Relativity Model Synopsis

 

Relativity Model Postulates

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1. A physical dimension is intrinsically spatial.

 

2. As a curved geometry is required by the radial length contraction of angular momentum, a curved geometry is a geometry involving a globally experienced dimension in contrast to the singular dimensions of linear geometry. Radial length contraction reveals a global spatial dimension perpendicular to circumference while the other spatial dimensions, in expressing a cubical symmetry of right angles, are tangent to circumference. Consequentially, fourth-dimensional length contraction is perpendicular to three-dimensional circumference and is therefore identical to gravitation. As mass is localized energy, a system of angular momentum is an area of mass. The greater the velocity of angular momentum, the greater the mass of the system and therefore the greater the radial length contraction that is equivalent to gravitation.

 

3. The fourth dimension is a spatial dimension, the oscillation of which is time (the direction of which is entropy), and the inertia to which is gravitation. 

 

4. N-dimensional global coordinates correspond to n-dimensional manifolds.

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5. The Schwarzschild radius is the four-dimensional global coordinate of the four-dimensional manifold and is the radius of mass for which there is zero space between particles.

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6. The combination of two or more equal rank-2 tensors is a rank-3 tensor. 

Whereas Gμν = κTμν, Gμν + Λgμν = κTμνξ, a (4 x 4 x 2) rank-3 tensor (showing a fourth-dimension perpendicular to three dimensions).

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7. A Lorentz invariant, four-boson, fundamental interaction, is a U(2) interaction.

 

​8. As opposite and mutually exclusive states cannot simultaneously exist for a given subject, bipolar quantum states exist in a state of quantum oscillation, not in a state of quantum superposition.

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9. As a subject cannot be derived from the absence of what constitutes it, something must always exist for anything to exist.

Energy is neither created nor destroyed but is either transferred or transformed.

As energy is neither created nor destroyed, energy always is and is always either transferring or transforming.

Energy that is always either transferring or transforming is a global (i.e. c²) activity taking place over an unbounded period of time.

Energy transference taking place over an unbounded period of time requires globally symmetric, counter-directional, adjacent spaces of oscillation.

As the edge of a bounded oscillating space cannot be globally symmetric, an unbounded space is required for globally symmetric energy transference (i.e. every oscillating space must be globally surrounded by equally oscillating spaces that facilitate the energy transference to the space [via a π₄(S³) symmetry]: c² → 1/c² ← c²).

The activity of unbounded time requires unbounded space.

The perpetual oscillation of a globally symmetric unbounded space is an unbounded spacetime.

Spacetime is necessarily infinite.

 

Singularity

 

Singularity (1/c) is the condition of spacetime reduced to zero with mass/energy inversely increased to infinity.

Singularity is the physically unobtainable consequence of the Lorentz factor to result from mass obtaining causal velocity.

Singularity must occur with causal velocity mass (mc = 1/c).

Causal velocity mass must occur with the Schwarzschild radius (2m = mc).

Singularity that must occur with causal velocity mass must occur with the Schwarzschild radius (2m = 1/c).

The physically unobtainable consequence of singularity makes the Schwarzschild radius a physically unobtainable mass

(mass compressed to its Schwarzschild radius, requiring zero space/motion between its particles, is prohibited by zero-point energy).

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""Schwarzschild singularities" do not exist in physical reality...for the reason that matter cannot be concentrated arbitrarily...due to the fact that...the constituting particles would reach the velocity of light."

-Albert Einstein​

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Relativity

 

Relativity (p/r) [or t/d, the inverse of speed (d/t)] is the contraction of spacetime experiencing momentum as measured against the velocity of causality, the contraction being the curvature of three-dimensional space into the contracting fourth dimension. THE VELOCITY OF MASS IS INTRINSIC TO RELATIVITY. In short, relativity is the phenomenon of mass density (i.e. inertia) increasing with velocity due to the decreasing size and quantum activity of the mass [whereas p = mv, t = m → v (i.e. E = M → c²) or 1/mv, thus v increases for p as v decreases for t]. As classical motion increases, quantum motion decreases and vice versa. Relativity is ultimately just the temporal conservation of momentum. 

 

mv ∝ 1/mv

mv/c = γ∆t/γ∆x

mv/c² = γ∆t/γ∆x, γ∆y, γ∆z

 

Relativistic equations to determine the measure of spacetime contraction for a given mass naturally involve the mv (or v/c) factor.

Equations such as P = K₂ρ^4/3 and M = 1/m² that do not measure the velocity of mass do not provide relativistic outcomes.[1]

Actual relativistic equations such as γ = mv/c² and γ = mv²/2 (as well as h/mv) show a condition of zero volume mass (m/c) to be unobtainable. 

