arXiv subjects

Tejinder P. Singh

Publications and source records attributed to Tejinder P. Singh.

At least 37 records · Page 2Linked to original sources

arXiv2024

Causal Fermion Systems and Octonions

We compare the structures and methods in the theory of causal fermion systems with approaches to fundamental physics based on division algebras, in particular the octonions. We find that octonions and, more generally, tensor products of division algebras come up naturally to describe the symmetries of the vacuum configuration of a causal fermion system. This is achieved by associating the real and imaginary octonion basis elements with the neutrino and charged sectors of the vacuum fermionic projector, respectively. Conversely, causal fermion systems provide octonionic theories with spacetime structures and dynamical equations via the causal action principle. In this way, octonionic theories and causal fermion systems complement each other..

math-ph↗

arXiv2024

Theoretically motivated dark electromagnetism as the origin of relativistic MOND

The present paper is a modest attempt to initiate the research program outlined in this abstract. We propose that general relativity and relativistic MOND (RelMOND) are analogues of the broken electroweak symmetry. That is, $SU(2)_R \times U(1)_{YDEM} \rightarrow U(1)_{DEM}$ (DEM stands for dark electromagnetism), and GR is assumed to arise from the broken $SU(2)_R$ symmetry, and is analogous to the weak force. RelMOND is identified with dark electromagnetism $U(1)_{DEM}$, which is the remaining unbroken symmetry after spontaneous symmetry breaking of the darkelectro-grav sector $SU(2)_R \times U(1)_{YDEM}$. This sector, as well as the electroweak sector, arise from the breaking of an $E_8 \times E_8$ symmetry, in a recently proposed model of unification of the standard model with pre-gravitation, this latter being an $SU(2)_R$ gauge theory. The source charge for the dark electromagnetic force is square-root of mass, motivated by the experimental fact that the square-roots of the masses of the electron, up quark, and down quark, are in the ratio 1:2:3, which is a flip of their electric charge ratios 3:2:1 The introduction of the dark electromagnetic force helps understand the weird mass ratios of the second and third generation of charged fermions. We also note that in the deep MOND regime, acceleration is proportional to square-root of mass, which motivates us to propose the relativistic $U(1)_{DEM}$ gauge symmetry as the origin of MOND. We explain why the dark electromagnetic force falls inversely with distance, as in MOND, and not as the inverse square of distance. We conclude that dark electromagnetism is a good mimicker of cold dark matter, and the two are essentially indistinguishable in those cosmological situations where CDM is successful in explaining observations, such as CMB anisotropies, and gravitational lensing.

gr-qc↗

arXiv2023

Spontaneous localisation from a coarse-grained deterministic and non-unitary dynamics

Collapse of the wave function appears to violate the quantum superposition principle as well as deterministic evolution. Objective collapse models propose a dynamical explanation for this phenomenon, by making a stochastic non-unitary and norm-preserving modification to the Schrödinger equation. In the present article we ask how a quantum system evolves under a {\it deterministic} and non-unitary but norm-preserving evolution? We show using a simple two-qubit model that under suitable conditions, quantum linear superposition is broken, with the system predictably driven to one or the other alternatives. If this deterministic dynamics is coarse-grained and observed over a lower time resolution, the outcomes appear random while obeying the Born probability rule. Our analysis hence throws light on the distinct roles of non-unitarity and of stochasticity in objective collapse models.

quant-ph↗

arXiv2023

CKM matrix parameters from the exceptional Jordan algebra

We report a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e. left-chiral states) as superposition of mass eigenstates (i.e. the right-chiral states) weighted by square-root of mass. Flavor mixing for quarks is mediated by the square-root mass eigenstates, and the mass ratios used have been derived in earlier work from a left-right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, they can be listed as follows - the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, the quaternions $\mathbb{H}$ and the octonions $\mathbb{O}$. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also the action of various Spin Groups on these representations too can be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as $θ_{12}=11.093^o, θ_{13}=0.172^o, θ_{23}=4.054^o$. In comparison, the corresponding experimentally measured values for these angles are $13.04^o \pm 0.05^o, 0.201^o \pm 0.011^o, 2.38^o \pm 0.06^o $. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account.

hep-ph↗

arXiv2023

Gravitation, and quantum theory, as emergent phenomena

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.

physics.gen-ph↗

arXiv2023

Left-Right symmetric fermions and sterile neutrinos from complex split biquaternions and bioctonions

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 $E_6$.

hep-ph↗

arXiv2023

The exceptional Jordan algebra, and its implications for our understanding of gravitation and the weak force

The exceptional Jordan algebra is the algebra of $3\times 3$ Hermitian matrices with octonionic entries. It is the only one from Jordan's algebraic formulation of quantum mechanics which is not equivalent to the conventional formulation of quantum theory. It has often been suggested that this exceptional algebra could explain physical phenomena not currently explained by the conventional approach, such as values of the fundamental constants of the standard model of particle physics, and their relation to gravitation. We show that this is indeed the case; and this also unravels the connection between general relativity and the weak force. The exceptional Jordan algebra also predicts a new $U(1)$ gravitational interaction which modifies general relativity, and which provides a theoretical basis for understanding the Modified Newtonian Dynamics (MOND).

physics.gen-ph↗

arXiv2022

Why do elementary particles have such strange mass ratios? -- The role of quantum gravity at low energies

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infrared. Using the octonions as space-time coordinates, we construct a pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries of this non-commutative space unify the standard model of particle physics with $SU(2)_R$ chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time.

