Related papers: Noncommutativity and relativity
In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The…
Lorentz transformation on two-dimensional spacetime is obtained without assumption of linearity. To obtain this, we use the invariance of wave equations, which is recently proved to be equivalent to the causality preservation.
Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must…
Research in quantum gravity strongly suggests that our world in not fundamentally spatiotemporal, but that spacetime may only emerge in some sense from a non-spatiotemporal structure, as this paper illustrates in the case of causal set…
An odd look at "standard" physics (Galileo, Newton, Einstein, Dirac) leading to a radical change of our concept of inertial motion and to new heuristic approaches of gravitation and the cosmological constant.
The cosmological constant problem is principally concerned with trying to understand how the zero-point energy of quantum fields contributes to gravity. Here we take the approach that by addressing a fundamental unresolved issue in quantum…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
We present the theory of special relativity here through the lens of differential geometry. In particular, we explicitly avoid any reference to hypotheses of the form "The laws of physics take the same form in all inertial reference frames"…
Special relativity turns out to be more than coordinate transformations in which the constancy of the speed of light plays the central role between two inertial reference frames. Special relativity, in essence, is a theory of…
Several physical concepts, including the concept of time, are clarified herein by taking into account existing experimental data. In addition, the missing links among these physical concepts are established. This allows us to take another…
In this paper we consider the observables describing fundamental spatiotemporal properties and relations in the context of Quantum Gravity (QG). As we will show, in both Loop Quantum Gravity and in String Theory, these observables are…
The developments of special relativity and quantum mechanics marked the beginning of the modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity -- the space-time interval --…
We present a classical theory of gravity, which is singularity free at short distances and reduces to General Relativity at large distances. We discuss its implications.
The problem of relativity of motion in quantum vacuum is addressed by considering a cavity moving in vacuum in a monodimensional space. The cavity is an open system which emits photons when it oscillates in vacuum. Qualitatively new effects…
We emphasize that noncommutative (NC) spacetime necessarily implies emergent spacetime if spacetime at microscopic scales should be viewed as NC. In order to understand NC spacetime correctly, we need to deactivate the thought patterns that…
We feel that non-commutative geometry is to particle physics what Riemannian geometry is to gravity. We try to explain this feeling.
Traditional derivations of general relativity from the graviton degrees of freedom assume space-time Lorentz covariance as an axiom. In this essay, we survey recent evidence that general relativity is the unique spatially-covariant…
The quantization of gravity offers a solution to the presence of singularities in cosmology. Infinities are removed because of the existence of finite quanta of spacetime. This is one of the most important prediction of Loop Quantum…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
Popular wisdom amongst theoretical physicists says that the continuum structure of spacetime is probably not elementary, but rather emergent. While many arguments to support that view arise from speculative ideas, the argument can also be…