1905 miraculous year

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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS

J. Phys. B: At. Mol. Opt. Phys. 38 (2005) S437S448 doi:10.1088/0953-4075/38/9/001

1905a miraculous year

Jurgen Renn and Dieter Hoffmann

Max Planck Institute for the History of Science, Wilhelm Street 44, 10117 Berlin, Germany

E-mail: [email protected] and [email protected]

Received 15 February 2005

Published 25 April 2005

Online at stacks.iop.org/JPhysB/38/S437

AbstractThe article discusses Einsteins famous papers of 1905his miraculous year

and deals with their physical and historical context as well as their fundamental

impact on modern physics. It shows that the papers are not isolated, but

connected with each other by Einsteins deep-seated conviction of physical

atomism and his criticism of an ether. They are concerned with specific

problems that can be characterized as borderline problems since they go

beyond the traditional divisions between mechanics, electrodynamics, and

thermodynamics.

The year 1905 is generally considered Albert Einsteins annus mirabilis. It was not only a year

of miracles for him personally, but it was also a miraculous year for the further development

of physics. In this year, besides several book reviews, Einstein published five papers that

revolutionized the basic principles of physics.

The titles of Einsteins papers were comparatively unspectacular: On a heuristic point of

view concerning the production and transformation of light (completed 17 March, 1905); A

new determination of molecular dimensions (30 April); On the movement of small particles

suspended in liquids at rest required by the molecular kinetic theory of heat (11 May); On the

electrodynamics of moving bodies (30 June); and Does the inertia of a body depend upon its

energy content? (27 September), see figure 1. Every one of these works [1] had far-reaching

consequences for a physical understanding of the world.

Thus, the paper on electrodynamics contained the basics of Einsteins theory of special

relativity, and laid the foundation for a new concept of space and time. This paper led him to

the most famous physical formula, E = mc2.

Einsteins work on the creation and transformation of light was based on Max Planckstheory of blackbody radiation, and asserted the existence of so-called light quanta. This meant

that, contrary to the then well-established and highly successful electromagnetic wave theory,

light possessed characteristics of particlesa bold and revolutionary hypothesis at the time.

Ultimately, Einsteins study of Brownian motion was a major factor in the final acceptance

in physics of atomic theory, which was still controversial at the time.

What was it that turned this 26-year-old examiner at the Swiss Patent Office in Bern,

who, far from the leading physical research centres of the time, led more of a modest

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S438 J Renn and D Hoffmann

Figure 1. Facsimile of the title pages of Einsteins 1905 papers. From [16].

scientific existence (an outsider, and a loner as well), into the greatest revolutionary in the

world of physics since Isaac Newton? The oft-used reference to the physical genius of

Einstein romanticizes him more than it explains who he wasand not only because of todays

inflationary use of that term, which also places sports stars in the same category. Whoever

deals with the myth of Einstein simply by referring to his genius is, not least, neglecting the


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1905a miraculous year S439

Figure 2. Einstein at the Patent Office around 1906.

specific conditions for his insights and the circumstances of his life that allowed both Einsteins

personality and his gift for physics to unfold. We will briefly examine these factors below.

Albert Einstein was born on March 14, 1879 in Ulm as the son of a Jewish family [2].

His father was at first based in Munich, where the family moved in the summer of 1880.

Later in 1894 they moved to northern Italy where they worked in the electrical industry. At

the age of 16 Einstein followed his parents to Italy for a short time, after conflict with the

authoritarian German school system. He caught up on his diploma in the Swiss town of Aarau

in 1896, and went from there to study physics and mathematics at the Federal Polytechnic

Academy in Zurich (later called the Swiss Federal Institute of Technology). Although much

of the Einstein literature insists on calling him a wayward pupil and an unsuccessful student,

he was in actuality neither. But his behaviour did indicate a high level of individuality and

independence from an early age. As a young man he was called an Einspaenner or loner,

for whom reading physics textbooks was usually more important than going regularly to

lectures. In the summer of 1900, Einstein succeeded in graduating with a Diploma as a

Technical Instructor for Mathematics. Unfortunately, he could not at first find any regularemployment, as applications for assistantships with his Zurich teacher Adolf Hurwitz as well

as with Wilhelm Ostwald in Leipzig or Heike Kamerlingh-Onnes in Leiden were rejected [3].

Thus Einstein had to make do with work as a tutor and substitute teacher in various Swiss

schools and boarding schools.

