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In this article we investigate the application of complex split biquaternions and bioctonions to the standard model. We show that the Clifford algebras Cl(3) and Cl(7) can be used for making left-right symmetric fermions. Hence we incorporate right-handed neutrinos in the division algebras based approach to the standard model. The right-handed neutrinos, also known as sterile neutrinos, are a potential dark-matter candidate. We discuss the left-right symmetric fermions and their phenomenology using the division algebra approach. We describe the gauge groups associated with the left-right symmetric model and prospects for unification through division algebras. We investigate the possibility of obtaining three generations of fermions and charge/mass ratios through the exceptional Jordan algebra $J_3(O)$ and the exceptional groups $F_4$ and $E_6$., Comment: 20 pages, 2 figures, accepted for publication in Advances in Applied Clifford algebras

There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for constructing such a theory, which is also a unification of the standard model with gravitation, are : (i) the pre-quantum theory of trace dynamics – a matrix-valued Lagrangian dynamics, (ii) the spectral action principle of non-commutative geometry, (iii) the number system known as the octonions, for constructing a non-commutative manifold and for defining elementary particles via Clifford algebras, (iv) a Lagrangian with $E_8 \times E_8$ symmetry. The split bioctonions define a sixteen dimensional space (with left-right symmetry) whose geometry (evolving in Connes time) relates to the four known fundamental forces, while predicting two new forces, $SU(3)_{grav}$ and $U(1)_{grav}$. This latter interaction is possibly the theoretical origin of MOND. Coupling constants of the standard model result from left-right symmetry breaking, and their values are theoretically determined by the characteristic equation of the exceptional Jordan algebra of the octonions. The quantum-to-classical transition, precipitated by the entanglement of a critical number of fermions, is responsible for the emergence of classical spacetime, and also for the familiar formulation of quantum theory on a spacetime background.

Perforated gastrojejunal ulcers are a known complication following Roux-en-Y gastric bypass (RYGB) surgery requiring emergent surgical repair. The robotic approach has not been evaluated for emergency general surgery. A retrospective cohort study from 2015 to 2019 was performed identifying all patients who underwent repair of perforated gastrojejunal ulcers after RYGB at a single institution. Patient characteristics and outcomes were compared by robotic or laparoscopic approach. Of the 44 patients analyzed, there were 24 robotic and 20 laparoscopic repairs of perforated gastrojejunal ulcers. No patients were initially approached with open surgery. In-room-to-surgery-start time was significantly faster in the robotic group than the laparoscopic group (25 versus 31 min, p = 0.01). Complication rate, complication severity, operating time, hospital length of stay, postoperative vasopressor requirement, discharge to home, hospital length of stay and 30-day readmission were all improved in the robotic group, although these were not statistically significant. Both total inpatient and procedural costs were more in the robotic group than the laparoscopic group. Perforated hollow viscus is not a contraindication for the use of the surgical robot, which may improve outcomes.

This article gives an elementary account of the recently proposed theory of spontaneous quantum gravity. It is argued that a viable quantum theory of gravity should be falsifiable, and hence it should dynamically explain the observed absence of quantum superpositions of space-time geometries in its classical limit., Comment: v2: 28 pages, 1 figure, Typos corrected

We have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics. This is a Lagrangian dynamics in which the matrix degrees of freedom are made from Grassmann numbers, and the Lagrangian is trace of a matrix polynomial. Matrices made from even grade elements of the Grassmann algebra are called bosonic, and those made from odd grade elements are called fermionic: together they describe an `aikyon'. In the present article we provide a basic definition of spin angular momentum in this matrix dynamics, and introduce a bosonic (fermionic) configuration variable conjugate to the spin of a boson (fermion). We then show that at energies below Planck scale, where the matrix dynamics reduces to quantum theory, fermions have half-integer spin (in multiples of Planck's constant), and bosons have integral spin. We also show that this definition of spin agrees with the conventional understanding of spin in relativistic quantum mechanics. Consequently, we obtain an elementary proof for the spin-statistics connection. We then motivate why an octonionic space is the natural space in which an aikyon evolves. The group of automorphisms in this space is the exceptional Lie group $G_2$ which has fourteen generators [could they stand for the twelve vector bosons and two degrees of freedom of the graviton? ]. The aikyon also resembles a closed string, and it has been suggested in the literature that 10-D string theory can be represented as a 2-D string in the 8-D octonionic space. From the work of Cohl Furey and others it is known that the Dixon algebra made from the four division algebras [real numbers, complex numbers, quaternions and octonions] can possibly describe the symmetries of the standard model. In the present paper we outline how in our work the Dixon algebra arises naturally, and could lead to a unification of gravity with the standard model., v3. 26 pages, 2 figures, concluding paragraph on comparison with string theory added, references updated, typos corrected, accepted for publication in Zeitschrift fur Naturforschung A

