_{1}

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In the last decade, the need to arrive at a
Grand Unification Theory (GUT) has become more and more pressing, being able to open a new matter and universe knowledge. However, the difficulty arises from the fact that new particle discovery shall not resolve the conflict between the various main forces; that is the gravitation and quantum-relativistic theories. It is evident that new players must enter the scene together with extraordinary innovations from a conceptual point of view as they had already been shown in history when the revolutionary Newton and Einstein theories came into the scene. The study presents an attempt to make a connection between quantum
^{1} [1] physics and relativistic theories
^{2} [2] through the introduction of a new item from the peculiar concept of “precursive time”. The analysis was carried out starting from the plausible hypothesis that the time component is the subject of “curvature” as a result of the

In the theory of General Relativity^{3} [^{4} [

In the past century, there has been an exemplary computing progression to complement theory, confirming the validity and opening up the door to new horizons of science and new scientific awareness: relativistic space-time correlations and the physics of space-time-matter interactions^{5} [

Our analysis starts from this particular correlation to probe some elements that are being studied in recent years by many scientists and researchers related to difficulties in the interpretation of the phenomena involving matter and space-time interaction. Relativity conceptually described these phenomena perfect in a manner but poses some concerns on theory physical dynamics.

The study performed attempts a survey through the Einstein’s relativistic correlation theory, which can describe how matter curves space-time, but do not solve the physical dynamics of how space-time interacts with matter.

General Relativity (GR) has proved an extraordinary model able to describe and predict the S/t transformations, which generates a body immersed in space. However, the field equation behind this concept and the mathematical solution of the stress-energy tensor do not introduce specific elements about the actual points or places of infringement acting on space-time and which are at the origin of the S/t “curvature”.

In the GR theory, the calculation of gravitational forces and geodesic lines is expressed by the field equation (EFE, Einstein Field Equation):

It can be pointed out that the tensorial summation in the equality determines space-time curvature geometry, and the energy-momentum tensor assigns space-time vector flow M4.

The solution provides us with a geometric representation of space-time bound to matter where it is staying. The equation, therefore, describes how a body having a certain mass can “curve” space-time defining its geometry, but avoids describing how this interaction occurs physically.

The notion of curved space-time although understandable under a theory context, essentially expresses its physical synthesis related to mass density, where curvature tensors and vector/inherent to motion (Einstein tensor) introduce, however, a different correlation between space-time and matter.

Geodetic^{6} [

The phenomenon of gravitation and complimentarily of geodetics is assumed to be more physical than the relativistic geometric representation, intended as an “abstract curved space-time of arbitrary size, would state. The search for a particle of mediation^{7} [^{8} [

In our specific study, we examine the three primary players: matter-mass; spacetime; time.

There is intended as an element capable of generating a space-time “curvature ^{9}” [

In this first phase of development we put into the postulate the critical condition dictated by the GR theory^{10} [

Post. #1 Spacetime “curves” only in the presence of matter-mass.

It is essential to point out that the variation in space-time is determined only in the presence of a mass-matter, since, unlike space-time, it remains as is in an apparently flat or inertial condition.

Spacetime curvature in its geometric value is dictated by relativistic theory but in the physics of the phenomenon, the feedback is quite real, trajectories of asteroids or planets are true changes in a uniform or accelerated motion, not only fictitious observation points. The issue of “physical interaction between space-time and matter” comes back and affects the entire paradigm of the standard model: from wave-particle duality of Heisenberg’s indeterminacy principle, passing by direct entanglement interactions up to “dark matter” and “dark energy”. Theories and phenomena that detect a specific interaction established by matter with an imponderable entity that we can indicate now as space-time or simply as vacuum or the GR space-time conjugate.

Compared to the physical analysis of our problem, “curved” space-time involves a distortion of both space- time, which is evident through the description of the gravitational field, as well as conjugated time component.

In the GR statement about space-time curvature, it is agreed that time component undergoes a “curvature” although hardly conceivable and representable. In Minkowski^{11} [^{12} [

The need to use a theoretical-mathematical model, able to correlate spatial coordinates and time components of the chronotope, is the first point of our analysis.