In the summer of 1902 he managed at last, through the intercession of a friend, to find a

permanent position at the Swiss Patent Office in Bern. For the next seven years, he worked as a

technical expert third class andthen second class (see figure 2). But these years were influenced


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blinkers of specialization, bringing him closer to the internationalist spirit of science as well

as its worldview and political consequences.

Above all, this reading sharpened his awareness of scientific puzzles and unresolved

questions, characteristics that later were of great benefit to his revolutionary work.

The evidence that Einstein was occupied with original scientific problems even while inschool comes from a paper written when he was 16 years old which dealt with the effect of a

magnetic field on the dispersion of light in ether, speculating about the ether and asking how

a beam of light would look from the point of view of an observer also moving at the speed

of light. These were the problems, the Gedankenexperimente or thought experiments, that

would later be seen as precursors to Einsteins theory of relativity.

The image of the young Einstein must also include his early fascinationwhich he shared

with other great scientistswith the precision and beauty of mathematical thought. He taught

himself the basics of geometry as well as important areas of higher mathematics.

When Einstein graduated in the summer of 1900, there was no clear path for him to

embark upon professionally. This did not keep him from working on his own scientific profile.

His interests at the time centred on statistical physics, and in the years following he succeeded

in independently formulating, at about the same time and without any knowledge of the workof the American physicist Josiah Willard Gibbs, the basic principles of this field.

This achievement resulted from an attempt to expand on the work of Ludwig Boltzmann

to develop a kinetic theory of heat, in which among other things the electron theory of metals

as well as radiation theory could be used.

This parallel discovery of Einsteins would not have necessitated an annus mirabilis, as

his work in the area of statistical physics would have been more than enough to launch an

admirable career as a physicist. In fact, his first revolutionary paper of March 1905 would

actually have stood in the way of such a career at first, as opposed to furthering it. Einsteins

hypothesis of light quanta was, after all, a radical break with the traditions of optics and

electrodynamics of the nineteenth century, standing in diametric opposition to the large amount

of experimental as well as theoretical evidence that supported the electromagnetic wave theory

of light.

The fact that Einstein dared to advance this theory is related to his early work on statisticalphysics. This work attempted, e.g., to apply statistical mechanics to what was then the

prevailing problem of thermal radiation in thermodynamic equilibrium. In the fall of 1900,

Max Planck developed a formula that is still valid today for the dispersion of energy during

thermal radiation based on the precise measurements of heat radiation from a blackbody taken

at the Physikalisch-Technische Reichsanstalt in Berlin. However, the derivation of Plancks

radiation law, which introduced his quantum of action h to physics, was highly problematic.

Several physicists had already lodged protests, cf [6], and in the search for a physically

satisfying derivation of Plancks radiation formula Einstein could show, the higher the energy

density and wavelength of radiation, the more reasonable the theoretical foundations [of

Plancks formula] we have been using prove to be: However, they fail completely in the case

of low wavelengths and low radiation densities (in the area of validity of the so-called Wiens

radiation formula- JR/DH) [7, Doc. 14].Einstein especially alluded that the classical concept of electromagnetic radiation as

vibrations in a continuum is irreconcilable with the assumption of thermal equilibrium. The

number of wave frequencies in a continual ether would be infinite, but the law of dynamic

equilibrium states that every frequency must receive the same portion of energy. Thus Einstein

discarded the idea of a continual ether and asserted that the problems of Maxwells theory

in properly explaining electromagnetic radiation in a blackbody, i.e., radiation in thermal

equilibrium, could be overcome through a heuristic viewpoint, if one assumes that the


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energy of light is discontinuously distributed in space. According to the assumption considered

here, in the propagation of a light ray emitted from a point source, the energy is not distributed

continuously over ever-increasing volumes of space, but consists of a finite number of energy

quanta localized at points of space that move without dividing, and can be absorbed or

generated only as complete units [7, Doc. 14].Thus, the theory of light quanta was formulated, which not only made clear the principle

irreconcilability between Plancks radiation formula and classical physics, but was also a

theory with which Einstein could also explain for the first time various anomalies in the

electromagnetic theory of light.

This wasStokes formula for fluorescence, the ionization of gases through ultraviolet light,

and most importantly Philipp Lenards discovery in 1902 of the (qualitative) connection that

the energy of emitted electrons in the photoelectric effect is not dependent on the intensity of

the light, but on its frequency [8]. For this correlation, Einstein first formulated the well-known

photoelectric equation:

mv2/2 = hf P

where m is electron mass, v is maximum velocity of the freed electrons, f is frequency oflight, P is characteristic amount of work needed to free a single electron from a metal.

