ γ ν

ν

µ µ

∂

∂± ( ) =

Ψ Ψ Ψ Ψ

x l

s s

20

*.

A , Heisenberg d -

d d d d d. A “ ” d, d

q x d ; q d ; d , d

. W x, , d — ,

d — dd . H , d d Hume d Kant (Q

5.54, 5.55, 5.56). W d

— — d A . W Weyl:

Aristotelian philosophy considers matter as the determinable, in contrast

to the determining form. Matter is [the] possibility of becoming formed. In

a production process of several stages its matter appears “more formed” at

each step, and thereby the range of possibilities for further forming becomes

more restricted. And at the same time matter, the component of merely po-

tential rather than actual being, shrinks more and more. Substantiality is

ascribed to the forms rather than to matter. The forms push matter from po-

tentiality to actuality ….

—Hermannweyl, Philosophy of Mathematics and Natural Science [p. 178]

E d d “,” ,“ ” , -

d d d d— d-

d , dd— - q .S, , , x

d. M,

dd, d dd. A Q 5.57, New-ton d “d.” I d, d d

, , accidentia. B , ,

d? J d d , , dd. F Weisskopf,

Figure

5.170 Top: Quan-

tum numbers o

the three quarks,

u (up), d (down),

and s (strange),

and the three an-

tiquarks. Bottom:

the quark models

o some elemen-

tary particles (GEll-

Mann and GEorGE

zwEiG, 1964).

Proton Neutron

Hyperons

Q

I am convinced that we can discover by means of purely mathematical construction the conceptsand the laws connecting them with each other,which furnish the key to understanding of natural phenomena. Experience may suggestthe appropriate mathematical concepts, butthey most certainly cannot be deduced from it.Experience remains, of course the sole criterion of the physical utility of a mathematical construction.But the creative principle resides in mathematics.In a certain sense, therefore, I hold it true that purethought can grasp reality, as the ancients dreamed.

—einstein. Ideas and Opinions, 1954

Quotation 5.54And since I conceive that other beings can alsohave the right to say “I”, or that it can be said forthem, it is through this that I conceive what is calledsubstance in general.

—leibniz, Letter to Queen soPHie cHarlotte [p. 188]

QUANTUMMECHANICS

SPECIALTHEORY

GENERALTHEORY

Figure 5.198 I we compare this diagram with

Figure 5.1, we do not fnd here any clashing arrows that

o ld indicate kno n contradictions (in color in Fig re



575

it ity, cn nntss b usd t d dquty it pbms ting t

t big bng. By tis mn tt ty p t iv t sttmnts tt in ct

t t d nd tby vib tug pimnt.

It is nt t supising tt bstct cncpts nd tis cnnt b pssd in

cqui ngug. It is muc m supising tt n cn spk suc tings t

(s Bohr’s tugts in tis dictin, Quttin 0.9 nd Figu 5.197).

W nd ny c tt t cncptu systm Maxwell’s ty, t ct-

mgntic d, md vy gt dmnds n t bstctin cpcity t bst tink-

s t nintnt cntuy. T cnsquncs tis ty, ctmgntic vs,v nvtss ng bn gny ccptd—i m n tust tn undstnding.

5.7.6 Questions and Doubts Multiply

I smdy OE (ty vyting) is bn ut syntsis supsting

ty nd inftin ty, t t dg cn it b vid s t iztin

dm, t dm n ty tt mny pysicists dsi nd vn pss

in t tits ti bks ( mp, Dreams of a Final Teory )? I cmp

Figu 5.1 it Figu 5.198, s tt t n sut t m gu p-

snts t stting pint t tt gu. Wi t ctin n -ncm-pssing ty bing n nd t tis cntinuity? O i scinc b b t mk

simi sktc t t bginning t tnty-scnd cntuy, t stting

pint is givn by OE? T mny sink m t d “n.” Ty

cnsid it unccptb, indd gicy s, tt pincip ds nt ssum

nt, ying t dp v, n ic it cn b bsd. Ots biv tt n

ty ists tt ud b cpb pviding cmpt pntin t in-

MECHANICS OF RELATIVITY OF RELATIVITY

STANDARD MODEL

WS + QCD

BIG

BANG

GUT Grand Unication Theory

HiggsField

Quark–GluonPlasma

Accelerati onof the

Expansion

Ψ Ψ n

EPRParadox

TOE Theory of Everything

QUANTUMCOMPUTING

Neutrino

Oscillation

CP Violation Quark

Connement

Gravitational Waves

Dark

Matter

Proton

Decay

Ination

Bell Inequalities

would indicate known contradictions (in color in Figure

5.1). The Standard Model is unable to give answers to a

number o important questions but its assertions are not

in contradiction o any experimental acts. (Diagram is in

part ater G. vEsztErGoMBi.)

A summary o this sort presents even greater difculties at

the turn o this millennium than at the turn o the previous

century. In preparing the earlier fgure, we had knowledge

o all the new disciplines that would be established over the

century ahead. Thus we could defne the questions to be

answered and problems to be solved. In the leading journals,

such as Annalen der Physik and Physical Review , hundreds

o articles have been published in which new and newer

problems are continually solved that in turn, however, raise

a new set o problems. It is easy to decide what the relevant

problems were ater the act, the answers to which led to

the establishment o relativity theory and quantum mechan-

ics. However, we don’t know or certain—we only suspect

or antasize—about the syntheses to take place in the com-

ing century; we can thereore not maintain that the solution

o the selected questions in act represents the correct path

to the establishment o newer undamental laws.

