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Tejinder P. Singh

Publications and source records attributed to Tejinder P. Singh.

At least 19 recordsLinked to original sources
arXiv2026

Critical emergence of quantum theory, spacetime and gravity from generalised trace dynamics

Generalized trace dynamics (GTD) is a deterministic dynamics of aikyons (atoms of space-time-matter) whose near-equilibrium statistical mechanics yields quantum dynamics, while large anti-self-adjoint fluctuations drive spontaneous localisation and emergent classical spacetime. We separate two independent large limits: long-Connes-time coarse-graining of a finite system, which conditionally yields the quantum Ward identities, and the extensive many-aikyon/large-matrix limit required for a collective singularity. We turn the condensed-matter analogy of the E8 x omega E8 programme into a quantitative, falsifiable effective framework. Four coupled composite channels (bifermionic localisation, geometric soldering/Lorentz-Higgs, gauge-invariant electroweak, and matrix-valued flavour) define an exact susceptibility matrix and Legendre effective action, giving zero-mode and free-energy criteria for a common continuous or first-order transition. We pose the nonequilibrium problem in Schwinger-Keldysh form, define a projected fluctuation-dissipation defect and the martingale condition for Born probabilities, identify Newton's constant with the stiffness of the ordered geometric phase, and give conditions under which the Sakharov, constrained-BF, Jacobson, Padmanabhan and Verlinde descriptions of gravity are limits of one substrate. A regulated two-sector surrogate ensemble (a Myers-deformed geometric triple coupled to a matter matrix, with a Grassmann-regulated fermionic extension) shows that selected diagnostics are calculable: exact Adler-Millard charge conservation, a multi-channel first-order jump, a verified fluctuation-dissipation relation and its quench defect, and a fermionic spectral dimension d_s = 1.96 on the emergent two-sphere. The result is a calculational programme, not a completed derivation; the next step is the many-aikyon composite two-point matrix for GTD itself.

physics.gen-ph↗
arXiv2026

Gauge couplings of the Standard Model in the octonionic framework: invariant normalisations, a conditional weak-sector completion, and a scale-explicit matching ledger

We present a major revision of the gauge-sector account of the $E_8\otimes E_8$ octonionic unification programme. Exact identities within the specified algebraic construction, consequences of an effective support model, and microscopic hypotheses are kept separate. The recurrent 3/8 is the squared half-spacing of the adopted exceptional-Jordan family spectrum, while the exponential charge dependence is a multiplicative-character hypothesis motivated by the trace-dynamics action; the action parameter $α_{\rm TD}$ is not the fine-structure constant. On the real ladder space $H_6$, the real Schur lemma fixes the shape of a colour-singlet self-adjoint photon profile to be proportional to the identity; the resulting 1/6 dilution holds only if the Hilbert-Schmidt norm coincides with the norm induced by the projected gauge kinetic term. This gives the conditional boundary value $[α_γ^{(0)}]^{-1}=137.04006064$, while comparison with CODATA requires the calculable factor $Z_γ=1.0000296379$. We also repair the two-U(1) matter-current normalisation: for parent charges $c_1Y$, $c_2Y$ with $c_1+c_2=1$, a link field leaves the diagonal connection coupled to exactly the Standard-Model $Y$. Equal connection coefficients and zero kinetic mixing give the illustrative benchmark $g_Y^2/g_2^2=3/10$, $\sin^2θ_W=3/13$; trace-induced normalisation of the scaled generators gives a different result, so 3/13 is not an embedding-independent prediction; treated as exact, it lies about $13σ$ below the quoted $\overline{\rm MS}$ value. The colour bound $α_s/α_{\rm em}\leq 8$ is restricted to colour profiles individually commuting with the complex structure. Measured couplings enter only as inputs to scale and running diagnostics. The result is a falsifiable conditional programme and a normalization audit, not a parameter-free derivation of Standard-Model gauge couplings.

