## Introduction

#### Scope of the present volume

This volume presents Einstein's 49 contributions to *Annalen der Physik*, together with four introductory
essays based on recent historical studies. The first three essays, by David Cassidy, Jürgen Renn, and Robert
Rynasiewicz, discuss key aspects of the scientific revolution triggered by the pathbreaking papers of Einstein's
*annus mirabilis* 1905, which changed our understanding of space, time, matter, and radiation.Various
ramifications of these papers are worked out in Einstein's subsequent contributions to the *Annalen*. These
papers document Einstein's further exploration of the quantum hypothesis and the triumphs of statistical
physics as well as various stages of Einstein's journey from special to general relativity. General relativity
is the subject of the fourth historical essay, by Michel Janssen.

The earliest contributions were written just after Einstein graduated with a teacher's diploma from the
Swiss Federal Polytechnic School in Zurich; the latest while Einstein was working in Berlin as a member
of the Prussian Academy of Sciences and as director of the Kaiser-Wilhelm Institute of Physics. The rise
of Nazism in Germany put an end to this glorious period of the history of science. Einstein was forced to
emigrate from Germany in 1933 and was never to return again. This volume, published in the centenary of
Einstein's *annus mirabilis*, offers the reader a comprehensive overview of the breathtaking scope and depth
of the investigations of the towering figure of 20^{th}-century physics, focusing on his most productive years.
The dramatically changing historical circumstances under which these papers were written may also serve
as a reminder of the fragility of the scientific enterprise and the need both to reflect on its contexts and to
strengthen it by civil courage, just as Einstein has taught us.

#### 1 Foundation and role of the *Annalen*

The *Annalen der Physik*, one of the most influential journals in the history of physics, was founded in 1790
by Friedrich Albert Carl Gren, a professor of physics and chemistry at Halle University. As is described
in the masterful account of the rise of theoretical physics by Christa Jungnickel and Russel McCormmach
(*Intellectual Mastery of Nature*, University of Chicago Press), the original mission of the *Annalen* was to
familiarize its German-speaking readership with the results of investigations pertaining to the mathematical
and chemical parts of the theory of nature, including reports from other journals, foreign as well as German.
From the outset, the spirit of the journal was international and integrative and continued to be so under the
subsequent editors, in particular Ludwig Wilhelm Gilbert and Johann Christian Poggendorff, who succeeded
in turning it into a principal point of reference for the German-speaking scientific community in physics
and chemistry, which included not only university professors, but also teachers, doctors, and apothecaries.

Original contributions published in the *Annalen* were soon translated or reported in foreign journals.
In spite of the rising specialization, the editors paid close attention to the interconnections between the
broad variety of subjects treated in the articles. While the emphasis was on experimental work, the rising
significance of theoretical contributions was acknowledged as well. The wide distribution of the *Annalen*,
whichwas available not only in university libraries, but also in secondary and technical schools, furthered the
formation of a broadly accessible scientific culture. Accordingly, the *Annalen* remained open to contributions
not only from established physicists and institute directors, but also to articles submitted by students,
assistants, and teachers. Its role as an intellectual reference point was reinforced by the foundation of the
*Beiblätter*, which offered brief reports on work not published in the *Annalen*.

The subjects treated in the *Annalen* over the years reflect the development of research in 19th century
physics and chemistry. Under the editorship of Gustav Wiedemann, who took office after Poggendorff's
death in 1877, the broad perspective of the journal was maintained and occasionally even included articles
on the history of science. All in all, the journal was transformed into a means of communication oriented
towards the increasingly professionalized community of physicists. Yet the growing hints at the existence
and relevance of a microworld of atoms and molecules for the understanding of nature kept alive the promise
of unity in the dispersive multitude of results published in the *Annalen*.

#### The *Annalen* as food for thought

This was roughly the situation when the young Einstein began to avidly study the *Annalen*, which had been
edited since 1900 by Paul Drude. Drude's work on an atomistic theory of conduction in metals was of
special interest to Einstein and the precocious young student even entered into a controversy with Drude.

Einstein's originality is often attributed to his autodidactic training. But the possibility to learn independently
obviously very much depends on the availability of appropriate reading material. Although
academically isolated, it was the *Annalen* that offered Einstein an up-to-date overview of contemporary
physics, stimulating many of the original ideas he pursued during his student days and his time at the Swiss
patent office in Bern. His contemporary correspondence suggests that he often believed he just had to put
the pieces of a puzzle together in order to achieve a breakthrough, pieces he often found in papers he read
in the *Annalen*.

