This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis – Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka. The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry.

The vacuum structure for the massive charged scalar field in the region of two parallel, infinitely long and thin solenoids confining the fluxesn 1 andn 2 is studied. By using the Green function method, it is found that the vacuum expectation value of the system's energy has a finite mutual interaction term depending on the distance a between the solenoids, which implies an attractive force per unit length given by F n1n2 =−(ℏc/π2)(n 1 n 2)2/a 3.

The Casimir force between two neutral metallic plates is often considered conclusive evidence for the reality of electromagnetic zero-point fluctuations in ‘empty space’. However, it is not well known that the Casimir force can be derived from many different points of view. The purpose of this note is to supply a conceptually oriented introduction to a representative set of these different interpretations. The different accounts suggest that the Casimir effect reveals nothing conclusive about the nature (...) of the vacuum. (shrink)

The Casimir force between two neutral metallic plates is often considered conclusive evidence for the reality of electromagnetic zero-point fluctuations in ‘empty space’. However, it is not well known that the Casimir force can be derived from many different points of view. The purpose of this note is to supply a conceptually oriented introduction to a representative set of these different interpretations. The different accounts suggest that the Casimir effect reveals nothing conclusive about the nature (...) of the vacuum. (shrink)

The Casimir force between two neutral metallic plates is often considered conclusive evidence for the reality of electromagnetic zero-point fluctuations in 'empty space' (i.e. in absence of any boundaries). However, it is not well known that the Casimir force can be derived from many different points of view. The purpose of this note is to supply a conceptually oriented introduction to a representative set of these different interpretations. The different accounts suggest that the Casimir effect (...) reveals nothing conclusive about the nature of the vacuum. (shrink)

Conventional rockets are not a suitable technology for interstellar missions. Chemical rockets require a very large weight of propellant, travel very slowly compared to light speed, and require significant energy to maintain operation over periods of years. For example, the 722 kg Voyager spacecraft required 13,600 kg of propellant to launch and would take about 80,000 years to reach the nearest star, Proxima Centauri, about 4.3 light years away. There have been various attempts at developing ideas on which one might (...) base a spacecraft that would permit interstellar travel, such as spacewarps. In this paper we consider another suggestion from science fiction and explore how the quantum vacuum might be utilized in the creation of a novel spacecraft. The spacecraft is based on the dynamic Casimir effect, in which electromagnetic radiation is emitted when an uncharged mirror is properly accelerated in vacuum. The radiative reaction produces a dissipative force on the mirror that tends to resist the acceleration of the mirror. This force can be used to accelerate a spacecraft attached to the mirror. We also show that, in principle, one could obtain the power to operate the accelerated mirror in such a spacecraft using energy extracted from the quantum vacuum using the standard Casimir effect with a parallel plate geometry. Unfortunately the method as currently conceived generates a miniscule thrust, and is no more practical than a spacewarp, yet it does provide an interesting demonstration of our current understanding of the physics of the quantized electromagnetic field in vacuum. (shrink)

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell’s equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point (...) radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics. (shrink)

Covering the fundamentals as well as many special topics of current interest, this is the most concise, up-to-date, and accessible graduate-level textbook on quantum mechanics available. Written by Gerald Mahan, a distinguished research physicist and author of an acclaimed textbook on many-particle physics, Quantum Mechanics in a Nutshell is the distillation of many years' teaching experience. Emphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, the book proceeds from (...) solving for the properties of a single particle in potential; to solving for two particles ; to addressing many-particle systems. Applications include electron gas, magnetism, and Bose-Einstein Condensation; examples are carefully chosen and worked; and each chapter has numerous homework problems, many of them original. Quantum Mechanics in a Nutshell expertly addresses traditional and modern topics, including perturbation theory, WKBJ, variational methods, angular momentum, the Dirac equation, many-particle wave functions, Casimir Force, and Bell's Theorem. And it treats many topics--such as the interactions between photons and electrons, scattering theory, and density functional theory--in exceptional depth. A valuable addition to the teaching literature, Quantum Mechanics in a Nutshell is ideally suited for a two-semester course. The most concise, up-to-date, and accessible graduate textbook on the subject Contains the ideal amount of material for a two-semester course Focuses on the description of actual quantum systems, including a range of applications Covers traditional topics, as well as those at the frontiers of research Treats in unprecedented detail topics such as photon-electron interaction, scattering theory, and density functional theory Includes numerous homework problems at the end of each chapter. (shrink)

