I have been interested in astronomy, since I was 12 years old.
I attended a boarding school from age 10 to 14.
The school had a sizable collection of minerals that stirred
my interest. Asking a teacher for literature about minerals
he told me that he had nothing suitable for a person of my age,
but that he had some books about stars that might interest me.
I began to read the books he gave to me and became more interested
in astronomy. The r taught me Kepler"s laws of planetary motion.
With his help and a considerable collection of eye glasses and cardboard
cylinders in the teacher's possession, and with his help I built my first
refractor telescope. I became sure that I wanted to become an astronomer
when I were to enter university.
University Studies
At the beginnining of the summer semester 1970 I enrolled
at the Universität Münster. It was the university closest
to my hometown and the only university in Germany where one
could choose astronomy as the major subject. Sometime during
the semester Prof. Straßl, the director of the astronomical
institute, advised me to leave and go elsewhere because the
institute as he said was too small to provide me with a decent
education. He had a point: the instiute consisted of one
professor, his assistant and one student, me.
I set out to look for an alternative, first visiting Bonn where
I rented a room right away, applied for admission to study physics
in Heidelberg and finally visited Göttingen. I got admiitted for
study in Heidelberg, but when walking through the streets of
Göttingen, I knew that this was the town where i wanted to study.
A small town, breathing history on every corner, the place where
Gauss and Hilbert had worked, one of the birthplaces of quantum
mechanics and with an astronomical observatory built during Gauss'
lifetime.
Admission in Göttongen was also restricted and the application
deadline had already passed. I consulted Prof. Kippenhahn who
engaged in theoretical astrophysics and he suggested that I start
by studiyng mathematica first and switch to physics after the
Vordiplom (approx. B.Sc.). So I did. After 3 semesters I obtained
the Vordiplom. Meanwhile I had decided that I was no longer
interested in science and began to study English literature and
history for 3 semesters. Then my love for astronomy returned and
I switched again, to physics. Under the supervision of Willi Deinzer
I investigated the generation of magnetic fields in the cores of
massive stars.
M.Sc. Thesis
In my thesis I studied the mechanism of $\alpha$-effect dynamos driven
by turbulent plasma motion, when currents flow through magnetic
fields. The sun's and the earth's magnetic fields are
generated by such dynamo action. While research thus far had focussed on
$\alpha\omega$-dynamos, where the $\alpha$-effect and differential
rotation work together to produce magnetic fields, my work showed that
the $\alpha$-effect alone was sufficient. Such a dynamo is called an
$\alpha^2$-dynamo.
An unexpected side result with a model consisting of a convecrive core
surrounded by a radiative shell behaves quite different as a function
of $\alpha$-effect strength compared to $\alpha\omega$-dynamos. An
existing field decays extremely slowly, when the effect is weak
and begins to grow when a threshold is crossed.
Thesis Title
$\alpha^2$ Dynamos in den konvektiven Kernen
massereicher Sterne
$\alpha^2$ dynmos in the convective cores of massive stars
Publication
Manfred Schüßler, Arno Pähler
Diffusion of a Strong Internal Magnetic Field
through the Radiative Envelope of a 2.25 $M_{\odot}$ star
Astron. & Astrophys. 68, 57-62 (1978)
The publication was last cited in a research paper in July 2023.
Minerals had lead me to astronomy at the age of 12.
I studied astronomy and was intent on continuing this
path. While pondering my next steps, a part-time job
changed my future forever.
A scientist, Wolfram Saenger, at the Max-Planck-Institut
für experimentelle Medizin in Göttingen, was offering
a programmer part-time position. I interviewed and was
accepted. At the end of the interview he asked me whether
I would be interested to becocme a graduate student in
his research team. Initially I declined but left the final
decision open.
Disaster in Bonn
During a party at the Sternwarte in Göttingen one of my former professors
suggested that I contact Peter Mezger at the Max-Planck-
Institut für Radioastronomie. After having arranged a visit to Bonn
I discussed my options with Mezger. At the end everything
seemed settled: I would join his department as a graduate student and
a professor in Göttingen would act as my official thesis supervisor.
