Growing Up a Physicist
Physics focussed short autobiography of Dr Harvey A Cohen
I grew up in Coogee a seaside suburb of Sydney.
My father, Raymond Cohen, B.E., a civil engineer with the NSW State Railway system, had gained a Sydney University
Exhibition  which paid his University fees. Home boasted encyclopaedias,
and science oriented books for the young such as Lively Things for Lively Youngsters.
Selected in year 5 and 6 to attend the Opportunity Class at Woolahra Primary
for high IQ children then went to the Sydney (Boys) High School (SHS).
This school in that era was highly selective, drawing students from about half the area
of Sydney. Strongest memories are from High School Years 4 and 5 (Y10 and Y11)
when I was given keys to the Chemistry Lab, and was free to extend the scope of Physics Experiments.
I set up an Atwood Machine
 essentially a pulley system  in the middle of a staircase so that the weights desended and ascended
up and down the shaft, crashing to the basement with a great whoosh. [ Not appreciated
by teachers in adjoining classrooms  but my behaviour was tolerated as an elite student. ] In maths in Y11
I was not permitted to attend class  as I had an annoying habit of putting
up my hand after the teacher, Mr (Jim) Hamnett, had explained a point to the class, of offering a more succint explanation
or better proof.
My mother, rather more than my father, was very disappointed that after attending SHS I did not go to University to study Medicine,
as did her brothers Sam and Henry Pearlman (both medical specialists), but enrolled in Engineering.
At Sydney University I encountered Ms
Phyllis Nichols, who had been a tutor to my father, and after so many years had just then risen to Lectureship
status.
Many years before Nicolls, with professor Booth, had compiled a massive book of mechanics problems,
which undoubtedly influenced my grasp of qualitative physics. In the text,
Booth and Nichols, there are questions as to
How a Falling Cat Rights itself
In that period all second year engineering students
had a bridge design project. I can recall watching my old school (SHS)
competing in a rowing regatta on the Nepean River, Penrith,
and visualising the girder stresses as a flow (of momentum)
through a bridge that spanned the river over the rowing course.
At the University of Sydney having completed second year
electrical engineering, I could transfer
to the Science Faculty.
I was uncertain as to whether to proceed to an honours year in mathematics or physics.
But having gained a CSIRO Junior Postgraduate Award of £600 earmarked
for physics, that in fact was my major.
I lead a rather full life at the University, as office bearer in various societies.
I revived a then inactive student Physics Society, holding regular campus lunch hour lectures,
featuring such physics notables as laser/maser pioneer Dr Gilbert Chandler of the CSIRO.
I also organised tours to the various CSIRO Radiophysics field stations about Sydney,
and one memorable physics oriented tour to Canberra.
My PhD on computational methods in quantum electrodynamics is being covered elsewhere.
Following a postdoc at the University of Adelaide I became a senior lecturer at La Trobe University
originally in Mathematics
and later in Computer Science. My experiences of teaching undergraduate
mechanics during my early years at La Trobe lead to the collection of protocols of “loudthinking” student efforts in qualitative physics.
This lead me to devise what I termed "dragons" qualitative physics puzzles which naive physics students invariably
failed to correctly solve. Arguing with physics tyros gently failed to nudge their conclusion,
though an actual demonstraton of physical reality with yoyo, bike or whatever
would be shattering. More mature students and some professionals could either solve or at least
be nudged to recognise that
their original solution was faulty. And through discussion of powerful ideas  heuristics  could improve.
Thus in answer to the question
Which direction will YoYo roll ?
Initially I attempted to explain solving problems in qualitatve mechanics in terms of
the application of socalled mathematical models to a physical world scenario.
But I found that it wasn't the case that difficulties arose in adapting packaged models.
Some powerful ideas aka heuristics applied or malapplied lead to difficulties.
Thus for the YoYo puzzle above  students could agree to the verbal formula
"That things Go the Way They are pulled (or pushed) and hence the YoYo must roll to the right ( in both cases )
yet also perceive the YoYo as having a central axis about which it turned
with the applied string tension supplying an anticlockwise turning "force" (actually a torque)
suggesting that the YoYo would turn anticlockwise and so would roll to the left when
cord
lower than the YoYo's axis..
Some exposed to the model that wheels turn about their point of contact (on the ground)
could predict thereby clockwise rotation about the ground contact point,
yet be otherwise quite nonplussed by the situation, and could readily agree with
the nonphysical possibilty.
In the illustrated compilation A Dragon Hunter's Box
various talking (dragon!) heads voice these ( and other ) suggestions and antisuggestions
to naive forays onto YoYo
Amongst the set of qualiative problems that I devised 19713
all of which I termed Dragons
I found a powerful analogy between some of these Dragons and the monsters
of Imre Lakatos in his hallmark papers entitled Proofs and Refutations.
which had appeared in four parts in the
British Journal for the Philosophy of Science 196364. [ Discussed further
here. ]
An illustrated collection of graphically illustrated Dragons,
the Dragon Hunter's Box, published in December 1973,
served to introduce my nascent ideas to the MIT AI community.
At MIT, leading researchers Marvin Minsky ( the first author of a paper with
title including artificial intelligence )
and Seymour Papert (renowned author of Mindstorms
saw the development of qualitative physics within an AI framework
as vital for the field of Artificial Intelligence. I was offered
a role as Consultant to the LOGO Group, lead by Papert,
within the MIT Artificial Intelligence Laboratory
Seymour Papert, a maths PhD,
had been a researcher linked to Piaget in Geneva,
and in fact some of Piaget and Inhelders doctoral students were visitors
at the LOGO Group during my 1974 stay there.
Thus I had extensive exposure to Piaget's methodology,
and could see close relationship between my Dragons and Monsters, and Piagetial puzzles  especially those related to the Child's Conception of
Quantity, such as the Pepsi Game:


