# Weekly Papers on Quantum Foundations (43)

Everettian probabilities, the Deutsch-Wallace theorem and the Principal Principle. (arXiv:2010.11591v1 [quant-ph])

This paper is concerned with the nature of probability in physics, and in quantum mechanics in particular. It starts with a brief discussion of the evolution of Itamar Pitowsky’s thinking about probability in quantum theory from 1994 to 2008, and the role of Gleason’s 1957 theorem in his derivation of the Born Rule. Pitowsky’s defence of probability therein as a logic of partial belief leads us into a broader discussion of probability in physics, in which the existence of objective “chances” is questioned, and the status of David Lewis’ influential Principal Principle is critically examined. This is followed by a sketch of the work by David Deutsch and David Wallace which resulted in the Deutsch-Wallace (DW) theorem in Everettian quantum mechanics. It is noteworthy that the authors of this important decision-theoretic derivation of the Born Rule have different views concerning the meaning of probability. The theorem, which was the subject of a 2007 critique by Meir Hemmo and Pitowsky, is critically examined, along with recent related work by John Earman. Here our main argument is that the DW theorem does not provide a justification of the Principal Principle, contrary to claims by Wallace and Simon Saunders. A final section analyses recent claims to the effect that that the DW theorem is redundant, a conclusion that seems to be reinforced by consideration of probabilities in “deviant’ branches in the Everettian multiverse.

Quantum State Readout, Collapses, Probes and Signals. (arXiv:2010.11804v1 [quant-ph])

Theories involving localized collapse allow the possibility that classical information could be obtained about quantum states without using POVMS and without allowing superluminal signalling. We can model this by extending quantum theory to include hypothetical devices that read out information about the local quantum state at a given point, defined by considering only collapses in its past light cone. Like Popescu-Rohrlich boxes, these hypothetical devices would have practical and scientific implications if realisable. These include signalling through opaque media, probing the physics of distant or opaque systems without needing a reflected signal and giving detailed information about collapse dynamics without requiring direct observation of the collapsing system. These potential applications motivate systematic searches for possible signatures of these nonstandard extensions of quantum theory, and in particular for relevant gravitational effects, such as the validity of semi-classical gravity on small scales.

Identifying weak values with intrinsic dynamical properties through modal quantum mechanics. (arXiv:1812.10257v6 [quant-ph] UPDATED)

The so-called eigenvalue-eigenstate link states that no property can be associated to a quantum system unless it is in an eigenstate of the corresponding operator. This precludes the assignation of properties to unmeasured quantum systems in general. This arbitrary limitation of Orthodox quantum mechanics generates many puzzling situations such as for example the impossibility to define a universal work distribution, an essential building block of quantum thermodynamics. Alternatively, modal theories (e.g., Bohmian mechanics) provide an ontology that is specially suited to define intrinsic properties of general quantum systems that are not in eigensates of the corresponding operators. We prove here that Aharonov, Albert and Vaidman’s weak value can always be identified with intrinsic dynamical property of a quantum system described by a modal theory. Modal (non-Orthodox) theories thus provide a clear-cut physical interpretation of weak values. Furthermore, the fact that weak values are experimentally accessible (to a good approximation as a post-selected ensemble average of weak measurements) strengthens the idea that understanding the intrinsic (unperturbed) dynamics of quantum systems is possible and also useful despite the unavoidable quantum backaction due to the measurement. As an example of the physical soundness of these intrinsic properties, we discuss the Bohmian (intrinsic) dwell time, work distribution and high frequency electrical current.

History entanglement entropy. (arXiv:2009.02331v1 [quant-ph] CROSS LISTED)

Authors: Leonardo Castellani

A formalism is proposed to describe entangled quantum histories, and their entanglement entropy. We define a history vector, living in a tensor space with basis elements corresponding to the allowed histories, i.e. histories with nonvanishing amplitudes. The amplitudes are the components of the history vector, and contain the dynamical information. Probabilities of measurement sequences, and resulting collapse, are given by generalized Born rules: they are all expressed by means of projections and scalar products involving the history vector. Entangled history states are introduced, and a history density matrix is defined in terms of ensembles of history vectors. The corresponding history entropies (and history entanglement entropies for composite systems) are explicitly computed in two examples taken from quantum computation circuits.

How does physics bear upon metaphysics; and why did Plato hold that philosophy cannot be written down?

Publication date: Available online 21 October 2020

Source: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

Author(s): Howard Stein

Searching for dynamical black holes in various theories of gravity. (arXiv:2010.11790v1 [gr-qc])

We construct models of Einstein and $f(R)$ gravity with two scalar fields, which admit analytical solutions describing time-varying dynamical black holes. Their thermodynamics is investigated in the adiabatic approximation. In addition to the Misner-Sharp-Hernandez quasilocal mass, we provide time-dependent thermodynamical quantities, including the Hawking temperature, Helmholtz free energy, entropy, and thermodynamical energy. The latter does not always coincide with the Misner-Sharp-Hernandez mass at the horizon, although they coincide in the static limit. For Schwarzschild-type (i.e., $g_{tt}g_{rr}=-1$) black holes in Einstein gravity, one of the two scalars is always a ghost with negative kinetic energy. We show that this ghost can be avoided in $f(R)$ gravity.

