Einstein's Tautological Maths and Field Equations. The heart of the Relativity confusion.

Circular illogic. Unproven assumptions. Apriori claims. Made up constants. Contrived metrics to force an answer. No physical proofs. About as anti-science as one will find.

Einstotle sharing some laughs with the kids.

Georg Wendel writes: “He (Einstotle) accepts certain errors of older physicists or mathematicians…he accepts four-dimensional space, a thought from Riemann and Helmholtz….accepts the errors of non-Euclidean geometry…accepts the doctrine of finite space…

Palagyi rightly says…’playing with transformations is a dangerous tautology, since it gives the appearance that it contains a demonstration of the principle of relativity while it only expresses the logical-methodical principle that we represent the absolute regularity of a movement in differential equations...’” (in ‘100 Authors against Einstein’, 1930, p. 65, 69)

Relativity is a mathematical-magic show.

Absurdity

When Relativity was first proposed in 1905, almost immediately, many perceptive scientists and mathematicians noticed the tautological nature of Einstein’s calculus. The equations themselves are circular and of little value. It is not hard to spot and is explained below. As part of the author’s quotidian existence he is involved with tensor calculus equations deployed in data analysis. He knows full well that you can create complex tensor and field equations that no one understands, to generate a desired output, or parse the data in a certain desired manner. This is often done to prove an apriori or confirmation bias.

A few posts have assessed the tautology of the transformation equations which is the foundation of Relativity. The Einstotle’s philosophy that everything, time and space, all objects, all grids, all motion, all aspects of life is ‘Relative’, was based on flawed maths which are called, ‘Einstein Field Equations’. As you would expect these are canonical ‘laws’ within ‘science’ and ‘education’. Memorise, regurgitate, repeat.

Einstotle’s Tautology

The cornerstone of General Relativity or ‘GTR’ is the Einstein field equations (EFE), which describes the unproven and frankly ridiculous curvature of spacetime in relation to the distribution of mass and energy within it. The most common expression of EFE is:

Where:

1. G_μν is the Einstein tensor, which describes the curvature of spacetime

2. Λ is the cosmological constant

3. g_μν is the metric tensor, which defines the geometry of spacetime

4. T_μν is the stress-energy tensor, which describes the distribution of mass and energy

5. G is the gravitational constant.

6. c is the speed of light

To be blunt the above equation is rubbish¹. To wit:

1. G_μν is purloined from Ricci and his tensor equation, and simply assumes that a curvature of spacetime is valid. This is unproven and anti-reality. Space and Time cannot be merged. Space is objective, Time is a subjective change of events, which must be measured (and only humans measure time).

   Relativity and its deliberate confusion over Time and Space.

2. Λ is the cosmological constant, which is simply a ‘fudge constant’, with the initial assumption by Einstein, that the universe was static, not expanding. This is equivalent to a similar constant used by Newton. It contravenes the modern dogma that the universe is expanding at different rates of velocity in all directions. You will be pleased to know that this Λ constant, which marked universal stasis, is now ‘revived’ to be equated with ‘Dark Energy’ and the expanding universe! So much science!

3. g_μν is the ‘forced metric tensor’, which defines the ‘geometry of spacetime’, which is unproven, unknown and can never be physically verified.

4. T_μν is the stress-energy tensor, which is again tautological. This ‘stress tensor’ describes the distribution of mass and energy within ‘spacetime’. It represents the ‘source’ of gravity in the equation, without identifying the ‘source’! Again it assumes a 4^th dimension which does not exist in reality. Einstein also based this on E=Mc2 which is incorrect.

5. G is the gravitational constant which is disputed, roughly calculated to be 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻² (gravity is a weak force).

6. c is the speed of light, assumed to be invariant, but is indeed variant as thousands of experiments have shown (Sagnac, Light interferometer experiments, Miller, etc).

She blinded me with maths

Within the above equation, the indexes of the tensors, the μ and the ν, assume values 0,1,2,3, representing the 4 dimensions of space time. This is the key assumption. As written previously, this assumption of 4 dimensions can only be supported by someone who is insane.

The 4th dimensional assumption, invariant light speed and the equivalency of energy and mass are the basis of EFE and all are wrong.