We have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics. This is a Lagrangian dynamics in which the matrix degrees of freedom are made from Grassmann numbers, and the Lagrangian is trace of a matrix polynomial. Matrices made from even grade elements of the Grassmann algebra are called bosonic, and those made from odd grade elements are called fermionic. In the present article, we provide a basic definition of spin angular momentum in this matrix dynamics, and introduce a bosonic(fermionic) configuration variable conjugate to the spin of a boson(fermion). We then show that at energies below Planck scale, where the matrix dynamics reduces to quantum theory, fermions have half-integer spin (in multiples of Planck’s constant), and bosons have integral spin. We also show that this definition of spin agrees with the conventional understanding of spin in relativistic quantum mechanics. Consequently, we obtain an elementary proof for the spin-statistics connection.

Spontaneous localisation is a falsifiable dynamical mechanism which modifies quantum mechanics, and explains the absence of position superpositions in the macroscopic world. However, this is an ad hoc phenomenological proposal. Adler's theory of trace dynamics, working on a flat Minkowski space-time, derives quantum (field) theory, and spontaneous localisation, as a thermodynamic approximation to an underlying non-commutative matrix dynamics. We describe how to incorporate gravity into trace dynamics, by using ideas from Connes' non-commutative geometry programme. This leads us to a new quantum theory of gravity, from which we can predict spontaneous localisation, and give an estimate of the Bekenstein-Hawking entropy of a Schwarzschild black hole., v3: 46 pages, 2 figures, Minor typos in v2 corrected. Accepted for publication in Zeitschrift fur Naturforschung A

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This theory offers the prospect of unifying internal symmetries of the standard model with pre-gravitation. We explain why such a quantum gravitational dynamics is in principle essential even at energies much smaller than Planck scale. The dynamics can also predict the values of free parameters of the low energy standard model: these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the exceptional Jordan algebra $J_3(8)$ which describes the three fermion generations. We use the octonionic representation of fermions to compute the eigenvalues of the characteristic equation of this algebra, and compare the resulting eigenvalues with known mass ratios for quarks and leptons. We show that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios. In conjunction with the trace dynamics Lagrangian, these eigenvalues also yield a theoretical derivation of the low energy fine structure constant., Comment: v2: 67 pages, 11 figures, minor changes in text so as to improve clarity; accepted for publication in `The European Physical Journal Plus'; arXiv admin note: substantial text overlap with arXiv:2110.02062

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued La-grangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal symmetries of the standard model with gravity. It can also predict the values of free parameters of the standard model, because these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the algebra J3 (O) [exceptional Jordan algebra] which in turn is related to the three fermion generations. The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional Lie group F4. These matrices admit a cubic characteristic equation whose eigenvalues are real and depend on the invariant trace, determinant, and an inner product made from the Jordan matrix. Also, there is some evidence in the literature that the groups F4 and E6 could play a role in the unification of the standard model symmetries, including the Lorentz symmetry. The octonion algebra is known to correctly yield the electric charge values (0, 1/3, 2/3, 1) for standard model fermions, via the eigenvalues of a U (1) number operator, identified with U (1)em. In the present article, we use the same octonionic representation of the fermions to compute the eigenvalues of the characteristic equation of the Albert algebra, and compare the resulting eigenvalues with the known mass ratios for quarks and leptons. We find that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios for quarks and charged leptons. We also propose a diagrammatic representation of the standard model bosons, Higgs and three fermion generations, in terms of the octonions, exhibiting an F4 and E6 symmetry. In conjunction with the trace dynamics Lagrangian, the Jordan eigenvalues also provide a first principles theoretical derivation of the low energy value of the fine structure constant, yielding the value 1/137.04006. The Karolyhazy correction to this value gives an exact match with the measured value of the constant, after assuming a specific value for the electro-weak symmetry breaking energy scale.