From postulate #1, we can be inferred that:

Post. #2: Spacetime curvature is a property of matter mass as an “entity itself”.

Consistently with GR enunciation we define that:

Post. #3: The “curvature” is an alteration of the symmetry inertia state in which space-time exists in its rest state when a matter-mass is not present.

The study model raises the hypothesis that “space-time curvature” is determined primarily by a shift of time component, setting time as variable and space as a dependent function.

In

We describe the event “P” in (x_{0}, y_{0}, z_{0}, t_{0}).

We extend the representation of point “P” to an imaginary correlated time layer, which we call Krl (Krono Layer).

To represent the coordinates system of time layer, we use the “hypersphere^{13}” [

Then, we proceed as follows:

We broaden the projection of Minkowski plane time component (t_{0}) to hypersphere and call (e_{0}) as time correlated with point P.

We consider tangent points (tj, tj_{n}) as hypersphere “T”, and we put (e_{0}) as the center point of hypersphere.

We describe the projection of imaginary time correlated point “P” in:

where (e^{+}) and (e^{−}) specify the correlated components for time layer, respectively delayed and in advance, next to the neighborhood of event P (e_{0}).

We can characterize the point “P” as chronotope (P_{k}) of the plane M4, in function of the correlated projection of time layer Krl.

We describe the correlation according to Hurwitz^{14} [

In summary, we generated two time coordinates (t_{0}), (e_{0}) at two different layers: (t_{0}) indicates time component of chronotope (P_{k}), and (e_{0}) marks the imaginary correlated time component of the imaginary hyperplane (Krl). this allows us to operate on two correlated layers: M4 e Krl. Time component (t_{0}) is conjugated to the imaginary time component. (e^{−}, e_{0}, e^{+}).

The method used enables us to postulate time curvature correlations.

Under a model representation perspective, the curvature of time hyperplane is understandably representable at a hypersphere shift compared to space-time plane. The trend is comparable to a “torsion” effect, where space-time is curved following the dragging action of the imaginary time layer. In this first phase of demonstration, this hypothesis produces no change neither on field equation geometry nor on gravitational geodesics calculation, but poses a hypothesis only in correlation to an imaginary plane.

We can express graphically space-time representation that curves around itself like a phenomenon resulting from the twist of the imaginary time component, as shown in

This figure shows the aberration that is determined as a result of Krono layer curvature between the points [t_{0}, e_{0}] and the resulting deviation of → (t_{0} ≠ e_{0}) correlation.

Following hypersphere shift, chronotope P_{k} (t_{0}) shall correlate to a new imaginary time layer of reference:

In _{0}) correlated to the point (t_{0}) of chronotope “P_{k}” shifts of a certain quantity (Δt_{0}) → e_{01}.

Consequently, we shall determine the new interrelated components of imaginary time layer:

Chronotope “P_{κ}” with time component (t_{0}), establishes a new correlation compared to the Krono layer; (e_{01}) becomes the new point of hypersphere center.

In summary, we have:

・ The reference point (t_{0}) of chronotope time component expressed by plane M4 is correlated and in phase with its imaginary time component (e_{0}) when in a flat space-time condition.

・ Otherwise, in the presence of a space-time curvature, that is coming from a shift of the imagery correlated time layer, the point (t_{0}) loses its timing (t_{0} ® e_{0}) and generates a resulting correlation with the next imaginary time point (t_{0} ® e_{01}) which becomes the center of hypersphere and a new timing point.

Conceptually, the hypotheses of a time layer curvature introduce a correlation between real-time component (t_{0}) expressed by the Minkowski plane and a hyperplane in time domain graphically represented by hypersphere geometry having (e^{+}, e_{0}, e^{−}), coordinates as a component, that is (e^{+}) as delay component; (e_{0}) as in phase coordinate and (e^{−}) as in advance component, respectively. The method allows us to “curve” space-time operating in time domain, which has no spatial-vector coordinate but only imaginary scalar components. The components (e^{+}, e_{0}, e^{−}) indicate the “twistingmoment” of “mass” effect, acting on the GR space-time curvature.

