Phys/Hsci4121 Take-Home Exam #3 / C. David Kearsley

I. Stepping Stones to a Nuclear Bomb

A. The Discovery of the Neutron

The early investigations conducted by Frederic Joliot and Irene Curie involving neutral radiation emission (a Polonium-Beryllium source bombarding Hydrogen) and the subsequent discovery of the neutron by James Chadwick (1932) via expansion of the earlier experiment to (Po-Be bombarding Hydrogen, Helium and Nitrogen), both expanded and completed the casting of atomic constituents to three (p+, n, e-), and at the very same time confirmed the instability of certain atomic nuclei due to direct neutron emission.

B. Deuterium

The discovery (1932) of the first heavy hydrogen isotope deuterium (H2) by Harold Urey, F. G. Brickwedde, and G. M. Murphy, provided confirmation that the atomic masses of elements was not necessarily fixed (because the nuclei of heavier isotopes of a given element contained extra neutrons), and that this phenomenon was extendable even to the simplest element in the universe. On a more practical level, it provided the prospect for a highly manageable future source of donor neutrons, the substance later known as “heavy water” with H2 replacing H1.

C. The 7 th Solvay Council: The Consolidation of Modern Nuclear Physics

The 7th Solvay Council (Paris, October 1933) gathered together the principal investigators in nuclear physics of the time (theorists and experimentalists), with the notable exception that only one American, E. O. Lawrence, was present. The meeting’s investigative focus was the atomic nucleus. Foremost among the subjects of inquiry was the phenomenon known as beta decay, the process by which the neutron decays to become a proton (p+), an electron (e-) and an (at the time unknown) electron anti-neutrino (). This problem was a vexing one which at first glance challenged the laws regarding the conservation of mass and energy. Due to its pan-European constituency, the conference also provided the opportunity for significant theoretical cross-pollination at a very critical geo-political juncture, since the National Socialist (Nazi) Party had recently risen to power in Germany.

D. Beta-Decay

The development of the correct model for beta-decay by Enrico Fermi (1933) confirmed the instability of the neutron and introduced yet another particle into the framework of nuclear physics, the neutrino (). From a conceptual standpoint, the discovery of the correct beta decay model also went a long way in establishing the concept of the “mass/energy defect” when looking for an apparently “missing” constituent in a nuclear reaction. The mass defect concept played a central role in constructing the final theoretical and experimental frameworks pursuant to the development of a nuclear weapon.

E. Nuclear Fission

The discovery in Germany of nuclear fission by O. Hahn and F. Strassmann placed everyone in the now trans-Atlantic physics community on notice that a vast potential source of nuclear energy was available

to humanity. The experimental results obtained by Hahn and Strassmann; high and low-energy alpha particles (He4) resulting from neutron bombardment of uranium, were duplicated by Otto Frisch and several other investigators in short order. The ramifications were clear. Given sufficient energy, nuclear fission could result in the precipitous release of vast amounts of energy as a result of a nuclear chain reaction. The timescale over which this energy release was observed to occur was sufficiently small that, given a critical amount of neutron emitting material, an explosion of unprecedented proportions would be an unavoidable result.

II. The Equivalence Principle

A. General Theory of Relativity, Beta-Version: Crude & Heuristic

From 1907 to 1912 Albert Einstein began to wrestle with the logical theoretical extension to both Newton’s Laws of Gravitation, and his own Special Theory of Relativity (SR). This effort upon was undertaken not without significant difficulty, principally because the underlying concepts were at least as counterintuitive as those which formed the foundation of SR. The descriptive framework was also problematic, because in extremis, the phenomena which constituted the subject of Einstein’s investigation were all-encompassing in scope, and both quantum and cosmological in scale.

The most succinct initial dynamical description given by Einstein regarding the laws of motion under GR, is known as the “Principle of Equivalence” (Crude), and stipulated that:

1. Acceleration within a gravitational field is equivalent to being at rest outside of a gravitational field.

2. Acceleration outside of a gravitational field is equivalent to being at rest within a gravitational field.

A further extension of this model, expressed by the “Principle of Equivalence” (Heuristic), employed the use of the Minkowski space-time already established for use in SR, and proposed that gravitational fields produced specific phenomena when modeled using Minkowski space-time, specifically:

1. Clocks run slower in the presence of gravitational fields. That is to say, a clock will run slower when placed in a gravitational potential. This phenomenon is known as the gravitational red-shift, and can be observed in radiation emitted from compact stars.

2. The region in proximity to a gravitational potential is defined by a non-Euclidean spatial geometry; that is to say, a spatial geometry in which the shortest distance between two points is not a straight line segment. This arises because units of measure for inertial and accelerated frames of reference are observed to differ.

3. As a consequence of [2], light paths are necessarily non-linear in the presence of gravitational fields. This effect is responsible for the phenomenon known as “gravitational lensing”.

This observation led Einstein in the direction of proposing that gravitational fields could be geometrically represented by local curvature of otherwise Euclidean (or “flat”) space-time. This would have been fine, but for a flaw in his formalism. To this point Einstein had treated the inertial field and

the gravitational field as separate entities. Or more precisely, he had treated the gravitational field and the Minkowski space-time as separate entities. This deconstructive flaw, albeit subtle, resulted in contradictions with regard to the linearity of the associated field equations when considering observers in a gravitational potential.

