Moving objects in retarded gravitational potentials of an expanding spherical shell/Cosmology of retarded interaction

Gravitational redshift Conclusion Cosmology of retarded interaction Modern astrophysics is based on the general theory of relativity (GR) because it has been confirmed by experiments such as the perihelion precession of Mercury or the detection of gravitational waves. A new model must prove that it also correctly describes all the effects that the general theory of relativity explains geometrically. To devise a disruptive cosmology that relies solely on classical, relativistic, and retarded gravitational potentials and dispenses with all ad hoc and a priori hypotheses – such as the equivalence principle of general relativity, cosmological constants, dark matter, dark energy, homogeneity, or isotropy – we must return to a dynamic field approach. To this end, the differential geometry required for general relativity can be replaced by a model that relies on pseudo-Euclidean geometry in Minkowski space. The central challenge is that classical Newtonian gravity acts instantaneously. To construct a consistent cosmology, retarded gravitational potentials can be introduced. This leads to an inherent time dependence and dynamics of the universe without the need to postulate an expansion of spacetime. In what follows, a draft of the cosmology of retarded interaction (CRI) is outlined. The axioms of retarded interaction Established physics is based on three pillars, which are used to build the cosmology of retarded interaction: Classical mechanics: The force as the basis of the acceleration of a mass . Relativistic kinematics: time dilation and length contraction according to the special theory of relativity, but without the curvature of spacetime. Retarded gravitation: The gravitational effect propagates at the speed of light . The potential at a point at time depends on the state of the source at time , where . The mathematical core For the mathematical formulation, the gravitational potential can be substituted into the wave equation: To calculate the gravitational potential at a given location at a specific time , one must not use the current mass distribution ; rather, the mass distribution must be considered at a retarded time : The solution to this wave equation is the retarded potential: In a universe with massive objects, gravity never acts instantaneously but always depends on the mass’s past position. This creates a phase shift between mass and force, as well as an attenuation of the retarded gravitational potentials. Since the particle horizon of a spherical kinematic universe expands at the speed of light in a vacuum, the density depends heavily on the distance from the observer. Observers at the centre see the edges as they were in the past, when the universe was still smaller and denser. For observers in the centre () of a mass distribution within a sphere with the radius the integral above can be simplified with the linear shell mass densities (in kilogram per metre) at their surfaces : The retarded radius of the surface of a sphere at the retarded time that moves away with the speed is given by: The maximum radius that can be experienced by an observer in the centre of the universe is the observable horizon at the retarded time that moved away with speed of light. It is given by the following limit: At a certain point in time with a homogeneous mass distribution , the retarded mass density is given by: Due to the effect of the retarded potentials the mass distribution becomes increasingly inhomogeneous over time. The gravitational potential in the centre at bocomes more and more flat, and the mass density in the out regions at becomes higher and higher over time. Furthermore, the the radial velocity component of all mass points is increasing over time as well: with This leads to an accelerated expansion with the acceleration : An time-dependent inhomogenous mass distribution can be expressed by the dimensionless function with the dimensionless parameter : with and With: The Lorentz factor can also be taken into account. In special relativity it describes the increased relativistic mass of a particle with the velocity and the rest mass as well as the increased mass density of an appropriate space element with the rest mass density : Then the relativistic and retarded mass density distribution is given by the initial shell mass density at the radius at the time : with Cosmological mechanisms The apparent expansion In general relativity, redshift is a stretching of spacetime. In the cosmology of retarded interaction, it is the result of a dynamic retardation in both time and space. Since the gravitational effect arrives retarded, the force of mass lags behind. In a system consisting of many particles, this leads to a continuous kinematic shift in their trajectories. When we receive light from distant sources, we do not observe an expansion of spacetime, but rather the cumulative effect of the net gravitational potentials on the propagation of light (gravitational redshift) and the relativistic potentials due to the motion of the source (Doppler redshift). A replacement for dark matter In the standard model of cosmology respectively the Lambda cold dark matter model (Lambda-CDM model or ΛCDM model), the flat rotation curves of galaxies are explained by dark matter which is even changing over time. In the cosmology of retarded interaction, they result from the retarded effect of the baryonic matter accreted by the galaxies. The stars in the outer regions of a galaxy respond to the gravitational potential of the center as it was millions of years ago. The force does not decrease as because the time delay generates an additional force component, similar to the Liénard–Wiechert potentials in electrodynamics. A replacement for dark energy In the cosmology of retarded interaction, accelerated expansion is interpreted as a cosmic phenomenon. The retarded gravitational potentials of homogeneously distributed masses – located in a spherical shell outside the sphere’s surface on which a moving test mass rests – lead to an net outward acceleration of the test mass, since masses in front of the test mass cause stronger retarded forces than opposing masses that reach the test mass with attenuated retarded forces. Consequently, all mass points