Time curvature is conceivable and similar to an elastic twist able to produce an aberration in the classical relativistic space-time, where, however, in our case, time “curves” around itself assigning to space a hyperplane on which unfold.

It is important to point out that:

This correlation is understood as an interpretive hypothesis and indicates a non-connective conjugation between two different entities: Space Î Time.

In the summary of this section, we assume (

We set the above through a “timespace quadrant” representation (

(_{01}”.

(_{t}) depends on the “twistingmoment” exercised by mass-matter.

In this meaning, we can formulate spacetime curvature as a function of the imaginary time component:

The point (

In the hypothesis here described, time hyperplane twist is assumed as a postulate. However, “curvature”, as shown by Minkowski and extended to GR, introduces an inclusively bonded close correlation between the two parameters, and this consistently implies that also time variable should undergo a resulting derived curvature. The notion of space-time that “incurves” around itself is not only a representation model of a proven geometry but shows the exceptional event of an entity that loses its status isotropy.

However, despite the innovative concept of―no invariance―of reference planes, time variable still repeats itself in the classic scalar reference on the becoming event abscissa.

Our hypothesis insinuates a new idea of the concept of “time” that integrates the so far acquired notion: the concept of time as a mediator entity of space-time changes.

From the step (1) of this exposure we remarked that: space-time “curves” around itself only in matter-mass presence; this triggers an insurmountable, not only ontological but above all physical conflict, as a matter entity cannot interact with a “non-material” entity if not mediated by a complex variable.

Time curvature introduces in space-time description three complex coordinates (e^{+}, e_{0}, e^{−}), able to correlate time component M4 of chronotope to time hyperplane illustrated by hypersphere. With such complex coordinates, you can generalize a space-time curvature as illustrated by “time-space quadrant”.

In particular, the (Dq_{t}) gap determines a lag time between (t_{k} Ü t_{0}), this is due to the twist effect, for which the curvature defined by the point (s_{i}) shall trace point progress of the imaginary space, such that:

Consequently, it establishes a “precursive” correlation between:

^{15} [

We update the quadrant of the latest correlations:

In the description of time hyperplane torsion, we showed that this hypothesis generates an imaginary space in which time component is shifted compared to time component of chronotope of a certain quantity depending on the specific mass-matter density.

The lag time between _{i}” as precursive than plane M4.

The “space-time” curvature model allows us to build a hyperplane, able to describe and calculate the theoretical curves as a function of the changes generated by mass-matter:

The mass-matter ratio and the (Δq_{τ}) are a function as follows:

Inertial mass (

From a conceptual point of view, the principle of precursive space is deduced from the intuitable conformation of a folded and contracted space that reduces chronotope extension compared to reference space.

The contraction effect is the result of space formatting resulting by time curvature.

It is clear that physically a “space” cannot be contracted as also cannot be curved for intuitable reasons that have been exposed, however, following the study assumption, the geometry of space (s_{j}) is drawn from time coordinates (t). Therefore, space becomes a projection of physically quantifiable precursive time points

Space points that draw the imaginary layer curvature are a projection function according to precursive time quantities.

The model dynamics proposes the twist action exerted by mass-matter on space as an origin of the combined effect:

> space contraction º lower space Þ lower travelling time.

The equation means that to a lesser travelling time corresponds a mass-interaction between matter and space with lower times on plane M4 (

The interaction between space and “mass-matter” becomes, therefore, a precursive interaction.

Compared to physical analysis, time curvature is the difference that is established between chronotope time (real time) and hyperplane time, in this order the variables are characterized in:

time Þ time discrepancy

space Þ precursive space

energy Þ

We carry out a zoom on the quadrant TS:

The correlation between time matrix (t_{n}_{n}) and the projection of respective points (s_{m}_{n}) show how the progression of time variables

We can enunciate that:

Space becomes a theoretical entity formatted by time curvature under a mass-matter action.