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The Schwarzschild solution shows spacetime contraction to be symmetric for all dimensions (i.e. spatially 4, not spatially 3 + 1 non-spatial).

There is neither observation nor sufficient reason for why spacetime contraction should be asymmetric for the fourth dimension.

The three-dimensional global coordinate of the Schwarzschild solution is purely geometric and is in no way shown to be physical.

Nothing claimed to be within a Schwarzschild radius is known to be physical as no spacetime interior can exist for a Schwarzschild radius.

As mc is the physical consequence of 2m, any coordinate manipulation for claiming r = 2m as being a coordinate singularity is inherently invalid.[2]

The approach to causal velocity and the approach to the Schwarzschild radius are necessarily the same physical event.[3]

As spacetime does not curve itself, the gravitation of a mass can never increase the density of that mass.

Spacetime curvature prohibitive of causal escape velocity is curvature prohibitive of gravitational waves, relativistic jets, and angular momentum.

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Due to a constant temporal moving frame, mass can only exist as a variable radius around the Schwarzschild origin point, never at that point.

The four-dimensional symmetry of spacetime contraction requires the Schwarzschild radius as the four-dimensional global coordinate.

Four-dimensional moving mass can never exist at a three-dimensional global coordinate and can never completely contract to a Schwarzschild radius.

 

Unified Field Equations

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General Relativity and Quantum Mechanics are unified in the expression of temporal symmetry (i.e. the oscillation of the fourth dimension).

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General Relativity; the curvature of spacetime caused by the inertia of mass to the expansive force of fourth-dimensional oscillation.

Quantum Mechanics; the relative flatness of spacetime accompanying the motion of mass caused by fourth-dimensional oscillation.

 

Gmhc/l = 2MG/c² * h/2mc = (mv/c² * h/mv) = h/c².

 

T = (h/c² → h) = Gμν + Λgμν = κTμνξ = SU(1) x U(1) x U(2) x SU(3) or 𝔼⁰(𝔼).

 

General Relativity (Gμν / Tμν0 / mv/r / 1/c² / M/c²: mass; the trough (h/c²) of the U(1) fourth-dimensional standing wave)

Fundamental Forces (Λgμν / Tμν1 / r/mv / c² / Mc²: energy; the crest (h) of the U(1) fourth-dimensional standing wave)

 

0D = (2⁰) = 𝔼⁰ = T000, T001 = S⁰ = the SU(1) symmetry (the h/c² → h amplitude of the U(1) fourth-dimensional standing wave),[4]

1D = (2¹) = 𝔼⁰(𝔼¹) = T100, T101 = S¹ = the U(1) symmetry (the one-dimensional temporal interaction),

2D = (2²) = 𝔼⁰(𝔼²) = T200, T201, T210, T211 = S³ = the U(2) symmetry (the two-dimensional temporal interaction),[5]

3D = (2³) = 𝔼⁰(𝔼³) = T300, T301, T310, T311, T320, T321, T330, T331 = π₄(S³) = the SU(3) symmetry (the three-dimensional temporal interaction).

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True Planck Units

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Energy: h

Mass: h/c²

Space: h/c²

Time: h/c³ 

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Energy and mass (as well as the cosmological constant and gravitation) are the opposite directions (i.e. c² and 1/c²) of fourth-dimensional motion.

Together, kinetic energy (mv²/2 / r/mv / Λgμν) and density (2m/c² / mv/r / Gμν) reveal the intrinsic U(1) symmetry of the fourth dimension. As density increases (h → h/c² / mv/c² / mv/r), kinetic energy must also increase (h/c² → h / mv²/2 / r/mv) in counter to it. Indeed, at no point does density ever increase without a source of kinetic energy to increase it (h/c² → h ∝ h → h/c²) making density the fourth-dimensional interaction of kinetic energy and counter kinetic energy that can never be physically removed. Thus, r/mv (i.e. RKE) is the reaction to G which itself is the reaction to Λ. As kinetic energy is an irremovable property of the U(1) temporal symmetry, its existence does not permit an asymmetric transformation of the fourth dimension.

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Relativistic Descriptions of Ascribed Quantum Phenomena

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Quantum entanglement, or a two-particle Einstein-Rosen bridge, is the occurrence of two particles coming together and separating on the x-axis while remaining together on the t-axis where they share a common oscillating time dilation that is orthogonal and thus non-local to three-dimensional space.[6]

 

The circumambient force of the cosmological constant upon galactic angular momentum results in a condition of amplified angular momentum that is gravitational vorticity (Λ + L = Gω).

 

The universe is one of an infinite number of universes that expand as matter (c²/e) in a mass to energy conversion (2M/c² → Mc²/2) when adjacent regions of reflected CPT symmetry are undergoing compression and compress as antimatter (e/c²) in an energy to mass conversion (Mc²/2 → 2M/c²) when adjacent regions of reflected CPT symmetry are undergoing expansion thus forming an eternally oscillating multiverse (← Mc²/2 → 2M/c² ← Mc²/2 → 2M/c² ←) with every expansion initiated at a Cosmological Trough.