hep-ph↗
arXiv2026

The CKM sector of the exceptional-Jordan programme: finite-Dirac mass moduli, two conditional angle estimates, and the weak-to-mass bridge

The Standard Model does not determine quark masses or the CKM matrix. In the exceptional-Jordan programme, square-root masses occupy short $\operatorname{Sym}^{3}(\mathbf{3})$ chains. Compressing the symmetric-cube lift onto occupied nodes gives a root-mass operator whose square yields the proposed mass ratios, packaging that spectrum and relative left frames in one finite Dirac operator without deriving the frames. Conditional on the transport, virtual-node-amplitude, real-$(2,3)$ and balanced-quadrature choices, the no-fit layer gives $|V_{us}|=0.2371$ ($5.3\%$ high) and $|V_{cb}|=0.0422$ ($0.8\%$ high) at $M_Z$. The relation $|V_{ub}|/|V_{cb}|=\sqrt{m_u/m_c}$ is a factor two low; one complex long edge is fitted. The two balanced orientations give branches $(\varepsilon,ω)=(0.002079,288.2^\circ)$ and $(0.005358,202.2^\circ)$, so the former $\varepsilon$ ratio is not robust and raw $ω$ is convention-dependent. For an adopted $F_1$--$F_2$ family embedding, we construct an exact Peirce-changing Albert lift in $\mathfrak f_4(\mathbb C)$, reproducing conjugate up/anti-down transport and $φ_{12}=-2χ$. For an adopted cyclic Majorana placement and real-linear projection, its completion has real $(e_4,e_3,e_6)$ support while the $e_1$ quadrature vanishes; $J_\ell=0$ and $δ^\ell_{CP}=0$ or $π$ are compatibility results in this class. The minimal radial-quartic cyclic truncation has equal-magnitude full-rank extrema or a flat direction; a mixed Albert cubic gives stable alignment only in a chosen three-edge subspace. Six diagonal mass links plus three directed Peirce links would form a connected one-cycle nine-link graph if the Yukawa block is linear in the projected bridge. This is a candidate Arkani-Hamed et al. texture skeleton, not a derivation: family-vacuum selection, chiral projection and right-frame locking remain open.

hep-ph↗
arXiv2026

A Proposed $E_8 \times E_8$ Kinematic Scaffolding for the Standard Model with Pre-Gravitation

We present a proposed $E_8 \times E_8$ kinematic scaffolding for the standard model with pre-gravitation. The notation $E_8\timesωE_8$ used below records a split-complex exchange grading of two factors; it is not a tensor product of groups. Each factor branches through $SU(3)\times E_6$ and thence through trinification, $E_6 \rightarrow SU(3)^3$. The first factor supplies representation labels associated with the standard-model lineage, and the second supplies a mirror, pre-gravitational lineage. The identification of a single vector-like colour group across the two factors, and the proposed gravitational reading of the right-sector $SU(2)$, remain dynamical hypotheses. Physical chiral fermions are not assigned to the $E_8$ adjoints: they are modelled by minimal ideals of the complex Clifford algebra $Cl_6(\mathbb C)$, while the $496$ adjoint dimensions are used only as a representation-label ledger. The numerical split $208+288$ is therefore a declared roster-matching convention, not an invariant decomposition and not a particle count. Spacetime enters through a selected six-dimensional split-biquaternionic vector space with a separately specified quadratic form of signature $(3,3)$. Its full frame group is $SO(3,3)$; deriving a soldering form and the proposed $BF$/Plebański dynamics remains open. The conventional Clifford--Dirac operator is constructed independently and exactly: $J_2(\mathbb H_s)$ realises the vector space $\mathbb R^{3,3}$ through its determinant, and after choosing $\mathbb H_s\cong M_2(\mathbb R)$ its matrix gradient and adjugate act between real four-dimensional Weyl modules and factorise the wave operator in both orderings. The rank-two algebra supplies the quadratic spacetime layer, whereas $J_3(\mathbb O_{\mathbb C})$ supplies the proposed internal, generation and cubic spectral layer through the magic-star decomposition of $\mathfrak e_8^{\mathbb C}$.

