Completely real? A critical note on the claims by Colbeck and Renner

Following an early suggestion by Dirac, contemporary quantum mechanics (QM) and measurement theory are used to stepwise construct a conceptual framework to chemistry. In QM arbitrary physical quantum states are represented by linear superpositions. Base sets and quantum states are clearly distinguished; the latter are sets of ordered complex numbers. The generator of time evolution $$\fancyscript{H}$$ is shown to have besides the molecular hamiltonian H=H C+K N, the electron–phonon and spin–orbit operators.H is shown diagonal in a product base set formed with generalized electronic diabatic (GED) and nuclear wave functions; the latter represented in a plane wave base set and unique inertial frame; these functions form the GEDM base set. Chemical species are assigned to particular GED base functions and a chemical quantum state is given as a linear superposition in the GEDM base set. Thus, given a fixed number of electrons and nuclei, the GEDM base set includes all electronuclear quantum states from clusters, supermolecule, molecular aggregates, asymptotic states, and ionized states (continuum electron states) to all plasma states. Experimentally measurable quantum states are given by linear superpositions. A chemical process is sensed by amplitude changes involving different electronic states in the linear superposition; vibration states intervene in excitation–relaxation processes; a time evolution of a global quantum 1-system is the feature. If sufficient time is allowed to an isolated system, with a given total energy E, unitary time evolution with $$\fancyscript{H}$$ (but not H) ensures that the system will evolve from the initial state to get amplitudes different from zero for all energy conserving final states. Response towards external dynamic couplings, e.g. electromagnetic fields, is given by changes of amplitudes and expressed in correlation functions. For a quantum state, the amplitude at a given base function reflects the possibility for the system submitted to excitation sources to respond with its spectral signatures; if the experiment is done, and the amplitude is different from zero, then, there will be a response. Algorithms permitting to relate Hilbert space to real space events are discussed. A chemical compound (analyte) is identified to (i) a fixed electronic quantum state; (ii) linear nuclear base states superpositions; (iii) zero amplitude for all other electronic base states. To get this implies either the action of a chemist introducing constraints to bottle the analyte or an accidental change of external (to the box) conditions producing spontaneous separations.

We propose, formulate and examine novel quantum systems and behavioral phases in which momentary choices of the system's memories interact in order to source the internal interactions and unitary time evolutions of the system. In a closed system of the kind, the unitary evolution operator is updated, moment by moment, by being remade out of the system's `experience', that is, its quantum state history. The `Quantum Memory Made' Hamiltonians (QMM-Hs) which generate these unitary evolutions are Hermitian nonlocal-in-time operators composed of arbitrarily-chosen past-until-present density operators of the closed system or its arbitrary subsystems. The time evolutions of the kind are described by novel nonlocal nonlinear von Neumann and Schrödinger equations. We establish that nontrivial Purely-QMM unitary evolutions are `Robustly Non-Markovian', meaning that the maximum temporal distances between the chosen quantum memories must exceed finite lower bounds which are set by the interaction couplings. After general formulation and considerations, we focus on the sufficiently-involved task of obtaining and classifying behavioral phases of one-qubit pure-state evolutions generated by first-to-third order polynomial QMM-Hs made out of one, two and three quantum memories. The behavioral attractors resulted from QMM-Hs are characterized and classified using QMM two-point-function observables as the natural probes, upon combining analytical methods with extensive numerical analyses. The QMM phase diagrams are shown to be outstandingly rich, having diverse classes of unprecedented unitary evolutions with physically remarkable behaviors. Moreover, we show that QMM interactions cause novel purely-internal dynamical phase transitions. Finally, we suggest independent fundamental and applied domains where the proposed `Experience Centric' Unitary Evolutions can be applied natuarlly and advantageously.

This chapter is a translation by E. Crull and G. Bacciagaluppi of Grete Hermann’s hitherto unpublished manuscript on ‘Determinism and Quantum Mechanics’ from 1933. In this fascinating manuscript, sent by Hermann to Bohr, Dirac and Heisenberg, and rediscovered by us in the Dirac Archive, Hermann criticises known arguments for the incompatibility of quantum mechanics and determinism, including the theorem in von Neumann’s 1932 book, and sketches what a completion of quantum mechanics might have to look like.