Apart from Drude's work on the electron theory of metals, which eventually stimulated Einstein's development
of statistical mechanics, he also read Max Planck's work on black-body radiation and Philipp
Lenard's studies of the photoelectric effect, which triggered his work on the light quantum hypothesis. Also
Wien's report on the problematic attempts to detect the translatory motion of the ether offered an important
stepping stone towards the rejection of the ether and the formulation of the special theory of relativity.

#### The *Annalen* as a source of income

The *Annalen* also served as a source of modest additional income for Einstein, who wrote more than twenty
reports for its *Beiblätter* - mainly on the theory of heat - thus demonstrating an impressive mastery of the
contemporary literature. This activity started in 1905 and probably resulted from his earlier publications in
the *Annalen* in this field. Going by his publications between 1900 and early 1905, one would conclude that
Einstein's specialty was thermodynamics.

#### Beginners' papers

The collection begins with what Einstein later designated his two "worthless beginners' papers," one on
capillarity published in early 1901 and the other on dilute salt solutions published in 1902. Both are dedicated
to an investigation of the nature of molecular forces through the effect of such forces on phenomena in liquids,
a subject Einstein also planned to investigate for his dissertation, a plan he then abandoned.

His early exploration of a molecular theory of solutions nevertheless helped shape many of the techniques
used in the dissertation he did complete in 1905. It dealt with the determination of molecular dimensions.
It was published in the *Annalen* in 1906 and is included in this collection. The investigations documented
by Einstein's first papers also provided a motivation for generalizing the methods of the kinetic theory, and
for establishing statistical mechanics independently from Josiah Gibbs.

#### Statistical mechanics

The pivotal role of statistical mechanics in Einstein's early work is clearly visible in this collection. While
its development was obviously driven by his early atomistic speculations, the statistical framework he
established between 1902 and 1904 provided the backbone for his papers on the light quantum and on
Brownian motion of 1905. It pointed to the crucial role of fluctuations in discerning the non-classical
character of heat radiation, and revealed atomic dimensions in his analysis of Brownian motion.

#### The *annus mirabilis* 1905

Without detracting from the singularity of Einstein's 1905 papers in the history of science, this collection
may help to frame these contributions in the context of his intellectual development, as is discussed in
the historical essays opening this volume. The 1905 papers deal with subjects as diverse as heat radiation,
Brownian motion, and the electrodynamics of moving bodies. How were these topics related in Einstein's
mind? In viewof his earlier publication record and of insights gained from his contemporary correspondence,
it seems plausible to assume that one unifying theme goes back to Einstein's early pursuit of atomistic ideas,
which includes both the quest for evidence for the existence of atoms and speculative ideas such as that of
a corpuscular constitution of light.

Later these speculations turned into the exploration of the limits of classical physics, as Einstein encountered
them when critically reading the *Annalen*. His perception of these limits was sharpened by the
philosophical acumen he had developed through his reading of authors such as Hume, Kant, Mach, and
Poincaré. All three of the revolutions that Einstein initiated in 1905 originated from problems at the borders
between the major conceptual domains of classical physics; mechanics, electrodynamics, and thermodynamics.
Special relativity emerged from the electrodynamics of moving bodies, an area at the intersection
of electrodynamics and mechanics; the light quantum hypothesis can be seen as an attempt to cope with
the problem of heat radiation, a problem at the intersection of electrodynamics and thermodynamics; while
Einstein's work on Brownian motion deals with a borderline problem of mechanics and thermodynamics.

The year 1905 was just the beginning of Einstein's career and of the scientific revolution triggered by his
pathbreaking contributions. This becomes evident from his own subsequent publications, which show that
Einstein's contributions should not be seen a series of isolated achievements, but as integrated in a lively
scientific context, involving collaborative efforts and discussions - polemics even - with his colleagues.

#### Electrodynamics in moving media

Einstein's 1908 paper with Jakob Laub on the electrodynamics of moving media was, for instance, a direct
continuation of his 1905 work on the electrodynamics of moving bodies, which focused on microscopic
electron theory, extending it, following prior work by Minkowski, to the macroscopic theory of electromagnetic
and optical phenomena in polarizable and magnetizable material media in motion. It was in this
context that Einstein was first confronted with the four-dimensional spacetime formalism developed by
Minkowski. In their own work, Einstein and Laub avoided this formalism, the value of which Einstein only
gradually learned to appreciate.

#### Specific heats

The present collection also documents Einstein's early efforts to further explore the consequences of his
revolutionary interpretation of Planck's formula for black-body radiation as hinting at a non-classical foundation
of physics. Such an exploration was needed all the more since Einstein's interpretation - in particular
the light quantum hypothesis - met, in contrast to his other 1905 achievements, with little sympathy from
his established colleagues.