 Q: Which height will Pepsi be if poured from this beaker into that ?
A (fouryear old) The same
A (six year old) The same
The Pepsi is poured confirming predictions. Again:
Q: Which height will Pepsi be if poured into this (narrow) vessel?
A (fouryear old) The same of course
A (six year old) Higher of course

In MIT sometimes on the same day I observed the conduct of
Piagetian interviews with children
while collecting further records
of expert/nonexpert attempts to solve my Dragons.
On one remarkable day, a rather bright 4 year old,
explained the unexpected outcome of the Pepsi Game, by saying "The Sides are pushing it up"
while moving his flattened hands together as he spoke.
Clearly this child had invoked a fictitious intermediate state where the Pepsi was
poured into a tall beaker of identical diameter to the beaker,
which was then transformed as he
moved his flattened hands together.
The same day  having alerted a MIT professor that his solution to the
Milko dragon was the canonical false one  he conceived
of a milk bottle with tiltable sides  which
moved with his hands  making the same gesture as the child.
At the MIT AI Lab
I encountered
Minsky's Frames concept for the
organization of knowledge whilst putting together my
research on qualitative physics problem solving, which I incorporated into
MIT Memo 338. When I returned to Australia in 1975,
the original MIT Memo 338 was
further elaborated to become the (downloadable)
The Art of Snaring Dragons.
Back in Australia
I conceived the educational robotics project
OZNAKI
inspired by LOGO. Unlike MIT LOGO,
OZNAKI was to be microcomputer based.
With R.S. Francis
developed microprocessor software development scheme highlighted in
IEEE Computerin 1979.
Wuth the marketing by Votrax of the first speech chip in 1981 I was able to
develop an early Talking Communicator for severely disabled nonspeech children.