Thus Einstein had found uses for Plancks quantum constant h outside of thermal radiation

theory, thereby demonstrating its general significance for the world of physics. But Planck

himselflike most other physicistswas at first unwilling to go along with Einsteins

far-reaching conclusions. This was less because Einstein would have a long wait for a

quantitative confirmation of his photoelectric formula, but most importantly because most

physicists hoped to preserve the electromagnetic wave theory of light and, along with it,

classical physics.

In the end, Einsteins light quantum theory opened up a new, non-classical understanding

of radiation and matter. In this sense it was not Planck, but Einstein with his 1905 work on

light quanta, through whom the problem of thermal radiation became the crucial starting point

for quantum theory, cf [6].

It was not only his light quantum theory, however, that made Einstein a central figure

in this process. More importantly, the light quantum theory became the starting point for

intensive research into the questions of quantum theory, which would make Einstein by far the

most important pioneer in the early history of quantum theory and which would considerably

support the insight that the development of this theory would be connected with a deeply

significant transformative effect on the foundations of classical physics.

Thus in 1907 Einstein was able, using the quantum hypothesis, to lay the foundations for

the first non-classical theory of specific heat in solids. In 1909, while considering blackbody

radiation, he introduced the idea of lights dual nature as both a wave and a particle, and

in 1912 formulated the law of photochemical equivalence. Further milestones in Einsteins

activities with quantum theory were a new derivation of Plancks radiation formula in 1916, in

which the term transitional probability for spontaneous and induced emission and absorption

of radiation was introduced, thereby laying the theoretical foundations for the invention of thelaser. Finally, in 19241925 he developed BoseEinstein statistics, an equation describing the

statistical distribution of certain types (todays so-called bosons) of identical particles in an

ideal gas.

His participation in the Solvay Conferences, which had taken place since 1911 (see

figure 3), did much to promote acceptance of quantum theory; but in the 1920s his appearances

at these summit meetings of leading contemporary physicists were increasingly characterized

by determined opposition to the so-called Copenhagen Interpretation of quantum mechanics.


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Figure 3. The first Solvay Conference, Brussels 1911.

He consistently rejected a statistical interpretation of quantum mechanics because of its

putative incomplete description of physical reality. In discussions with Niels Bohr and other

pioneers of modern quantum mechanics, Einstein always pointed out gaps in the theory and

expressed his belief that all natural processes follow deterministic paths. His now-classic

saying, formulated in a letter to his friend Max Born on 4 December, 1926, the old one

. . . is not playing at dice [9], stands for this belief just as it does for his final significant

contribution to quantum theory, the paper published in 1935 together with Boris Podolsky

and Nathan Rosen, in which questions about the completeness of a quantum mechanical

description of physical reality came to a head through the so-called EinsteinPodolskyRosen

paradox [10].

Thus it was not only the young Einstein who rebelled against the physics establishment.

Just how unconventional and strange Einsteins light quantum hypothesis was is made clear,

for instance, by the fact that it had to struggle for recognition much longer than quantum

theory itself. Up to the 1920s, it stood alone in the world of physics. Starting in 1914, the

American physicistRobert Andrew Millikan conducteda long series of precision-measurement

experiments in order to disprove Einsteins bold light quantum theory and his explanation of

the photoelectric effect. Although Millikans measurements resulted rather quickly in a basicagreement between the theory and experimental reality, for a long while he only wanted

to admit that this confirmation was nothing more than the quantitative confirmation of the

photoelectric equivalence, especially since yet another precision method for determining

Plancks active quantum had been found, thanks to his work. The light quantum hypothesis

itself seemed to him fully unacceptable until the early 1920s.

Even Max Planck himself, after all the father of quantum theory and one of Einsteins

strongest supporters, who once called Einstein his most important discovery, said in 1913


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during a laudatory address for Einsteins election to membership in the Prussian Academy that

Einsteins contributions to physics had been so great that the scientific world should not be

too critical if he once in a while has shot past the mark, like for instance with his hypothesis

about light quanta. . . . Because without the ability to take risks, even the most exact natural

science cannot introduce any true advances [11].It is an irony of the history of science that Einsteins light quantum theoryhis discovery

of the law of the photoelectric effectwon him the Nobel Prize for physics in 1921. This

had less to do with the scientific foresight of the selection committee than with the fact that

Alfred Nobels testament specifically preferred effects to theories, and Einsteins general

theory of relativity seemed to be insufficiently confirmed and in addition was considered highly

controversial [12].