A first milestone of this exploration was Einstein's 1907 paper on the specific heat of solid bodies, which
exploited the insight into the non-classical behavior of atomic oscillators for a new understanding of the
thermal properties of solid bodies, in particular at lower temperatures. The experimental confirmation in
Nernst's laboratory of the prediction of the decrease of specific heats with temperature turned out to be
crucial for Einstein's career and his eventual move to Berlin in 1914.

#### Elastic behavior of solids

This line of research is continued in a paper of 1911 about the relation between molecular vibrations and
optical wavelengths in the infrared region, which exploits the connection that Einstein had established between
molecular vibrations and specific heats. He thus succeeded in propagating the quantum discontinuity
from its original locus in radiation theory to yet another range of physical phenomena, identifying, very
much in the vein of his early atomistic speculations, a link between the thermal and mechanical properties
of a solid.

#### Collaboration with Hopf

Planck and others remained skeptical of Einstein's claim that a newradiation theorywas required. Challenged
by this skepticism, Einstein in 1910 published two papers together with Ludwig Hopf on the statistical
properties of the radiation field. Their main purpose was to provide support for the claim that classical
radiation theory leads to unacceptable implications for heat radiation and that Planck's radiation formula
does imply a break with classical physics.

#### Critical opalescence

Einstein's 1910work on critical opalescencewas both a direct continuation of his earlierwork on fluctuations
and a reaction to a contemporary issue raised by the Polish physicist, Marian von Smoluchowski, who in
1905 had analyzed independently from Einstein the statistical properties of Brownian motion. In 1908
Smoluchowski published a paper on critical opalescence in the *Annalen*, which dealt with the optical effects
occurring near the critical point of a gas and near the critical point of a binary mixture of liquids. In his
paper, Einstein provided a quantitative derivation of the effect from a treatment of density fluctuations. His
key insight was that both critical opalescence and the blue color of the sky can be explained with the help
of such density fluctuations, which originate from the atomistic constitution of matter.

#### Photochemical equivalence law

Another contribution illustrating Einstein's attempts to explore the quantum hypothesis at a time when he
had already begun to despair about ever capturing it in a coherent theory is his influential 1912 paper about
the photochemical equivalence law, the beginning of a line of research that would lead him in 1916 to his
ground-breaking rederivation of Planck's law based on the concepts of spontaneous and induced emission.

#### Zero-point energy

The 1913 paper by Einstein and Otto Stern also testifies to the early struggle to understand the status of
Planck's radiation law and its implications for applying the quantum hypothesis to the atomistic conception
of matter. Einstein and Stern attempted to develop a quantum theory of rotating diatomic molecules, which
show that the notion of zero-point energy - first introduced by Planck in his "second quantum theory" -
could be used to interpret measurements of the specific heat of hydrogen at low temperatures. But Einstein
soon became skeptical of some of the arguments in this paper and considered zero-point energy, as he put
it in a letter to his friend Paul Ehrenfest, "as dead as a doornail."

#### Light deflection

While ever more desperate about the quantum, Einstein became increasingly involved with the idea of
formulating a relativistic field theory of gravitation, modeled on electromagnetic field theory. As early as
1907, whileworking on a reviewof special relativity, he had realized that, if such a theory were to incorporate
Galileo's principle that all bodies fall with the same acceleration, it would require yet another fundamental
revision of our concepts of space and time. This led Einstein to formulate his famous equivalence principle,
by which gravitation and inertia ultimately became as intertwined as the electric and the magnetic field in
the first relativity revolution.

This collection contains some of the early papers marking Einstein's path from special to general relativity
such as his 1911 paper predicting the deflection of light by the gravitational field of the sun.

#### Static gravitational fields

The collection also includes a number of papers illustrating some of the heuristic strategies Einstein adopted
as well as some of the obstacles he had to overcome in his search for a relativistic field theory of gravitation.
As documented by the papers in this volume, he started in 1912 by treating the special case of a static
gravitational field with the help of the equivalence principle, which allowed him to use knowledge about
acceleration in the absence of gravity to draw conclusions about physical effects in the presence of a
gravitational field.

While making impressive advances in this way, such as the prediction of light deflection and his recognition
of the need for non-Euclidean geometry, these early successes consolidated a framework of expectations
rooted in classical physics, many of which had to be abandoned or seriously modified before general relativity
could be established.

#### Controversy with Abraham

One can argue that, unlike special relativity, general relativity was essentially the achievement of a single
man. As a matter of fact, most of Einstein's established colleagues were skeptical about his attempt to build
a new theory of gravitation on the idea of curved spacetime described by a ten-component metric tensor
rather than the familiar scalar potential of Newton's theory.