Cross-term conservation relationships for electromagnetic energy, linear momentum, and angular momentum are derived and discussed here. When two or more sources of electromagnetic fields are present, these relationships connect the cross terms that appear in the traditional expressions for the electromagnetic (1) energy, (2) linear momentum, and (3) angular momentum, over to, respectively, (1) the sum of the rates of work, (2) the sum of the forces, and (3) the sum of the torques, that are due to the fields of (...) each charge or current source acting upon the other charge and current sources. These relationships, although not new, appear to be rarely recognized and used in the physics literature. As shown here, they can be extremely helpful for solving and gaining a deeper physical understanding into a rather diverse range of interesting problems in electrodynamics, including (1) aspects of Poynting's theorem when applied to charged point particles, (2) the detailed physical basis of electrostatic analysis, (3) understanding the connection between different techniques used in the past for solving Casimir force problems, and (4) reconciling the invalidity of Newton's third law in electrodynamics. (shrink)

The first classification of general types of transition between phases of matter, introduced by Paul Ehrenfest in 1933, lies at a crossroads in the thermodynamical study of critical phenomena. It arose following the discovery in 1932 of a suprising new phase transition in liquid helium, the “lambda transition,” when W. H. Keesom and coworkers in Leiden, Holland observed a λhaped “jump” discontinuity in the curve giving the temperature dependence of the specific heat of helium at a critical value. This apparent (...) jump led Ehrenfest to introduce a classification of phase transitions on the basis of jumps in derivatives of the free energy function. This classification was immediately applied by A.J. Rutgers to the study of the transition from the normal to superconducting state in metals. Eduard Justi and Max von Laue soon questioned the possibility of its class of “second-order phase transitions” -- of which the “lambda transition was believed to be the arche type -- but C.J. Gorter and H.B.G. Casimir used an “order parameter to demonstrate their existence in superconductors. As a crossroads of study, the Ehrenfest classification was forced to undergo a slow, adaptive evolution during subsequent decades. During the 1940s the classification was increasingly used in discussions of liquid-gas, order-disorder, paramagnetic-ferromagnetic and normal-super-conducting phase transitions. Already in 1944 however, Lars Onsagers solution of the Ising model for two-dimensional magnets was seen to possess a derivative with a logarithmic divergence rather than a jump as the critical point was approached. In the 1950s, experiments further revealed the lambda transition in helium to exhibit similar behavior. Rather than being a prime example of an Ehrenfest phase transition, the lambda transition was seen to lie outside the Ehrenfest classification. The Ehrenfest scheme was then extended to include such singularities, most notably by A. Brain Pippard in 1957, with widespread acceptance. During the 1960s these logarithmic infinities were the focus of the investigation of “scaling” by Leo Kadanoff, B. Widom and others. By the 1970s, a radically simplified binary classification of phase transitions into “first-order” and “continuous” transitions was increasingly adopted. (shrink)

An analysis is carried out involving reversible thermodynamic operations on arbitrarily shaped small cavities in perfectly conducting material. These operations consist of quasistatic deformations and displacements of cavity walls and objects within the cavity. This analysis necessarily involves the consideration of Casimir-like forces. Typically, even for the simplest of geometrical structures, such calculations become quite complex, as they need to take into account changes in singular quantities. Much of this complexity is reduced significantly here by working directly with the (...) change in electromagnetic fields as a result of the deformation and displacement changes. A key result of this work is the derivation that for such cavity structures, classical electromagnetic zero-point radiation is the appropriate spectrum at a temperature of absolute zero to ensure that the reversible deformation operations obey both isothermal and adiabatic conditions. In addition, a generalized Wien displacement law is obtained from the demand that the change in entropy of the radiation in these arbitrarily shaped structures must be a state function of temperature and frequency. (shrink)

This is a volume of specially commissioned essays of analytical philosophy, on topics of current interest in ethics and the philosophy of logic and language. Among the topics discussed are the making of wicked promises, G. E. Moore's early ethical views, as well as indexicals, tense, indeterminism, conventionalism in mathematics, and identity and necessity. The essays are all by former students of Casimir Lewy, until recently Reader in Philosophy at the University of Cambridge and an exponent of a particularly (...) thoroughgoing form of philosophical analysis. Together, they represent some of the best work in these areas at present, and express what may be described as a characteristic 'Cambridge' voice. (shrink)