PhD
ANU

Harvey Alan Cohen, Dispersion Theoretic Approach to Graph Theories of Charged Particles of Spin 0, 1/2, 1
, Instute of Advanced Study, Australian National University, May 1965.
Chapter 2
A New Approach to Calculations in the Quantum Field Theory of Charged particles
opens as follows: The calculations we perform in subsequent chapters comprise the first exposition of quantum electrodynamics
that does not involve the concept of renormalisation and yet does not reject graph theory.
Two principles guide us:
Principle A asserts the validity of the dispersion relations appropriate to the
quantities to be calculated, some of these DR being well known, others postulated by us for the first time. This principle is used to help us ascertain the graph
elements for new theories as well as providing our basic computational device.
Principle B asserts the correctness of the wellknown graph elements for Dirac spin 1/2, scalar spin zero,
and 5x5 β spin zero,
and prescribes that as much of Lagrangian formalism and DysonWick procedures as seem substantive be utilised
to determine the graph elements for previously unconsidered theories.

Published Papers on Theoretical and Mathematical Physics

1967

H. A. Cohen,
Covariant Wave Equations for Charged Particles
of Higher Spin in an Arbitrary Gravitational Field,
Il Nuovo Cimento, Serie X, Vol 52A, 1967 pp 12421253
Summary It is known that special difficulties are encountered in devising a wave equation to describe higher spin S≥3/2
particles in interaction with the electromagnetic field,
and Buchdahl has shown that like
difficulties arise when the gravitational field is introduced. We show
that just as a consistent electromagnetic interaction can be introduced,
so wave equations describing charged particles of spin S = 3/2 and of spin S = 2 in a universe endowed with a Riemannian metric can be devised.
The paper incorporates an account of Dirac γ matrices in general relativity.
RIASSUNTO (*)
È noto che sorgono pa ri ieolari difficoltà quando si vuole impostare un'equazione d'onda che descriva particelle di spin superiore o uguale a interagenti con un campo elettromagnetico, e Buchdahl ha mostrato come simili difficoltà sorgano anche quando si introduce un campo gravitazionale. In questo articolo si fa vedere che come si può introdurre una interazione elettromagnetica coerente, così si possano trovare equazioni d'onda descriventi particelle cariche di spin S 2 o S= 2 in un universo dotato di metrica Riemanniana. Nell'articolo si includono considerazioni sulle matrici y di Dirac in relatività generale.
(*) Traduzione a cura della Redazione.
The most recent citation of this 1967 publication is the following paper
in General Relativity and Quantum Cosmology:
Harold Erbin, Vincent Lahoche, Universality of tunnelling particles in Hawking radiation
arXiv:1708.00661 [grqc] Submitted Wed, 2 Aug 2017

1967

H. A. Cohen^{*} and J. Smith^{**},
The CConserving Decay Modes η → π^{0}e^{+}e^{} and
η → π^{0}μ^{+}μ^{}
* Mathematical Physics, University of Adelaide
** Institute for Theoretical Physics, State University of New York at Stony Brook
The Cconserving decay rate for η → π^{0}μ^{+}μ^{}
is of second order in the fine structure constant. A knowlege of the matrix elements
η →γγ and γγ → e^{+}e^{}
is sufficient to find the imaginary part of the matrix element
η → π^{0}μ^{+}μ^{}
from unitarity. The real part of the matrix element can be found from dispersion relations.
Recent theoretical estimates ^{(1)} of the decay rate for
η → π^{0}e^{+}e^{}
have assumed an interaction
ηπ^{0}F_{μν}F_{μν}
for the
ηπ^{0}γγ amplitude.^{(2)}
However, this interaction leads to the result that the decay rate into one π^{0}
is proportional to the square of the mass of the leptons. The rate is therefore much larger for muons^{(3)}
than for electrons, whereas the contrary conclusion is reached using the simple phase space argument. (which supposes
a constant matrix element).
One way to modify this result is to note that the Cconserving decay amplitude is
decomposible into two invariant amplitudes:
the first corresponding precisely to the Swave interaction given above and the second
to the Pwave interaction included in
ηπ^{0}P_{α}P_{β}F_{αμ}F_{βμ}
where P is the η four momentum. In this paper we
adopt the second interaction leading to a calculation that is parallel
to the calculation^{(3)} by the second author
based on the first interaction. We calculate both the
η → π^{0}e^{+}e^{} and
η → π^{0}μ^{+}μ^{}
decay rates