For the last 20 years, controversies in robotic surgery focused on cost reduction, development of new platforms and technologies, creation and validation of curriculum and virtual simulators, and conduction of randomized clinical trials to determine the best applications of robotics [Leal Ghezzi and Campos in World J Surg 40:2550–2557, 2016]. This review explores the robotic systems which are currently indicated for use or development in gastrointestinal/abdominal surgery. These systems are reviewed and analyzed for clinical impact in these areas. In a MEDLINE search of articles with the search terms abdominal, gastrointestinal, review and robotic surgery, a total of 4306 total articles as of 2021 were assessed. Publicly available information, highest cited articles and reviews were assessed by the authors to determine the most significant regarding clinical outcomes. Despite this increased number of articles related to robotic surgery, ongoing controversies have led to limitation in the use of current and future robotic surgery platforms [Connelly et al. in J Robotic Surg 14:155–165, 2020]. Newer robotic platforms have limited studies or analysis that would allow meaningful definite conclusions. A multitude of new scenarios are possible due to this limited information. Robotic surgery is in evolution to a larger conceptual field of computationally enhanced surgery (CES). Various terms have been used in the literature including computer-assisted surgery or digital Surgery [Ranev and Teixeira in Surg Clin North Am 100:209–218, 2020]. With the growth of technological changes inherent in CES, the ability to validate these improvements in outcomes will require new metrics and analytic tools. This learning feedback and metric analysis will generate the new opportunities in simulation, training and application [Julian and Smith in Int J Med Robot 15:e2037, 2019].

Short-term success following robotic-assisted ventral hernia repair (RVHR) is well established; however, data describing outcomes after the first year are limited. In this study, we followed a cohort of patients with an average of 1.8 years of follow-up to demonstrate the durability of this technique and examine risk factors for recurrence. A retrospective analysis of RVHR performed by a single surgeon from 2012 to 2016 was done. The technical approach for hernia repair consisted of tension-free primary fascial closure with placement of preperitoneal mesh when possible. The primary end point of hernia recurrence was determined based on physical examination or imaging documented in the medical record. A logistic regression model was used to identify patient risk factors for recurrence. One hundred and eight RVHRs were performed over 4 years. Mean age was 52.72 ± 13.61 years, BMI was 33.07 ± 7.82 kg/m2, and hernia defect size was 70.1 ± 86.3 cm2. In terms of patient characteristics, 17.6% of patients were diabetic, 13.9% were smokers preoperatively, 72.2% were ASA class 3 or higher, and 29.6% had prior VHR. Primary fascial closure was achieved in all RVHRs, with 23.1% requiring component separation. Mesh was used in 97.2% of patients: 79.5% had preperitoneal mesh and 17.6% had intraperitoneal onlay mesh. Ninety-eight percent of patients had long-term follow-up at a mean of 625.6 days. Recurrence rate was 12%, with one recurrence attributed to an inguinal hernia fixed concurrently with a midline defect. There were no statistically significant differences in gender, age, BMI, ASA class, incidence of diabetes, smoking status, or number of previous hernia repairs. Hernia defect size and perioperative complications including SSO, ileus, obstruction, or any other medical complication were not predictive of recurrence. Technical approach did not affect outcomes. RVHR is safe and durable with a low recurrence rate at a mean of 21 months postoperatively. Patient characteristics or type of repair were not predictive of recurrence.

We recall that in order to obtain the classical limit of quantum mechanics one needs to take the $\hbar\rightarrow 0$ limit. In addition, one also needs an explanation for the absence of macroscopic quantum superposition of position states. One possible explanation for the latter is the Ghirardi-Rimini-Weber (GRW) model of spontaneous localisation. Here we describe how spontaneous localisation modifies the path integral formulation of density matrix evolution in quantum mechanics. (Such a formulation has been derived earlier by Pearle and Soucek; we provide two new derivations of their result). We then show how the von Neumann equation and the Liouville equation for the density matrix arise in the quantum and classical limit, respectively, from the GRW path integral. Thus we provide a rigorous demonstration of the quantum to classical transition., v1: 17 pages, 2 figures; v2: 18 pages, 2 figures, Refs. 4-6 added; v3: 18 pages, parts of the paper rewritten to improve clarity, no change in conclusions; v4: 17 pages, edited in response to referee comments, accepted for publication in Zeitschrift fur Naturforschung A

