THE EINSTEIN GRAVITATIONAL FIELD LACKS A TRUE TENSOR

Cosmology scientists inform us that they definitely understand the universe expansion. They have proven from extensive scientific study that our universe was born 13.7 billion years ago in a Big Bang explosion. They can explain in minute detail the many stages of this process that have occurred since that explosion. However, the most astounding part of the Big Bang story is that our universe began as a singularity, which literally means a condition of infinite mass density. Cosmologists insist that our whole universe was microscopic in size at the instant of the Big Bang, and some claim it was smaller than a proton.

We are supposed to believe that the many tens of billions of galaxies of our universe, each containing as many as 100 billion stars, were initially squeezed into a microscopically small body, 13.7 billion years ago. This 13.7 billion-year age of our universe may seem like a long time, but it is only 3 times the age of our earth (4.6 billion years), and stars have been observed in our Milky Way galaxy that are at least 13.4 billion years old. To explain observational data, cosmologists have concluded that our present universe must consist primarily of dark energy and non-physical dark matter, which are unrelated to any energy or matter that we can observe on earth.

What is the basis for these science-fiction claims by cosmologists? Their research is based on computer studies of Einstein’s General theory of Relativity. Obviously, these conclusions must be correct. After all, who can doubt the great wisdom of Albert Einstein?

But Einstein strongly opposed singularity predictions of his theory. The cosmologists reply, “That does not matter. Since Einstein did not have a computer, he could not realize that his equations definitely require singularities. Our computer simulations of General Relativity have proven that the Big Bang must have begun as a singularity, and a massive neutron star must collapse to form a singularity that we call a Black Hole.” (According to Black Hole theory, all of the mass of a Black Hole is concentrated as a singularity at its center.)

Astronomers claim to have proven that Black Holes are physically real, because they are finding many highly compact, dark bodies that are too massive to be neutron stars, and must be Black Holes. Therefore, even though a singularity may seem like science-fiction, these astronomical observations have definitely proven that singularities actually exist in physical reality.

This is the claim made by cosmologists to support the physical reality of singularities. The fallacy of this reasoning is the assumption that the equations of General Relativity are absolutely correct. However, in 1945 Einstein admitted that his theory does not hold exactly under conditions of extreme density of field and matter, and so it cannot be used to predict a physical singularity. (See Article 1,1, page 18 and Reference 7.)

These issues show that to appreciate the true nature of our universe, the reader must understand cosmology, and this requires the knowledge of Einstein’s General theory of Relativity. “But that is impossible”, you say. “Everyone knows that only a few brilliant scientists can comprehend General Relativity!” That common belief is nonsense! In Article 1,1, this website provides a simple yet thorough and scientifically accurate explanation of General Relativity, which can be readily understood by anyone with a high-school knowledge of algebra.

The Einstein theory provides the basis for explaining the universe expansion. Einstein maintained that gravity is not an attractive force, as Newton claimed; gravity is a curvature of space. Within our solar system, the curvature of space produced by gravity is accurately approximated by Newton's theory, which assumes that celestial bodies are pulled together by gravitational forces. However, when we model the universe as a whole, the curvature of space produced by gravity manifests itself as an expansion of the universe.

Why did Einstein not recognize that the curvature of space embodied in General Relativity explains the universe expansion? The answer is simple. Einstein was unable to derive a complete gravitational field equation to specify his General theory of Relativity.

The Einstein Theory of Relativity

Einstein presented his basic (or “Special”) Relativity theory in 1905 to explain a paradox associated with measuring the speed of light. He concluded that the speed of light must be the same for all observers, regardless of their velocities. For this to be true, the instruments for measuring distance and time must appear to be different for observers travelling at different velocities. Yet, these apparent effects are not illusions; they are real.  

From this concept, Einstein derived some profound conclusions, which include the prediction that energy can be converted into matter, and matter into energy, in accordance with the famous Einstein formula (E = Mc²).  That prediction eventually led to the awesome power of the atomic nuclear bomb.

Einstein’s Special Relativity theory was based on the principle that the measured speed of light is exactly constant, regardless of the velocity of the observer. Then Einstein found that this does not hold when the velocity of the observer changes, i.e., when acceleration occurs. He concluded that acceleration and gravity are indistinguishable, and so the speed of light must also vary with gravity. Hence Einstein needed to generalize his Relativity theory to include the effects of gravity and acceleration. 

The measurements made by two observers can be regarded as measurements made relative to coordinates at the locations of the observers. Einstein recognized that the essential result achieved by his Special 

Relativity theory was to translate measurement data in a consistent manner from one set of coordinates to another. To generalize his Relativity theory, Einstein needed to achieve this same result when the two sets of coordinates operate under different accelerations and gravitational fields, as well as under different velocities. Einstein specified this requirement by his Principle of Covariance, which states that the laws of physics should be formulated in such a manner that they are “good” in all coordinate systems.

Einstein discovered that his Covariance principle could be satisfied by a mathematical theory published in 1901 by the Italian mathematician, Gregorio Ricci, with the help of his student, Tullio Levi-Civita. This theory was called “The Absolute Differential Calculus”. It was based on a mathematical principle for specifying curved space that was presented by the German mathematician Bernhard Riemann in 1852. The Riemann-Ricci mathematical theory of curved space provides complicated rules for translating data in a consistent manner from one coordinate system to another.

To incorporate relativity principles into the abstract Riemann-Ricci mathematical theory, Einstein concluded that gravity and acceleration must produce the curvature of space for this mathematical theory. Einstein achieved this by developing his “Gravitational Field Equation”, which specifies the effect of gravity and acceleration on the curvature of space. The elements of this equation are called “tensors”. These tensors must have precise mathematical characteristics, so that they transform into different coordinates according to the rigid rules of the Riemann-Ricci mathematical theory. Tensors that satisfy this requirement are called true tensors.

Einstein was able to derive a true tensor that specifies the effect of matter and energy on the curvature of space. He called this true tensor his “energy-momentum tensor”. He also tried to develop a true tensor to specify the energy of the gravitational field, but he could only achieve a “pseudo-tensor”, which could not be used in his gravitational field equation.   

The resultant gravitational field equation developed by Einstein has had remarkable success in predicting the tiny relativistic effects due to gravity that occur within our solar system. However, the Einstein equation cannot yield meaningful predictions of the much larger relativistic effects associated with cosmology, because the Einstein gravitational field equation lacks a true tensor to characterize the gravitational field. The science-fiction concepts derived by cosmologists from Einstein’s General theory of Relativity are the result of using an incomplete gravitational field equation. 

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