1968

H. A. Cohen,
Vacuum polarization in the Lee and Yang theory of charged spin one
,
Il Nuovo Cimento A Series 10
21 Luglio 1968, Volume 56, Issue 2, pp 467478
Summary:
The radiative correction, to ordere 2, to the photon propagator in the Lee and Yang theory of charged spinone bosons, is calculated in a dispersiontheoretic manner.
Some general aspects of the ξlimiting formalism are
discussed. A useful matrix treatment of Lorentz tensors is
presented in an Appendix.
Riassunto
Calcoliamo, servendoci della teoria della dispersione,
la correzione radiativa, di ordinee 2, al propagatore
fotonico nella teoria di Lee ed Yang dei bosoni di spin
uno carichi. Si discutono alcuni aspetti generali del
formalismo ξlimitante. In un appendice si presenta un
utile trattamento matriciale dei tensori di Lorentz.
HINDSIGHT: The DysonWick formalism that produced a manageable theory of elementary
charged particles of spin 1/2 and zero spin simply failed to handle spin one QED.
Lee and Yang attempted to develop a quantum electrodynamics of charged spin one
by introducing a ξlimiting formalism. Although no actual
values were determined for this most speculative spin1 QED, Lee and Yang proclaimed that their novel theory worked.
In this paper I showed this ws bsolutely false: I used the Cutkosky approach to finding the (finite)
discontinuities across the branch cuts in the complex momentum plane
for substitution in the relevant dispersion relation.
Contrary to Lee and Yang's claims of adequacy  these integrals  unlike those for spin zero and spin 1/2,
simply diverged and the ξlimiting process did not remove the infinities.

1969

A.J. Bracken and H. A. Cohen,
Five Classes of Transformations of Dirac Spinors
— The FreeParticle Dirac Equation Is Brought to “p_{0}, “p_{1}, “p_{2}, “p_{3} and “mLinear” Forms —,
Progress of Theoretical Physics, Vol 26, No 1, 1969, pp 816831.
Abstract:
The freeparticle Dirac equation has two remarkable features: (1) It
is linear in all four components of the energymomentum p_{μ}, and also in the mass m.
(2) For its solutions there are five distinct simple modes of the invariant scalar product
in the momentum representation. In this paper, a theorem presented by Case is generalized
and used to obtain five classes of transformations of the Dirac equation. Every transformation in a given class has two properties characteristic of the class: (1) The linearity in a corresponding one of the five quantities pµ, m is maintained in the transformed equation. (In this way ``p_0, ``p_1, ``p_2, ``p_3 and ``mlinear'' forms of the Dirac equation are obtained.) (2) A corresponding mode of the invariant scalar product is presented. Thus all five classes consist of canonical transformations. Included amongst the ``p_0linear'' forms are the FoldyWouthuysenTani equation, and the one commonly attributed to Cini and Touschek, together with equations appropriate to limiting situations other than the nonrelativistic and extreme relativistic ones. The ``canonical'' form proposed by Chakrabarti is of the ``mlinear'' type.
Belonging to all three of the ``p_{1}, ``p_{2} and ``p_{3}linear'' categories is a
``plinear'' form of significance for large p.

1969

A.J. Bracken and H. A. Cohen,
On Canonical SO(4,1) Transformations of the Dirac Equation,
Journal of Mathematical Physics, Vol 10, No 11, Nov. 1969, pp 2024.
Abstract: Certain matrix transformations of the freeparticle Dirac equation are described
as momentum dependemt SO(4,1) transformations. Such of these belonging to any one of five subgroups
G^{(α)}(α=0,1,2,3,4,5) are canonical, preserving the Lorentzinvariant product
in a corresponding one of five modes of expression. The Dirac equation itself is linear
in all five components p_{α}[p_{μ}(μ=0,1,2,3) is the
fourmomentum operator, p_{4}=m ] of the "fivevector" p^{~},
and a transformation in G^{(β)} has the additional property
that the component p_{β} appears linearly also in the transformed equation.
The Mendlowitz and the FoldyWouthuysenTani accordingly are in G^{(0)},
the SO(4) subgroup; and that proposed by Chakrabarti is in G^{(4)},
the SO(3,1) subgroup associated with homogeneous Lorentz transformations.
For any p^{~`} obtained from p^{~} by a momentumdependent
Lorentz transformation, there is a corresponding transform of the Dirac equation.
Where p_{α} appears in the transformed equation, p_{`α} appears in the transformed equation.
The ambiguities which arise in the specification of the transform leading to a given
such equation are associated with the existence of a "little group" for any such p^{~`}.