The final turning point in the general acceptance of Einsteins light quanta and therefore

the waveparticle dual nature of light was of course not provided by the Nobel Prize

committee, but by the discovery of the Compton effect in 1922, and his convincing theoretical

interpretation based on Einsteins light quantum hypothesis shortly afterwards [13]. Arnold

Sommerfeld, who had witnessed this during a trip to America, wrote about it to Niels Bohr:

The most interesting thing I experienced in terms of science in America was the workof Arthur Compton in St Louis. After this, the wave theory of x-rays will have to be

abandoned [14].

After it became clear to Einstein in the spring of 1905 that the problem of thermal radiation

in thermodynamic equilibrium not least made the concept of empty space insupportable, other

ideas in this regard in which he had engaged for quite some time, especially relating to the

electrodynamics of moving bodies, suddenly gained new significance. Letters from the years

between 1899 and 1903 show that Einstein was continually absorbed in these problems [4].

He drafted experiments to analyse the changes in the speed of light in a moving body or

the relative movement of the earth through the ether. But in trying to bring his ideas into reality,

he ran into insuperable problems that even with the intensive study of relevant textbooks and

other scientific literature could not be overcome. Special attention was given to the work of

the Dutch physicist Hendrik Antoon Lorentz on electrodynamics, which had climaxed in the

well-known electron theory.This theory, based on the commonly held notion of a stationary ether, still managed to

bring processes taking place in frames of reference in motion, with the help of auxiliary space

and time coordinates, into agreement with the experience of systems at rest. This reduction

held within it the seed of the so-called Lorentz transformations between moving frames of

reference.

Like Plancks derivation of his law of radiation, the derivation of Lorentzs theory from

classical physics proved complicated and connected with problematic additional assumptions.

Similarly to what he had done with his revolutionary work on light quanta, Einstein here

cut the Gordian knot in that he came up with a completely new interpretation of Lorentzs

transformation equations.

From the perspective that Einstein had gained during his research, the building blocks

of Lorentzs theory appeared in a new light. While for Einstein the ether, which was animportant basis of Lorentzs work, had become questionable, Lorentzs conclusions about

the relationship between electromagnetic measurements taken in moving frames of reference

seemed, in contrast, quite reliable. These conclusions were in agreement with the postulate that

in measuring electromagnetic and optical phenomena, it was impossible to tell the difference

between a framework at rest and a framework moving at a uniform speed. Still, Lorentz had

only been able to reach these conclusions, which had been proven by observation, with the

help of additional assumptions. He had therefore to introduce an auxiliary variable for time


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into his description of physical processes in moving frameworks that was different from time

in a system at rest. In addition, Lorentz assumed that the length of bodies is shortened in

the direction of their movement through the etherthis was the only way to explain why the

MichelsonMorley experiments had failed to detect any movement of the earth through the

ether.The results of these deliberations added up to an expansion of the relativity principle

already at the core of classical mechanics to electromagnetic and optical phenomena. Einstein

had expected such an expansion since he first considered a strange asymmetry in classical

electrodynamics: the interaction between a magnet and a conductor moving towards each

other was described differently depending on which was considered to be at rest, but the

physical effectelectricity induced in the conductoris always the same.

For Einstein, the success of Lorentzs electrodynamics was essentially a confirmation of

the principle of relativity. But it was simpler not to embark on the difficult path Lorentz

had adopted in order to see this confirmation, especially since his starting point of an etheric

medium was, from Einsteins perspective, highly questionable. It seemed much more plausible

to make the principle of relativity the starting point, thereby setting Lorentzs theory, so to

speak, on itsfeet instead of itshead. Einstein clearly hoped that hisanalogy of thermodynamics,which apart from its physical details was based on simple principles, would lead him to a theory

that was independent of the composition of electromagnetic phenomena, i.e., whether they

were waves or particles.

Thus he searched for the solution to the problem of the electrodynamics of moving bodies

on an entirely new and more profound level, whichsupported by his philosophical readings,

especially in a discussion with his friend Michele Besso in May of 1905he ultimately found

in kinematics: the doctrine of space and time. While new variables for time and length played

a supporting role in Lorentzs theory, they took on fundamental significance in Einsteins

deliberations. It was a kind of Copernican turning point in the formation of basic principles.