hep-ph↗
arXiv2026

Left-right symmetry breaking in $E_6^L\times E_6^R$ occurs only in spacetime -- with possible implications for strong $CP$

Two-sided octonionic $E_6^L\times E_6^R$ unification carries a nominal second colour $SU(3)_{c'}$ which, gauged, would colour the charged lepton and must be suppressed by hand. We argue no such device is needed: the left-right symmetry acts in spacetime, not internally -- in the gravi-weak reading $SU(2)_R$ is the gravitational frame group and the exchange is ordinary parity on the Dirac field; a spacetime operation cannot double the internal colour, so $SU(3)_{c'}=SU(3)_c$, one vector-like colour with a colour-singlet electron. The right sector contributes one colour-blind datum, $\sqrt m$ (values: the exceptional-Jordan trace split, an input; $N_R$ fixes only the colour representation). An anomaly no-go proven here shows every anomaly-free $U(1)$ on visible fermions lies in span$\{Q,B-L\}$, which the $\sqrt m$ pattern does not, in any sign or chirality assignment. The gauged dark-electromagnetic $U(1)_{dem}$ -- the mirror electroweak chain's unbroken remnant -- therefore carries the parity-mirror of electric charge on the dark sector: the visible fermions are dem-neutral (kinetic mixing the sole portal; no visible fifth force), and $\sqrt m$ enters visible physics only as the spectral label of the Jordan mass operator. The same recognition recovers hypercharge as the consistency relation $Y=Q-T^3_L$, $Q=N/3$, with no right-sector generator. As an application, the spontaneous parity forbids the QCD vacuum angle ($θ_{QCD}=0$, conditional on the gravi-weak identification), while the flavour rotors have real determinant, so $\arg\det M=0$ at tree level (exact for the Cabibbo rung, texture-contingent in full), coexisting with a nonzero CKM phase. Loop stability -- where minimal gauged-$SU(2)_R$ parity solutions fail -- is plausibly evaded (no gauged $W_R$) but open, pending the Higgs-bridge matrix elements. We tag throughout what is derived, what is input, and what is open.

hep-ph↗
arXiv2026

Experimental predictions of the $E_8 \times ωE_8$ octonionic unification program : A falsification-oriented catalogue for quantum foundations, particle physics, gravitation, and cosmology

The $E_8\timesωE_8$ octonionic unification programme makes empirical claims across quantum foundations, particle physics, gravitation, and cosmology. This catalogue assembles them as possible failure modes rather than a success list, classified by logical strength and distinctiveness. Standing entries include collapse in time with an attosecond cutoff, $m_τ/m_μ=m_s/m_d$, the first-generation $1{:}4{:}9$ pattern, and $α_s(M_Z)/α_{\rm em}(0)=16$. Version~2 upgrades every sector to the dedicated 2026 papers. Neutrinos: the v1 maximal leptonic phase, a removable-rephasing artifact, is corrected to conditional CP conservation, $δ_{CP}^{\ell}\in\{0,π\}$; the minimal Majorana branch commits to inverted ordering with masses $(49.1,\,49.8,\,0.76)$~meV, $Σm_ν\simeq0.10$~eV, $m_{ββ}=18.2\pm1.2$~meV; the three right-handed neutrinos become diluted $\sim\!40$~eV relics closing the matter budget, with a two-epoch dark-radiation fingerprint ($ΔN_{\rm eff}\simeq0.19$ at BBN, $0.05$ at recombination). The second Higgs becomes a full electroweak quartet in a CP-conserving 2HDM near alignment, mass undetermined. Gravitational parity-blindness is derived via three screening theorems, residual violation confined to a quantified operator basket, with CMB TB/EB correlations observable if $r\gtrsim\text{few}\times10^{-3}$ and a Galactic-supernova triple-timing test at $3\times10^{-9}$. CKM: two of four degrees of freedom parameter-free ($|V_{us}|=0.237$, $|V_{cb}|=0.042$), the remainder one complex bridge element, fragilities disclosed. The Tsirelson-bound violation is recorded as mechanism-and-sign with magnitude underived, hence not yet falsifiable.