A study of various central and connected topics in philosophical logic and the theory of meaning. There are important sections on the relation between linguistic and abstract entities, on necessity and convention, on meaning, sense and reference, and on entailment. Dr Lewy proposes a number of original solutions to problems which have been widely discussed in literature, and there is in particular a sharp and sustained criticism of conventionalism and reductionism. These are among the most difficult and intricate issues in (...) contemporary philosophy, but Dr Lewy writes with great clarity and a minimum of technicality. Where his views are controversial they are explained and supported in a detail which makes it both possible and necessary for potential critics to state their disagreement precisely. The book should therefore be of value as an advanced textbook as well as an original contribution to philosophical logic. (shrink)

H.B.G. Casimir's life, interests and works are intertwined with the important developments that have taken place in physics during this century. This book was compiled by his friends and admirers in honour of his 80th birthday and concentrates mainly on Casimir's achievements in the field of physics, though without ignoring the peripheral areas of the history and philosophy of physics in which he was greatly interested. The book is divided into four parts. Part I describes Casimir's teachers, (...) Ehrenfest, Bohr and Pauli, and will be of general interest due to the key role which these physicists played in modern developments. The articles do give new facts and provide new insights into the history of modern physics. Part II consists of essays on recent developments in various areas of physics in which Casimir has taken an active interest, such as the modern concept of time, statistical foundations of electrodynamic theory and field theory. The subjects covered in Part III have been selected because of Casimir's efforts in the industrial research area of physics. They cover past, present and future expectations in research. (shrink)

The history of women has been defined by a world enmeshed in woes, frustration, oppression, maltreatment and inequalities. Feminism as a philosophy of change sought to fight, end and change this woeful scenario of women that denied their self respect, dignity and led to a loss of self confidence. Fundamentally, feminist philosophy sought for explanations and justifications why women were denied a voice and why they were historically not treated as coequals of men. The basis of inequality is historically rooted (...) in cultural and philosophical falsities that were not evidenced based but were used to justify oppression against women. The Universal Declaration of human rights gave women and the world the platform that empowered them with rights and led to fresh processes that sought to end oppression and their underdevelopment inspired by inequality, iniquities, denial of opportunities for growth and empowerment. The millennium development goal of ending inequality and oppression against women should achieve equality and women’s empowerment in Africa. Since the declaration of the MDGS, considerable gains had been made inAfricabut challenges and problems are still identified in the areas of cultural inequality complicated by the weakness of the major governance institutions and corruption. Other challenges centre on women’s lack of genuine empowerment, violence against women, trafficking in women, denial of human rights, lack of participation in policy and governance. Since empowerment is the key to achieving mainstreaming and gender equality, this paper seeks to redefine the concept of empowering women as the platform to ending inequality, social injustice and achieving equality in the context of the unique challenges of underdevelopment facingAfrica. It will identify the policy implications of establishing empowerment structures that address multiple challenges facing gender inequality and how these structures will assist in building the necessary feminine human resources that will make women as partners of sustainable growth and development after 2015. (shrink)

Casimir Lewy; On the “Justification” of Induction1, Analysis, Volume 6, Issue 5-6, 1 September 1939, Pages 87–90, https://doi.org/10.1093/analys/6.5-6.87.

It has been suggested by some that the acquisition of symbolic capital in terms of honor, prestige, and power translates into an accumulation of material capital in terms of tangible belongings, and that on the basis of these goods high reproductive success may be achieved. However, data on completed fertility rates over more than one generation in so-called traditional societies have been rare. Ethnographic and demographic data presented here on the pastoral Bakkarwal of northern India largely corroborate the hypothesis concerning (...) the interdependence between the attainment of various cultural goals and differential reproduction rates and indicate that the numbers of (especially male) surviving offspring and siblings are crucial to a man’s position in society. (shrink)

