Pitts, J. Brian (2020) Conservation of Energy: Missing Features in Its Nature and Justification and Why They Matter. Foundations of Science. ISSN 1233-1821

Lewis, Peter J. (2017) Collapse Theories. [Preprint]

Lewis, Peter J. (2018) Bohmian Philosophy of Mind? [Preprint]

Lewis, Peter J. (2019) On Closing the Circle. [Preprint]

We reconsider the black hole firewall puzzle, emphasizing that quantum error-correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation.

According to an elementary result in quantum computing, any unitary transformation on a composite system can be generated using 2-local unitaries, i.e., those which act only on two subsystems. Beside its fundamental importance in quantum computing, this result can also be regarded as a statement about the dynamics of systems with local Hamiltonians: although locality puts various constraints on the short-term dynamics, it does not restrict the possible unitary evolutions that a composite system with a general local Hamiltonian can experience after a sufficiently long time. We ask if such universality remains valid in the presence of conservation laws and global symmetries. In particular, can k-local symmetric unitaries on a composite system generate all symmetric unitaries on that system? Interestingly, it turns out that the answer is negative in the case of continuous symmetries, such as U(1) and SO(3): unless there are interactions which act non-trivially on every subsystem in the system, some symmetric unitaries cannot be implemented using symmetric Hamiltonians. In fact, the difference between the dimensions of the Lie algebra of all symmetric Hamiltonians and its subalgebra generated by k-local symmetric Hamiltonians with a fixed k, constantly increases with the system size (i.e., the number of subsystems). On the other hand, in the case of group U(1), we find that this no-go theorem can be circumvented if one is allowed to use a pair of ancillary qubits. In particular, any unitary which is invariant under rotations around z, can be implemented using Hamiltonians XX+YY and local Z on qubits. We discuss some implications of these results in the context of quantum thermodynamics and quantum computing.

This note is a part of my efforts for getting rid of nonlocality from quantum mechanics (QM). Quantum nonlocality is two faced Janus, one face is L\”uders projection nonlocality, another face is Bell nonlocality. This paper is devoted to disillusion of the latter. The main casualty of Bell’s model with hidden variables is that it straightforwardly contradicts to the Heinsenberg’s uncertainty and generally Bohr’s complementarity principles. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as it is. The original Einstein-Podolsky-Rosen (EPR) argument was based on the Heinseberg’s principle, but EPR did not question it. Hence, the arguments of EPR and Bell differ crucially. It is worth to find the physical seed of the aforementioned principles. This is the {\it quantum postulate}: the existence of indivisible quantum of action. Bell’s approach with hidden variable straightforwardly implies rejection of the quantum postulate. Heisenberg compared the quantum postulate with constancy of light’s velocity in special relativity. Thus attempts to explain long distance correlations within the Bell model can be compared with attempts to construct models violating the laws of relativity theory. Following Zeilinger, I search for the fundamental principles of quantum mechanics (QM) similar to the principles of relativity and consider the quantum action and complementarity principles as such principles.

It is conjectured that the exceptional-point (EP) singularity of a one-parametric quasi-Hermitian $N$ by $N$ matrix Hamiltonian $H(t)$ can play the role of a quantum phase-transition interface connecting different dynamical regimes of a unitary quantum system. Six realizations of the EP-mediated quantum phase transitions “of the third kind” are described in detail. Fairly realistic Bose-Hubbard (BH) and discrete anharmonic oscillator (AO) models of any matrix dimension $N$ are considered in the initial, intermediate, or final phase. In such a linear algebraic illustration of the changes of phase, all ingredients (and, first of all, all transition matrices) are constructed in closed, algebraic, non-numerical form.

