Digital computers carry out algorithms coded in high level programs. These abstract entities determine what happens at the physical level: they control whether electrons flow through specific transistors at specific times or not, entailing downward causation in both the logical and implementation hierarchies. This paper explores how this is possible in the light of the alleged causal completeness of physics at the bottom level, and highlights the mechanism that enables strong emergence to occur. Although synchronic emergence of higher levels from (...) lower levels is manifestly true, diachronic emergence is generically not the case; indeed we give specific examples where it cannot occur because of the causal effectiveness of higher level variables. (shrink)

There has been much controversy over weak and strong emergence in physics and biology. As pointed out by Phil Anderson in many papers, the existence of broken symmetries is the key to emergence of properties in much of solid state physics. By carefully distinguishing between different types of symmetry breaking and tracing the relation between broken symmetries at micro and macro scales, I demonstrate that the emergence of the properties of semiconductors is a case of strong emergence. This is due (...) to the existence of quasiparticles such as phonons. Furthermore time dependent potentials enable downward causation as in the case of digital computers. Additionally I show that the processes of evolutionary emergence of living systems is also a case of strong emergence, as is the emergence of properties of life out of the underlying physics. A useful result emerges: standard physics theories and the emergent theories arising out of them are all effective theories that are equally valid. (shrink)

Entanglement has been called the most important new feature of the quantum world. It is expressed in the quantum formalism by the joint measurement formula. We prove the formula for projection valued observables from a plausible assumption, which for spacelike separated measurements is an expression of relativistic causality. The state reduction formula is simply a way to express the joint measurement formula after one measurement has been made, and its result known.