What consequences did Lorentzs electron theory have for the kinematic behaviour of

bodies in motion? How would it be possible to determine whether systems in motion behaved

in the way Lorentz had asserted? It was questions such as these that led Einstein to the

problem of simultaneity in two systems moving with uniform velocity with respect to eachother, thereby causing him to take the crucial step that would eventually solve this problem.

In order to determine simultaneity he developed a method that was based on calibrating

two clocks separated by distance through light signals. This method disclosed a certain amount

of arbitrariness in the determination of simultaneity in systems moving towards each other,

because the concept was at first only defined in one frame of reference. This arbitrariness

could be eliminated in two ways. One could assume that the determination of simultaneity

with Einsteins method would lead to the same results regardless of motion of the framework;

that would make it possible to conclude the validity of the concept of absolute time, which

was the basis for conventional physics. Alternatively one could introduce the hypothesis that

it was not time but the speed of light that would remain the same regardless of the motion

within the framework.

Einstein chose the latter hypothesis, despite counterintuitive consequences like therelativity of simultaneity. It allowed him to derive the main results of Lorentzs

electrodynamics based on two simple principles, that of relativity and the non-classical

principle of the constancy of the speed of light. This in turn made it possible for him to

extend the scope of the principle of relativity from classical mechanics over the entirety

of physics, whereby the classical Galileo transformations between frameworks in motion

were replaced by Lorentz transformations. With its seemingly paradoxical consequences like

shortening of length and time dilatation, or the so-called twin paradox, these transformations


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guaranteed that all inertial systems are physically equal, i.e., the laws of physics are retained

in these transformations and the speed of light remains constant.

In a supplementary paper Does the inertia of a body depend on the energy it contains?

Einstein in the fall of 1905 derived another consequence of his theory of special relativity.

In relation to this, he wrote to his friend Conrad Habicht: One other consequence ofelectrodynamic work has occurred to me. The principle of relativity in relation to Maxwells

equations demands that mass is a direct measurement of the energy of a body; that light carries

mass. A noticeable decrease in mass must then occur in the case of radium. The thought is

funny and infectious; but whether God is laughing and has led me by the nose, I do not know

[15].

As we know today, God was not leading Einstein by the nose at all, rather he was leading

Einstein to the most famous physical equation of all time as well as to his scientific fame and

popularity.

Einsteins special relativity theory from 1905 received the form in which it is usually

expressed today from Hermann Minkowski, Einsteins Zurich mathematics professor. In

1908, he gave it the form of four-dimensional spacetime geometry. This four-dimensional

formulation tied in with the further development of the relativity theory by Max von Laue,Arnold Sommerfeld and other physicists, in whose frameworks more fundamental conceptual

insights, like, for instance, the role of the four-dimensional energy impulse tensor, provided

material for the understanding of inertia and eventually gravitation as well.

Another breakthrough of Einsteins annus mirabilis was his analysis of Brownian motion.

This work also has a hidden connection to the more famous relativity and quantum theory

papers. It is rooted just as deeply as the others in Einsteins occupation with questions of

statistical physics. While the controversy was still raging among physicists at the turn of the

century about the legitimacy of assuming the existence of atoms in order to explain thermal

phenomena (as well as other physical processes), Einstein turned the issue on its head and

instead questioned whether classical thermodynamics could correctly describe the movement

of particles suspended in fluid.

From the point of view of thermodynamics, such particles should behave like macroscopic

bodies, which after a certain amount of time reach equilibrium. From the point of view ofthe kinetic theory of heat, these particles differ from real atoms in size only. When they are

exposed to the buffeting of their smaller siblings, they should pick up on the thermal movement

and thereforeas had, in fact, been observedbegin moving in random motion at a constant

rate.

The laws of mechanics were used to calculate the average rate of motion of the particles

as related to their share of the thermal energy, but it became clear that it was impossible to

reconcile the calculated rate of motion of the suspended particles with the observed rate. In

his work on Brownian motion, Einstein analysed this phenomenon as a statistical process, a

stochastic process.

Thus Einstein used the strange, in-between world of fluctuations, the best example of

which is Brownian motion, to bridge the macrocosm of our everyday environment and the

microcosm of atoms and moleculesin order to make the latter more comprehensible. Brownianmotion became the key to proving the existence of atomseven though their characteristics

no longer fit into the classical image of moving particles.

Remarkably, it was Einsteins atomic interpretation of Brownian motion that was the first

to be understood and accepted. Its experimental verification, which was from 1908 advanced

by the French physicist Jean Perrin, was an impressive and crucial confirmation of the atomic

structure of matter, and contributed immensely to the final acceptance of atomic theory in

physics.


