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Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though, leading us to consider the implications of using realistic probes in defining an effective spacetime geometry. As an example, we consider de Sitter spacetime and employ the centroid of various composite probes to obtain its effective sectional curvature, which is found to depend on the probe's internal energy, spatial extension, and spin. Possible refinements of our approach are pointed out and remarks are made on the relevance of our results to the quest for a quantum theory of gravity.

In this paper, we have tried to explore the twin paradox in the ellipsoidal coordinate system. We have investigated that the traveling twin travels away from the gravitational source in the first case while in the other it moves towards the source. We then tried to compare it with the special relativistic case where the static twin ages faster as compared to his traveling counterpart.

‘Internal spacetime’ is a modification of general relativity that was recently introduced as an approximate spacetime geometric model of quantum nonlocality. In an internal spacetime, time is stationary along the worldlines of fundamental (dust) particles. Consequently, the dimensions of tangent spaces at different points of spacetime vary, and spin wavefunction collapse is modeled by the projection from one tangent space to another. In this paper, we develop spinors on an internal spacetime, and construct a new Dirac-like Lagrangian ${ℒ}=\bar{\psi }(i\partial /-\widehat{\omega })\psi$ whose equations of motion describe their couplings and interactions. Furthermore, we show that hidden within ${ℒ}$ is the entire standard model: ${ℒ}$ contains precisely three generations of quarks and leptons, the electroweak gauge bosons, the Higgs boson, and one new massive spin-$2$ boson; gluons are considered in a companion paper. Specifically, we are able to derive the correct spin, electric charge, and color charge of each standard model particle, as well as predict the existence of a new boson.

A composite model of the standard model particles was recently derived using the Dirac Lagrangian on a spacetime where time does not advance along the worldlines of fundamental dust particles, called an ‘internal spacetime’. The aim of internal spacetime geometry is to model certain quantum phenomena using (classical) degenerate spacetime metrics. For example, on an internal spacetime, tangent spaces have variable dimensions, and spin wavefunction collapse is modeled by the projection from one tangent space to another. In this article, we show that the combinatorial structure of the internal Dirac Lagrangian yields precisely the standard model trivalent vertices, together with two new additional (longitudinal) $Z$ vertices that generate the four-valent boson vertices. In particular, we are able to derive electroweak parity violation for both leptons and quarks. We also obtain new restrictions on the possible spin states that can occur in certain interactions. Finally, we determine the trivalent vertices of the new massive spin-$2$ boson predicted by the model.

From the theory of the multiverse cosmology, it is possible that our universe collides with other universes locally in its history, which may result in local changes of the curvature of the spacetime. In this paper, we propose a method to probe the multiverse using gravitational wave observations for the first time. Our method firstly makes triangles using two detected gravitational wave sources and the Sun, and then measures the curvature of the triangles. We use 11 gravitational wave sources detected by LIGO and Virgo during O1 and O2, and make 55 triangles by combining them to measure their curvature. The curvature is measured by comparing the distance between two gravitational wave sources estimated by the gravitational wave observations with the one obtained with assumption of a simple model of the cosmological evolution.

As a result, we found that, for 43 of 55 triangles, the distances estimated by the model are greater than the ones obtained by the gravitational wave observations. This indicates a negative curvature, which may be due to the simplification of the cosmological evolution. For the rest 12, the distances are not determined because of uncertainty of the parameters of the gravitational wave observations. Further gravitational wave observations and more sophisticated model of the cosmological evolution is essential to test the multiverse cosmology observationally.