We present a new, falsifiable, quantum theory of gravity, which we name Non-commutative Matter-Gravity. The commutative limit of the theory is classical general relativity. In the first two papers of this series, we have introduced the concept of an atom of space-time-matter [STM], which is described by the spectral action in non-commutative geometry, corresponding to a classical theory of gravity. We used the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derived the spectral equation of motion for the gravity part of the STM atom, which turns out to be the Dirac equation on a non-commutative space. In the present work, we propose how to include the matter (fermionic) part and give a simple action principle for the STM atom. This leads to the equations for a quantum theory of gravity, and also to an explanation for the origin of spontaneous localisation from quantum gravity. We use spontaneous localisation to arrive at the action for classical general relativity [including matter sources] from the action for STM atoms., Comment: v1: 25 pages (this paper is a follow-up of arXiv:1903.05402v2 and arXiv:1906.08248v3). This version v2: minor changes, references updated, to appear in Zeitschrift fur Naturforschung A

We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu-Goto + Kalb-Ramond string . We explain why this is a significant gravitational theory, and in what sense classical general relativity is an approximation to it. We propose that a non-commutative generalisation of this theory (in the sense of Connes' non-commutative geometry and Adler's Trace Dynamics) is a `quantum theory of gravity'. The theory is in fact a classical matrix dynamics with only two fundamental constants -- the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of non-commuting coordinates.The action for this non-commutative torsion gravity can be elegantly expressed as an invariant area integral, and represents an atom of space-time-matter. The statistical thermodynamics of a large number of such atoms yields the laws of quantum gravity and quantum field theory, at thermodynamic equilibrium. Spontaneous localisation caused by large fluctuations away from equilibrium is responsible for the emergence of classical space-time and the field equations of classical general relativity. The resolution of the quantum measurement problem by spontaneous collapse is an inevitable consequence of this process. Quantum theory and general relativity, are both seen as emergent phenomena, resulting from coarse-graining of the underlying non-commutative geometry. We explain the profound role played by entanglement in this theory: entanglement describes interaction between the atoms of space-time-matter, and indeed entanglement appears to be more fundamental than quantum theory or space-time. We also comment on possible implications for black hole entropy and evaporation, and for cosmology., v2: 32 pages, 1 figure, Section I borrows some text (overview of trace dynamics) from arXiv:1701.09132v1 [quant-ph], revised in response to reviewer comments: list of revisions appended after bibliography; accepted for publication in Zeitschrift fur Naturforschung

By invoking an asymmetric metric tensor, and borrowing ideas from non-commutative geometry, string theory, and trace dynamics, we propose an action function for quantum gravity. The action is proportional to the four dimensional non-commutative curvature scalar (which is torsion dependent) that is sourced by the Nambu-Goto world-sheet action for a string, plus the Kalb-Ramond string action. This `quantum gravity' is actually a non-commutative {\it classical} matrix dynamics, and the only two fundamental constants in the theory are the square of Planck length and the speed of light. By treating the entity described by this action as a microstate, one constructs the statistical thermodynamics of a large number of such microstates, in the spirit of trace dynamics. Quantum field theory (and $\hbar$) and quantum general relativity (and $G$) emerge from the underlying matrix dynamics in the thermodynamic limit. The statistical fluctuations that are inevitably present about equilibrium, are the source for spontaneous localisation, which drives macroscopic quantum gravitational systems to the classical general relativistic limit. While the mathematical formalism governing these ideas remains to be developed, we hope here to highlight the deep connection between quantum foundations, and the sought for quantum theory of gravity. In the sense described in this article, ongoing experimental tests of spontaneous collapse theories are in fact also tests of string theory!, v1: 7 pages, one figure; v2: 7 pages, one figure, minor modifications, accepted for publication in Zeitschrift f\"ur Naturforschung

There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang-Mills fields, and fermions. The definition of spin in this theory leads us to an eight dimensional octonionic space-time. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions., Comment: 9 pages, honorable mention in Gravity Research Foundation Essay Contest 2021, v2: references updated. arXiv admin note: substantial text overlap with arXiv:2110.02062

