Schrödinger's cat in a realist quantum mechanics Arthur Jabs Alumnus, Technical University Berlin. Vossstr. 9, 10117 Berlin, Germany arthur.jabs@alumni.tu-berlin.de (1 November 2016) Abstract. There is no paradox with Schrödinger's cat in a realist interpretation. In particular, a closer look at the temporal aspect shows that the two macroscopic wave functions (alive and dead) of Schrödinger's cat are not to be compared with two superposed parts of a microscopic quantum wave function. Keywords: Schrödinger's cat, macroscopic states, superposition In the thought experiment of Schrödinger's cat in the box [1] consider the superposition c1ψ1 + c2ψ2, (1) where ψ1 is the wave function of the alive and ψ2 that of the dead cat. Actually ψ1 may contain the alive cat together with the undecayed radioactive nucleus and ψ2 the dead cat together with the decayed nucleus, but we neglect this because in our present argumentation it is not essential. The probability of finding, in a measurement (opening the box), an alive cat is |c1ψ1|2 and that of the dead cat |c2ψ2|2. So there seems to be no objection to write the wave function of the cat inside the closed box as the superposition (1), where ψ1 and ψ2 are probability amplitudes and (1) is the wave function of neither a dead nor an alive cat but a superposition of both. Now take the stand of a realist interpretation, where the particles are wavepackets, ψ represents real matter, and reduction (collapse) is independent of measurement [2], [3]. And should the cat die, this occurs during a definite short time interval around, say, t0, even if nobody takes notice of it. The wavepackets ψ1 and ψ2 here represent still the same cat (either definitely alive or definitely dead) but at different times: ψ1 before t0, ψ2 after t0. The superposition (1) then superposes the same real object at different times. If we accepted this we would also have to accept the superposition of an electron wavepacket of today with the same packet of tomorrow. Such a superposition is however nowhere met, not even for microscopic objects, in the formalism of quantum mechanics, independent of the particular interpretation adopted. The less it can justify the superposition (1) of the macroscopic cat wavepackets. 2 What is considered in the γ emission process of the radioactive nucleus is the transition amplitude T= ( φ2(t2), U(t2, t1)φ1(t1) ) , in which U(t2, t1)φ1(t1) means the wavepacket φ1(t2) at the time t2 > t1, after its unitary temporal development from t1 to t2, and T includes the reduction of φ1(t2) to φ2(t2). There is no superposition of φ1(t1) and φ2(t2) as they stand [4], [5]. The decay of the nucleus releases the poison and initiates a process in the cat which ends with its death. This process can in principle be described by the (many-particle) Schrödinger equation plus possible 'internal' reductions among the wavepackets representing the atoms etc. that make up the cat's body [2, Chap. 3]. This is quite different from cases like the Stern-Gerlach experiment. There, a hydrogen atom passes through an inhomogeneous magnetic field, and its wave function is fanned out into a superposition of two spatially separated parts, a spinup part and a spin-down part. The parts reach the screen beyond the magnetic field at the same time, and there the superposition is reduced to one part only. In the Copenhagen view one then compares the spin up part with the alive and the spin down part with the dead cat, and the reduction in the screen with the opening of the cat's box. In realism the difference to the cat wave functions is, however, that both atom wave functions together represent the atom at the same time. Thus, although the superposition (1) for the cat is rejected in a realist interpretation, this does not mean that there is no superposition at all of wavepackets representing macroscopic objects. The restriction is that these wavepackets must represent something that really exists at the same time. Examples can be seen in [6]. Ref. [7] reports on molecules of 1.7 × 10−23 kg (≈ 104 protons) and 5 nm diameter that pass through gratings with slit separation (period) of 266 nm, where interference effects between the parts coming from different slits are indeed observed. Experiments with even larger objects are under way [6], though one difficulty of observing interferences with ever greater objects, such as the cat as a whole, is the increasing importance of environmental decoherence. References [1] Schrödinger, E.: Die gegenwärtige Situation in der Quantenmechanik, Die Naturwissenschaften 23, 807-812, 823-828, 844-849 (1935), the cat appears in §5, p. 812; English translation in: Proc. Am. Philos. Soc. 124, 323-338 (1980) and in: Wheeler, J.A. and Zurek, W.H. (eds.): Quantum Theory and Measurement (Princeton University Press, Princeton, 1983) p. 152-167 [2] Jabs, A.: Quantum mechanics in terms of realism, arXiv:quant-ph/9606017 (2016) [3] Jabs, A.: A conjecture concerning determinism, reduction, and measurement in quantum mechanics, arXiv:1204.0614 (2016) (Quantum Stud.: Math. Found. 3 (4), 279-292 (2016)) 3 - [4] Messiah, A.: Quantum Mechanics (North-Holland Publishing Company, Amsterdam, 1970) Vol. II, Chapter XVII.2 [5] Dirac, P.A.M.: The Principles of Quantum Mechanics (Oxford University Press, London, 1967) Sec. 44 [6] Arndt, M. and Hornberger, K.: Testing the limits of quantum mechanical superpositions, arXiv:1410.0270 (Nature Physics 10, 271-277 (2014)) [7] Eibenberger, S., Gerlich, S., Arndt, M., Mayor, M., Tüxen, M.: Matter-wave interference with particles selected from a molecular library with masses exceeding 10 000 amu, arXiv:1310.8343 (Phys. Chem. Chem. Phys. 15, 1469614700 (2013)) ----------