hep-ph↗
arXiv2026

Fermion Mixing Matrices and the Exceptional Jordan Algebra

We extend the exceptional-Jordan spectral framework for fermion mass hierarchies to the problem of quark and lepton mixing. Following the companion mass paper~\cite{Teli:2026jgr}, each fermion sector is associated with a Hermitian element of $J_3(\mathbb{O}_{\mathbb{C}})$, where adjacent square-root mass ratios are obtained from cubic ladders in $\mathrm{Sym}^3(\mathbf 3)$. Here, these ratios are used as inputs to an adjacent-edge lift from spectral hierarchy data to two-generation mixing angles. The lift is derived from a Fritzsch-type two-state texture~\cite{Fritzsch:1977za, Fritzsch:1979zq} and should be regarded as an effective bridge ansatz rather than a theorem of the Jordan spectrum alone. The exact CP-transport input is supplied by the companion CP Letter~\cite{GuptaTeli:2026aqf}. In the quark sector, the octonionic ladder operator $α_2$ generates a real local rotor in the $(e_1,e_3)$ plane, and the up- and down-sector local Cabibbo-edge amplitudes are complex conjugates, giving the exact local law $ϕ_{12}=-2χ$. This is a transport-level Cabibbo-rung phase law, not by itself a prediction of the standard CKM Dirac phase. With the fitted companion mass ratios, the minimal two-angle extraction from the measured $|V_{us}|$ gives an effective Cabibbo-block phase $ϕ_{12}\simeq 105.7^\circ$; this number is a bridge diagnostic, while the balanced octonionic rotor remains the distinguished quadrature reference point. The $(2,3)$ sector requires a phenomenological normalization $κ_{23}\simeq0.56$, and the direct $(1,3)$ element remains a long-edge bridge problem. [Truncated]

hep-ph↗
arXiv2026

Leptonic CP Conservation and the Quark CP Phase from Octonionic Flavor Structure

One generation of standard-model fermions can be realized on the complexified octonions through the Clifford algebra $\mathcal{C}l(6)$; the octonionic unification programme extends this to three generations, with generation transport implemented by $G_2$ automorphisms or by rotors built from the ladder operators. We prove a localization theorem for the CP-violating phases of this structure, using only the $\mathcal{C}l(6)$ construction and the stated three-generation representatives, independently of the wider programme. For quarks, the first-to-second generation step is the occupation flip of one ladder mode, with the up and down species coupling to conjugate ladder directions; a conjugation theorem forces $A_d=A_u^*$ for every real transport, and the most general rung-generated rotor yields the exact one-parameter law $ϕ_{12}=-2χ$: the $(1,2)$ transport phase is twice one Yukawa orientation angle. The programme's geometric rotor sits exactly at the quadrature-balanced point $|ϕ_{12}|=π/2$; the companion analysis reproduces the Cabibbo \emph{magnitude} $|V_{us}|$ with a single real tilt, leaving the rung near quadrature, but it does not extract a CKM CP phase, so the quark Dirac phase is fixed only once the underlying Yukawa orientation is computed. For leptons we prove a reality theorem: every charged-lepton and every neutrino transport amplitude is exactly real for every $G_2$ automorphism and every rotor that does not mix the identity line $\mathbb C\cdot1$ with the lepton--flavor plane $\mathrm{span}(e_7,e_5,e_2)$ a class that contains the entire quark-rung family--and identity--flavor mixing across that plane is the unique possible source of a leptonic phase. [Truncated]