B. General Theory of Relativity 1.0: Mature

In The Foundation of the General theory of Relativity, Einstein abandons the deconstructive treatment of the gravitational field and spatial geometry in favor of a comprehensively constructive mathematical framework which treats inertial fields and gravitational fields as different components of the same system of covariant (applying to all coordinate systems) field equations:

“Inertia and gravity are of an identical nature [wesensgleich]. […] It follows that [one and the same field, which we now call the inertio-gravitational field, represented by the metric tensor field ] describes the metrical properties of space, the inertial behavior of bodies in space, and the effects of gravity”

—“On the Foundations of the GeneralTheory of Relativity,” March 1918.

In this constructive framework, the gravitational field and the spatial geometry that defines it are not regarded separately, but rather as manifestations of the same overall structure, a direct analogue to the synthesis of the electric and magnetic fields required for the eventual development of Special Relativity.

III. Weak Neutral Currents as Social Constructs

In Constructing Quarks, Andrew Pickering introduces the concept of “interpretive procedures” as vehicle used to explain the means by which elementary particle theorists and experimentalists attempted to describe the results of the experimental impact on the evolving models which comprised elementary particle theory during the 1960’s and early 1970’s. It is an interesting albeit misguided turn of phrase, which somehow suggests that the primary responsibility for the existence of physical phenomena rests with the observer, as opposed to the actual events as they occur in the universe. Pickering’s “interpretive procedures” (IP) construct is merely convenient cover for the fact that theoretical models of the way the universe might work are invariably constrained by experimental observations of how the universe actually does work. When new experimental data becomes available, those theoretical models conflicting with the new observations find themselves in jeopardy and must either be altered or abandoned altogether. However, for Pickering to allow for this eventuality would irreparably damage the sociological IP argument that he so painstakingly attempts to craft.

With regard to his proposal that the quark-gauge theory of elementary particles “should be seen as a culturally specific product”, one is compelled to inquire: To which specific culture does Pickering refer? It is true that within the high energy physics (HEP) community there exist subgroups whose memberships are roughly defined by specific areas of inquiry, but the degree to which Pickering describes factionalism within the HEP community is overstated. The aforementioned subgroups overlap significantly. There is no doubt that a competitive spirit exists between teams of scientific investigators within a given discipline. It is also the case that there exist traditions and codes of conduct peculiar to theoretical and experimental physics that are worthy of sociological inquiry. However, Pickering extends his sociological modeling into the areas of theoretical development and experimental

methodology, and thereby endangers his credibility. By referring to astrophysicists and cosmologists as “outsiders” with regard to HEP, Pickering reveals his ignorance as to the interdisciplinary nature of the HEP community, and why HEP is considered to be of (quite literally) fundamental importance with regard to the development of a unified model of cosmic structure. By way of example, the fact that Steven Weinberg shared the 1979 Nobel Prize with Sheldon Glashow and Abdus Salam, "for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including inter alia the prediction of the weak neutral current", did not prevent him from also publishing a 600-page tome (in 1972) entitled Gravitation & Cosmology: Principles and Applications of the General Theory of Relativity.

With specific regard to the weak neutral current investigations conducted by Cargamelle (CERN) and the Harvard-Wisconsin-Pennsylvania-Fermilab (HPWF) team at Fermilab in the 1960’s and 1970’s, Pickering makes repeated references to these IP constructs with regard to the experimental results produced by the respective investigations. He characterizes the IP employed by Cargamelle to deduce the existence of the weak neutral current as having “differed significantly from those which had supported the opposite conclusion in earlier analyses” and describes the IP employed in the HPWF weak neutral current report as “potentially questionable”. The final evidence of Pickering’s apparent disregard for “facts in the universe” rests on the following point however. His references to the IP employed by “the 1960’s order”, which “pointed to the non-existence of the neutral current” having been “displaced in the 1970’s by a new order in which a new set of interpretive procedures made the neutral current manifest”, ignore the central reality of both elementary particle theory and experimental HEP. The ISR at CERN (p+p-, colliding-beam) came on-line in 1971 with an initial maximum beam energy of ~31GeV (per beam). The Fermilab Main Ring (p+, fixed-target) came on-line in 1972 with an initial maximum beam energy of 500GeV. The rest energy of the Z0 (weak neutral current mediator) is ~91GeV. Prior to 1972 then, the accelerator beam energies required to reliably produce the weak neutral current in the laboratory were simply unavailable, regardless of the “interpretive procedures” one might have chosen to employ.

References

The Foundation of the General Theory of Relativity, A.Einstein, 1918.

Introduction to Experimental Particle Physics, R.Fernow, Cambridge University Press, 1992.

Review of Particle Physics: Particle Physics Booklet, Physical Review D-66, K.Hagiwara et al, 2002.

Constructing Quarks: A Sociological History of Particle Physics, A.Pickering, Edinburgh University Press, 1984.

Phys/HSci-4121: History of 20th Century Physics: Lecture Notes & Slides, M.Janssen, University of Minnesota, 2007.

Nobel Laureates in Physics: 1901-Present, Stanford Linear Accelerator (SLAC) Library, 2006.