physics.gen-ph↗

arXiv2022

A Lagrangian with $E_8\times E_8$ symmetry for the standard model and pre-gravitation I. -- The bosonic Lagrangian, and a theoretical derivation of the weak mixing angle

Building on earlier work, we propose an elementary Lagrangian for the unification of the standard model with pre-gravitation, assumed to have an unbroken $E_8 \times E_8$ symmetry. The Lagrangian is patterned after the kinetic energy of a free particle in Newtonian dynamics, generalising it to the matrix-valued Lagrangian dynamics of a 2-brane on a split bioctonionic space. Symmetry breaking gives rise to the standard model quarks and leptons of three generations along with the known gauge interactions, and a novel right-handed counterpart $SU(3)_{grav}\times SU(2)_R \times U(1)_g$ identified as pre-gravitation. The goal of the present series of papers is to investigate if this pre-quantum, pre-spacetime matrix-valued Lagrangian dynamics can lead to the emergence of quantum field theory for the standard model, and classical general relativity, possibly with some additional corrections. In this paper we work out the bosonic part of the Lagrangian, and show how the anticipated 32 gauge bosons are recovered from the elementary Lagrangian. As an application, we show that the asymptotic low energy weak mixing angle $θ_W$ is given by a solution of the equation $1 = (1/2)\sqrt{ \cos(θ_{W}/2)}+ \sqrt {\sin(θ_{W}/2)}$, yielding $\sin^2θ_W \approx 0.24996$.

hep-ph↗

arXiv2022

A violation of the Tsirelson bound in the pre-quantum theory of trace dynamics

The term Bell's theorem refers to a set of closely related results which imply that quantum mechanics is incompatible with local hidden variable theories. Bell's inequality is the statement that if measurements are performed independently on two space-like separated particles of an entangled pair, the assumption that outcomes depend on hidden variables implies an upper bound on the correlations between the outcomes. Quantum mechanics predicts correlations which violate this upper bound. The CHSH inequality is a specific Bell inequality in which classical correlation (i.e. if local hidden variables exist) can take the maximum value of 2. Quantum mechanics violates this bound, allowing for a higher bound on the correlation, which can take the maximum value $2\sqrt{2}$, known as the Tsirelson bound. Popescu and Rohrlich showed that the assumption of relativistic causality allows for an even higher bound on the CHSH correlation, this value being 4. Why is the bound coming from causality higher than the Tsirelson bound? Are there relativistic causal dynamical theories which violate the Tsirelson bound? In the present paper we answer this question in the affirmative. We show that the pre-quantum theory of trace dynamics, from which quantum theory is emergent as a thermodynamic approximation, permits the CHSH correlation to take values higher than $2\sqrt{2}$. We interpret our findings to suggest that quantum theory is approximate, and emergent from the more general theory of trace dynamics.

quant-ph↗

arXiv2022

Quantum gravity effects in the infra-red: a theoretical derivation of the low energy fine structure constant and mass ratios of elementary particles

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.

physics.gen-ph↗

arXiv2022

Relativistic weak quantum gravity and its significance for the standard model of particle physics

There ought to exist a reformulation of quantum theory, even at energy scales much lower than Planck scale, which does not depend on classical time. Such a formulation is required also for the standard model of particle physics, at the low energies at which it is currently observed. We have proposed such a formulation, by replacing 4D Minkowski spacetime by an octonionic space. Doing so allows us to naturally construct spinor states which describe quarks and leptons having properties as in the standard model. We conclude that the aforesaid reformulation of quantum theory helps understand why the standard model is what it is. We do not need experiments at ever higher energies to understand the low energy standard model. Instead, we need a better understanding of the quantum nature of spacetime at low energies, such that the quantum spacetime is consistent with the principle of quantum linear superposition. In the present short review article, we give a summary of our ongoing research programme which aims to address these issues.

physics.gen-ph↗

arXiv2022

Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions

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 $SU(3)_{color} \times SU(2)_L \times U(1)_Y$.

hep-ph↗

arXiv2022

Quantum theory without classical time: octonions, and a theoretical derivation of the fine structure constant 1/137

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.

physics.gen-ph↗

arXiv2021

The Life and Science of Thanu Padmanabhan

Thanu Padmanabhan was a renowned Indian theoretical physicist known for his research in general relativity, cosmology, and quantum gravity. In an extraordinary career spanning forty-two years, he published more than three hundred research articles, wrote ten highly successful technical and popular books, and mentored nearly thirty graduate students and post-doctoral fellows. He is best known for his deep work investigating gravitation as an emergent thermodynamic phenomenon. He was an outstanding teacher, and an indefatigable populariser of science, who travelled very widely to motivate and inspire young students. Paddy, as he was affectionately known, was also a close friend to his students and collaborators, treating them as part of his extended academic family. On September 17, 2021 Paddy passed away very unexpectedly, at the age of sixty-four and at the height of his research career, while serving as a Distinguished Professor at the Inter-University Centre for Astronomy and Astrophysics, Pune. His untimely demise has come as a shock to his family and friends and colleagues. In this article, several of them have come together to pay their tributes and share their fond memories of Paddy.

physics.hist-ph↗

arXiv2021

Trace dynamics, and a ground state in spontaneous quantum gravity

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 Schrödinger 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.

physics.gen-ph↗

arXiv2020

Trace dynamics and division algebras: towards quantum gravity and unification

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.

hep-th↗

arXiv2020

Quantum gravity, minimum length, and holography

The Karolyhazy uncertainty relation is the statement that if a device is used to measure a length $l$, there will be a minimum uncertainty $δl$ in the measurement, given by $(δl)^3 \sim L_P^2\; l$. 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.

gr-qc↗