Then came Mezger"s final question: "Und wovon wollen Sie leben?"
- "How do you want to cover your living expenses?".
This one question ended my astronomical career. I pointed out to him
that the Max-Planck-Gesellschaft offered grants for graduate
students. He demured, telling me that he had no money to
support me. It was likely not meant seriously: I was contacted
multiple times thereafter asking when I would move to Bonn.
I never replied but ultimately got tired and sent a reply that
I woudl never come.
I returned to Göttingen the same afternoon, talked to Saenger
and asked whether he still wanted me as a grauate student.
He said yes and from that moment on I became a protein
crystallographer, spending most of my scientific career in
that field.
Professional Activities
I have worked in research institutes, universities
and pharmaceutical companies in Germany, the USA and Japan.
Most of that time was spent in Japan, where I lived and worked
for 16 years.
Research Institutes
MPI für experimentelle Medizin, Göttingen, DE
PERI, Osaka, JP
RIKEN, Harima, JP
Universities
MIT, Cambridge, MA, US
Universität Göttingen, Göttingen, DE
Freie Universität Berlin, Berlin, DE
Columbia University, New York, NY, US
Osaka University,s Osaka, JP
Companies
Taisho Seiyaku, Ohmiya, JP
Mitsubishi Kagaku, Yokohama, JP
Syrrx, San Diegp, CA, US
Multi-wavelength Anomalous Diffraction (MAD)
The most important contibution that I made to protein
crystallography was my involvement in the development
of multi-wavelength anomalous difraction. The method was
mostly developed by W. Hendriclson and J. Smith. I made
minor contributions to the theory and was the first person
to successfully apply it, jointly with Hendrickson and
Smith, to determine an unknown structure with this technique.
It is now the standard method in the field, together with
single-wavelength anomalous diffraction.
Publication
W. A. Hendrickson, A. Pähler, J. L. Smith,
Y. Satow, E. A. Merritt, R. P. Phizackerley
Crystal structure of core streptavidin determined from
multiwavelength anomalous diffraction of synchrotron radiarion
PNAS 86, 2180-2184 (1989)
My earliest exposure to computers was at the age of 16,
when I took a correspondence course "Programming of Hollerith
Machines". They work with punched cards, switchboards and cables
to program them. The next step was learning Algol-60 in my second
semester as a mathematics student.
While I studied mathematics, I took a courseabout numerical
mathematics.The two terms I liked best were ADI for alternating
directions implicit (method) and SOR for successive
overrelaxation. Both are used to solve partial differential
equations.
One rule that we were told to always respect was: If you need
to divide more than once by the same value, calcuate the reciprocal
of that vallue and mutliply by it. That is, because even today,
division is much slower than multiplication.
Programming languages
My first "programming language" was of course switchboards and
cables. After that in 1971 Algol-60 and from 1973 Fortran and
more modern variants of Fortran. Since then I have learned a
substantial number of languages, some of which are listed
below in mostly chronological order. My favorite and almost
exclusively used language is Python. Languages that I
currently actively use are underlined..
Tools like HTML, CSS and Javascript that I use to develop
this website I do not usually employ. HTML is generated via
Pug/Jade and CSS via Stylus. The framework is Flask. The entire code
consists of Python, Pug/Jade, CSS and Javascript. HTMl is created
on the fly from Pug templates with PyPugJS. Bootstrap or Foundation
and jQuery scripts and Bootstrap or Foundation CSS are also used.
Algol-60
Fortran
Assemblers
Pascal, Modula
C / C++
Tcl / Tk
Python
Ada
Cuda, OpenCL
Julia
Algebra
Algebraic Structures
One can arrange algebraic structures by increasing gemerality. The most
commonly known structures are
Monoids
Groups
Rings
Fields
This describes a hierarchy, such that for instance groups are more general
than monoids, but have a monoid structure as well as a group structure.
Sloppily once could write
Sets are at the heart of modern mathematics. Sets are collections of
objects, such that an object's membership in a set is defined by some
predicate(s). They were formalized by Dedekind and Cantpr in the late
19th century and have become an indispensible construct of modern
mathematics.