hep-ph↗
arXiv2026

Fermion mass ratios from the exceptional Jordan algebra

The origin of the three fermion generations and their highly hierarchical mass spectra remains one of the most profound puzzles in particle physics. We show that the complexified exceptional Jordan algebra $J_{3}(\mathbb{O}_{\mathbb{C}})$, the natural mathematical framework for the exceptional Lie group $E_{6}$, provides a unified explanation for both. The three generations arise from the three off-diagonal Peirce slots of $J_{3}(\mathbb{O}_{\mathbb{C}})$, each carrying an isomorphic $Cl(6,\mathbb C)$ minimal-ideal fiber and permuted cyclically by triality $S_3\subset\mathrm{Out}(\mathrm{Spin}(8))$; pre-breaking, the three families are identical by symmetry. After triality breaking the residual $SU(3)_F$ flavor symmetry organises the three generations of each family as a $\mathrm{Sym}^{3}(\mathbf{3})$ multiplet, the minimal $S_3$-symmetric degree-3 arena consistent with the cubic structure of the Jordan determinant and the unique $E_6$-invariant Yukawa. The mass-ratio formula follows from a one-line diagonal-action theorem: when $\langle X\rangle$ is Jordan-diagonalised to $\mathrm{diag}(a,b,c)$, the induced action $X^{\odot 3}$ on the $\mathrm{Sym}^{3}(\mathbf{3})$ monomial basis is diagonal with eigenvalues $a^pb^qc^r$, so a fermion identified with the weight state $|p,q,r\rangle$ has $\sqrt m\propto a^pb^qc^r$ and adjacent generations related by an edge move have $\sqrt m$-ratios that depend only on the edge type ($c/a$, $b/a$, $c/b$). We refer to this as $\textit{edge universality}$; it is monomial arithmetic, not a Clebsch-Gordan cancellation. The universal Jordan eigenvalue spectrum $(q-δ, q, q+δ)$ with $δ^{2}=3/8$ is fixed by the cubic on the coassociative slice of $J_3(\mathbb O_\mathbb C)$. [abstract truncated]

hep-ph↗
arXiv2026

The Residual $288$ of the $E_8\timesωE_8$ Program as Adjoint-Lineage Scaffolding Labels: an Ontology, and the Status of the Bifermionic Lagrangian

In the $E_8\timesωE_8$ octonionic unification program, each $E_8$ branches as $SU(3)_{st}\times E_6$, supplying one geometric $SU(3)_{st}$ per branch, while the split-complex unit $ω$ grades the visible and pre-gravitational branches; matter and gauge content is carried by $E_6\times E_6$, with chiral fermions realized as Cl(6) minimal-ideal spinors rather than $E_8$ representation components -- which places the chiral sector outside the Distler-Garibaldi no-go theorem. Comparing the 496-label two-branch adjoint reservoir with the 208 structures matched in the Generalized Trace Dynamics Lagrangian leaves a residual 288. We argue that this 288 is an adjoint-lineage representation-label ledger -- bookkeeping for the scaffolding -- and not a particle spectrum. The bifermionic seed is Hermitian, with $E_6$-covariant channels classified by $\bar{27}\otimes 27 = 1\oplus 78\oplus 650$: each branch's 78 supplies the gauge currents and a composite electroweak doublet, while the $E_6$ singlet is electroweak-inert. The charge-sum sector A is absent from the bare seed, and the 252 $SU(3)_{st}$-charged labels cannot be matter bilinears in any reservoir, conditional on the spinor ontology. The size of $E_8\timesωE_8$ is thus the dimension of a label ledger, not a count of particles; beyond the Standard Model, the framework's content is sterile neutrinos and a second composite scalar.

hep-ph↗
arXiv2026

Candidate collapse-noise correlators from Generalized Trace Dynamics: a Hubble-scale spectral line under structural assumptions

