Related papers: What do we know about the geometry of space?
Since the dawn of civilization, humanity has grappled with the big questions of existence and creation. Modern cosmology seeks to answer some of these questions using a combination of mathematics and measurement. The questions people hope…
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…
The Cosmological Principle states that the universe is both homogeneous and isotropic. This, alone, is not enough to specify the global geometry of the spacetime. If we were able to measure both the Hubble constant and the energy density we…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
Recent astronomical observations verify the new scenario resulting from new conservation laws and a new relativity principle fixed either by dual properties of light or by new gravitational (G) tests and the Einstein's equivalence…
The possibility to describe the laws of the Universe in a computational way seems to be correlated to a principle that the density of information is bounded. This principle, that is dual to that of a finite velocity of information, has…
In this essay we discuss the difference in views of the Universe as seen by two different observers. While one of the observers follows a geodesic congruence defined by the geometry of the cosmological model, the other observer follows the…
Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…
No matter how counterintuitive they are, quantum phenomena are all simple consequences of the laws of Quantum Mechanics. It is not needed to extend the theory with hidden mechanisms or additional principles to explain what Quantum Mechanics…
A natural geometric framework of noncommutative spacetime is symplectic geometry rather than Riemannian geometry. The Darboux theorem in symplectic geometry then admits a novel form of the equivalence principle such that the…
While many observations support the validity of Einstein's general relativity as the theory of gravity, there are yet many that suggest the presence of new physics. In order to explain the high-redshift supernovae Ia observations together…
Modern observations based on general relativity indicate that the spatial geometry of the expanding, large-scale Universe is very nearly Euclidean. This basic empirical fact is at the core of the so-called "flatness problem", which is…
Weyl famously argued that if space were discrete, then Euclidean geometry could not hold even approximately. Since then, many philosophers have responded to this argument by advancing alternative accounts of discrete geometry that recover…
It is shown that the theory of dark matter can be derived from the first principles. Particles representing a new form of matter gravitate but do not interact electromagnetically, strongly and weakly with the known elementary particles.…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4-dimensional space where time intervals are always a measure of geodesic arc lengths, i.e.…
Most scientists would hold that science has not established that the cosmos is physically comprehensible - i.e. such that there is some as-yet undiscovered true physical theory of everything that is unified. This is an empirically…
While purely philosophical in the early times, and still very speculative at the beginning of the twentieth century, Cosmology has gradually entered into the realm of experimental science over the past eighty years. It has raised some…