For instance, the collection ..., -1, 0, 1, ... is the set
of all integers, written $\mathbb{Z}$. This set is a subset of rational
numbers $\mathbb{Q}$ and the rationals are called a superset of the
integers, expressed by
Operations like $\text{Union}\ \cup$ or $\text{Intersection}\ \cap$
can be performed on pairs of sets, thus creating new sets. The intersection
of two sets S and T, for instance, consiste of all objects that belong to
S as well as T.
Mappings
Mappings, together with the sets they operate on, are the second
of two buildong blocks used to define algebraic structures. A mapping
between two sets S and T can be written as
With sets and mappings between sets explained, one can proceed to define
algebraic structures. Mappings between such structures are usually called
homomorphisms when they preserve the algebraic structure of the sets they
operate on.
The basics of the structures mentioned above can be defined by a few simple
axioms. When defined they are abstract, but have far-reaching uses in
modern physics. Groups in particular are an indispensible tool in pjysics.
Together with Noether's theorem they lead to all the conservation
laws of physics, conservation of energy, linear and angular momentum and
so on.
Monoids
Monoids in general are not as familiar as the other three structures
mentioned above. Simply put, they are groups
without imverse elements. Therefore grpups are also monoids.
They consist of a set M and a mapping $\circ : M\times M\mapsto M$ with
the following properties
$$
\begin{gather}
\circ:\ M\times M\mapsto M\quad (a,\,b)\mapsto\ a\circ b\\
\forall a,\,b\in M\quad a\circ b\in M\\
a\circ(b\circ c) = (a\circ b)\circ c\\
\exists e\in M\ \forall a\in M\quad e\circ a = a\circ e = a
\end{gather}
$$
It is easy to show that the unit element e is unique along the lines
one can often find in mathematical texts:
"The proof is trivial and left as an exercise for the reader."
Monoids are not as rare as one might think. For instance, the set of
integer numbers $\mathbb{Z}$ with multiplication as the mapping is a
monoid, but not a group. On the other hand $\mathbb{Z}$ with addition
is a group.
Groups
Next in the hierrachy of algebraic structures are groups. Groups are an
extremely important structure in modern physics and can occur in
many manifestations. There are finite groups with a defined number of
elements $|G| < \infty$ and groups with an infinite number of elements.
They extend monoids by introducing an inverse.
Again it is eas to show that the inverse of every element is unique and
that $g\circ h = h\circ g$.
When $\forall a,\,b\in G\quad a\circ b = b\circ a$,
the group is called commutative or abelian. Not every group is abelian.
Examples
$\mathbb{Z}$ with adition is an infinite abelian group. The simplest
finite group may be $\{-1,\,1\}$ with multiplication. 1 is the unit element
and each element is its own inverse. Such objects are called idempotent
$a\circ a = e$. This subset of integers is the only set of integers that
forms a group under multiplication. It is not a group under addition,
because $1 + 1 = 2\notin \{-1,\,1\}$.
$2\mathbb{Z}$, the subset of even integers, is a group under addition,
but the subset of odd integers $2\mathbb{Z}+1$ is not, because the sum
of two odd integers is even. $2\mathbb{Z}$ is called a subgroup of
$\mathbb{Z}$. It is a normal subgroup defined by
Monoids and groups are sets endowed with one kind of mapping. Rings and
Fields extend the concept by introducing a second kind of mapping. In the
structures that most people are familiar with, rational, real and complex
numbers, these mappings are called addition and multiplication.
The simplest way to characterize the ring structure of a set R with
mappings + and $\times$ written as $(R, +, \times)$, is:
(R, +) is an abelian group
$\forall a,\,b,\,c\in R\,: a\times (b\times c) = (a\times b)\times c$
$\forall a,\,b,\,c\in R\,: a\times (b + c) = a\times b + a\times c$
$\forall a,\,b,\,c\in R\,: (a + b)\times c = a\times c + b\times c$
Rule 4 is necessary because (R, $\times$) need not be commutative.
An example is a ring formed by matrices that may or may not have
multiplicative inverses for some or all elements (e.g. det M = 0).