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal symmetries of the standard model with gravity. It can also predict the values of free parameters of the standard model, because these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the algebra $J_3(\mathbb O)$ [exceptional Jordan algebra] which in turn is related to the three fermion generations. The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional Lie group $F_4$. These matrices admit a cubic characteristic equation whose eigenvalues are real and depend on the invariant trace, determinant, and an inner product made from the Jordan matrix. Also, there is some evidence in the literature that the group $F_4$ could play a role in the unification of the standard model symmetries, including the Lorentz symmetry. The octonion algebra is known to correctly yield the electric charge values (0, 1/3, 2/3, 1) for standard model fermions, via the eigenvalues of a $U(1)$ number operator, identified with $U(1)_{em}$. In the present article, we use the same octonionic representation of the fermions to compute the eigenvalues of the characteristic equation of the Albert algebra, and compare the resulting eigenvalues with the known mass ratios for quarks and leptons. We find that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios for up, charm and top quark. We also propose a diagrammatic representation of the standard model bosons, Higgs and three fermion generations, in terms of the octonions, exhibiting an $F_4$ symmetry. We motivate from our Lagrangian as to why the eigenvalues computed in this work could bear a relation with mass ratios of quarks and leptons. In conjunction with the trace dynamics Lagrangian, the Jordan eigenvalues also provide a first principles theoretical derivation of the low energy value of the fine structure constant, yielding the value $1/137.04006$. The Karolyhazy correction to this value gives an exact match with the measured value of the constant, after assuming a specific value for the electro-weak symmetry breaking energy scale.

We have recently proposed a Lagrangian in trace dynamics, to describe a possible unification of gravity, Yang-Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity - called the aikyon - is invariant under global unitary transformations, and as a result possesses a novel conserved charge, known as the Adler-Millard charge. In the present paper, we derive an eigenvalue equation, analogous to the time-independent Schr\"{o}dinger equation, for the Hamiltonian of the theory. We show that in the emergent quantum theory, the energy eigenvalues of the aikyon are characterised in terms of a fundamental frequency times Planck's constant. The eigenvalues of this equation can, in principle, determine the values of the parameters of the standard model. We also report a ground state, in this theory of spontaneous quantum gravity, which could characterise a non-singular initial epoch in quantum cosmology., Comment: 18 pages, published in Mod. Phys. Lett. A

We provide theoretical evidence that the neutrino is a Majorana fermion. This evidence comes from assuming that the standard model and beyond-standard-model physics can be described through division algebras, coupled to a quantum dynamics. We use the division algebras scheme to derive mass ratios for the standard model charged fermions of three generations. The predicted ratios agree well with the observed values if the neutrino is assumed to be Majorana. However, the theoretically calculated ratios completely disagree with known values if the neutrino is taken to be a Dirac particle. Towards the end of the article we discuss prospects for unification of the standard model with gravitation if the assumed symmetry group of the theory is $E_6$, and if it is assumed that space-time is an 8D octonionic space-time, with 4D Minkowski space-time being an emergent approximation. Remarkably, we find evidence that the precursor of classical gravitation, described by the symmetry $SU(3)_{grav} \times SU(2)_R \times U(1)_{grav}$ is the right-handed counterpart of the standard model $SU(3)_{color} \times SU(2)_L \times U(1)_Y$., Comment: v2. 39 pages, 2 figures, partly rewritten in response to reviewer recommendations so as to improve clarity, results unchanged, accepted for publication in Journal of Physics G: Nuclear and Particle Physics

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., v4. 70 pages, 4 figures, references updated, published online in Zeitschrift fur Naturforschung A

We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also space-time points, are raised to the status of matrices [equivalently operators]. These matrices obey a deterministic Lagrangian dynamics at the Planck scale. By coarse-graining this matrix dynamics over time intervals much larger than Planck time, one derives quantum theory as a low energy emergent approximation. If a sufficiently large number of degrees of freedom get entangled, spontaneous localisation takes place, leading to the emergence of classical space-time geometry and a classical universe. In our theory, dark energy is shown to be a large-scale quantum gravitational phenomenon. Quantum indeterminism is not fundamental, but results from our not probing physics at the Planck scale., Comment: v2: 8 pages; Typo corrected, Honourable mention, GRF essay contest 2020. Accepted for publication in Int. J. Mod. Phys. D

We propose that space-time results from collapse of the wave function of macroscopic objects, in quantum dynamics. We first argue that there ought to exist a formulation of quantum theory which does not refer to classical time. We then propose such a formulation by invoking an operator Minkowski space-time on the Hilbert space. We suggest relativistic spontaneous localisation as the mechanism for recovering classical space-time from the underlying theory. Quantum interference in time could be one possible signature for operator time, and in fact may have been already observed in the laboratory, on attosecond time scales. A possible prediction of our work seems to be that interference in time will not be seen for `time slit' separations significantly larger than 100 attosecond, if the ideas of operator time and relativistic spontaneous localisation are correct., Comment: v2: 12 pages, 6 figures, clarifying remarks added, has text overlap with arXiv:1806.01297 [gr-qc], to appear in Zeitschrift f\"ur Naturforschung A