It is important to realize, however, that Einstein was not only supported by some friends and collaborators
such as his Swiss companions Marcel Grossmann and Michele Besso and by the astronomer Erwin
Freundlich, but that he also had to face competitors and opponents who provided his endeavor with a scientific
context that was crucial for the emergence of general relativity. It was Max Abraham, for instance,
and not Einstein, who first formulated a comprehensive gravitational field theory in 1912, thus challenging
Einstein to integrate his own considerations based on the equivalence principle into a coherent theory as
well. Our collection contains the papers resulting from these efforts while offering some glimpses of the
heated controversy in which this early competition resulted.

#### Nordström's special relativistic theory of gravitation

While Einstein was initially convinced that the problem of gravitation could not successfully be addressed
within the framework of special relativity,Abraham's failed attempt to provide such a theorywas followed by
a more convincing theory developed by Gunnar Nordströmin the years between 1912 and 1913. Nordström's
theory was a serious competitor of nascent general relativity. It might well have become the dominating
relativistic theory of gravitation for some time had it not been for Einstein's philosophically motivated
quest to combine such a theory with the attempt to generalize the principle of relativity. This collection
features a paper resulting from a collaboration with Adriaan Fokker and showing how Nordström's theory
can be reformulated in terms of the absolute differential calculus, the mathematical language Einstein had
adopted in his own search for a field theory of gravitation. In this way, it became possible to compare the
two approaches more directly and to reveal the assumptions underlying Nordström's theory. At the same
time it suggested that Nordström's theory, like Einstein's, went beyond special relativity and would likewise
involve curved space-time.

#### Foundations of general relativity

It took Einstein eight years, from 1907 to 1915, to attain his goal of a relativistic field theory of gravitation
that preserved both the heritage of mechanics and that of field theory. The drama of this struggle with the
conceptual foundations of classical and special relativistic physics is documented by Einstein's research
manuscripts, by his correspondence, by several intermediary publications, and in particular by the famous
sequence of communications to the Prussian Academy of November 1915.

A comprehensive reconstruction of this drama including key sources appears elsewhere (The Genesis
of General Relativity, Kluwer Academic Publishers, edited by J. Renn). The present collection features the
outcome of this quest - the general theory of relativity - in the form of Einstein's first masterful exposition
of the finished theory in his famous 1916 contribution to the *Annalen*. This paper bears clear traces of the
gestation period of the theory, as is demonstrated in the historical essay of Michel Janssen.

#### Cosmology

Einstein's subsequent work on general relativity is no longer extensively documented in the *Annalen*. As
a newly minted member of the Prussian Academy in Berlin, his outlet of choice in this period are the
Academy's own *Sitzungsberichte*. Both the four celebrated papers of November 1915 documenting the final
breakthrough in Einstein's search for a relativistic field theory of gravity and the famous paper on cosmology
of 1917 appeared in the *Sitzungsberichte*. This volume, however, does contain a short but important paper of
1918 on the foundations of general relativity, in which Einstein formally introduced what he called "Mach's
Principle," the requirement that matter fully determines the metric field. The volume ends with a short paper
of 1922 providing at least a hint at the fate of general relativity, which was subsequently turned from a
philosophically motivated integration of the classical knowledge about gravitation with the kinematics of
relativity into the theoretical foundation of modern cosmology describing an expanding universe. In this
1922 paper, Einstein reacted to a proposal by Franz Selety for resolving Einstein's objections to Newtonian
cosmology of 1917 by what he called a "hierarchical molecular world." Einstein rejected this proposal
because it did not, in his view, comply with Mach's principle. He also rejected the interpretation of the spiral
nebulae as galaxies similar to our own milky way, referring to the evidence of contemporary observations.
The cosmological mission of general relativity was yet to be accomplished.

#### Perspective

The present collection offers a first entry point into Einstein's work, which is being published comprehensively
in an annotated documentary edition by the *Collected Papers of Albert Einstein* (Princeton University
Press). Here the reader will find more extensive commentaries and annotations that offer insights into the
genesis and historical context of Einstein's papers. In line with Einstein's legacy and spirit of broadly
sharing scientific knowledge, the Editor-in-Chief of the *Annalen*, Ulrich Eckern, and WILEY-VCH have
consented, in agreement with the Albert Einstein Archives at the Hebrew University Jerusalem and the
*Collected Papers*, and in collaboration with the Max Planck Society, to make the papers in this collection
freely accessible on the Internet.

Acknowledgements I would like to thank Lindy Divarci for her role as editorial assistant in the preparation of this
volume.

Jürgen Renn (Berlin)

This text is taken from "*Einstein’s Annalen Papers*", WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2005