The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex valued Gaussian, looking for relevance to quantum mechanics. Here we show that the Gaussian, with all terms fully complex, acting as a propagator, leads to Schrodinger nonrelativistic equation including scalar and vector potentials, assuming only that the norm is conserved. No prior physical laws need to be postulated. It thereby presents as a process of irregular motion analogous to the real random walk but executed under the rules of the complex number system. Inferences are 1. There is a standard view that Schrodinger equation is deterministic, while wavefunction collapse is probabilistic by Born’s rule. This is opposed by the now demonstrated linkage to the central limit theorem, indicating a stochastic picture for the foundation of Schrodinger equation itself. 2. This picture is also consistent with the dynamic origin of probabilities suggested for the Born rule in the de Broglie Bohm pilot wave theory. Reasons for the primary role of C are open to discussion. The present derivation is compared with recent reconstructions of the quantum formalism, which have the aim of rationalizing its obscurities.

The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or some combination of these. The Bell inequality applicable to data is thus a purely mathematical result independent of experimental test. Correlations of simultaneously cross-correlated variable pairs do not in general all have the same form, and vary with the physical system considered and its experimental configuration. It is the form of correlations of associated data sets that may be tested, and not whether they satisfy the Bell inequality. In the case of pairs of spins or photons, a third measured or predicted value requires a different experimental setup or predictive computation than is used to obtain data from pairs alone. This is due to the quantum non-commutation of spin and photon measurements when there is more than one per particle of a pair. The Wigner inequality for probabilities, with different probabilities for different variable pairs, may be obtained from the four variable Bell inequality under a simple symmetry condition. Neither the probability or correlation inequality is violated by correlations computed from quantum probabilities based on non-commutation.

Authors: Nathan Hagen

Textbooks in physics use science history to humanize the subject and motivate students for learning, but they deal exclusively with the heroes of the field and ignore the vast majority of scientists who have not found their way into history. What is the role of these invisible scientists — are they merely the worker ants in the colony of science, whose main utility is to facilitate the heroes of the field?

Authors: Gia Dvali

We establish that unitarity of scattering amplitudes imposes universal entropy bounds. The maximal entropy of a self-sustained quantum field object of radius R is equal to its surface area and at the same time to the inverse running coupling evaluated at the scale R. The saturation of these entropy bounds is in one-to-one correspondence with the non-perturbative saturation of unitarity by 2-to-N particle scattering amplitudes at the point of optimal truncation. These bounds are more stringent than Bekenstein’s bound and in a consistent theory all three get saturated simultaneously. This is true for all known entropy-saturating objects such as solitons, instantons, baryons, oscillons, black holes or simply lumps of classical fields. We refer to these collectively as “saturons” and show that in renormalizable theories they behave in all other respects like black holes. Finally, it is argued that the confinement in SU(N) gauge theory can be understood as a direct consequence of the entropy bounds and unitarity.

Abstract

The free energy principle says that any self-organising system that is at nonequilibrium steady-state with its environment must minimize its (variational) free energy. It is proposed as a grand unifying principle for cognitive science and biology. The principle can appear cryptic, esoteric, too ambitious, and unfalsifiable—suggesting it would be best to suspend any belief in the principle, and instead focus on individual, more concrete and falsifiable ‘process theories’ for particular biological processes and phenomena like perception, decision and action. Here, I explain the free energy principle, and I argue that it is best understood as offering a conceptual and mathematical analysis of the concept of existence of self-organising systems. This analysis offers a new type of solution to long-standing problems in neurobiology, cognitive science, machine learning and philosophy concerning the possibility of normatively constrained, self-supervised learning and inference. The principle can therefore uniquely serve as a regulatory principle for process theories, to ensure that process theories conforming to it enable self-supervision. This is, at least for those who believe self-supervision is a foundational explanatory task, good reason to believe the free energy principle.