We present a conditional construction of candidate CSL-type collapse-noise correlators inspired by Generalized Trace Dynamics (GTD). The construction is not a parameter-free derivation from the minimal GTD Grassmann algebra. It rests on a chain of explicit structural postulates, listed in Section 1; within that auxiliary structure the spectral form and amplitude follow by computation rather than by phenomenological fitting. The resulting narrow-band spectrum at the Hubble scale lies outside the bands of current CSL bounds, so the framework is not in tension with existing high-frequency data. We compute the two-point function of a candidate collapse-noise operator associated with the GTD aikyon decomposition $q_i = q_B + a_0β_i q_F$. In the minimal Grassmann algebra, $q_F$ appears only multiplied by Grassmann generators $β_i$, the reduction of $\mathrm{Tr}(q_F^\daggerΓ^μq_F)$ to ghost-mode operators is obstructed by the nilpotent $δβ= β_2 - β_1$, and the pure-fermion coefficient $β_1β_2$ has no ordinary sign, modulus, or inverse. We therefore introduce an auxiliary canonical fermionic Fock-space sector for $q_F$, equivalently replacing the nilpotent pure-fermion coefficient by an ordinary effective scalar body parameter. This replacement is an independent structural postulate, not a consequence of the original minimal action. Under this auxiliary postulate, together with a scalar bilinear $J = \mathrm{Tr}(q_F^\dagger q_F)$ as bath operator, positive-norm canonical quantization, and an effective sign choice $σ= \pm1$ for the scalarized pure-fermion sector, elementary Wick contraction gives a Wightman line at $|ω| = 2ω_0$ with amplitude $A_J = (\hbar/2m_Rω_0 L_{\mathrm{aik}}^2)^2\cdot N\cdot D$. The cosmological identification $ω_0 \sim H_0$ places the line at twice the Hubble scale. [truncated]

quant-ph↗
arXiv2026

Gravity and electroweak sector from symmetry breaking of an $SO(3,3)$ BF theory

An $SO(3,3)$ BF-type gauge theory is formulated on a six-dimensional spacetime of split signature $(3,3)$, interpreted as the pre-electroweak-symmetry-breaking phase. A MacDowell--Mansouri-type symmetry breaking to $SU(2)\times SU(2)$ is implemented, and the corresponding stabilizer and coset structures are computed. The curvature decomposes into chiral sectors, and effective tetrads are introduced using components of the higher-dimensional connection. The resulting left and right sectors are formulated as constrained BF/Plebanski-like theories with appropriate simplicity and reality conditions. The six-dimensional theory yields two overlapping four-dimensional Lorentzian sectors of opposite signature, related via gluing constraints across their intersection. In the first sector, the selfdual two-forms ($Σ^{(+)}$) satisfy simplicity constraints that select the non-degenerate branch and reproduce Einstein gravity. Subsequently, the $SU(2)_R\times U(1)_{Y{\rm dem}}\to U(1)_{\rm dem}$ breaking pattern is outlined which admits an ultra-soft regime consistent with current phenomenological bounds under sufficiently suppressed couplings. In the second sector, the antiself dual two-forms ($Σ^{(-)}$) satisfy analogous simplicity constraints, realizing weak gauge dynamics as gravity on the opposite-signature sector. Subsequently, the $SU(2)_L\otimes U(1)_Y$ electroweak symmetry is realized within the Yang--Mills branch of the BF theory which incorporates the standard Higgs mechanism $SU(2)_L\otimes U(1)_Y \to U(1)_{\mathrm{EM}}$, recovering the conventional electroweak $W^\pm$, $Z$, and photon spectrum.

hep-th↗
arXiv2026

Causal Fermion Systems, Non-Commutative Geometry and Generalized Trace Dynamics

We compare the structures and methods in the theory of causal fermion systems with generalized trace dynamics and non-commutative geometry. Although the three theories differ on many aspects, they agree in that the geometric structure to be recovered in the continuum limit is not the bare spacetime but a suitable fiber bundle. Furthermore, the comparison leads us to the conclusion that the key innovation in causal fermion systems lies in the manner in which the relation between different spacetime points is encoded. The role of Synge's classical world function $σ(x,y)$ that encodes the geodesic distance between any two points in the manifold, is taken by a generalized two-point correlator. We show that this idea can be transferred to non-commutative geometry and generalized trace dynamics.

math-ph↗
arXiv2026

In models of spontaneous wave-function collapse, why only fermions collapse, not bosons?