Rather than a chaotic quantum foam at the foundation of reality, a temporal oscillation exists from which all of the fundamental forces are generated. Rather than origination from a one-time Big Bang, the expanding universe originates from a periodic Cosmological Trough, oscillating in tandem with other oscillating universes via a π₄(S³) symmetry. From spacetime (h/c² → h → h/c²) to the cosmos (2M/c² → Mc²/2 → 2M/c²), reality is an infinite temporal wave fundamentally described by the Schwarzschild solution.

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​***

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[1] The general theory of relativity is not a theory of gas. Gas equations do not measure the relativistic density of mass. A modified ideal gas equation (P = K₂ρ^4/3) that doesn't measure the velocity of mass (mv), being called a 'relativistic' equation of state, makes such an equation pseudo-relativistic while intentionally altering the Schwarzschild solution for the sole purpose of bringing it into conformity with the result of the pseudo-relativistic equation is a pseudoscientific endeavor. In essence, the natural physics of symmetric dimensional contraction as shown by the Schwarzschild solution is consciously rejected in preference for a purely geometric and thus physically impossible result from a contrived asymmetric contraction. THE FOURTH-DIMENSIONAL SYMMETRY OF THE FOUR-DIMENSIONAL MANIFOLD IS DENIED SOLELY FOR THE PURPOSE OF JUSTIFYING A PREFERRED THREE-DIMENSIONAL ORIGIN POINT AS BEING GLOBAL. This exercise of an arbitrary preference for a three-dimensional origin point is not an exercise of science. A three-dimensional origin point is a mathematical reality, not a physical one. A three-dimensional origin point is only global for a three-dimensional manifold. IT IS GEOMETRICALLY IMPOSSIBLE FOR A THREE-DIMENSIONAL COORDINATE TO BE GLOBAL FOR A FOUR-DIMENSIONAL MANIFOLD. The global coordinate of a four-dimensional manifold naturally requires four dimensions. Whereas the Schwarzschild radius (in conformity with both the Lorentz factor and zero-point energy) is a consequence of physics, the tortoise coordinate singularity is the consequence of a geometric coordinate upon a non-physical coordinate frame. The Schwarzschild radius singularity, called 'non-physical', is symmetrically four-dimensional and is physically impossible due to mass having to obtain the physical limit of causal velocity while the tortoise coordinate singularity, called 'physical', is a three-dimensional geometric origin point upon a non-physical coordinate frame and is physically impossible due to mass having to obtain the non-physical limit of infinite velocity. As is apparent, the consequence of one physical impossibility is infinitely less aligned to the physical world than the other. The physical impossibility/violation of physics begins at the Schwarzschild radius and only increases ad infinitum towards r = 0. Claiming that mass can contract to the Schwarzschild radius is the physically impossible condition that facilitates the physical impossibility of the r = 0 singularity. A Schwarzschild radius can only be reached by ignoring the prohibitive physics of the Lorentz factor (e.g. the unbounded relativistic kinetic energy that counters contraction) and of zero-point energy (e.g. the energy of particles confined to h/2mc producing identical additional particles that counters overall contraction) which are selectively ignored in order to claim an unpreventable contraction to a three-dimensional global coordinate. In consequence, the acknowledged problem of the physical singularity to arise from the use of the tortoise coordinates only exists with the arbitrary decision to treat a geometric singularity as being physical. The problem is automatically resolved with the recognition that mass which is physically prohibited from obtaining causal velocity is automatically prohibited from obtaining infinite velocity. Causal velocity is the unobtainable limit to the velocity of mass and is only ignored due to the existence of a geometric preference for which an asymmetric contraction of the fourth dimension must be contrived despite violation of the Lorentz factor. The tortoise coordinates are used to produce a manufactured result that is then proclaimed to be the actual result of general relativity. THE TORTOISE COORDINATE SINGULARITY IS LITERALLY CHOSEN TO EXIST CONTRARY TO THE RESULT OF THE SCHWARZSCHILD SOLUTION THAT DOES NOT PERMIT ITS PHYSICAL EXISTENCE. In essence, a singularity that is naturally revealed to not physically exist is nevertheless insisted upon physically existing (via the tortoise coordinates) with the open acknowledgement that such a singularity cannot physically exist! The general theory of relativity is then blamed for the prediction of this result even though the fourth-dimensional symmetry of general relativity has to be ignored and even mathematically countered by nullifying the interior Schwarzschild solution to intentionally arrive at the impossible result. As such, a 'theory' of geometric singularity should never be confused with the general theory of relativity in which physical singularities (prohibited by the Lorentz factor/zero-point energy) are in no way a physical prediction. The relativistic equation of state (considered to be relativistic not by measuring the velocity of a mass but by merely altering the numerator in the exponent of a gas equation), in excluding the Lorentz factor, is observably not a relativistic equation as it is not an equation reflective of a four-dimensional manifold while the Lorentz factor itself (at the very foundation of relativity), in prohibiting the causal velocity of mass, clearly prohibits any mass from ever being contracted to its Schwarzschild radius. The increase of relativistic kinetic energy (γ = mv²/2) from the increase of relativistic density (γ = mv/c²) is accurately determined by calculation of the Lorentz factor not by the mere change of numerator in the exponent of a gas equation. This increase of relativistic mass/energy corresponds directly to the interior Schwarzschild solution, intrinsically linking it to the dilation of time. Thus, the claimed condition of a physical singularity only arises upon the exercised choice to ignore the physical consequence of the Lorentz factor; γ = mv²/2 ∝ mv/c², mc²/2 ∝ mc/c² = 2mG/c², γ = mv²/2 🛇 2mG/c². 