1971

H. A. Cohen,
On the Derivation of the PryceFoldyWouthuysen transformation,
American Journal of Physics,
Vol 39, April 1971, pp 409412.
Abstract: A simple and instructive derivation of the PryceFoldyWouthuysen transformation
is given in terms of rotations in two dimensions.

1972

H. A. Cohen,
On Time NonSpecial Quantum Mechanics, Acta Physica Austrica, Suppl. IX, 1972
pp 851855.
Abstract: A reformulation of quantum mechanics is described
in which the z coordinate is described in which the z coordinate has the special role with
regard to the three other spacetime coordinates that the time t
has in the usual formulation.

1973.1

E.F. Carter and H. A. Cohen,
The Classical Problem of Charge and Pole, American Journal of Physics, Vol 41, Issue 8, Aug 1973, pp 944950.
Abstract: In this paper the classical dynamics of interacting electrically charged particles
where one or both possess magnetic charge is reviewed. The equations of motion are
obtained, and the vector constants of motion are derived. A consistent canonical
formalism is developed while related aspects such as scale
invariance and the geometry of the motion are also discussed.

1973.2

H. A. Cohen, On the Dirac Monopole Potential,
Prog. Theor. Phys. Vol. 50 No. 2 (1973) pp. 691696 Abstract:
The GrönblomJordan picture of the Dirac magnetic monopole is reviewed.
The role of the string in a singlevalued vector potential describing a magnetic
monopole is demonstrated. First Page Only

1974

H. A. Cohen and M.Z. Shaharir The Action Principle
in Quantum Mechanics,
International Journal of Theoretical Physics, Vol. 11 No. 5 (1974) pp. 289303
Abstract:
The EulerLagrange equation derived from Schwinger's action
principle (1951) has been shown by Kianget al. (1969) and
Linet al. (1970) to lead to inconsistencies for quadratic
lagrangians of the form
ˆL(
[Tex] $$\bar L(\dot q,q) = \tfrac{1}{2}\dot q^j g_{jk} (q)\dot q^k  V(q)$$
except in the Euclidean case g_{jk} =δ_{jk} . This inadequacy is linked to Schwinger's specification that the variations of operators becnumbers. We reformulate the action principle by introducing the concept of ‘proper’ Gauteaux variation of operators to find the most general class of admissible variation consistent with the postulated quantisation rules. This new action principle, applied to the LagrangianL, yields a quantum Euler equation consistent with the HamiltonHeisenberg equations.

1974

H. A. Cohen, Is There a
Quantization Condition for the Classical
Problem of Charge and Pole,
Foundations of Physics, Vol. 4 No. 1 (1974) pp. 115120
Abstract: In elementary derivations of the quantization of azimuthal angular momentum
the eigenfunction is determined to be exp(imφ), which is "oversensitive" to the rotation
φ → φ +2π, unless m is an integer. In a recent paper Kerner examined
the classical system of charge and magnetic pole and expressed Π,
a vector constant of motion for the system, in terms of a physical
angle ψ,
to deduce a remarkable paradox. Kerner pointed out that
Π(ψ)
is "oversensitive"
to ψ → ψ +2π, unless a certain charge quantization
condition is met. Our
explicandum of this paradox highlights the distinction
between coordinates in classical and quantum physics.
It is shown why the singlevaluedness requirement on Π(ψ)
is devoid of physical significance.
We are finally led to examine the classical analog
of the quantum mechanical argument
that demonstrates the quantization of magnetic charge,
to show that there is "no hope" of
a classical quantization condition.
