The Science of Divinity

The geometry of space–time–matter

The Generalization of the Periodic Table: The 'Periodic Table' of 'Dark Matter'

In this paper we present a new point of view on space–time–matter (STM) theory. First, some weak points from earlier research papers on STM theory are presented. Then, we obtain in a covariant form the fully general \(4D\) equations of motion for STM theory. This enables us to classify the \(5D\) motions and to give a new definition of the fifth force in \(4D\) physics.

The Karolyhazy uncertainty relation states that if a device is used to measure a length l, there will be a minimum uncertainty \(\delta l\) in the measurement, given by \((\delta l)^3 \sim L_{\mathrm {P}}^2 l\). This is a consequence of combining the principles of quantum mechanics and general relativity. In this letter 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 (STM) 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 classical space–time background is not 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.

In the standard Einstein’s theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space–time. In this work we present a generalization of those so called Weyl solutions to a space–time–matter metric in a five-dimensional manifold within a non-compactified Kaluza–Klein theory of gravity. The arising field equations reduce to those of vacuum Einstein’s gravity when the metric function associated to the fifth dimension is considered to be constant. The calculation of the geodesics allows to identify the existence or not of different behaviours of test particles, in orbits on a constant plane, between the two metrics. In addition, static solutions on the hypersurface orthogonal to the added dimension but with time dependence in the five-dimensional metric are also obtained. The consequences on the variation of the rest mass, if the fifth dimension is identified with it, are studied.

We study the relationship between space–time–matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they are equivalent to each other. First we demonstrate that STM predicts local and nonlocal high-energy corrections to general relativity in 4D, which are identical to those predicted by brane-world models. Secondly, we point out that in brane models the usual matter in 4D is a consequence of the dependence of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is independent of the extra dimension, then the brane is void of matter. Thus, in brane theory matter and geometry are unified, which is exactly the paradigm proposed in STM. Consequently, these two 5D theories share the same concepts and predict the same physics. This is important not only from a theoretical point of view, but also in practice. We propose to use a combination of both methods to alleviate the difficult task of finding solutions on the brane. We show an explicit example that illustrate the feasibility of our proposal.

We study the correspondence between two theoretical frameworks for describing dark energy: f(R) gravity and higher-dimensional space–time–matter (STM) or induced matter theory. We show that the Hubble expansion parameter in f(R) gravity can be associated with a combination of metric functions in STM theory, and consider a specific example whose properties are consistent with late time acceleration.

Stated succinctly, the original version of the Campbell–Magaard theorem says that it is always possible to locally embed any solution of four-dimensional general relativity in a five-dimensional Ricci-flat manifold. We discuss the proof of this theorem (and its variants) in n dimensions, and its application to current theories that postulate that our universe is a four-dimensional hypersurface Σ0 within a five-dimensional manifold, such as space–time–matter (STM) theory and the Randall and Sundrum (RS) braneworld scenario. In particular, we determine whether or not arbitrary spacetimes may be embedded in such theories, and demonstrate how these seemingly disparate models are interconnected. Special attention is given to the motion of test observers in five dimensions, and the circumstances under which they are confined to Σ0. For each five-dimensional scenario considered, the requirement that observers be confined to the embedded spacetime places restrictions on the 4-geometry. For example, we find that observers in the thin braneworld scenario can be localized around the brane if its total stress–energy tensor obeys the five-dimensional strong energy condition. As a concrete example of some of our technical results, we discuss a ℤ2 symmetric embedding of the standard radiation-dominated cosmology in a five-dimensional vacuum.

Exploiting Network Science for Feature Extraction and Representation Learning

A generalized scalar–tensor (GST) theory is investigated whose cosmological (or quintessence) term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space–Time–Matter (STM) theory is noted. Analytic solutions are found for the scale factor, scalar field and cosmological term. Models with free parameters of order unity are consistent with recent observational data and could be relevant to both the dark matter and cosmological "constant" problems.