Duncan, Anthony and Janssen, Michel (2002) Quantization Conditions, 1900–1927. [Preprint]

De Haro, Sebastian (2019) The Heuristic Function of Duality. Synthese, 196. pp. 5169-5203. ISSN 1573-0964

Abstract

Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws (the role of determining local inertial structure). I raise two objections to this inertial functionalism. First, it depends on a prior assumption about which coordinate systems defined in a theory are reference frames, and hence on assumptions about which geometric structures are spatiotemporal. This makes Knox’s account circular. Second, her account is vulnerable to several counterexamples, giving the wrong result when applied to topological quantum field theories and parity- and time-asymmetric theories. I advance an alternative account on which our spacetime concept is a cluster concept. On this view, the notion of metaphysical fundamentality may feature in the cluster, in which case spacetime functionalism may be uninformative in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate.

Christian, Joy (2020) Oversights in the Respective Theorems of von Neumann and Bell are Homologous. [Preprint]

Author(s): Stella Seah, Stefan Nimmrichter, and Valerio Scarani

We discuss a self-contained spin-boson model for a measurement-driven engine, in which a demon generates work from thermal excitations of a quantum spin via measurement and feedback control. Instead of granting it full direct access to the spin state and to Landauer’s erasure strokes for optimal per…

[Phys. Rev. Lett. 124, 100603] Published Tue Mar 10, 2020

Ritson, Sophie (2016) The Many Dimensions of the String Theory Wars. PhD Thesis – University of Sydney.

De Haro, Sebastian and van Dongen, Jeroen and Visser, Manus and Butterfield, Jeremy (2020) Conceptual Analysis of Black Hole Entropy in String Theory. Studies in History and Philosophy of Modern Physics, 69. pp. 82-111. ISSN 1355-2198

van Dongen, Jeroen and De Haro, Sebastian and Visser, Manus and Butterfield, Jeremy (2020) Emergence and Correspondence for String Theory Black Holes. Studies in History and Philosophy of Modern Physics, 69. pp. 112-127. ISSN 1355-2198

Abstract

The Frauchiger–Renner Paradox is an extension of paradoxes based on the “Problem of Measurement,” such as Schrödinger’s Cat and Wigner’s Friend. All these paradoxes stem from assuming that quantum theory has only unitary (linear) physical dynamics, and the attendant ambiguity about what counts as a ‘measurement’—i.e., the inability to account for the observation of determinate measurement outcomes from within the theory itself. This paper discusses a basic inconsistency arising in the FR scenario at a much earlier point than the derived contradiction: namely, the inconsistency inherent in treating an improper mixture (reduced density operator) as a proper, epistemic mixture. This is an illegitimate procedure that is nevertheless endemic if quantum theory is assumed to be always unitary. In contrast, under a non-unitary account of quantum state reduction yielding determinate outcomes, the use of a proper mixture for measurement results becomes legitimate, and this entire class of paradoxes cannot be mounted. The conclusion is that the real lesson of the FR paradox is that it is the unitary-only assumption that needs to be critically reassessed.

Abstract

The indistinguishability of bosons and fermions has been an essential part of our ideas of quantum mechanics since the 1920s. But what is the mathematical basis for this indistinguishability? An answer was provided in the group representation theory that developed alongside quantum theory and quickly became a major part of its mathematical structure. In the 1930s such a complex and seemingly abstract theory came to be rejected by physicists as the standard functional analysis picture presented by John von Neumann (in his book Mathematical Foundations of Quantum Mechanics) took hold. The purpose of the present account is to show how indistinguishability is explained within representation theory.

Nature Physics, Published online: 09 March 2020; doi:10.1038/s41567-020-0822-z

Small-angle neutron scattering measurements show that the vortices of the heavy-fermion compound UPt3 possess an internal degree of freedom in one of its three superconducting phases, implying the breaking of time-reversal symmetry in the bulk.

Nature Physics, Published online: 09 March 2020; doi:10.1038/s41567-020-0807-y

The modes of the radiation field generated from an emitter are usually determined by the eigenstates of the surrounding environment. However, this scenario breaks down in a non-Hermitian system, at the spectral degeneracy known as an exceptional point.