The twentieth century consigns to the current a unda-

mental problem that it struggled over or decades: the

measurement process itsel and the evaluation o results

or, ormulated quite generally, the “interace” between

mankind and nature.

the “decoherence” o the quantum state, resulting in loss o inormation, due tothe quantum system’s interaction with its environment. Irrespective o whether new practical applications might be successully implemented, these techniques and the

SupernovaExplosion

Figure

5.199 Critical



578

p pp g y p , qaccompanying new experimental acts will create momentum in the investigationso basic quantum-mechanical problems such as the riddle o the measurement pro-

cess (Figure 5.77) or that o the EPR paradox with Bell’s inequalities (Figure 5.78).

5.7.7 “Between Nothing and Infnity”

Te eternal and unchanging Aristotelian world encompassing the Sun, the Moon,ve planets, and the stars embedded in a crystalline sphere was orced to cede itsplace to a dynamic universe resembling a giant laboratory ull o exquisite objectsthat change in exquisite ways.

From a smallish planet orbiting an average star located at the edge o a galaxy o

average size, mankind observes the divine drama o cosmic events. We can con-dently say that we belong in the fow o these cosmic processes with every drop o our blood. Biologists trace the origins o lie back to protein molecules as initialbuilding blocks; but the hydrogen contained in our bodies also took part in theprimordial processes o the universe, and every iron nucleus in human blood origi-nated within a massive star, went through a supernova explosion beore it couldbecome, via the development o a new star system, a component o our solid earthand now play an important role our biological unction (Figure 5.199).

Te grandeur o all o human history is dwared, shrivels to nothing, and is lost

in the enormous currents o the cosmos (Quotation 5.63), and yet this terrestrial world is not insignicant, or alongside all the marvelous objects in the universe,next to pulsars, quasars, and black holes, the great cosmic creation brought orthin this place the human brain and human consciousness with its capacity to beaware o both the innitely small and the innitely large (Figure 5.200).

Here is where natural knowledge leads us: if it is not true, there is no truth

in man; and if it is true, he nds in it a great source of humiliation, forced to

humble himself one way or another.

And since he cannot subsist without believing this knowledge, before enter-

ing into greater explorations of nature, I want him to consider nature bothseriously and at leisure just once, and also to reect upon himself and to

judge, in a comparison of these two objects, whether any proportion holds

between them.

Let man then contemplate the whole of nature in its lofty and full majesty,

and let him avert his view from the lowly objects around him. Let him behold

that brilliant light set like an eternal lamp to illuminate the universe. Let the

earth seem to him like a point in comparison with the vast orbit described

by that star. And let him be amazed that this vast orbit is itself but a very

small point in comparison with the one described by the stars rolling around

the rmament. But if our gaze stops here, let our imagination pass beyond.It will sooner tire of conceiving things than nature of producing them. This

whole visible world is only an imperceptible trace in the amplitude to na-

ture. No idea approaches it. However much we may inate our conceptions

beyond these imaginable spaces, we give birth only to atoms with respect to

the reality of things. It is an innite sphere whose center is everywhere and

circumference nowhere. …

p

Origin of theSolar System

Ultraviolet Radiationfrom the Sun

Origin of the Amino Acids

and Nucleotides

P r i m i t i v

e A t m o s p h ere

steps in cosmic

evolution that

eventually led

to the mosthighly orga-

nized orm o

matter: lie.

The heavy

elements

were created

(perhaps) dur-

ing a super-

nova explosion.

The physical

conditions—

the narrow

temperatureand pressure

range, appro-

priate liquid,

gaseous, and

solid phases

o materials—

conducive to

the continued existence o

the sensitive,

ragile, and

extremely com-

plex protein molecules, which combine reproducible stability with

the necessary variability, were ensured by our solar system. For

the initial formation o the building blocks, electrical phenomena

in the primitive atmosphere may have been responsible. Once

sel-reproducing units were ormed, the tempo o evolution was

dictated by the laws o biology.

Let man, returning to himself, consider what he is with respect to what exists.

Let him regard himself as lost in this remote corner of nature, and from the

little cell in which he nds himself lodged, I mean the universe, let him learn

h l f h h k d d h lfc

m )



579

to estimate the just value of the earth, kingdoms, cities, and himself.

What is a man in the innite?

But to present him with another equally astonishing prodigy, let him exam-ine the most delicate things he knows. … Let him lose himself in wonders as

astonishing in their minuteness as the others are in their extent! For who

will not marvel that our body, imperceptible a little while ago in the universe,

itself imperceptible inside the totality, should now be a colossus, a world, or

rather a whole, with respect to the nothingness beyond our reach? …

For what, in the end, is man in nature? A nothing compared with the innite,

an everything compared to the nothing, a midpoint between nothing and

everything. …

This is our true state. It is what makes us incapable of certain knowledge

or absolute ignorance. We oat on a vast ocean, ever uncertain and adrift,

blown this way and that. Whenever we think we have some point to which

we can cling and fasten ourselves, it shakes free and leaves us behind. And

if we follow it, it eludes our grasp, slides away, and escapes forever. Nothing

stays still for us. …

All things, then, are caused and causing, supporting and dependent, mediate

and immediate; and all support one another in a natural, though impercep-

tible chain linking together things most distant and different. So, I hold it is

as impossible to know the parts without knowing the whole as to know the

whole without knowing the particular parts. …

Man is to himself the most prodigious object of nature, for he cannot con-

ceive what body is, still less what mind is, and least of all how a body can be

unied to a mind. This is the culmination of his difculties, and yet it is his

very being. The way the spirit is united to the body cannot be understood by

man, and yet it is man. [Modus quo corporibus adhaerent spiritus comprehendi

ab hominibus non potest, et hoc tamen homo est; Saint Augustine, City of God ,

XXI.10.]

—blaise Pascal, Pensées [pp. 58–62]

L e

n g t h ( c

M a s

s ( g )

L i f e S p a n ( s )

Figure 5.200 The place o mankind between

“nothing” and the “infnite.”

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