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SCHWARZSCHILD SOLUTION: Four-Dimensional Manifold - Four-Dimensional Global Coordinate - Bounded by Causal Velocity. 

TORTOISE COORDINATE SOLUTION: Four-Dimensional Manifold - Three-Dimensional Global Coordinate - Exceeds Causal Velocity. 

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Of the two solutions, one is symmetric and is bounded by physics while the other is asymmetric and violates physics.

One, bounded by the Lorentz factor, does not allow for singularities while the other, centered upon a three-dimensional global coordinate, is literally centered upon singularity. The tortoise coordinate singularity is unavoidable, not because of physics, but because of inherent choice. The singularity is inherent to the choice of choosing r = 0 as the global coordinate of a four-dimensional manifold. It has nothing to do with the natural consequences of physics (which is why the Lorentz factor must be ignored at the Schwarzschild radius in order to obtain it). The tortoise coordinates do not reveal the Schwarzschild solution to be asymmetric. The tortoise coordinates are intentionally imposed to nullify the interior Schwarzschild solution to make the four-dimensional Schwarzschild solution asymmetric thereby resulting in a three-dimensional singularity. Any solution (or coordinate transformation) intended to bypass the Schwarzschild radius automatically bypasses the physical singularity of the Lorentz factor thereby resulting in a purely geometric (i.e. non-physical) singularity. Despite the endeavor to make the Schwarzschild solution asymmetric via the tortoise coordinates, the fact of there being a Schwarzschild radius where an event horizon is claimed to exist is the fact of there being a spatial fourth-dimensional symmetry that requires the Schwarzschild radius to exist. The simple fact of the matter is that a non-spatial fourth dimension results in a physical impossibility whereas a spatial fourth dimension does not. When the fourth dimension is denied spatial recognition, inconsistencies arise. When the fourth dimension is spatially recognized, the inconsistencies are resolved. The choice of singularity necessitates fourth-dimensional asymmetry and vice versa. Without fourth-dimensional symmetry, reality must be a singularity.

 

[2] As a coordinate singularity is a coordinate discontinuity upon a non-physical coordinate frame, 2m cannot be a coordinate singularity as the coordinate designation of '2' is not discontinuous upon the coordinate frame. The only place that the coordinate frame becomes discontinuous is at the three-dimensional origin point of r = 0 where the density of m = ∞. This means that the coordinate designation of r = 0 is the literal coordinate singularity that is automatically resolved by the fourth-dimensional symmetry of the four-dimensional manifold. FOURTH-DIMENSIONAL SYMMETRY PROHIBITS r = 0 FROM EVER BEING PHYSICAL while the Lorentz factor prohibits r = 2m from ever being realized. The designation of '2m' marks a physical degree of mass at radius '2' that must have causal velocity gravitation and therefore the physical consequence of singularity to result from the causal velocity contraction of mass (i.e. 2m = mc = Gc). This is clearly not the 'illusionary' consequence of a coordinate frame and therefore cannot be a coordinate singularity. As the Schwarzschild radius is the global coordinate of the four-dimensional manifold, the Schwarzschild radius cannot be a coordinate singularity of the four-dimensional manifold, therefore the tortoise coordinates are used as an intentional manipulation to bypass the natural fourth-dimensional consequence of the Schwarzschild solution. Without the tortoise coordinate manipulation to result in the r = 0 singularity (i.e. r = ∞m), no excuse exists for the claim of a r = 2m coordinate singularity (or of the time coordinate somehow being a ‘bad choice’ of coordinates for application in a four-dimensional solution). The fact that 2m ∝ c is a condition prohibited by the fact that γ = 1/√[1 - (v/c)²]. 