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 localization 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 [Formula: see text], forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about [Formula: see text] 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 [Formula: see text].

There ought to exist a reformulation of quantum theory which does not depend on classical time. To achieve such a reformulation, we introduce the concept of an atom of space-time-matter (STM). An STM atom is a classical noncommutative geometry (NCG), based on an asymmetric metric, and sourced by a closed string. Different such atoms interact via entanglement. The statistical thermodynamics of a large number of such atoms gives rise, at equilibrium, to a theory of quantum gravity. Far from equilibrium, where statistical fluctuations are large, the emergent theory reduces to classical general relativity. In this theory, classical black holes are far from equilibrium low entropy states, and their Hawking evaporation represents an attempt to return to the [maximum entropy] equilibrium quantum gravitational state.

This essay is a nontechnical primer for a broader audience, in which I paint a broad-brush picture of modern cosmology. I begin by reviewing the evidence for the big bang, including the expansion of our Universe, the cosmic microwave background, and the primordial abundances of the light elements. Next, I discuss how these and other cosmological observations can be well explained by means of the concordance model of cosmology, putting a particular emphasis on the composition of the cosmic energy budget in terms of visible matter, dark matter, and dark energy. This sets the stage for a short overview of the history of the Universe from the earliest moments of its existence all the way to the accelerated expansion at late times and beyond. Finally, I summarize the current status of the field, including the challenges it is currently facing such as the Hubble tension, and conclude with an outlook onto the bright future that awaits us in the coming years and decades. The text is complemented by an extensive bibliography serving as a guide for readers who wish to delve deeper.

With its strong economy, the country wants to play a bigger role on the world science stage.

The brain is a complex system, composed of multiple neural units interconnected at different spatial and temporal scales. Diffusion MRI allows probing in vivo the anatomical connectivity between different cortical areas through white matter tracts. In parallel, functional MRI records neural-related signals of brain activity. Particularly, during rest (in absence of specific external task) reproducible dynamical patterns of functional synchronization have been shown across different brain areas. This rich information can be conveniently represented in the form of a graph, a mathematical object where nodes correspond to cortical regions and are connected by edges representing anatomical connections. On the top of this structural network, or brain connectome, individual nodes are associated to functional signals representing neural activity over observation periods. Network science has fundamentally contributed to the characterization of the human connectome. The brain is a small-world network, able to combine segregation and integration aspects. These properties allow functional specialization on the one side, and efficient communication between distant brain areas on the other side, supporting complex cognitive and executive functions. Graph theoretical methods quantify brain topological properties, and allow their comparison between different populations and conditions. In fact, brain connectivity patterns and interdependences between anatomical substrate and functional synchronization have been proved to be impaired in a variety of brain disorders, and to change across human development and aging. Despite these important advancements in the understanding of the brain structure and functioning, many questions are currently unanswered. It is not clear for instance how structural connectivity features are related to individual cognitive capabilities and deficits, and if they have the concrete potential to distinguish pathological subgroups for early diagnosis of brain diseases. Most importantly, it is not yet understood how the connectome topology relates to specific brain functions, and how the transmission of information happens on the top of the structural connectivity infrastructure in order to generate observed functional dynamics. This thesis was motivated by these interdisciplinary inputs, and is the result of a strong interaction between biological and clinical questions on the one hand, and methodological development needs on the other hand. First, we have contributed to the characterization of the human connectome in health and pathologies by adapting and developing network measures for the description of the brain architecture at different scales. Particularly, we have focused on the topological characterization of subnetworks role within the overall brain network. Importantly, we have shown that the topological alteration of distinct brain subsystems may be a biomarker for different brain disorders. Second, we have proposed an original network model for the joint representation of brain structural and functional connectivity properties. This flexible spatio-temporal framework allows the investigation of functional dynamics at multiple temporal scales. Importantly, the investigation of spatio-temporal graphs in healthy subjects have allowed to disclose temporal relationships between local brain activations in resting state recordings, and has highlighted functional communication principles across the brain structural network.