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Figure 4. Schematic forborderline problems.

(This figure is in colour only in the electronic version)

Einsteins essential conviction of atomic theory, which he gained at the very latest in his

early student days, must also be seen as the connecting element in all his key works of 1905,

because in all these works it played a crucial heuristic role.

In this context, however, we can see yet another connective element among these works.

Einsteins works during his annus mirabilis are all concerned with problems of a certain

kind; they go beyond the divisions among mechanics, electrodynamics and thermodynamics,

the three main areas of classical physics, and therefore can be characterized as borderline

problems (see figure 4).

Mechanics, the oldest discipline in physics, was long considered the basis upon which

all physical phenomena could be explained. Besides mechanics, electrodynamics and

thermodynamics had established themselves since the middle of the nineteenth century as

relatively independent areas with their own theoretical foundations. Their reduction to

mechanics was attempted, but this proved in the end to be both impossible and unnecessary.Instead, a whole series of problems emerged that affected at least two of the three domains of

classical physics.

The problem of thermal radiation in thermal equilibrium was just such a borderline

problem between thermodynamics and electrodynamics, that of the electrodynamics of moving

bodies bordered both electrodynamics and mechanics, and Brownian motion lay between

thermodynamics and mechanics. It is no coincidence that the scientific revolution Einstein

initiated in 1905 was sparked by just such borderline problems. Because these borderline

problems were not isolated, they were, so to speak, problems that dealt with the overlap zones

among the continents of classical physics, where highly integrated knowledge systems meet.

Since this degree of integration came not least from model concepts like the notions of the

ether and the atom, it is not surprising that the inner conceptual conflicts of classical physics

were replaced in these model concepts. Against this background we can understand how the

seemingly specialized works of Einstein during his miraculous year of 1905 ultimately led to

the elimination of the ether and the acceptance of the existence of atoms, and also led to the

surprising conclusion that light is not a wave after all, but has a quantum nature.

References

[1] For a documentary edition of the papers (with comments), see Stachel J et al (ed) 1989 Collected Papers of

Albert Einstein (CPAE) vol 2 (Princeton, NJ: Princeton University Press)


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[2] For Einsteins biography see Folsing A 1997 Albert EinsteinA Biography (New York: Viking)

[3] Stachel J (ed) 1987 Collected Papers of Albert Einstein (CPAE) vol 1 (Princeton, NJ: Princeton University

Press) pp 2889

[4] Renn J and Schulmann R 1992 Albert EinsteinMileva MaricThe Love Letters (Princeton, NJ: Princeton

University Press)

[5] Einstein A 1993 Letters to Solovine, 19061955 (New York: Citadel Press) p 142

[6] Kuhn T S 1978 Black-Body Theory and the Quantum Discontinuity 18941912 (Oxford: Clarendon)

[7] Stachel J (ed) 1989 Collected Papers of Albert Einstein (CPAE) vol 2 (Princeton, NJ: Princeton University

Press)

[8] Lenard P 1944 Wiss. Abh. Lpz. 3 251 ff

[9] Einstein A, Born M and Born H 1971 The correspondence between Albert Einstein and Max Born and Hedwig

Born from 1916 to 1955, with commentaries by Max Born The BornEinstein Letters (New York: Walker)

p 88

[10] EinsteinA, PodolskyB andRosen N 1935Can quantum-mechanical description of physicalreality be considered

complete? Phys. Rev. 47 77780

[11] Planck M 1975 Wahlvorschlag fur Albert Einstein, Berlin 12.6.1913 Physiker uber Physiker I ed C Kirsten and

H-G Korber (Berlin: Akademie) p 202

[12] Friedman R M 2001 The Politics of Excellence: Behind the Nobel Prize in Science (New York: Freeman)

p 119 ff

[13] See Stuewer R 1975 The Compton Effect: Turning Point in Physics (New York: Science History Publications)

[14] Eckert M and Marker K (ed) 2004 A Sommerfeld: Wissenschaftlicher Briefwechsel vol 2 (Berlin: Diepholz)

p 144 (A Sommerfeld to N Bohr, 21 January 1923)

[15] Klein M J et al (ed) Collected Papers of Albert Einstein (CPAE) vol 5 (Princeton, NJ: Princeton University

Press) p 33 (A Einstein to C Habicht, Bern, June 1905)

[16] Renn J (ed) 2005 Einsteins Annalen Papers (Weinheim: Wiley)

1905 miraculous year

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