As the intentional alteration of an existing coordinate to obtain a preferred geometric outcome does not make the original state of that coordinate a 'bad choice', the denial of a necessary physical consequence (along with the avoidance of actual relativistic equations that show the physical consequence) in preference for the tortoise coordinate manipulation for claiming an asymmetric contraction is sheer pseudoscience in violation of the principle of general covariance. To state that there is no singularity at the Schwarzschild radius is to state that either causal velocity mass does not result in singularity or that causal velocity mass does not occur with the Schwarzschild radius. Since an event horizon where nothing of c velocity can escape is claimed to be at the Schwarzschild radius, the occurrence of causal velocity mass cannot be denied. This means that the singularity of causal velocity mass must somehow be denied thereby making such a denial a refutation of relativity itself. What manner of physical interaction must be imagined to nullify the physical consequence of the Lorentz factor at the Schwarzschild radius? As a physical consequence is invariant to coordinate transformations, the Lorentz factor clearly requires a physical singularity at the Schwarzschild radius which no mere manipulation of coordinates can ever remove. Singularity is solely dependent upon the physical consequence of mass obtaining causal velocity, not upon the geometric manipulation of coordinates. The consequences of physics are not determined by the geometric manipulation of coordinates. It doesn't matter what type of coordinate system is used to justify a three-dimensional manifold global coordinate for a four-dimensional manifold, the global coordinate of the sphere cannot be manipulated into being the global coordinate of the hypersphere. Unless the physical consequence of the Lorentz factor is being refuted by only equating the occurrence of singularity with mass obtainment of infinite velocity, it is a physical impossibility for r = 2m to be a coordinate singularity (or 'an illusion') as an absence of singularity at the Schwarzschild radius necessitates an absence of the light barrier and therefore an absence of validity for both the Lorentz factor and zero-point energy. The concept of an event horizon (that results from the concept of a fourth-dimensional asymmetry) automatically violates the limit of causal velocity (i.e. the light barrier) and therefore the physics of relativity itself. FOURTH-DIMENSIONAL SYMMETRY IS PHYSICAL WITH A DIRECT CORRESPONDENCE TO THE LORENTZ FACTOR WHILE FOURTH-DIMENSIONAL ASYMMETRY IS A VIOLATION OF CAUSAL VELOCITY THAT IGNORES THE CONSEQUENTIAL SINGULARITY AT THE SCHWARZSCHILD RADIUS. The tortoise coordinates are used to ignore the consequence of the Lorentz factor at the Schwarzschild radius (which, due to time dilation, includes ignoring the fact that all motion must come to a halt thereby referring to it as being 'an illusion'). This is nothing less than the intentional manipulation of data to obtain a false result presented as being correct. The only reason for denying the physical necessity of a singularity at the Schwarzschild radius is the knowledge that the existence of such a singularity would automatically preempt the occurrence of a singularity at the preferred three-dimensional origin point. So long as that singularity is being claimed, the necessary physical consequence of the Lorentz factor at the Schwarzschild radius must be declared to somehow be 'an illusion' (i.e. 'an illusion' declared upon mathematically cancelling the infinite RKE/ZPE at the Schwarzschild radius with a negative infinity to result in the claim of an infinite spacetime curvature). 

​Whereas 2m = the Schwarzschild radius, mc = causal velocity mass, and 1/c = singularity, 

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2m = mc 

mc = 1/c 

2m ≠ 1/c 

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though any two of the above can be correct, one of the above must be incorrect. 

The Schwarzschild singularity is literally the physically required consequence of relativity. To say that the singularity is an illusion is to say that the light barrier is an illusion. To say that the singularity can be removed is to say that the light barrier can be removed. The physical consequence of singularity can’t be valid for a restricted special case of relativity yet invalid for relativity in general. The physical consequence of singularity from the movement of mass restricted to one dimension (i.e. mc/c or zero activity/infinite density mass) is the physical consequence of singularity from the movement of mass in all dimensions (i.e. mc/c² or zero empty space/infinite density mass). Consequentially, length contraction in special relativity is just as omni-dimensional as contraction in general relativity. Mass does not simply contract in the dimension of its velocity but contracts in all of its dimensions due to contraction in the fourth dimension. The physical consequences of causal velocity mass in either special relativity or general relativity are exactly the same as the time dilation common to both is simply fourth-dimensional length contraction (i.e. gravitation). Therefore, any coordinate system designed to ignore the physical consequence of the Lorentz factor at the Schwarzschild radius is a system of coordinates that fails to correspond to physical spacetime. Transforming a coordinate to mathematically ignore the unbounded increase of relativistic kinetic energy that accompanies causal velocity mass automatically results in the inverse condition of unbounded densityignores the necessary consequence of relativity. Either singularity is the indisputable physical consequence of causal velocity mass or the theory of relativity is invalid.