The Ghirardi-Rimini-Weber theory of spontaneous collapse offers a possible resolution of the quantum measurement problem. In this theory, the wave function of a particle spontaneously and repeatedly localises to one or the other random position in space, as a consequence of the hypothesised quantum jumps. In between jumps, the wave function undergoes the usual Schrödinger evolution. In the present paper, we suggest that these jumps take place in Hilbert space, with no reference to physical space and a physical three-dimensional space arises as a consequence of localisation of macroscopic objects in the universe. That is, collapse of the wave-function is responsible for the origin of space. We then suggest that similar jumps take place for a hypothetical time operator in Hilbert space and classical time, as we know it emerges from localisation of this time operator, for macroscopic objects. More generally, the jumps are suggested to take place in an operator space-time in Hilbert space, leading to an emergent classical space-time.

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

The Karolyhazy uncertainty relation is the statement that if a device is used to measure a length $l$, there will be a minimum uncertainty $\delta l$ in the measurement, given by $(\delta l)^3 \sim L_P^2\; l$. This is a consequence of combining the principles of quantum mechanics and general relativity. In this note we show how this relation arises in our approach to quantum gravity, in a bottom-up fashion, from the matrix dynamics of atoms of space-time-matter. We use this relation to define a space-time-matter foam at the Planck scale, and to argue that our theory is holographic. By coarse graining over time scales larger than Planck time, one obtains the laws of quantum gravity. Quantum gravity is not a Planck scale phenomenon; rather it comes into play whenever no classical space-time background is available to describe a quantum system. Space-time and classical general relativity arise from spontaneous localisation in a highly entangled quantum gravitational system. The Karolyhazy relation continues to hold in the emergent theory. An experimental confirmation of this relation will constitute a definitive test of the quantum nature of gravity., Comment: v2. 15 pages, one figure, title changed, introductory remarks added, references updated, to appear in Pramana - Journal of Physics

Excessive fat accumulation in the gastrointestinal tract is pathologic. Gastric mucosal polyposis due to excessive submucosal fat infiltration in a bariatric partial gastrectomy specimen was encountered, which has not been described in the literature. This observation prompted us to assess the extent of fat in gastric submucosa and study the incidence of mucosal polyposis due to submucosal fat accumulation in morbidly obese patients. Archived pathology slides of 128 bariatric partial gastrectomy specimens including the index case and 89 control cases obtained from Whipple’s procedure were examined. The amount of submucosal fat was categorized as 0 (no fat), 1 (up to 70% fat), and 2 (> 70% fat). The maximum submucosal fat thickness was measured with the interval cutoff of 5 mm and 10 mm. Of the 128 cases, 90 (70.3%) were category 1 and 31 (24.2%) were category 2. Maximum submucosal fat thickness was > 10 mm in 3 (2.3%) cases including the index case. The extent of submucosal fat accumulation correlated with the body mass index. The frequencies of category 2 and > 10 mm of fat thickness were higher in the bariatric patient group compared with the control group. We propose a submucosal fat thickness of > 10 mm and diffuse (> 70%) fat accumulation as diagnostic criteria for gastric lipohyperplasia. Using these criteria, the prevalence of gastric lipohyperplasia in the morbidly obese population is 2.3%. A subset of these may present as gastric mucosal polyps.

In our recently proposed quantum theory of gravity, the universe is made of `atoms' of space-time-matter (STM). Planck scale foam is composed of STM atoms with Planck length as their associated Compton wave-length. The quantum dispersion and accompanying spontaneous localisation of these STM atoms amounts to a cancellation of the enormous curvature on the Planck length scale. However, an effective dark energy term arises in Einstein equations, of the order required by current observations on cosmological scales. This happens if we propose an extremely light particle having a mass of about $10^{-33} \ {\rm eV/c^2}$, forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about $10^{122}$ such particles in the observed universe. Their net effect on space-time geometry is equivalent to dark energy, this being a low energy quantum gravitational phenomenon. In this sense, the observed dark energy constitutes evidence for quantum gravity. We then invoke Dirac's large number hypothesis to also propose a dark matter candidate having a mass halfway (on the logarithmic scale) between the proton and the dark energy particle, i.e. about $10^{-12}\ {\rm eV/c^2}$., Comment: v2: 11 pages, material added at the end (Eqn. 8 onwards): (i) a quantum-classical duality (ii) role of Planck length in explaining the quantum-classical transition. This version v3: 21 pages. Discussion section and Appendix added in response to referee comments. Ref. 19-24 newly added. Conclusions unchanged. Accepted for publication in Mod. Phys. Lett. A

