On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

Interactive Marine Spatial Planning: Siting Tidal Energy Arrays around the Mull of Kintyre

The rapid development of the offshore renewable energy sector has led to an increased requirement for Marine Spatial Planning (MSP) and, increasingly, this is carried out in the context of the ‘ecosystem approach’ (EA) to management. We demonstrate a novel method to facilitate implementation of the EA. Using a real-time interactive mapping device (touch-table) and stakeholder workshops we gathered data and facilitated negotiation of spatial trade-offs at a potential site for tidal renewable energy off the Mull of Kintyre (Scotland). Conflicts between the interests of tidal energy developers and commercial and recreational users of the area were identified, and use preferences and concerns of stakeholders were highlighted. Social, cultural and spatial issues associated with conversion of common pool to private resource were also revealed. The method identified important gaps in existing spatial data and helped to fill these through interactive user inputs. The workshops developed a degree of consensus between conflicting users on the best areas for potential development suggesting that this approach should be adopted during MSP

Pig farmers’ willingness to pay for management strategies to reduce aggression between pigs

When deciding whether to invest in an improvement to animal welfare, farmers must trade-off the relative costs and benefits. Despite the existence of effective solutions to many animal welfare issues, farmers’ willingness to pay for them is largely unknown. This study modelled pig farmers’ decisions to improve animal welfare using a discrete choice experiment focused on alleviating aggression between growing/finishing pigs at regrouping. Eighty-two UK and Irish pig farm owners and managers were asked to choose between hypothetical aggression control strategies described in terms of four attributes; installation cost, on-going cost, impact on skin lesions from aggression and impact on growth rate. If they did not like any of the strategies they could opt to keep their current farm practice. Systematic variations in product attributes allowed farmers’ preferences and willingness to pay to be estimated and latent class modelling accounted for heterogeneity in responses. The overall willingness to pay to reduce lesions was low at £0.06 per pig place (installation cost) and £0.01 per pig produced (running cost) for each 1% reduction in lesions. Results revealed three independent classes of farmers. Farmers in Class 1 were unlikely to regroup unfamiliar growing/finishing pigs, and thus were unwilling to adopt measures to reduce aggression at regrouping. Farmers in Classes 2 and 3 were willing to adopt measures providing certain pre-conditions were met. Farmers in Class 2 were motivated mainly by business goals, whilst farmers in Class 3 were motivated by both business and animal welfare goals, and were willing to pay the most to reduce aggression; £0.11 per pig place and £0.03 per pig produced for each 1% reduction in lesions. Farmers should not be considered a homogeneous group regarding the adoption of animal welfare innovations. Instead, campaigns should be targeted at subgroups according to their independent preferences and willingness to pay