K₂ρ^4/3 ≠ mv/c².

γ = 1/√[1 - (v/c)²] ∝ mv/c². 

γ = 1/√[1 - (c/c)²] ∝ mc/c² = 2mG/c².

 

[3] As relativistic momentum corresponds to relativistic density [mv ∝ mv/c²], a mass accelerated to causal velocity is a mass contracted to the length of its Schwarzschild diameter [mc = 2m(r) = 2(r)m]. This is reflective of the fact that gravitational velocity corresponds to spacetime curvature (Gv ∝ Gμν). As velocity corresponds to degrees of spacetime curvature, the limit to fourth-dimensional symmetric contraction (i.e. the Schwarzschild radius) corresponds to the limit of velocity (as the velocity of causality and time i.e. 'ct' are necessarily linked). Without this natural limit imposed by fourth-dimensional symmetry, velocity would be unlimited. As the Lorentz factor is the consequential expression of fourth-dimensional symmetry, ignoring fourth-dimensional symmetric contraction requires ignoring the Lorentz factor and its consequential singularity. The world is observed to be a four-dimensional manifold. The fact of relativity applying to angular momentum is the fact of a fourth spatial dimension as there can’t be length without space thus radial length contraction perpendicular to three-dimensional circumference reveals a fourth spatial dimension. Apart from the radial length contraction of angular momentum, both the math (i.e. the exterior (mv/r) and interior (r/mv) Schwarzschild solutions) and physical observation (i.e. gravitation (Gμν) and the cosmological constant (Λgμν)) show there to be a spatial fourth dimension. As a three-dimensional coordinate can only be global for a three-dimensional manifold and a four-dimensional coordinate can only be global for a four-dimensional manifold, the unreasonable endeavor to make a three-dimensional coordinate global for a four-dimensional manifold can only facilitate non-physical consequences. Based upon the concept of Minkowski space, the fourth dimension has always been assumed, never demonstrated, to be non-spatial (while both gravitation and the cosmological constant have always revealed the opposite spatial directions of the fourth dimension). As the Schwarzschild solution shows spacetime to be spatially four-dimensional, the tortoise coordinates are applied to make the solution spatially three-dimensional, thereby resulting in a singularity - a physical impossibility. Thus, WITHOUT PHYSICAL CONFIRMATION OF THE FOURTH DIMENSION BEING NON-SPATIAL, NO SCIENTIFIC JUSTIFICATION EXISTS FOR THE APPLICATION OF THE TORTOISE COORDINATES. Violations of physics automatically occur when the global coordinate of a three-dimensional manifold is insisted upon being physically acknowledged in place of the Schwarzschild radius. Such a notion is observably impossible as it requires the physical impossibility of mass at the Schwarzschild radius contracting into zero empty space (via a force of infinite gravitation by which spacetime curves itself). This involves mv/r whereas mv < 2 and r > 2 is the physical condition of mass/energy in spacetime that becomes 1 (i.e. singular) at 2/2 beyond which an increasing mass (mv > 2) must impossibly exceed a decreasing space (r < 2) that can no longer physically contain it. This physical impossibility is the direct consequence of ignoring the Lorentz factor which shows in a reciprocal function that 2/2 can never be reached (as when mv approaches c, m increases towards 2 while r decreases towards 2 and KE increases towards ∞). Contracting a mass to its Schwarzschild radius requires an infinite amount of energy from a finite amount of space. A contained subject cannot match or exceed the dimensions of its containing agent and still be physically contained. Infinities arise when physical limits are ignored. As contraction requires empty space for a subject to contract into, claiming mass to be able to contract into zero empty space is equivalent to claiming to move north of the north pole. Mass cannot contract into a Schwarzschild radius as there is literally zero spacetime for the mass to contract into thereby requiring infinite energy. It is a situation of infinite energy literally appearing out of nothing while the volume of mass literally disappears into nothing as there is literally no physical place for the mass to go. This corresponds to the fact that the fourth dimension is symmetric, not asymmetric, thereby requiring ct to terminate at r = 2, not at r = 0. The three-dimensional r = 0 singularity is not the global coordinate of the four-dimensional manifold. Any physics based upon r = 0 being the global coordinate of the four-dimensional manifold is based upon a demonstrable falsehood. A THREE-DIMENSIONAL GLOBAL COORDINATE CANNOT BE PHYSICAL FOR A FOUR-DIMENSIONAL MANIFOLD. This geometric fact is the sole reason for the imposition of asymmetry upon the fourth dimension despite its physical impossibility. As asymmetry is used to bring about a result known to be physically impossible, the imposition of the asymmetry itself manifests the physical impossibility which begins at the Schwarzschild radius (i.e. m2/r2) by mathematically cancelling the ∞KE (which is zero-point energy) with a negative infinity (i.e. r* = r + 2MG ln |r/2MG – 1|). This involves the fact that every dimension is symmetric in being composed of two opposite directions (←→), therefore the tortoise coordinates are applied to the fourth dimension to separate the t-coordinate into its two opposite directions (→←) to eliminate one of those directions (← i.e. c² or the interior Schwarzschild solution) thereby leaving the asymmetry of the remaining direction (→ i.e. 1/c² or the exterior Schwarzschild solution) to automatically result in the gravitational singularity. The problem of the gravitational singularity is intentionally created by the application of the tortoise coordinates, effectively eliminating zero-point energy by transforming the Schwarzschild radius from a two-dimensional impenetrable shell where all time/motion must come to a halt into a unidirectional membrane that ignores the Lorentz factor. The Schwarzschild solution is simply altered to eliminate the consequence of the Lorentz factor at the Schwarzschild radius and suit a perspective of space that the unaltered solution and the Einstein unified field equation both show to be invalid. Rejecting the result of a standard solution but altering that solution to obtain a preferred yet untenable result (that is then blamed upon the theory from which the unaltered solution had been derived) is not a method of science. The global coordinate of a sphere cannot be the global coordinate of a hypersphere. The Schwarzschild radius singularity is the necessary consequence of the Lorentz factor, a physical consequence that no degree of coordinate manipulation can ever remove.

