“Every description of natural processes must be based on ideas which have been introduced and defined by the classical theory.” — Niels Bohr, 1923 1 “There must be quite definite and clear grounds, why you repeatedly declare that one must interpret observations classically, which lie absolutely in their essence.... It must belong to your deepest conviction—and I cannot understand on what you base it.” — Erwin Schrödinger to Niels Bohr, 13 October 1935 2 1.

Einstein’s philosophy of physics (as clarified by Fine and Howard) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed “physical thought ” and “physical laws ” to be impossible. Bohr’s philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio’s Theorem in algebraic quantum theory that within a suitable class of physical theories Einstein’s doctrine is mathematically equivalent to Bohr’s, so that quantum mechanics accommodates Einstein’s Trennungsprinzip if and only if it is interpreted à la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in a constructive way, since in its early phase their debate was blurred by an undue emphasis on the uncertainty relations, whereas in its second stage it was dominated by Einstein’s flawed attempts to establish the “incompleteness ” of quantum mechanics. These two aspects of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein on the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein’s off-the-cuff characterization of Bohr as a ‘Talmudic philosopher ’ was spot-on.

What is commonly known as the Copenhagen interpretation of quantum mechanics, regarded as representing a unitary Copenhagen point of view, differs significantly from Bohr’s complementarity interpretation, which does not employ wave packet collapse in its account of measurement and does not accord the subjective observer any privileged role in measurement. It is argued that the Copenhagen interpretation is an invention of the mid-1950s, for which Heisenberg is chiefly responsible, various other physicists and philosophers, including Bohm, Feyerabend, Hanson, and Popper, having further promoted the invention in the service of their

Abstract The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the Church-Turing hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinate-free mathematical language which is both constructive and non-local to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagram can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of Church-Turing and quantum theories. It has constructively to bridge the non-local chasm between the weak anticipation of mathematics and the strong anticipation of physics.

Einstein and Bohr – No names loom larger in the history of twentieth-century physics, and rightly so, Albert Einstein and Niels Bohr being the figures most prominently associated with the 1 relativity and quantum revolutions. Their names dominate, likewise, the history of philosophical reactions to the new physics of the twentieth century, Bohr for having identified complementarity 2 as the chief novelty in the quantum description of nature, Einstein for having found vindication in 3 relativity theory for either positivism or realism, depending upon whom one asks. Famous as is each in his own domain, they are famous also, together, for their decades-long disagreement over the future of fundamental physics, their respective embrace and rejection of quantum indeterminacy being only the most widely-known point of contention. A well-entrenched narrative tells the story of the Einstein-Bohr debate as one in which Einstein’s tries, from 1927 through 1930, to prove the quantum theory incorrect via thought experiments exhibiting in-principle violations of the Heisenberg indeterminacy principle, only to have Bohr find the flaw in each, after which Einstein shifts his direction of attack, faulting the quantum theory now not as incorrect, but incomplete. In 1935, the Einstein, Podolsky, and Rosen (EPR) paper, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” (Einstein, Podolsky, Rosen 1935) represents the high-water mark of this critique. It is met by Bohr’s deep and devastating reply (Bohr 1935), after which Bohr grows ever more in stature and influence as the sage of Copenhagen, while Einstein slips into senility in Princeton, meddling, perhaps commendably, in the politics of the atomic bomb, but no longer capable of constructive contributions to physics, itself. 4-2-That something is seriously wrong with this triumphalist narrative has been remarked upon 5 by various authors for more than twenty years. More than anyone else, however, it was Mara Beller,