Objective collapse models are often implemented so that collapse acts only on the fermionic (matter) sector, while bosonic fields do not undergo fundamental collapse. In generalized trace dynamics (GTD), spontaneous localization is expected to arise when the trace Hamiltonian has a significant anti-self-adjoint component. In this note we show, starting from the STM-atom (spacetime-matter atom) trace Lagrangian written in terms of two inequivalent matrix velocities $\dot Q_1$ and $\dot Q_2$, that the purely bosonic subsector admits a self-adjoint Hamiltonian, whereas the fermionic sector carries an intrinsic anti-self-adjoint contribution. The key structural input is that making the trace Lagrangian bosonic requires insertion of two \emph{unequal} odd-grade Grassmann elements $β_1\neq β_2$. Assuming natural adjoint properties for these elements, we compute the trace Hamiltonian explicitly via trace-derivative canonical momenta (with bosonic and fermionic variations treated separately) and isolate the resulting anti-self-adjoint term. This provides a first-principles mechanism, within GTD, for why only fermionic degrees of freedom act as collapse channels.

physics.gen-ph↗
arXiv2026

A Relativistic MOND

We present a minimal relativistic completion of MOND in which (i) General Relativity is recovered exactly in the high-acceleration regime, while (ii) the Bekenstein--Milgrom (AQUAL) equation emerges in the low-acceleration regime, without introducing additional propagating fields beyond those already present in a right-handed gauge sector. The construction is motivated by an $E_6\times E_6$ framework in which $SU(3)_R\rightarrow SU(2)_R\times U(1)_{Y'}\rightarrow U(1)_{\rm dem}$, leaving a healthy repulsive $U(1)_{\rm dem}$ interaction whose charge is the square-root mass label. Gravity itself arises from the $SU(2)_R$ connection via a Plebanski/MacDowell--Mansouri mechanism, yielding an emergent tetrad and the Einstein--Hilbert action. MOND is implemented by an infrared (IR) metric deformation $ΔS_{\rm IR}[g]$ that is UV-vanishing (so GR is recovered) while its deep-MOND/static limit is fixed by a symmetry principle: in three spatial dimensions, the deep-MOND action is conformally invariant with a 10-parameter group isomorphic to $SO(4,1)$ (the de Sitter group). The single MOND acceleration scale is set by a de Sitter radius selected dynamically in the IR, $a_0=c^2/(ξ\,\ell_{\rm dS})$ with $ξ={ O}(1)$ fixed by matching to the static limit. MOND resides in perturbations and quasistatic systems; the homogeneous FRW background is controlled by the IR vacuum kinematics rather than an ad hoc cosmological constant.

gr-qc↗
arXiv2025

Time-like Extra Dimensions: Quantum Nonlocality, Spin, and Tsirelson Bound

The $E_8 \otimes E_8$ octonionic theory of unification suggests that our universe is six-dimensional and that the two extra dimensions are time-like. These time-like extra dimensions, in principle, offer an explanation of the quantum nonlocality puzzle, also known as the EPR paradox. Quantum systems access all six dimensions, whereas classical systems such as detectors experience only four dimensions. Therefore, correlated quantum events that are time-like separated in 6D can appear to be space-like separated and, hence, nonlocal, when projected to 4D. Our lack of awareness of the extra time-like dimensions creates the illusion of nonlocality, whereas, in reality, the communication obeys special relativity and is local. Bell inequalities continue to be violated because quantum correlations continue to hold. In principle, this idea can be tested experimentally. We develop our analysis after first constructing the Dirac equation in 6D using quaternions and using the equation to derive spin matrices in 6D and then in 4D. We also show that the Tsirelson bound of the CHSH inequality can in principle be violated in 6D.

physics.gen-ph↗
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↗