 

The Chandrasekhar limit, not the Schwarzschild solution, predicts a three-dimensional manifold, gravitational singularity.

The Schwarzschild solution of Einstein’s general theory of relativity predicts the physical consequence of the Lorentz factor.

The premeditated application of the tortoise coordinates mathematically cancels the physical consequence of the Lorentz factor

(thereby resulting in a non-relativistic, non-physical, geometric singularity).

 

Simply stated:

 

N-dimensional global coordinates correspond to n-dimensional manifolds.

The global coordinate of the three-dimensional manifold is not the global coordinate of the four-dimensional manifold.

As the Schwarzschild radius is the global coordinate of the four-dimensional manifold, the Schwarzschild radius cannot be a coordinate singularity of the four-dimensional manifold.

The singularity of the Schwarzschild radius is the consequence of the Lorentz factor and therefore can neither be tenably removed nor physically obtained. 

As spacetime does not curve itself and infinite spacetime curvature cannot arise from a finite curvature agency, contraction to a Schwarzschild radius is physically unobtainable as it is prohibited by the unbounded increase of relativistic kinetic energy (i.e. zero-point energy).

 

Spacetime is not an active agent of curvature and therefore does not curve itself. As such, spacetime is incapable of increasing the density of the mass that curves it. The curvature of spacetime cannot exceed the curvature of the density responsible for it. Any process to require the increased density of mass from the inactive curvature of spacetime is a process of pseudoscience. This includes the notion of there being a limit to degeneracy pressure for non-composite particles. Upon sufficient force existing to compress the quarks of a quark-gluon plasma to half their range (h/2mc), such force will be converted into the creation of additional quarks thereby increasing the volume of the mass and bringing the force of contraction to a halt. Thus, there is no physical limit to degeneracy pressure and no physical process of unlimited increasing density. When an unobserved violation of physics is unnecessarily insisted upon as being physically real, the subject is no longer one of physics but is one of magic.

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[4] h/c² → h for any given space simultaneously causes h → h/c² for the accompanying adjacent space thereby facilitating fourth-dimensional U(1) oscillation (i.e. ← h → h/c² ← h → h/c² ←) and three-dimensional motion i.e. the electromagnetic wave (as the SU(1) symmetries of G and KE form the oscillating U(1) symmetry of t directly resulting in c). For this reason, though the interior Schwarzschild solution would appear to reveal a Schwarzschild radius devoid of interior spacetime (as the interior spacetime must contract away from the three-dimensional origin point to meet the exterior contraction at the Schwarzschild radius), this is only from a three-dimensional perspective. Fourth-dimensionally, the interior and exterior Schwarzschild solutions reveal the Schwarzschild radius to be the intersection of maximal, opposite, fourth-dimensional forces (i.e. ← Mc²/2 → 2M/c² ← Mc²/2 →) between which there can be neither space nor motion. The Schwarzschild radius is simply the limit of counter cosmological constant movement (i.e. gravitation) a part of the fundamental gauge symmetries that are reflected at the cosmic scale [i.e. the cosmological constant; SU(1), motion in any non-temporal dimension; U(1), the four-dimensional space of the universe; U(2), the oscillation of the four-dimensional space of the universe with its adjacent space; SU(3)].

