# | PROBLEM 3: Einstein’s Field Equations – incorrectness in the General Theory of Relativity.

The content of this web page is excerpts of the published printed book in Bulgaria
The Special Theory of Relativity – a Classical Review,
that almost corresponds to the e-book “The Special Theory of Relativity – the Biggest
Blunder in Physics of the 20th Century”©, published at Smashwords and at Amazon.

In the General Theory of Relativity, Einstein shows that the time and space are not absolute and depend on gravitational forces. The mass of the celestial bodies distorts the space and the time. Space reacts with distortion and contraction when a mass object is present. The bending of the trajectory of light due to the geometric distortion of space, observed during a total solar eclipse, is the first experimental test of the general theory of relativity. In areas with a stronger gravitational field, the space is shrunk (length contraction) – i.e. the unit of length “meter” is shortened; the time goes slower (time dilation) – i.e. the unit of time “second” is extended. However, in an area where the intensity of the gravitational field is the same and unchanging, as in our local time-spatial domain “near the surface of the Earth”, the base units of measurement of time and length are constant.

In fact, however, there are two considerable reasons why Einstein’s field equations are not correct from the point of view of physics. This actually means that the search for their mathematical solutions is meaningless.

### Two considerable reasons proving that Einstein’s field equations are not correct:

1) The first reason for the incorrectness of the field equations: Neglecting the paramount importance of the units of measurement for the theoretical physics.

Actually, the first reason why Einstein’s field equations are not correct from the point of view of physics lies in the answer to the question:

“What is the difference between the mathematical equations and the equations of the theoretical physics?”

For many scientists in the field of relativity and cosmology it is a mistake that they (it seems unconsciously and unintentionally) overlook the following fundamental difference:

•  In the mathematical equations, we work only with numbers. Actually, the mathematical equation is an assertion of the equality of two pure numeric expressions.

•  In physics, however, the use of mathematics (writing/ creation of an equation of the theoretical physics), is possible only with the help of the measurement units of the physical quantities involved in the equation. Each equation of the theoretical physics is written on the basis of a certain system of units of measurement – for example, the International System of Units (SI).

That’s why the units of measurement are of paramount importance for the theoretical physics.

So, we can highlight:

The units of measurement are the primary, the most basic physical constants, which we have defined and chosen to be constants!

It is precisely: with the help of these primary physical constants we have the opportunity to use mathematics in the field of physics!

In this way, the sign of equality between the physical expressions in the equations of theoretical physics (formed by means of units of measurement), represents, in fact, the relationships between the physical quantities in nature. On the base of the equations of theoretical physics, we have discovered the physical laws and have determined the physical constants (like the speed of light in vacuum c, the gravitational constant G, the electric constant ε0 (vacuum permittivity), the magnetic constant µ0 (vacuum permeability), the Planck’s constant, the Boltzmann constant etc. All these physical constants are actually secondary constants, because they are obtained on the basis of the defined (and accepted) primary physical constants – the measurement units. That is why, we have different numerical values for physical constants when we use units of measurement of other measurement system.

In conclusion, we must emphasize again that the equations of theoretical physics can exist only if the units of measurement are constant and do not change inside the scope of the given equation. Only then, the use of the “equality sign” between the expressions on both sides of the equations is correct! The disregard of this important fact leads to the nonsense of the work of many scholars.

### One simple example that shows the importance of the units of measurement:

Let us compose a physical equation for the average speed of a seagoing ship between two points A and B.  Obviously, it is equal to V = S/t, where S is a real number showing how many times the used unit of length (meter) is applied to the distance between points A and B; t is the real number showing the number of elapsed seconds (the used unit of time), for which the ship passes the distance between the two points. The result obtained for the average speed is again an exact real number, but with a certain dimension (m/s), which shows the units of measurement, used to obtain the resulting number. This example undoubtedly shows that mathematically, everything is accurate and true…, but remember that the base units of length and time do not change within the scope of the equation – they are constant, defined at the sea level!

However, if A is our Earth, and B is another planet or a star on the opposite side of our Galaxy? In this case, during the voyage, the spacecraft will pass through areas with different strength of the gravitational field, where the unit of length (meter) and time unit of time (second) will be different. Defined on the Earth “meter” can contract to a millimeter in a strong gravitational field, and the “second” there to be equal to minutes or hours on the Earth. Obviously, that if we write the equation for the average speed of the spacecraft between points A and B: (V = S/t), on the basis of the defined units of length and time on the surface of the Earth, then this equation in terms of physics would not be true. In fact, we do not know either the number of miles (the length of the unit “meter” is changed) nor the duration of the voyage (the duration of the unit “second” changes) in the scope of this equation. Therefore, the average speed of the ship will be indeterminable. In this sense, it appears that, in addition to the uncertainty principle in quantum mechanics, it turns out that we have actually uncertainty in the “macro-world”, too (in the Universe).

Let us return to Einstein’s Field Equations(EFE) – the set of nonlinear partial differential equations in Albert Einstein’s General Theory of Relativity.