Tests of Quantum Gravity near Measurement Events. (arXiv:2010.11811v1 [gr-qc])

Authors: Adrian Kent (Centre for Quantum Information and Foundations, DAMTP, University of Cambridge and Perimeter Institute for Theoretical Physics)

Experiments have recently been proposed testing whether quantum gravitational interactions generate entanglement between adjacent masses in position superposition states. We propose potentially less challenging experiments that test quantum gravity against theories with classical spacetimes.

Explanation for why the Early Universe was Stable and Dominated by the Standard Model. (arXiv:1911.04648v3 [hep-ph] UPDATED)

Authors: Mark P. HertzbergMudit Jain

The Standard Model (SM) possesses an instability at high scales that would be catastrophic during or just after inflation, and yet no new physics has been seen to alter this. Furthermore, modern developments in quantum gravity suggest that the SM degrees of freedom are not unique; that a typical low energy effective theory should include a large assortment of hidden sector degrees of freedom. It is therefore puzzling that cosmological constraints from BBN and CMB reveal that the early universe was almost entirely dominated by the SM, when the inflaton $\phi$ could have decayed into many sectors. In this work we propose the following explanation for all of this: we allow the lowest dimension operators with natural coefficients between the inflaton and both the Higgs and hidden sectors. Such hidden sectors are assumed to be entirely natural; this means all unprotected masses are pushed up to high scales and project out of the spectrum, while only massless (or protected) degrees of freedom remain, and so the inflaton can only reheat these sectors through higher dimension (and suppressed) operators. On the other hand, the SM possesses a special feature: it includes a light Higgs $H$, presumably for life to exist, and hence it allows a super-renormalizable coupling to the inflaton $\phi H^\dagger H$, which allows rapid decay into the SM. We show that this naturally (i) removes the instability in the Higgs potential both during and after inflation due to a tree-level effect that increases the value of the Higgs self-coupling from the IR to the UV when one passes the inflaton mass, (ii) explains why the SM is dominant in the early universe, (iii) allows dark matter to form in hidden sector/s through subsequent dynamics (or axions, etc), (iv) allows for high reheating and baryogenesis, and (v) accounts for why there so far has been no direct detection of dark matter or new physics beyond the SM.

Quantum electrostatics, Gauss’s law, and a product picture for quantum electrodynamics; or, the temporal gauge revised. (arXiv:2003.07473v2 [hep-th] UPDATED)

Authors: Bernard S. Kay (York)

We provide a theoretical foundation for the notion of the quantum coherent state of the electrostatic field of a static external charge distribution introduced in a 1998 paper and rederive formulae there for the inner products of a pair of such states. Contrary to what one might expect, these inner products are non-zero whenever the total charges of the two charge distributions are equal, even if the charge distributions themselves differ. We actually display two different frameworks for these same coherent states, in the second of which Gauss’s law only holds in expectation value. We propose an experiment capable of ruling that out. The first framework leads to a ‘product picture’ for full QED — i.e. a reformulation of standard QED in which it has a total Hamiltonian, arising as a sum of a free electromagnetic Hamiltonian, a free charged-matter Hamiltonian and an interaction term, acting on a ‘physical subspace’ of the full tensor product of charged-matter and electromagnetic-field Hilbert spaces. (The traditional Coulomb gauge formulation of QED isn’t a product picture because, in it, the longitudinal part of the electric field is a function of the charged matter operators.) We do this for both Maxwell-Dirac and Maxwell-Schr\”odinger QED. For all states in the physical subspace of each of these systems, the charged matter is entangled with longitudinal photons and Gauss’s law holds on the physical subspace as an operator equation; albeit the electric field operator and the Hamiltonian, while self-adjoint on the physical subspace, fail to be self-adjoint on the full tensor-product Hilbert space. Analogues of our coherent state inner products and of the product picture play a role in the author’s matter-gravity entanglement hypothesis. Also, the product picture amounts to a temporal gauge quantization of QED which appears to be free from the difficulties of previous versions.

Effective relational cosmological dynamics from Quantum Gravity. (arXiv:2008.02774v2 [gr-qc] UPDATED)

Authors: Luca MarchettiDaniele Oriti

We discuss the relational strategy to solve the problem of time in quantum gravity and different ways in which it could be implemented, pointing out in particular the fundamentally new dimension that the problem takes in a quantum gravity context in which spacetime and geometry are understood as emergent. We realize concretely the relational strategy we have advocated in the context of the tensorial group field theory formalism for quantum gravity, leading to the extraction of an effective relational cosmological dynamics from quantum geometric models. We analyze in detail the emergent cosmological dynamics, highlighting the improvements over previous work, the contribution of the quantum properties of the relational clock to it, and the interplay between the conditions ensuring a bona fide relational dynamics throughout the cosmological evolution and the existence of a quantum bounce resolving the classical big bang singularity.

