![]() Not least of all, determining the speed of gravity would help physicists debunk theories that contradict Einstein's general relativity. This scientific advancement has broad implications for fundamental physics and our understanding of the cosmos. Previous measurements of gravitational waves had allowed scientists to narrow the range of possibles speeds of gravity to within 55 and 142 percent of c.īut this observation allowed them to narrow the difference between the speed of gravity and c further to within -3 x 10^-15 and 7 x 10^-16 of c - meaning the speed of gravity is practically the speed of light. In this situation tensor calculus plays no role.These two sets of data from the kilonova allowed scientists to compare the speed of the gamma-ray light to the speed of the gravitational waves, giving us a much clearer understanding of the speed of gravity than ever before. This already explains that in otherwise flat space a moving front in the embedding field can be observed to move with superluminal speed. One of the ingredients is that the universe continuously expands. If GR draws the wrong conclusion, then either it applies the wrong differential calculus or it implements the Lorentz transform or tensor calculus in the wrong way. ![]() Next the Lorentz transform and tensor calculus help to compute what the observer will perceive. Thus the differential calculus is the primary descriptor of the dynamics of the field. Any deformation of the embedding field influences the information path and enforces the application of tensor calculus to understand the effect of the differential calculus that controls the behavior of the field at the situation of the observed event. Also in flat space the same hyperbolic coordinate conversion that introduces time dilation and length conversion takes place. Simple mathematics then shows that the Lorentz transform describes the involved coordinate transformation from the Euclidean format in which physical reality presents its data to the spacetime format in which the observers perceive. Also in that situation the embedding field transports the information from the event to the observer. Special relativity already plays at the location and the instant of the observed event when a difference exist between the observed event and the observer. This defines the eigenspace of such defined operator as a sampled continuum or with other words, as a sampled field. This fact can be exploited for defining a category of defined operators that use the eigenvectors of the reference operator and that specify the eigenvalue for an eigenvector as the target value of a selected quaternionic function that corresponds with the eigenvalue of the reference operator as parameter value for that function. When equipped with Cartesian and polar coordinate systems this reference operator can manage the private parameter space of the separable Hilbert space. For example all rational values of a quaternionic number system can together form an eigenspace of a special reference operator. As eigenvalues of operators they can store discrete sets of such values in the eigenspace of operators that reside in separable Hilbert space. The quaternions are ideally suited for the storage of dynamic geometric data in the form of a scalar time-stamp and a three-dimensional spatial location vector. The real numbers, the complex numbers and the quaternions. Hilbert spaces can only cope with number systems that are division rings. Hilbert spaces exist as separable Hilbert space and as non-separable Hilbert space. ![]() A suitable platform that is familiar for many physicists is a Hilbert space. ![]()
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