We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
This is the first ever English translation of Heisenberg’s unpublished response to the EPR paper. In this chapter, Heisenberg uses his famous cut argument to argue against the possibility of hidden variables.
Schrödinger’s reaction to the EPR paper is less widely known than, say, Bohr’s, and yet our analysis shows that it fits rather nicely with contemporary concerns in foundations of quantum mechanics. Taking the lead both from the EPR paper and from Pauli’s remarks in their correspondence, Schrödinger shows that EPR’s locality considerations lead to the assignment of values to all quantum mechanical observables, but that under apparently mild assumptions this then leads to contradictions of the von Neumann type. This dilemma (as he explicitly calls it) is thus similar to more recent debates between nonlocality on the one hand and no-go results on the other (whether through violation of the Bell inequalities, the Kochen–Specker theorem, or what you will). We shall first look at Schrödinger’s fundamental worries in the years leading up to 1935. The chapter then discusses in detail the direct reaction by Schrödinger to EPR. It will, however, not exhaust our discussion of Schrödinger, who is a recurring character in the book, having poked and prodded his peers on EPR during the whole summer and autumn of 1935.
This is a reprinting of Bohr’s response to the EPR paper, wherein Bohr relies on his principle of complementarity to demonstrate an ambiguity in the criterion of reality as described by EPR and to argue that quantum mechanics is in fact a complete description of reality given the bounds of complementarity.
This is a reprinting from Jammer (1974) of Podolsky’s unpublished response to Kemble’s criticisms of the EPR paper. Podolsky rightly criticises Kemble for missing the point of EPR’s argument and adds a few comments agreeing with Kemble that a statistical interpretation of quantum mechanics is best – yet Podolsky maintains such an interpretation is incomplete.
This is a reprinting of Flint’s response to EPR, originally signed only as ‘H.T.F.’ Flint begins with a fairly accurate outline of the argument in the EPR paper – with which he agrees – but then he expresses doubts as to the validity of the reality criterion. Without describing the nature of these doubts, he concludes by further agreeing with EPR in desiring a more direct description of reality than the one currently provided by quantum mechanics.
This chapter presents a collection of letters between the main protagonists in the EPR debate as analysed in the present volume. Among many other letters, it includes the first ever complete English translation of the correspondence Schrödinger held concerning the EPR paper with, e.g., Einstein, Bohr, Pauli, Born and Teller. He kept these letters in a special folder labelled ‘The Einstein Paradox’, only a small portion of which has previously been discussed in the foundations literature. These historical documents, many of which are published here for the first time, form the basis of our analysis in the beginning chapters of this book.
This chapter introduces in more comprehensive fashion than elsewhere in the literature the interesting role of Heisenberg in the EPR debate. Although we have already published an analysis of Heisenberg’s posthumously published draft response to EPR, only now are we able to situate this excellent primary source in its fullest context, by contributing a chapter describing, for example, Heisenberg’s thinking prior to EPR about interacting systems and hidden variables, the crucial role of Grete Hermann for Heisenberg’s thinking about separability, completeness and observational context, and describing the correspondence between Heisenberg and Bohr discussing Heisenberg’s manuscript.
This is a reprinting of Bohr’s note to Nature advertising his forthcoming response to the EPR paper. It is very brief but contains in essence the argumentative tack Bohr would in fact employ in his full response to EPR.
This is a reprinting of Furry’s response to EPR. Although his response misses the mark, his discussion of an example is intriguing for other aspects of the foundations of quantum mechanics.
This chapter provides a complete list and brief analyses of published and unpublished responses to EPR in 1935 (virtually all of which are reprinted as later chapters in this book). We invite a renewed consideration of certain contributors not much discussed elsewhere in the literature. These include going beyond Kemble’s short criticism of EPR to his ensuing disagreement with Margenau about the viability of an ensemble interpretation of the wavefunction, and also a response to Kemble’s note on EPR by Podolsky himself. We also examine the correspondence between Margenau and Einstein in the wake of EPR, discussing the role of the collapse postulate, and finally we discuss two papers by Furry, which although not entirely satisfactory qua a response to EPR’s arguments, are nevertheless of great potential interest for the foundations literature more generally.