The existence of a multiplicative unit element is not required,
but also not excluded. The latter care clled rings with unity.
Hence with respect to multiplication R may be less than a monoid.
Other examples of rings are $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$,
the second one being the ubtegere modulo n. a finite ring, as the
underlying set consists of the integers from 0 to n - 1 inclusive.
In bozj cases, as already mentioned in the Group section, there are no
multiplicative inverses.
Elements $a\in R$ of a ring such that $\exists b\ne 0 \in R$ with
$a\times b = 0$ are called zero divisors. An example would be
$\mathbb{Z}/4\mathbb{Z}$, since $2\times 2 = 0$ modulo 4. More generally
any n that is the square of another number, $n = k^2\quad k\times k = 0$
modulo n.
Fields
If, additionally, a ring (R, + $\times$) under multiplication, is not just
associative, but a group, it is called a field. The additive unit element
must however be excluded from the multiplicative set, but not from the
field itself. Multiplication of any element of R with 0 is 0.
The definition of (F, +, $\times$) thus is:
F is a ring
(F \ {0}, $\times$) is an abelian group
In the hierarchy
$\mathbb{N}\subset\mathbb{Z}\subset\mathbb{Q}\subset\mathbb{R}\subset\mathbb{C}$
all of them are rings, but fields start with $\mathbb{Q}$.
A less familiar example of a field is $\mathbb{Z}/p\mathbb{Z}$, the set of
integers modulo a prime number p. 1 is always its own inverse and for p = 5
we have 2 x 3 = 3 x 2 = 4 x 4 = 1. 0 and p are not part of the multiplicative
set, 0 by definition and p because p = 0 modulo p. The number of elements in
the set is p - 1.
Special Relativity
Origin
In 1905, following the failure osf the Michelson-Morley experiment
to prove the existence of an ether as the carrier medium of light,
Albert Einstein published two seminal papers.
The first introduced the concept of photons to explain the photoelectric
effect. This paper earned him the 1921 Nobel prize in physics.
The second paper, "Zur Elektrodynamik bewegter Körper" established the
theory of special relativity.
Underlying it is the concept of inertial frames of reference. Two objects
moving relative to each other and each having attached a local frame of
reference (coordinte system).
Inertial frames of reference are those
moving with constant velocity. Zhey neither change their speed nor their
direction of motion.
Two Principles of SR
No object can move faster than the speed of light in vacuum.
The laws of physics are the same in all inertial reference frames.
Gravitation has no place in this theory. That comes later with GR.
The consequences nevertheless are profound. The relation between
two inertial frames is described by the Lorentz transform. Time and
space are both parts of a 4-dimensional spacetime. Effects like time
dilation and length contraction, increase of mass-weight with
increasing speed, the equivalence of mass and energy. These are all
effects that have been experimentally confirmed, most dramatically
$E = m\,c^2$ in nuclear weapons, for instance hydrogen bombs, as the
difference $4\times m_H - m_{He} > 0$ is converted into energy.
The same process takes place inside stars like the the sun, making life
on earth possible.
Spacetime and Lorentz Transform
Space and time do not exist as separate entities, but jointly form a
4-dimension space, named spacetime. Its coordinates are
Given one inertial frame of reference with coordinates $\vec{x'}$ and
another one with coordinates $\vec{x}$ and constant inter-frame velocity
$\vec{\beta} = c^{-1}\vec{v}$ and with the Lorentz factor defined as
$\gamma = (1 - \vec{\beta}\cdot\vec{\beta})^{-1/2}$ the Lorentz transform
is defined by
In the equations $\vec{X} = (x,\,y,\,z)$ is the spatial component
of $\vec{x}$ In the literature one may find equations, where the x-axis
is chosen parallel to the direction of motion. The component of $\vec{X}$
normal to the direction of motion remains unchanged.
Boost and Rotation
.h4tag.sp1.
The transform shown above is only one part of the full Lorentz transform.
