Related papers: Relativity for games
The theory of relativity showed that several Newtonian ideas about spacetime are imperfect. We present here some relativistic concepts related to these ideas: simultaneity of events and synchronization of clocks (both along a line in the…
We develop a formalism for General Relativistic N-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives…
A logic of reciprocity between inertial frames in relative uniform motion is investigated. Relativity allows any reference frame to apply Lorentz Transformation while reciprocity would require the relative frame to use Inverse…
Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of…
Reinforcement learning (RL) is successful at learning to play games where the entire environment is visible. However, RL approaches are challenged in complex games like Starcraft II and in real-world environments where the entire…
In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…
The Principle of Relativity has so far been understood as the {\it covariance} of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of {\it…
We study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in…
In the framework of special relativity, all particles are point-like or string-like. This nature of particles has caused the divergence difficulties in quantum field, string and superstring theories. In the framework of special relativity,…
By attaching three anticommuting Lorentz scalar (colour) property coordinates to space-time, with an appropriate extended metric, we unify gravity with chromodynamics: gauge transformations then just correspond to coordinate transformations…
Fictitious play (FP) is one of the most fundamental game-theoretical learning frameworks for computing Nash equilibrium in $n$-player games, which builds the foundation for modern multi-agent learning algorithms. Although FP has provable…
The formula for the relativistic Doppler effect is investigated in the context of two compelling invariance axioms. The axioms are expressed in terms of an abstract operation generalizing the relativistic addition of velocities. We prove…
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…
A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski…
Video game playing is an extremely structured domain where algorithmic decision-making can be tested without adverse real-world consequences. While prevailing methods rely on image inputs to avoid the problem of hand-crafting state space…
It has been more than a century since first Lorentz and later Einstein explored relativistic events and still important consequences of that remains unclear to everybody. The present study extensively focus on Lorentz (Length) contraction…
After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is…
Theoretical and observational arguments are listed in favor of a new principle of relativity of units of measurements as the basis of a conformal-invariant unification of General Relativity and Standard Model by replacement of all masses…