Within the narrative, the EFE’s within the infinite number of reference frames are ‘symmetrical tensors’ and generate 10 unique equations within the one tensor equation, which can be applied ad infinitum across infinity frames. In reality an EFE generates an infinite number of possible outcomes. This means by default that they are rubbish and of no value.

Few understand what any of the above might actually mean. It is as simple as that.

The ‘science’ and its high priests will rave that the tensor calculus from Einstotle is ‘beautiful’, ‘elegant’, ‘simple’, ‘incisive’, and ‘works in every reference frame’. This is a deception. The reference frames or ‘coordinates’ used are entirely arbitrary and made up; and deny any absolutes. The constants plugged into the equations are meaningless premised on guesswork or what is needed to generate the ‘right answer’. These tortured equations are then applied to the only ‘proofs’ for Relativity which we have discussed and rejected, namely, ‘Mercury’s orbit’ and ‘Stellar aberration’.

Einstein the chef. Cooking up the alphabet soups.

Infinity insanity

Most normal people admit that 2+3=5. This is a straightforward Euclidean-linear equation which can be supported by mechanical, physical proof. I can take 2 apples, and 3 oranges and line them and do a linear-Euclidean count to 5. Not so with the Einstotle. Within the EFE’s I could generate an infinity set of possible solutions for 2 + 3 within his spacetime curvature.

Einstein’s tortured theory uses nonlinear partial differential equations. By default, mathematically, I can produce an infinite number of solutions. This is the mathematical crux of Relativity and why it is a fraud.

• Nonlinearity: This means that the gravitational field itself contributes to the source of gravity. A tautology! What produces the field to start with and how does a field produce gravity? Never explained. Einstein’s theory of gravity cannot explain any of the observable effects of gravity on this planet. It is useless.

• Infinite Solutions: I can now take the EFE’s and reconfigure them anyway I want because I can claim a different ‘reference frame’ within ‘spacetime’. This is called a ‘metric’ which tautologically describes the geometry of spacetime in the presence of various distributions of mass and energy. As discussed, the variables for mass and energy are based on the incorrect equation of E=Mc2 which is wrong.

• Mass and Energy: The values of mass and energy used in the EFE equations are arbitrary and obtained through interpretations of experimental data in different reference frames. They are calculated using Newton’s gravitation theory and Kepler’s third law. GTR is not used. Further, depending on the object in question, there is often no objective mass or energy ‘source’ for these constants which is verified, or the mass calculations vary. An example will be the mass of Jupiter which we will discuss in a future post and show why Relativity adds no value to assessing the Sun’s gravitational pull on Jupiter (as just one example).

• Mass and energy inputs come from assumptions made within the chosen reference frame, an example might be, the universe rotates around the merry-go-round. Imagine that I need to estimate the mass and energy involved in this reference frame, basing the calculations on the law of inertial mass. Now I shift the reference frame to the universe moving around an unproven ‘blackhole’ and now need to invoke the ‘Schwarzschild solution’ which tries to describe the unproven, assumed spacetime around a non-rotating, spherically symmetric mass. Simply put the inputs and constants are very inexact and are estimations. More on this in future posts.

Making it up

Measurements to estimate mass and energy within the circular-logic EFE’s include:

1. Gravitational Effects: The mass of celestial bodies can be deduced based on astronomical guesswork. However, as expected, it is again circular logic. We can look at the Moon for example and calculate the orb’s mass using Newton’s equations for gravity; however, ‘The Science’ will employ the equations of General Relativity with all of their absurd assumptions! So I used GTR to confirm GTR!

2. Gravitational Lensing: Which does not exist. GL is used as a ‘proof’ of GTR but it is no proof whatsoever. GL proposes that light refraction due to the plasma, aether and gravity is somehow proof of GTR! So again I use GTR to prove GTR! ‘Dark Matter’ is now used within GL dogma to explain the slight refraction of starlight around our Sun for example, as viewed from this planet. Anything but admit to an aether.

3. Radial Velocity: Planet’s wobble in their orbits, a fact known to the ancients and catalogued by Ptolemy. Gravitational attraction of large planets on smaller orbs account for this and is explained by Newtonian physics.