It is called the Lorentz boost and is complemented by a
rotation about an axis which need not conincide with $\vec{\beta}$, but
usually lies in the 3-dimensional subspace formed by the spatial
component. Mathematically nothing would exclude a rotation about the
"time" axis.
.h4tag.sp1.
The inverse transform is easily obtained by simply inverting the direction
of $\beta$, $\vec{\beta'} = -\vec{\beta}$. The two effects following directly
from the transform are
time dilation
length contraction
The equivalence of mass and energy $E = m_0\,c^2$ follows from the concept
of four-vectors and the expansion of $\gamma$ in a power series in
$\beta = \sqrt{\vec{\beta}^2}$.
The first term in the expansion $E_0 = \gamma(\beta = 0)\,E = m_0\,c^2$
ist the "rest" energy, that an object with $m > 0$ has, when it is not
moving. The second term $m_0\,c^2\,\beta^2 / 2 = m_0\,v^2 / 2$ is the
classical kinetic energy. Higher-order terms would bes undetectable
in most laboratory settings, but high.energy particle physics with
particle velocities appoaching c do indeed measure an increas of mass
as a function of velocity.
All these efects of course only exist for the oberver at rest relative
to the moving particle. For the particle itself, in its reference frame,
nothing changes. Instead, if it could observe the observer, it would
assign the same effects to her or him. In the paricle's frame the
particle is at rest and the observer is moving.
Minkowski Space
The mathematical structure of spacetime was first explained in some detail
in a talk that Hermann Minkowski gave 1908 in Göttingen.
He described the nature of spacetime and its associated metric. They are
now known as Minkowski space and the Minkowski metric.
Expressed by a a rank-2 mmetric tensor $\eta$ and co- and contravariant
rank 1 tensors the relations are
This describes a flat hyperbolic space. There are two signature
conventions, the one above, sometimes called the East Coast
convention and the West Coast convention. The naming refers to the
prevalence of usage at academic institutions on the east and west coast
of the USA.
The west coast convention was introduced by Hermann Weyl in his
1919 book "Raum, Zeit, Materie" about general relativity. He set
$x^0 = i\,c\,t$ as an imaginary number. Calculating a conventional
$L_2$ norm produces the minus sign for the 0-component.
Laplace and d'Alembert Operators
The Laplace operator in $\mathbb{R}^3$ is defined as
$\Delta = \nabla^2 = \sum_{i=1}^3\,\partial_i\,\partial^i$.
It constitutes the spece part of the d'Alembert operator which is its
equivalent for spacetime and was known long before Minkowski
introduced the concept of spaceatime. The d'Alambert operator is
defined as
The quantization $E\to\mathrm{i}\,\hbar\,c\,\partial_0$ and
$\vec{p}\to -\mathrm{i}\,\hbar\,\nabla$, with $E_m = m_0\,c^2$ leads
to the inhomogenous Klein-Gordon equation
The d'Alembert operator can thus be viewed as the quantization
of the momentum (or energy) four-vector.
Fourier Components
The homogenous Klein-Gordon equation $\square\,\psi = 0$ is hyperbolic,
the four-version of the Laplace equation, and describes a wave with the
solution $A\,e^{\mathrm{i}\,(\omega\,t - \vec{k}\cdot\vec{x})}$amd, with
$a = \ln\,A$ and $z = a + \mathrm{i}\,(\omega\,t - \vec{k}\cdot\vec{x})$,
can be written as $e^z$..
Conventional Fourier components involve frequency $\omega$, time t, wave
vector $\vec{k} = \vec{p}\,/\,\hbar$ and spatial vector $\vec{x}$ in the
combination $\omega\,t - \vec{k}\cdot\vec{x}$.
Defining $E_\omega = \hbar\,\omega$ and
$\vec{E}_p = c\,\vec{p}\ $ one obtains
Here $\{E^\mu\} = \{E_\omega,\,\vec{E}_p\}$ is the four-energy
(equivalent to four-momentum) and $\{x^\nu\} = \{c\,t,\,\vec{x}\}$
is the Minkowski spacetime coordinate. In SI units both numerator
and demominator have dimenion $J\,m$. and the fraction, as it should,
is dimensionless.