The long-standing conceptual controversies concerning the interpretation of nonrelativistic quantum mechanics are argued, on one hand, to be due to its incompleteness, as affirmed by Einstein. But on the other hand, it appears to be possible to complete it at least partially, as Bohr might have appreciated it, in the framework of its standard mathematical formalism with observables as appropriately defined self-adjoint operators. This completion of quantum mechanics is based on the requirement on laboratory physics to be effectively confined to a bounded space region and on the application of the von Neumann deficiency theorem to properly define a set of self-adjoint extensions of standard observables, e.g. the momenta and the Hamiltonian, in terms of certain isometries on the region boundary. This is formalized mathematically in the setting of a boundary ontology for the so-called Qbox in which the wave function acquires a supplementary dependence on a set of Additional Boundary Variables (ABV). It is argued that a certain geometric subset of the ABV parametrizing Quasi-Periodic Translational Isometries (QPTI) has a particular physical importance by allowing for the definition of an ontic wave function, which has the property of epitomizing the spatial wave function “collapse.” Concomitantly the standard wave function in an unbounded geometry is interpreted as an epistemic wave function, which together with the ontic QPTI wave function gives rise to the notion of two-wave duality, replacing the standard concept of wave-particle duality. More generally, this approach to quantum physics in a bounded geometry provides a novel analytical basis for a better understanding of several conceptual notions of quantum mechanics, including reality, nonlocality, entanglement and Heisenberg’s uncertainty relation. The scope of this analysis may be seen as a foundational update of the multiple versions 1.x of the Copenhagen interpretation of quantum mechanics, which is sufficiently incremental so as to be appropriately characterized as Copenhagen 2.0.

Prior to her extended stay in Leipzig and her 1935 essay on the foundations of quantum mechanics, Grete Hermann had written a manuscript on ‘Determinism and Quantum Mechanics’, which she had sent to some of the main quantum physicists at the time but had since disappeared. This manuscript was rediscovered by us in the Dirac Archive and appears in translation as Chap. 14 of this volume. In this chapter we give a first analysis of this fascinating manuscript, in which Hermann criticises known arguments for the incompatibility of quantum mechanics and determinism, including the theorem in von Neumann’s 1932 book, and sketches what a completion of quantum mechanics might have to look like.

Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical spacetime is modified or disordered. It is then possible that the right quantum theory of gravity will also be a completion of quantum mechanics in which the foundational puzzles in both are addressed together. I review here the results of a program, developed with Roberto Mangabeira Unger, Marina Cortes and other collaborators, which aims to do just that. The results so far include energetic causal set models, time asymmetric extensions of general relativity and relational hidden variables theories, including real ensemble approaches to quantum mechanics. These models share two assumptions: that physics is relational and that time and causality are fundamental.

Two thought experiments are analyzed, revealing that the quantum state of the universe does not contain definitive evidence of the wavefunction collapse. The first thought experiment shows that unitary quantum evolution alone can account for the outcomes of any combination of quantum experiments. This is in contradiction with the standard view on quantum measurement, which appeals to the wavefunction collapse, but it is in full agreement with the special state proposal (L.S. Schulman in Phys Lett A 102(9):396-400, 1984; J Stat Phys 42(3):689-719 1986; Time's arrows and quantum measurement, Cambridge University Press, Cambridge 1997) that there are some rare states that account for quantum experiments by unitary evolution alone. The second thought experiment consists in successive measurements, and reveals that the standard quantum measurement scheme predicts violations of the conservation laws. It is shown that the standard view on quantum measurements makes some unnecessary assumptions which lead to the apparent necessity to invoke wavefunction collapse. Once these assumptions are removed, a new hope of a measurement scheme emerges, which, while still having open problems, is compatible with both the unitary evolution and the conservation laws, and suggests means to experimentally distinguish between full unitarity and discontinuous collapse.

