THE END OF BROKEN SPACETIME

Xavier Terri Castañé

**ABSTRACT**: Any tetradimensional theory of gravity that was a consistent generalization of special relativity and no tolerating outstanding observers will get superior speeds to the local light speed in void. In this article the theory of general relativity from Einstein is refused because it is unable of carry out this requirement, therefore a new alternative generalization is propose, the connected theory that eliminates the black holes. A different light raises where the absolutely darnkness was before.

**KEYWORDS**: special relativity, general relativity, connected theory, black hole, inertial, inertial-no inertial dichotomy, connected system, metric, equivalence principle, connection principle, gravitational redshift, invariance, fundamental equation of the connected dynamic, Einstein's field equations, generalized principle of inertia, 'c' constant, Newton, Einstein, Hawking.

**1. Widespread official of special relativity: general relativity**

Our current vision of the cosmos is based on two theories: quantum mechanics, which constructs an entire microcosm, and general relativity, which is supposedly valid for describing macrocosms. The latter was a product of the urgent historical imperative to generalise special relativity, a theory presented in 1905 as an alternative to the Newtonian theories but which, in contrast to these, had the serious drawback of being unable to describe gravitational interaction. It was only applicable to reference systems or very special observers, ones which would today be called “inertial” observers, whose corresponding spacetime metric is characterised by a four-dimensional “flat”, or Minkowski, metric.

According to general relativity, gravitational forces curve spacetime. The metric ceases to be that of Minkowski—such as it is determined by field equations or Einstein equations—and falling bodies simply follow the shortest route in this curved spacetime—with movement, or geodesic, equations, determining the route. With this four-dimensional description of gravitation, it is not only possible to predict already known events, those that the Newtonian theories already predicted, but also to explain three “anomalies” or predictions that escaped the comprehension of the Newtonian theories: gravitational redshift, the residual advance of the perihelion of Mercury and the deflection of light rays that tangentially affect the edge of the solar disk. Such anomalies, corroborated in experiments, demand a high level of precision from any new theory. They represent a difficult test, known as the three classic tests, that any good theory of gravitation must be capable of passing. General relativity is generally said to have passed these tests successfully, but this article will explain that: 1) it is not true that it predicts gravitational redshift coherently, which leads to all types of contradictions and singularities, event horizons and black holes, points where spacetime breaks (points here the Schwarzschild metric breaks); 2) general relativity is a theory that contradicts the thesis that privileged observers do not exist; and 3) an alternative to general relativity exists which truly passes the three classic tests without singularities, does not contradict general relativity, is the only coherent four-dimensional generalisation of special relativity for the purpose of making it compatible with gravity and gives rise to new predictions, the theory of reference systems connected to the gravitational medium, or simply connected theory.

Einstein, faced with the historic imperative of generalising special relativity, applicable only to inertial systems and in the absence of gravitation, tried to find a bridge to connect the gravitational field with the concept of the inertial observer. This conceptual bridge is what as known as the equivalence principle. It establishes the following: “an observer in a gravitational free fall is locally inertial”. Something which seems to mean that the timespace metric for that observer alone will be an infinitesimal spacetime environment (locally), a flat, or Minkowski, metric, precisely as postulated by the special relativity theory for its inertial observers. The equivalence principle establishes, therefore, a relationship between the gravitational phenomenon, symbolised by an observer in a gravitational free fall, and special relativity, whose domain of applicability, although very restricted, seems to be assured by decreeing the existence of locally inert observers. Einstein attempted to generalise special relativity using this bridge. Ten years later he presented his theory of gravitation: general relativity, inspired by the equivalence principle and, as the name itself indicates, supposedly valid —invariable—for all possible observers in nature (that a theory is applicable to the entire system of mathematical coordinates is a merit inherent in the mathematical calculation instruments—tensorial calculus—that it uses. But it does not necessarily mean that it is in agreement with the invariability of physical laws for all possible observers in nature). But, what is the exact meaning of the “inertial” concept that appears in the logic of the equivalence principle? Does it not seem strange that a theory that aspires to surpass special relativity, a theory that had in turn already surpassed the theories of Newton, is based on a concept that originates in theories that are already obsolete? Is general relativity the fruit of precipitation and of historic urgencies?

**2. The dichotomy inertial vs non-inertial**

**The old second Newtonian law, which is the fundamental equation of the classic dynamic and which establishes a relationship between force and three-dimensional acceleration, is nothing more than a simple generalisation of the classic principle of inertia. From here it can be deduced that a three-dimensionally free body (the net force that acts upon it is null) remains in repose or uniform rectilinear movement. But this only occurs when it is observed from a “privileged” system of inertial reference. To try to explain the accelerations that three-dimensionally free bodies sometimes exhibit, Newtonian mechanics finds itself obliged to introduce the opposite concept: that of the non-inertial observer. According to these types of observers, certain specific forces would exist that are called fictitious, apparent or inertial, which would be held responsible for causing the accelerations of three-dimensionally free bodies (those that do not seem to exhibit any “real” interaction with their environment). Adding “fictitious” forces to Newton's second law—which then ceases to be an invariable equation—is the means of trying to justify the accelerations of three-dimensionally free bodies. Succinctly, accepting Newtonian ideas implies accepting the existence of a dichotomy within the class of all possible observers in nature. the inertial–non-inertial dichotomy. It is in this dichotomy where one finds the historic origin of the “inertial” concept on which the equivalence principle rests. Paradoxically it is this old absolute principle that becomes the key when it comes to generalising special relativity for the purpose of arriving at a theory that is applicable to any possible observer.**

It is necessary to generalise special relativity. It is necessary to construct, in effect, a new theory of gravitation which is consistent with the universal invariability of physical laws, which is also applicable to those observers that cease to be inertial because of gravitation. But it does not seem very sensible to have to build this new theory on a principle, the equivalence principle, that does nothing more than re-establish the existence of “privileged” inertial observers. General relativity is undoubtedly applicable to the entire system of mathematical coordinates (thanks to tensorial calculus), but it violates the universal invariability of physical laws. It violates the equality of all possible observers in nature from the moment that it “locally” resurrects the inertial–non-inertial dichotomy through the equivalence principle that sustains it.

We will have made no progress if, having refuted the absolutism of Newton’s theories, we then resurrect it by declaring the existence of absolute observers. We will have made no progress if, having separated the earth from its privileged place as the “centre of the universe”, we then make the sun the new centre. (In fact, general relativity even contradicts itself, with its equivalence principle and its geodesics, as it is not difficult to demonstrate that, for a relativistic stationary observer, the acceleration—the second derivation of the radial coordinate with respect to the “coordinated time”—of a falling body depends on its speed. Then it would not even be true for relativity itself that a free falling—“inertial”—observer would locally nullify the gravitational field: strictly speaking, bodies with different speeds will exhibit different accelerations, pág. 3 )

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