We present simulations of causal dynamical wavefunction collapse models of field theories on a 1 + 1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We suggest that a procedure of coarse graining and renormalizing the fundamental field can overcome its noisiness and argue that this coarse grained renormalized field will show interesting structure if the state vector does on the coarse grained scale. We speculate on the implications for quantum gravity.
We present simulations of causal dynamical wavefunction collapse models of field theories on a 1 + 1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We suggest that a procedure of coarse graining and renormalizing the fundamental field can overcome its noisiness and argue that this coarse grained renormalized field will show interesting structure if the state vector does on the coarse grained scale. We speculate on the implications for quantum gravity.
Quantum many-body systems are comprised of complex networks of microscopic interactions that work together to produce novel collective phases and phenomena. \nFor strongly-interacting systems, the connection between the underlying atomic-scale behaviour and the resulting emergent observable phenomena is exponentially (and, in practice, infinitely) complicated such that it becomes impossible to fully understand the connection between the physics at the microscopic and macroscopic levels. \nThe most promising theoretical approaches to addressing this infinite complexity utilize microscopic coarse-graining along with powerful computational simulations and strategies. \nIn this thesis, we apply numerical methods to effective lattice models and field theories with the goal of shedding light onto universal critical behaviour and exotic low-temperature phases in condensed matter physics. \n \nWe start by exploring universal features of critical non-interacting systems, for which several analytical strategies are readily available for calculating certain observables. \nWe study the behaviour of the system's entanglement for various entangling geometries, and utilize numerical techniques in order to isolate new universal features of Gaussian fixed points, which provide insight into the underlying critical theory's renormalization group flow. \nWe then proceed to examine computational strategies and, in particular, Monte Carlo simulations for studying more general interacting models. \nWe focus on the application of such strategies to the field of high-temperature superconductivity, for which we develop a coarse-grained model, simulate macroscopic observables and compare our results with those of recent experiments. \nWe conclude that lattice field theories together with innovative computational methods offer new perspectives on both universality and emergent phenomena in quantum matter.
We present Chronon Field Theory (CFT), a covariant framework in which large–scale spacetime geometry—including temporal order and causal structure—emerges from the coarse–grained dynamics of a single future–directed timelike field Φμ(x). Within this approach, both the unit–norm property of Φμ and the Lorentzian signature of gμν are not postulated but arise uniquely from random microscopic chronon dynamics under broad symmetry and locality assumptions. Quantum phenomena are reinterpreted in this geometric setting: double–slit interference results from phase–coherent Φ–threads rather than superposed particle paths, and measurement appears as a boundary–induced alignment of microscopic orientations with the apparatus’s macroscopic field, yielding definite outcomes without collapse or branching. Schrödinger’s cat is then a straightforward macro–micro coupling with no persistent macroscopic superposition, while EPR–type entanglement reflects shared Φ–thread ancestry across spacelike separations. The Born rule follows from the unbiased martingale structure of alignment dynamics and from coarse–graining symmetries, making it an emergent statistical law; the uncertainty principle appears as a statistical bound on chronon fluctuations, with ℏ arising as the variance of coarse–grained action. CFT thus provides a covariant and ontologically economical framework linking spacetime symmetries to quantum measurement, and predicts scale–dependent effects—such as nonlinear decoherence and curvature–sensitive timing shifts—that are open to experimental test.
This paper proposes a quantum renormalization group (RG)-based theoretical framework aimed at cooperatively emerging spatial geometry and temporal causal structurefrom a background-independent quantum gravity ground state. Traditional renormalization methods primarily focus on coarse-graining spatial degrees of freedom, while time istreated as an external parameter. This study introduces spatio-temporal joint renormalization transformations, unifying temporal evolution with spatial scaling behavior, andconstructs RG transformations based on the spatio-temporal tensor network category,where the transformations are implemented by a series of local quantum operations thatpreserve causal structure. The research proves that at specific fixed points of the RGflow, the system spontaneously emerges with a clear arrow of time, manifested as thebreaking of scale invariance of causal correlation functions. Through numerical simulations of a (1+1)-dimensional quantum lattice model, the cooperative scaling behavior ofspacetime structure is verified. This paper provides a concrete dynamical mechanism for“time emerging from quantum processes” and offers a new path for quantum gravity andholographic duality research.
We present a quantum framework grounded in micro-causality and spacetime quantization, where spacetime is composed of discrete, causally ordered units rather than a continuous manifold. This intrinsic structure naturally generates fundamental quantum features—wave–particle duality, energy quantization, and the Heisenberg uncertainty principle—without invoking canonical quantization, matter-wave postulates, or harmonic-oscillator models. Consequently, this paradigm eliminates the long-standing paradoxes of wavefunction collapse, self-interference, and non-local spooky correlations in entanglement.Within this causal lattice spacetime, quantum commutation relations emerge from finite shift operators, and the uncertainty principle arises geometrically from non-commutativity at the fundamental level. Unlike standard quantum field theory (QFT), which predicts infinite vacuum energy and requires renormalization, the present framework removes zero-point energy, ultraviolet divergences, and fine-tuning. Moreover, U(1) symmetry is broken geometrically on the lattice, leading to mass generation without a Higgs mechanism.The Casimir effect is reinterpreted as a temperature-dependent imbalance in thermal radiation pressure rather than the consequence of vacuum fluctuations, predicting that the Casimir force should vary with ambient temperature. Experimental confirmation of such dependence would directly support the lattice interpretation and challenge the QFT view of vacuum energy.By unifying key quantum behaviors through discrete causal geometry, this model offers a divergence-free and physically grounded alternative to continuum-based QFT. It opens new avenues for quantum unification, cosmology, and the understanding of fundamental constants, without speculative constructs, singularities, or infinities.
Coarse-graining renormalization aims to reformulate a tensor network model with a coarse-grained one at a larger scale. It has attracted particular attention in recent years because it opens a new avenue to unveil the entanglement structure of a tensor network model under the scaling transformation. This chapter reviews and compares the tensor renormalization group (TRG) and other coarse-graining methods developed in the past two decades. The methods can be divided into two groups according to whether or not the renormalization effect of the environment tensors is incorporated in the optimization of local tensors. The local optimization methods include TRG, HOTRG (a variant of TRG based on the higher-order singular value decomposition), tensor network renormalization (TNR), and loop-TNR. The global optimization methods include the second renormalized TRG and HOTRG, referred to as SRG and HOSRG, respectively. Among all these coarse-graining methods, HOTRG and HOSRG are the only two that can be readily extended and efficiently applied to three-dimensional classical or two-dimensional quantum lattice models.