In many quantum information processing applications, it is important to be able to transfer a quantum state from one location to another — even within a local device. Typical approaches to implement the quantum state transfer rely on unitary evolutions or measurement feedforward operations. However, these existing schemes require many accurate pulse operations and/or precise timing controls. Here, we propose a one-way transfer of the quantum state with near unit efficiency using dissipation from a tailored environment. After preparing an initial state, the transfer can be implemented without external time dependent operations. Moreover, our scheme is irreversible due to the non-unitary evolution, and so the transferred state remains in the same site once the system reaches the steady state. This is in stark contrast to the unitary state transfer where the quantum states continue to oscillate between different sites. Our novel quantum state transfer via the dissipation paves the way toward robust and practical quantum control.

This conference was lauded by Heisenberg as, “officially, the completion of the quantum theory,” while Langevin remarked it was, “where the confusion of ideas reached its peak.” The conference was held just as the theory had reached maturity, only two years after Heisenberg’s matrix mechanics was invented. De Broglie argued for his pilot wave theory, which was shot down by Pauli using an incorrect argument and in later years was re-introduced as the de Broglie–Bohm theory. Heisenberg and Dirac debated the meaning of superposition and the “collapse” of the wave function. Bohr and Einstein engaged in their legendary debate. In the conference proceedings, we see the main contributors to the new theory attempt to come to terms with its enigmas.

<i>The Historical Development of Quantum Theory. Volume 6: The Completion of Quantum Mechanics, 1926-1941</i>

In Episode 53, we described the origins of Fermi’s group in Rome. After the completion of quantum mechanics it had become more and more clear that research had to be redirected from the atomic shell to the nucleus. Accordingly, a cloud chamber and also Geiger–Müller counters were built by the group and put in use.

The Einstein–Bohr Debate on the Completion of Quantum Mechanics and Its Description of Reality (1931–1936)

Bell’s theorem implies that any completion of quantum mechanics which uses hidden variables (that is, preexisting values of all observables) must be nonlocal in the Einstein sense. This customarily indicates that knowledge of the hidden variables would permit superluminal communication. Such superluminal signaling, akin to the existence of a preferred reference frame, is to be expected. However, here we provide a protocol that allows an observer with knowledge of the hidden variables to communicate with her own causal past, without superluminal signaling. That is, such knowledge would contradict causality, irrespectively of the validity of relativity theory. Among the ways we propose for bypassing the paradox there is the possibility of hidden variables that change their values even when the state does not, and that means that signaling backwards in time is prohibited in Bohmian mechanics.

In 1809 Carl Friedrich Gauss' masterpiece “Theoria Motus Corporum Coelestium in sectionibus conicis solem ambientium” on the motion of celestial bodies was published. This book contains also a first version of the famous error propagation formula, which is still the basis of modern metrology and of any relevant national and international standard. Gauss' ideas are reflected in the GUM, the “Guide to the Expression of Uncertainty in Measurement”, published in 1993 by ISO, which is a key document for national measurement institutes and industrial calibration laboratories for evaluating uncertainty in the output of a measurement system. Uncertainty constitutes the main problem of any measurement theory. Because uncertainty is investigated in stochastics, any serious measurement theory should necessarily take into account the state of the art in stochastics. Stochastics was initiated by Jakob Bernoulli in his masterpiece “Ars conjectandi”, which appeared posthumously in 1713, i. e., about 100 years before Gauss established the basis of metrology. The difference between Jakob Bernoulli and Carl Friedrich Gauss is the following: Bernoulli aimed at quantifying and measuring uncertainty, while Gauss aimed at quantifying and measuring a measurement error. In this paper a modern measurement theory based on stochastics is briefly outlined. Subsequently, the antiquated concepts and methods as recommended in the GUM, which go back to the early 19th century, are discussed and their weaknesses are listed.

The usual no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we investigate a relation between the no-cloning theorem and the projective measurement theory that the results of measurements are either + 1 or − 1. We introduce the Kochen-Specker (KS) theorem with the projective measurement theory. We result in the fact that the two quantum states under consideration cannot be orthogonal if we avoid the KS contradiction. Thus the no-cloning theorem implies that the two quantum states under consideration are identical in that case. It turns out that the KS theorem with the projective measurement theory says a new version of the no-cloning theorem. Next, we investigate a relation between the no-cloning theorem and the measurement theory based on the truth values that the results of measurements are either + 1 or 0. We return to the usual no-cloning theorem that the two quantum states are identical or orthogonal in the case.