Trace dynamics and division algebras: towards quantum gravity and unification. (arXiv:2009.05574v3 [hep-th] UPDATED)

Authors: Tejinder P. Singh

We have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang-Mills fields, and fermions. Dynamical variables are described by odd-grade (fermionic) and even-grade (bosonic) Grassmann matrices. Evolution takes place in Connes time. At energies much lower than Planck scale, trace dynamics reduces to quantum field theory. In the present paper we explain that the correct understanding of spin requires us to formulate the theory in 8-D octonionic space. The automorphisms of the octonion algebra, which belong to the smallest exceptional Lie group $G_2$, replace space-time diffeomorphisms and internal gauge transformations, bringing them under a common unified fold. Building on earlier work by other researchers on division algebras, we propose the Lorentz-weak unification at the Planck scale, the symmetry group being the stabiliser group of the quaternions inside the octonions. This is one of the two maximal subgroups of $G_2$, the other one being $SU(3)$, the element preserver group of octonions. This latter group, coupled with $U(1)_{em}$, describes the electro-colour symmetry, as shown earlier by Furey. We predict a new massless spin one boson [the Lorentz boson] which should be looked for in experiments. Our Lagrangian correctly describes three fermion generations, through three copies of the group $G_2$, embedded in the exceptional Lie group $F_4$. This is the unification group for the four fundamental interactions, and it also happens to be the automorphism group of the exceptional Jordan algebra. Gravitation is shown to be an emergent classical phenomenon. Whereas at the Planck scale, there is present a quantised version of the Lorentz symmetry, mediated by the Lorentz boson. We argue that at sub-Planck scales, the self-adjoint part of the octonionic trace dynamics bears a relationship with string theory in eleven dimensions.

Mathematical languages shape our understanding of time in physics

Gisin, Nicolas (2020) Mathematical languages shape our understanding of time in physics. Nature Physics, 16. pp. 114-119.

Real Numbers are the Hidden Variables of Classical Mechanics

Gisin, Nicolas (2020) Real Numbers are the Hidden Variables of Classical Mechanics. Quantum Studies: Mathematics and Foundations, 7. pp. 197-201.

PROPENSITIES IN A NON-DETERMINISTIC PHYSICS*

Gisin, Nicolas (1991) PROPENSITIES IN A NON-DETERMINISTIC PHYSICS*. Synthese, 89. pp. 287-297. ISSN 1573-0964

Neural Oscillations as Representations

Manolo, Martínez and Marc, Artiga (2020) Neural Oscillations as Representations. [Preprint]

Free will and (in)determinism in the brain: a case for naturalized philosophy

Vervoort, Louis and Blusiewicz, Tomasz (2020) Free will and (in)determinism in the brain: a case for naturalized philosophy. THEORIA. An International Journal for Theory, History and Foundations of Science, 35 (3). pp. 345-364. ISSN 2171-679X

Isotopy and energy of physical networks

Nature Physics, Published online: 19 October 2020; doi:10.1038/s41567-020-1029-z

Recently, a framework was introduced to model three-dimensional physical networks, such as brain or vascular ones, in a way that does not allow link crossings. Here the authors combine concepts from knot theory and statistical mechanics to be able to distinguish between physical networks with identical wiring but different layouts.

Fundamental mentality in a physical world

Abstract

Regardless of whatever else physicalism requires, nearly all philosophers agree that physicalism cannot be true in a world which contains fundamental mentality. I challenge this widely held attitude, and describe a world which is plausibly all-physical, yet which may contain fundamental mentality. This is a world in which priority monism is true—which is the view that the whole of the cosmos is fundamental, with dependence relations directed from the whole to the parts—and which contains only a single mental system, like a brain or computer. Because some properties of the whole are fundamental under priority monism, it follows that that the mental properties of a cosmos-encompassing brain or computer system may be fundamental in a priority monist world. Yet such a world need not contain anything physically unacceptable: the mental properties of the cosmos-encompassing brain or computer can be characterized in a physicalism-friendly functionalist or identity-theoretic way. Thus, as I see it, physicalism need not be false in such a world. This constitutes a challenge to those who hold the view that physicalism is inconsistent with the existence of fundamental mentality.

Do symmetries “explain” conservation principles? The modern converse Noether theorem vs pragmatism

Brown, Harvey R. (2020) Do symmetries “explain” conservation principles? The modern converse Noether theorem vs pragmatism. [Preprint]