moving in the universe drift apart at an accelerating rate because the net acting forces, due to the retardation, cause a radially outward acceleration force. As a result, matter in the outer regions of the universe becomes increasingly dense, creating an inhomogeneous mass distribution (black shell) that continuously amplifies the effect of the retarded potentials. The cosmology of retarded interaction therefore does not align with metric expansion, it only presupposes a static pseudo-Euclidean space. If spacetime itself were expanding, this would call into question or modify the speed of light as a constant parameter for the retardation . The cosmology of retarded interaction would thus actively dispute the thesis of metric expansion and interpret it as an optical illusion. In the cosmology of retarded interaction, expansion is not necessarily linked to an event such as the Big Bang, but is rather a dynamic process. The retardation of gravity gives rise to inhomogeneity. When moving masses are far enough apart that the time delay effectively weakens and phase-shifts the effect of gravity, the objects begin to drift due to their kinetic motion. The farther they drift, the larger becomes, and the weaker the retarded forces from the opposite side from the universe become the expansion accelerates without the need for dark energy. The universe as a black hole In general relativity, a black hole is a region of extreme spatial curvature. However, since cosmology of retarded interaction rejects spatial curvature and replaces it with retarded potentials, the concept of a black hole would have to be radically redefined. In cosmology of retarded interaction, a black hole would not be a geometric point, but rather a region of high mass density in which the gravitational potentials are so strong that the escape velocity is reached. If our universe were the interior of such an object, we would find ourselves in a region where the retarded potentials are dominated by a massive external source which is located in the out regions of the universe. This region can be interpreted as a black shell. Since cosmology of retarded interaction is based on classical potentials, there is no mathematical necessity for a singularity. The retarded effect smooths out extreme gradients over time. A universe-black-hole in cosmology of retarded interaction would thus be more like a gigantic cluster of baryonic matter, within which we find ourselves. The observed physics would then be the superposition of the local forces and the global, retarded pull of the surrounding mass in the black shell. Comparison with the standard model of cosmology thumb|upright=2|Gravitational field in the cosmology of retarded interaction within a spherical black shell of an expanding universe with retarded gravitational potentials:Vector field showing the direction of gravitational forces by blue arrows.Corresponding scalar potential field indicating equipotential lines by red circles. The cosmology of retarded interaction does not rely on a priori hypotheses or ad hoc assumptions, which are taken for granted in the standard model of cosmology. + Comparision standard model of cosmology (ΛCDM) and cosmology of retarded interaction (CRI) Concept Standard model of cosmology (GR / ΛCDM) Cosmology of retarded interaction (CRI) Principle of equivalence Hypothesis (general theory of relativity) confirmed on earth within the margins of measurement accuracy No, gravitation has a scalar potential and its gradient is a force Homogeneity Ad hoc assumption (cosmological principle) No homogeneity, higher mass and energy densities in outer regions of a kinematic universe Isotropy Ad hoc assumption (cosmological principle) Only from the centre of a kinematic universe Copernican principle Ad hoc assumption Milky Way in Local Group near the centre of a kinematic universe Dark matter Ad hoc assumption (non-baryonic particles without electromagnetic interaction) Effect of retarded gravitational potentials Dark energy Ad hoc assumption (cosmological constant Λ) Effect of retarded gravitational potentials Rotation curves of spiral galaxies Ad hoc assumption (dark matter) Retarded gravitational potentials of accreted baryonic matter High-redshift objects Ad hoc assumption (cosmological redshift by expanding spacetime) Gravitational redshift due to baryonic matter in black shell Geometry Dynamic differential geometry Static pseudo-Euclidean geometry Spacetime Curved spacetime Minkowski spacetime Spatial evolution of particle horizon Accelerated expansion with superluminal speed Expansion with speed of light Spatial evolution of event horizon Accelerated expansion with superluminal speed Expansion of inner surface of massive mass shell with sub-light speed Gravitational potential within universe Constant Increasing decrease as the distance from the center increases Singularities Points with infinite mass and energy density, event horizonts with infinite gravitational redshift None Summary The spacetime is not expanding, and it is not curved. It is a system of masses distributed in flat space, whose mutual attraction is so retarded that the resulting trajectories and light signals create the illusion of an expanding geometry that is explained by dark matter and dark energy in the standard model of cosmology. The cosmology of retarded interaction consistently adheres to physical axioms (classical, relativistic, and retarded potentials). It dispenses with the geometric interpretation (no spatial curvature, no event horizon in the sense of general relativity) and regards everything as the result of forces, masses, and retardation. The dark components and spatial curvature are merely mathematical artifacts that arise when one attempts to describe the retarded force action using differential geometry. The universe is not viewed as a geometric black hole in the sense of general relativity, but rather as a huge massive and inhomogeneous system whose internal dynamics are governed by retarded potentials. Cosmology of retarded interaction is based solely on the view that the universe is a mechanical relativistic system with retardation. By introducing differential-geometric paradigms such as the curvature or stretching of spacetime, one departs from the disruptive paradigm of cosmology of retarded interaction and returns to general relativity.