Nigeria is a country blessed with abundant human and material resources. Pre-independent Nigeria had agriculture as the major foreign exchange and revenue earner. Other alternative revenue earners such as agricultural and mineral resources were explored and their proceeds used to support and foot the bill of government expenditures. Immediately the first oil field was discovered in 1956 at Olobiri in the Niger Delta, other alternative sources of revenue for Nigeria were abandoned and crude oil became the determinant of Nigeria’s mono-economic (...) status and the sole basis of all socio-economic transaction within and outside the country. The issue of appropriate pricing of petroleum products and the removal of government’s subsidy on petroleum price became a thorny controversial public policy issue. Successive governments, including the current President, have grappled with this problem of whether to remove the subsidy or not, without coming to a publicly endorsed solution to the debate. The last fuel subsidy removal on 1st January, 2012 sparked an uprising that almost led to a revolution. The thrust of the study is to examine the causes of the fuel subsidy removal, to identify the benefits of fuel subsidy removal, to describe the effects of the subsidy removal, and the socio-religious implications of the removal of fuel subsidy to the citizens of Nigeria. It is in the context of these socio-religious that one discovers the relevance of Professor Dukor theistic humanism and its implied need for African values to be applied to governance in the 21st century. The debate surrounding the subsidy removal and the subsidy scam running into trillions of Naira of stolen funds by independent marketers of petroleum products revolve around corruption and a bad commentary about how ethical African vales have been removed from public governance and the management of public resources. After pointing out these socio-religious implications for the Nigerian ethical and value re-orientation, the paper went ahead to recommend some ways of managing the subsidy money for the development of the country. (shrink)

To the question,“what is sports”, or what is a good sports activity or event, I am sure Plato would know what to say, using references to his philosophical division of man into three parts, namely: the appetite soul; the emotional soul and the reasonable soul. Plato would have said that sports comes from the human person and being, and so, for any particular sports to be accorded the accolade of goodness it must have the correspondence of the three constituent parts (...) of man’s true nature. The concept of the soul in Plato is what exploring just as that of Professor Maduabuchi Dukor’s expositions concerning the African philosophical concepts of soul, mind, spirit and body as they affect philosophy of sports and the discipline of physical education. The article will therefore analyze the link between Plato concept of the good sports, Professor Dukor’s ontological ideas about the African core values as they affect the balance, harmony and health both the mind and body of the human being. The central point here is the analytical framework of enquiry which Plato sustained in his Dialogues when he queries people:“what is this?”. By this he wants people to appreciate the fact that when they are in search of truth, they usually have the impression that they have all when, actually, they have only half-baked understanding of issues. It is important therefore to understand the issues involved in the disciplines of physical education, philosophy of sports, ethics and the ontological frame of African philosophy as profiled under Professor Dukor theistic humanism of African philosophy. Centrally, the dialectical link between Plato and Dukor will expose the ethical dimension to sports development since every thing is not wining and money or drugs should not be the ultimate motivation for sports and physical exercises. The exercise of sports should lead to the dual development and balance of both mind and body; the highest being the competition of the soul with itself and not with others in which laurels, gold or money is won or lost. The man who wins is the one, like in the communal spirit of the African ontology, who has conquered over his selfishness and sacrifices for the good of the community. (shrink)

Violent conflicts in emerging democracies or societies in transition threaten the stability of state governance institutions, which brings about insecurity of lives, property and deepens the vicious cycle of poverty and criminality in Africa. The first responsibility of any government is to provide security of lives and property. At no time since Nigeria’s civil war has the country witnessed the resurgence of violence and insecurity that claims hundreds of lives weekly. It is a sectarian insurgence of multiple dimensions. This article (...) makes the case that Boko Haram is not just a religious phenomenon but a reflection of a so- cio-political, economic and ethnic problem caused by bad governance. As a result, Boko Haram has witnessed a cross-border influence and impact which has expanded its frontiers beyondNigeriato neighboring countries in the West African region. The theoretical framework employed in this article posits that Boko Haram has its roots fundamentally in poverty caused by bad governance in the Northern Moslem bend, in Nigeria and the West African Region where corruption, human rights violations, marginalization of cultural, political and religious groups have created the situation whereby weak state structures have abysmally failed to deliver on the development promises made during elections. So the emergence of Nigeria’s Boko Haram violence, as a result of the street poverty and the rise of unemployed street beggars, popularly known as Almajiris, and their use for electoral and party violence, was encouraged by the neglect and abandonment of the masses by the governors and other elected leaders. The expansion and consolidation of the Boko Haram insurgence to other parts of the country and neighboring West African nations was made possible by the already existing failed state institutions, bad governance and corruption and the existing band of small criminal sectarian groups that depend upon their survival on aids from Al Quaeda, drug gangs and sea piracy. The religious dimension is a marginal factor fueled by fundamental socio-economic and political variables which have been thrown up in the first place by bad governance and leadership in Nigeria. (shrink)