Let us make a brief analysis (description) of the modified form of Einstein’s field equations (tensor record of these equations):

The expression on the left side of this equation represents unknown warping of the structure of space-time: (Rµν is the Ricci curvature tensor, R is the scalar curvature, gµν is the metric tensor, and Λ is the cosmological constant). The expression on the right side represents the known matter and energy (Tµν is the stress-energy tensor). The Newton’s universal gravitational constant G and the speed of light c appear as physical constants and π is a numeric constant. Therefore, the EFE are interpreted as a set of equations representing how the matter and energy (on the right side) determine the curvature of space-time (on the left side) in the Universe. They express the warping of the structure of the space-time, and “HOW THE UNITS OF MEASUREMENT ARE CHANGING IN THE UNIVERSE BY THE MATTER AND ENERGY”!

However, the scope of Einstein’s Field Equations is the entire Universe. The Universe consists of planets, stars and galaxies and the intensity of the gravitational field is different in different areas of the space-time of the Universe – and therefore, the units of measurement are different in any point, depending on the intensity of the gravitational field. However, the accepted base units of length and time in the EFE are the units defined on the surface of a small planet in the Solar System, and we use these units for the entire Universe! It is not funny, is it? The funny thing is when some physicists look for solutions to Einstein’s Field Equations. Usually, they demonstrate excellent mathematical skills and physically interprets there the irreproachably accurate mathematical “proofs”. As a result, they make wrong conclusions and then say:

##### “It is true, because it is mathematically proven!” …

Therefore, our conclusion about the Einstein’s field equations is that they express only a great, genius “idea”! However, the reader will agree that the use of “the equation sign” here is not correct… and the search for mathematical solutions of Einstein’s field equations is only a demonstration of mathematical skills, but they have no physical interpretation.

#### About tensors. We know that tensors are mathematical objects but are designed for engineering applications – for example, when calculating tensile and bending tensions in heterogeneous materials. One correct example in the engineering field:

If we calculate tensile and bending stress in a piece of heterogeneous material caused by external forces, we use units of a certain measurement system (like SI-system), which are defined in the time-spatial domain outside the material body. In our case, it is our time-spatial domain “near the Earth’s surface”, where the intensity of the gravitational field is uniform and the defined with great accuracy physical units are constant. The applied forces on the material body, as well as the calculated tension in any point of the piece of material, are in the “out of the body” coordinate system – the same system, where we have defined the units of measurement and where they are constant. Therefore, we can say that in this example, the physical equations are exact and mathematically and physically correct (the use of the equality sign is correct).

The reader sees, however, that the case “Einstein’s field equations” is not analogous.

Therefore, the Einstein’s field equations are not correct regarding the unchangeability of the units of measurement within the scope of the equations.

2) The second reason for the incorrectness of the field equations: THE PHYSICAL CONSTANTS (like the speed of light) are not absolute, unlike the mathematical constants.

The second reason why Einstein’s field equations are not correct from the point of view of physics refers to the fundamental physical constants:

“all physical constants change depending on the intensity of the gravitational field.” (Sharlanov, 2016).

In the current work, theoretical and experimental evidence is given that “the speed of light in vacuum is constant in the areas of Universe, where the intensity of the gravitational field is constant, but it is different in areas with different intensity of the gravitational field.

Einstein came himself to the conclusion in the article “On the Influence of Gravitation on the Propagation of Light” too, that the speed of light in vacuum depends on the gravitational potential (depends on the intensity of the gravitational field), and he deduced a formula how the speed of light changes. (Einstein, 1911).

If the measurement units of length and time change depending on the intensity of the gravitational field, then the physical constants will also change synchronously, as they are linked to the units of measurement. Here we must distinguish between the physical constants and the mathematical constants, which are non-variable purely numerical constants (such as the Archimedes’ constant π, Euler’s number e, Pythagoras’ constant √2, golden ratio φ,etc…).

Theoretically, the question of changing the physical constant “speed of light in vacuum, depending on the intensity of the gravitational field is discussed in detail in this book. Chapter 11 demonstrates that change of physical constants (such as “speed of light in vacuum”), can only be determined if we use the units of measurement, defined in another area but with different intensity of the gravitational field.

Experimentally, (using the units of measurement defined on the Earth’s surface), a slower speed of radar electromagnetic signals has been experimentally measured in the area with strong gravitation (near the Sun) by American astrophysicist Irwin I. Shapiro in 1964. This fact has been confirmed again highly accurately, using controlled transponders aboard “Mariner-6” and “Mariner-7” space probes, when they orbited the planet Mars.

In the Einstein’s field equations, whose scope is the entire Universe with all the unimaginable difference in the gravitation, exist: the local constant speed of light in vacuum c, the gravitational constant G, and the cosmological constant Λ (the value of the energy density of the vacuum of space, which is known as the Einstein’s “Biggest Blunder”). These physical constants are obtained on the basis of local units of measurement, defined on the surface of a small planet (the Earth) in a solar system on the outskirts of one of the galaxies.

These are the two considerable reasons, which undoubtedly show that
Einstein’s field equations are not correct from the point of view of physics, and this actually means

that the search for their mathematical solutions is meaningless.

In spite of this,

the general theory of relativity is a brilliant idea of a genius that breaks our perception about the absoluteness of time and space.