Macroscopic quantum Schro¨dinger and Einstein–Podolsky–Rosen paradoxes M. D. REID* and E. G. CAVALCANTI Physics Department, The University of Queensland, Brisbane, Australia (Received 15 February 2005; in final form 10 May 2005) We propose macroscopic generalizations of the Einstein–Podolsky–Rosen paradox in which the completeness of quantum mechanics is contrasted with forms of macroscopic reality and macroscopic local reality defined in relation to Schro¨dinger’s original ‘cat’ paradox. 1. Introduction In his famous 1935 essay, Schro¨dinger [1] discussed how ‘ridiculous’ it would be to set up a case where a cat would be described by a superposition of dead and alive states. The underlying assumption in Schro¨dinger’s remark is what we might call ‘macroscopic realism’. This premise states that, even if we accept that microscopic systems do not possess predetermined values for all physical quantities, as quantum mechanics tells us, there can be no such lack of a macroscopic predetermined value, so that the cat must be dead or alive. Leggett [2] discussed the possibility of tests of the existence of macroscopic superpositions. He introduced the idea of macroscopic variables, whose only essential characteristic is that ‘appreciably’ different values of the variable should correspond to macroscopically distinguishable states. In some cases, indeed, two states can be considered macroscopically distinguishable even when the number of particles is not strictly macroscopic. This view has in fact become increasingly frequent in the literature, as pointed out, for example, by Laloe¨ [3]. The work of Leggett and Garg [4] addressed the fundamental issue of proving an incompatibility of quantum mechanics with the premise of ‘macroscopic realism’ defined in conjunction with a ‘macroscopic non-invasive measurability’. This work illustrates the strength and simplicity of the fundamental approach along the lines considered by Bell [5], in which predictions of quantum mechanics are shown to disagree with those of well-defined classical premises, so that an experiment *Corresponding author. Email: margaret@physics.uq.edu.au Journal of Modern Optics Vol. 52, No. 16, 10 November 2005, 2245–2252 Journal of Modern Optics ISSN 0950–0340 print/ISSN 1362–3044 online # 2005 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/09500340500275678