Tautologically the Einstein cult will declare that the ‘Doppler shift’, or the apparent change in a wave's frequency (or wavelength) which can be observed when the source of the wave and the observer are moving towards or away from each other, confirms GTR! The Doppler shift has little to do with ‘Relativity’. Note that GTR does not allow for the motion of the observer within its calculus.

As many posts on here have outlined, none of the very few purported ‘proofs’ for Relativty, are valid.

Bottom Line

The edifice of Einstein’s flawed and quite fraudulent theory is his EFE’s. They violate mathematical rules and structure. They employ constants whose values are arbitrary or unproven. They are tautological. Any equation that produces an infinity of results within the non-existent ‘local reference frame’ which ignores the absolute of space and the absolute reference frame which is our universe, is junk science.

The EFE’s assume apriori without providing any proof, that Relative motion is correct (wrong), and that space and time are merged (wrong). We know that light speed is variant and that time has nothing to do with the objective reality of space or the active, energy-material rich aether, which Einstein denied. This means that the equations at their heart are invalid.

Further, EFE’s plug in measurements for mass and energy which are inaccurate and largely chosen based on estimations warped by worldviews and expected outcomes. There is no physical confirmation of any aspect, nor any single part of the EFE’s.

The deception of Einstein’s tensor calculus and metrical distortions is hard to tolerate. The fact that for 100 years ‘The Science’ has promoted this junk science to dogmatic narrative to be slavishly followed and venerated does not paint a pretty picture of our society, or our collective intelligence.

We have left ‘following the evidence’ and now erect fantasy worlds by ‘following the tensors’, enabled by censorship, aggressive scientistic totalitarianism, and the deadly sins of money, power, awards and privilege.

All hail.

Relativity's tautological maths, and issues with Mercury's perihelion and Einstein's gravity.

¹==Note on the gymnastics associated with the tensor nonsense.

As Misner, Thorne and Wheeler, Gravitation, pp. 409-410 put it: “The only conceivable modification that does not alter vastly the structure of the theory is to change the lefthand side of the geometrodynamic law G = 8πT. Recall that the lefthand side is forced to be the Einstein tensor, G_αβ = R_αβ ‒ ½R_αβ, by three assumptions: (1) G vanishes when spacetime is flat; (2) G is constructed from the Riemann curvature tensor and the metric and nothing else; (3) G is distinguished from other tensors that can be built from Riemann and g by the demands (1) that it be linear in Riemann, as befits any natural measure of curvature; (2) that, like T, it be symmetric and of second rank; and (3) that it have an automatically vanishing divergence, V ∙ G ≡ 0. Denote a new, modified lefthand side by “G,” with quotation marks to avoid confusion with the standard Einstein tensor.

To abandon V ∙ G ≡ 0 is impossible on dynamic grounds (see §17.2). To change the symmetry or rank of “G” is impossible on mathematical grounds, since “G” must be equated to T. To let “G” be nonlinear in Riemann would vastly complicate the theory. To construct “G” from anything except Riemann and g would make “G” no longer a measure of spacetime geometry and would thus violate the spirit of the theory.

After much anguish, one concludes that the assumption which one might drop with least damage to the beauty and spirit of the theory is assumption (1), that “G” vanish when spacetime is flat. But even dropping this assumption is painful: (1) although “G” might still be in some sense a measure of geometry, it can no longer be a measure of curvature; and (2) flat, empty spacetime will no longer be compatible with the geometrodynamic law (G ≠ 0 in flat, empty space, where T = 0). Nevertheless, these consequences were less painful to Einstein than a dynamic universe. The only tensor that satisfies conditions (2) and (3) [with (1) abandoned] is the Einstein tensor plus a multiple of the metric “G_αβ” = R_αβ - ½g_αβ + Λg_αβ= G_αβ + Λg_αβ….Thus was Einstein (1917) led to his modified field equation G + Λg = 8πT.” (Gravitation, p. 410).”

—>As stated above, it is all contrived maths and geometric arcana. Einstein wanted a ‘relativistic aether’ devoid of material and energy. A static universe, and a universe with no centre, completely decentralised, obeying in perpetuity the ‘laws’ of his maths. None of it is real.