This is a translation of the excerpts published in Naturwissenschaften of Grete Hermann’s 1935 essay on philosophy of quantum mechanics, recently translated into English. Her main thesis, in line with her natural-philosophical training and neo-Kantian commitments, is to argue that quantum mechanics does not refute the principle of causality. Quantum mechanics cannot be completed by, hidden variables, because it is already causally complete (albeit retroductively). In establishing this provocative thesis, she makes important use of Bohr’s principles of correspondence and complementarity and of Weizsäcker's version of the gamma-ray microscope, arguing that the lesson of quantum mechanics is the impossibility of an absolute description of nature independent of the context of observation.
This is a reprinting of the famous May 1935 paper in Physical Review by Einstein, Podolsky and Rosen. In this paper, the authors argued that the wavefunction fails to provide a complete description of reality unleashing the debate analysed in this volume.
This chapter details not only the prehistory of EPR but also examines the structure and logic of the EPR paper – including Einstein’s own preferred version of the argument for incompleteness. We here attempt a seamless interweaving of the excellent extant literature with additional details that have emerged from our work and the recent work of others. Some examples of new aspects in this prehistory of EPR include evidence of a ‘proto’ photon-box thought experiment Einstein had developed in connection with his ill-starred collaboration with Emil Rupp in 1926. We also describe the potential importance to this prehistory of Einstein’s paper with Tolman and Podolsky and of Einstein’s seminar and discussions with Schrödinger in Berlin in the early 1930s.
This is a reprinting of Edwin Kemble’s 1935 reply to the EPR paper. Kemble misses EPR’s point by taking their completeness criterion to be merely an epistemic concept; Kemble himself admits as much in a letter to Einstein later that year. His original response to EPR is nevertheless of interest, as Kemble there provides an argument for a statistical interpretation of the wavefunction – a view he attributes to Slater already in a 1929 paper, but for which Kemble provides greater clarity and motivation.
This is a reprinting of Furry’s response to Schrödinger’s cat paper and entanglement papers, as well as Furry’s response to other responses to the EPR paper, especially Bohr’s.
This is a reprinting of Schrödinger’s famous pair of papers delivered at the Cambridge Philosophical Society in late 1935 and 1936, wherein he first coins the term ‘entanglement’ to describe interacting quantum systems. The first paper (1935) is given here in full; section 4 of the second paper (1936) is reprinted as an appendix.
In this chapter, we dive deeply into Bohr’s views on (in)completeness and (non)locality. Perhaps the most outspoken and famous respondent to EPR, Bohr is generally thought to be obscure in his reply. We analyse it afresh (at least to our satisfaction), in particular in regard to its argumentative structure, the role of Bohr's examples and that of his 'non-mechanical disturbance'. We also assess its limitations as a reply to Einstein's wider concerns.
Guided by basic intuitions, we introduce the notion of a complete metric space and discover that we have in fact encountered it before in our study of mathematics. In particular, we learn that if the set of real numbers were not complete, bounded increasing (or decreasing) sequences would not have limits. Similarly, we realize that if time were not complete, Achilles would never catch the tortoise. In a slightly more advanced part, we show that criteria for convergence of functional series involve the notion of completeness of the space of continuous functions.
Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$-valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$, which is indeed the predicate version of monoidal t-norm based logic $\mathbf {MTL}$. The main aim of this paper is to give an algebraic proof of the completeness theorem for monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and some of its axiomatic extensions. Firstly, we survey the axiomatic system of monadic algebras for t-norm based residuated fuzzy logic and amend some of them, thus showing that the relationships for these monadic algebras completely inherit those for corresponding algebras. Subsequently, using the equivalence between monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and S5-like fuzzy modal logic $\mathbf {S5(MTL)}$, we prove that the variety of monadic MTL-algebras is actually the equivalent algebraic semantics of the logic $\mathbf {mMTL\forall }$, giving an algebraic proof of the completeness theorem for this logic via functional monadic MTL-algebras. Finally, we further obtain the completeness theorem of some axiomatic extensions for the logic $\mathbf {mMTL\forall }$, and thus give a major application, namely, proving the strong completeness theorem for monadic fuzzy predicate logic based on involutive monoidal t-norm logic $\mathbf {mIMTL\forall }$ via functional representation of finitely subdirectly irreducible monadic IMTL-algebras.