 

[5] It will be noticed that the Relativity Model corrects the Standard Model in that the weak interaction is observed to be of a U(2) symmetry, not a SU(2) symmetry. Unlike a SU(2) symmetry (S²) that is only representative of the three vector bosons, the U(2) symmetry is representative of the three vector bosons and the scalar Higgs boson (S² x S⁰) thereby representing all four bosons of the weak interaction (which is almost always presented with the three vector bosons displayed together with the Higgs boson separate from them as if not a part of the same fundamental interaction). The SU(2) symmetry is primarily claimed in order to fit an electroweak assumption that has never been experimentally confirmed and is even countered by Elitzur’s theorem which shows that the breaking of local gauge symmetries required for the proposed electroweak interaction [U(2)] to separate into the electromagnetic [U(1)] and weak [SU(2)] symmetries is simply not possible. This electroweak concept had originally been imagined to be a SU(2) symmetry composed of the two W bosons and the photon before being observed to be unfeasible and reconsidered to include a third weak boson without any notion of there being an additional Higgs boson. Thus, there had been an a priori commitment to realizing an electroweak symmetry regardless of actual findings. In order to claim validation for a SU(2) weak symmetry, the actual number of bosons has to be ignored to only consider the vector bosons as being symmetrically significant. This then conceptually allows for unification with the single vector boson of the U(1) symmetry to form the U(2) symmetry of the current electroweak hypothesis. Furthermore, claims of the electroweak hypothesis having been experimentally confirmed falsely refer to the experimental confirmation of the weak vector bosons as being electroweak confirmation. To this day, neither W₃ bosons nor B bosons have ever been confirmed to exist as verification of the electroweak hypothesis. As Elitzur’s theorem renders the spontaneous symmetry breaking of the electroweak symmetry to be untenable, it also renders the invoking of spontaneous symmetry breaking to be untenable for any of the grand unification theories that seek to show what the rank-3 unified field tensor of the Einstein field equations already shows. 

 

[6] As event horizons do not actually form and therefore cannot be the ends of wormholes, quantum entanglement is not the product of wormholes as currently described. The endeavor to describe quantum entanglement as wormholes is a part of the broader string theory endeavor to describe gravitation as being a quantum phenomenon. However, the entire string theory enterprise fails on two accounts to qualify as being an endeavor of scientific integrity. String theory had first emerged as an attempt to generalize the Euler beta function that had been applied to the scattering amplitude of mesons to being applied to the scattering amplitude of any number of particles. This attempted generalization had resulted in a description of gluons as being one-dimensional rotating strings between two quarks as well as in a prediction of spin-2 particles and in negative probabilities that could only be resolved with a result of negative mass and no less than 26 dimensions. As this inaccurate description of the strong interaction had been superseded by the theory of Quantum Chromodynamics, the focus of string theory had become the realization of the predicted spin-2 particle thought to be the graviton. It is at this point that string theory had been divorced from the history of scientific experimentation that had led to it and was then newly applied to a Planck scale of 10^-33 cm to become a Theory of Everything. Without a history of experimental observations and calculations to justify the notion of 10^-33 cm strings, string theory is without any scientific basis. It is the accumulated baggage of a failed hypothesis applied to an entirely different situation for which there is no scientific justification. The one-dimensional string gluons to have been concluded from the scattering of mesons provide no basis for the conclusion of non-gluonic 10^-33 cm strings that have absolutely zero experimental evidence behind them. Furthermore, as a theory of quantum gravity in pursuit of the validation of the graviton, string theory ignores the Weinburg-Witten theorem which states that “…in all theories with a Lorentz-covariant energy-momentum tensor, such as all known renormalizable quantum field theories, composite as well as elementary massless particles with j > 1 are forbidden.” As there are no natural particles above spin-1, there are no spin-2 gravitons for a quantum theory of gravity. This is otherwise evident by the fact that the fourth-dimensional vector of a graviton’s imagined gravitational force (1/c²) is orthogonal to the vector of its momentum. As momentum must be conserved, a fourth-dimensional force automatically prohibits any velocity orthogonal to it from obtaining causal velocity. A graviton would therefore be massive and incapable of directly facilitating the causal velocity effects of gravitation. As such, being fourth-dimensional, the massive graviton would have to be scalar (i.e. spin-0) in causing the curvature of spacetime and would therefore be no different than the Higgs boson. As for every vector of action there is equal opposite action, gravitation is the equal opposite action of the cosmological constant. Gravitation is simply the fourth-dimensional inertia to the cosmological constant as indicated by the Einstein Equivalence Principle and has no quantum explanation beyond the h → h/c² SU(1) activity of time. Spacetime contraction = fourth-dimensional inertia = gravitation. Gravitation is the reaction to the cosmological constant, the fourth-dimensional consequence of the third law of motion, not a quantum particle. The notion of quantum gravity has never been an idea based upon evidence. The notion of quantum gravity has always been an idea in search of evidence.