In the first paper of this series, we have introduced the concept of an atom of space-time-matter [STM], which is described by the spectral action of non-commutative geometry, corresponding to a classical theory of gravity. In the present work, we use the Connes time parameter along with the spectral action, to incorporate gravity into trace dynamics. We then derive the spectral equation of motion for the STM atom, which turns out to be the Dirac equation on a non-commutative space., Comment: v3: 7 pages, refs. updated; this paper is follow-up of arXiv:1903.05402v2 [gr-qc]; to appear in Zeitschrift f\"ur Naturforschung A - A Journal of Physical Sciences

The physical universe is made up of objects and events in space and time. We refer to them collectively as Things. How does the human mind convert things in the observed universe, into laws? What role does our consciousness play in this conversion process? We propose that the dynamic pathways connecting the neurons in our brains have a dual interpretation, as a thing-law. The pathways are things, by virtue of their material nature. However, our consciousness also accords a pathway the interpretation of a law, which could be a thought, an idea, an emotion, a number, a geometrical figure, a physical law, or a mathematical theorem. The mind’s conversion of things into laws is what we call the horizontal fundamental. But are laws different from things? In the emergent complex universe, apparently yes. However, as we dig deeper and deeper into the reductionist layers of reality, a process we call the vertical fundamental, laws and things become more and more like each other, until deepest down, they become one and the same.

Models of spontaneous wave function collapse predict a small heating rate for a bulk solid, as a result of coupling to the noise field that causes collapse. This rate is small enough that ambient radioactivity and cosmic ray flux on the surface of the earth can mask the heating due to spontaneous collapse. In this paper we estimate the background noise due to gamma-radiation and cosmic ray muon flux, at different depths. We demonstrate that a low-temperature underground experiment at a depth of about 6.5 km.w.e. would have a low enough background to allow detection of bulk heating for a collapse rate $\lambda$ of $10^{-16}$ s$^{-1}$ using presently available technology., Comment: v3: 11 pages, 9 figures, parts of the paper rewritten, no change in results, to appear in Phys. Rev. A

We derive the Schr\"{o}dinger-Newton equation as the non-relativistic limit of the Einstein-Dirac equations. Our analysis relaxes the assumption of spherical symmetry, made in earlier work in the literature, while deriving this limit. Since the spin of the Dirac field couples naturally to torsion, we generalize our analysis to the Einstein Cartan-Dirac (ECD) equations, again recovering the Schr\"{o}dinger-Newton equation., Comment: V3: 22 pages, typos and language corrected, clarifying paragraphs added, references added, accepted for publication in Phys. Rev. D

We formulate the Einstein-Cartan-Dirac equations in the Newman-Penrose (NP) formalism, thereby presenting a more accurate and explicit analysis of previous such studies. The equations show in a transparent way how the Einstein-Dirac equations are modified by the inclusion of torsion. In particular, the Hehl-Datta equation is presented in NP notation. We then describe a few solutions of the Hehl-Datta equation on Minkowski space-time, and in particular report a solitonic solution which removes the unphysical behavioiur of the corresponding Dirac solution. The present work serves as a prelude to similar studies for non-degenerate Poincare gauge gravity., Comment: 32 pages, 4 figures, Section 5.4 on plane waves rewritten

Compton wavelength and Schwarzschild radius are considered here as limiting cases of a unified length scale. Using this length, it is shown that the Dirac equation and the Einstein equations for a point mass are limiting cases of an underlying theory which includes torsion. We show that in this underlying theory the gravitational interaction between small masses is weaker than in Newtonian gravity. We explain as to why the Kerr-Newman black hole and the electron both have the same non-classical gyromagnetic ratio. We propose a duality between curvature and torsion and show that general relativity and teleparallel gravity are respectively the large mass and small mass limit of the ECSK theory. We demonstrate that small scale effects of torsion can be tested with current technology., Comment: 8 pages, 1 figure, Essay written for the Gravity Research Foundation 2018 Awards for Essays on Gravitation