It follows that space-time curvature condition is properly originated by the presence of an existing mass-matter as a logical consequence of the particular event.

Space intended as a physical body is isotropic and continuous:

This hypothesis is the only theoretical condition in which it may exist.

“Time-space” theory has as its fundamental principle of precursive space-time concept.

The plausibility of the model is supported by the theoretical hypothesis assuming that time component may vary as a result of the typical “space-time” curvature in the presence of mass-matter.

Under a physical analysis, time curvature provides a reading key of space-time according to a discretionary logic, that is in discrete and deferred, as well as divided quantities about complex time coordinates. This possibility allows us to operate in an analytical framework regardless of Lorentz transforms.

The model can be described operating on quadrant TS.

The quadrant TS extends the representation of “reference plan (x, y, z) ruled by a Cartesian logics” to complex time coordinates (ψ, τ, σ) and an imaginary space curvature (x_{h}, y_{h}, z_{h}), and puts chronotope time point (P_{k}) on the straight line (e^{+}, e_{0}, e^{−}) corresponding to the hypersphere circumference passing through the projection center. However, the complexity of correlations is simplified by the representation in quadrant TS as described above.

However, the understanding of a new interpretive representation of space, time and matter poses some hardships particularly to understand and imagine hyperplanes in complex time domains. We can subsume nevertheless that even for the Relativity theories, a large dispute survives over the complex logics of interpretation, which has introduced in the phenomenological reality.

The theory we are hereby exposing is in the making for over twenty years. A time which has begun to show more clearly elements of ideological conflicts related to quantum dynamics, as well as to “entanglement” correlations, alleged mediator particle of gravitational forces, and, even more, striking but troubling unaccountability of matter and dark energy.

It is evident that in this context, as scientists we must assume that a particular page is missing in our knowledge that should fill those conflict and re-establish a coherence with the new evidence.

We have always wondered in recent decades of theoretical labor, what could be the physical elements necessary to detect a possible hypothesis of new dimensional planes inevitably imponderable to any direct observation. An extra dimension is, in fact, a base having a different time layer from the reference one, that is, on a different time scale. Time component we typically refer to is still a scalar parameter, generally described as the event horizon in the classic sequence: past > present > future. It is usually depicted on an x-axis on which we noted new conventional reference values. Therefore, it would not have characteristics able to aspire a dimensional plans origination having complex coordinates.

Assuming TS introduces a new concept of time on a complex base and in function of a mass-matter precisely defined in relation to peculiarity: “precursive time” (y).

The “mass-matter” term is raised with greater distinction than the classic term of “mass”, since, as explained, the torsion phenomenon that gives rise to the curvature _{τ}).

The physical concept of mass, expressed by the theory introduces a notion of “mass^{16}” limited only by a multiplicative factor of the phenomenon while transfers to “matter” the action of the main cause of space-time curvature dynamics.

Therefore, to operate with an equation introducing the necessary variables, we have to convert the mass size/weight in mass-matter.

The quadrant TS lies on the straight line corresponding to the hyperplane time points _{p}”, that is Planck time, by:

Typically, Planck time is intended as a theoretical submultiple quantity of time scale; that is, 1 T_{p} = (_{}

In particular, in the TS model, Planck time indicates the quantity of scaling time precursive on the reference plane.

Our study hypothesis is based on the correlation between space-time quantization and time discrepancy arising from mass-matter.

We can apply quantization to time curvature in:

M (P_{k}) “chronotope mass (P_{k}) in value mass Planck”

The “

The

Time discrepancy that is generated is directly proportional to inertial mass:

It is interesting to observe that the equation when applied to mass of the Earth ≈ (

The value indicates the time curvature originated from the planet Earth^{17}.

The ^{18}:

The term defined by the Greek letter “Ψ” conceptually expresses the linear relationship that is established between the chronotope intended as mass-matter and the correlated time hyperplane.

For the calculation of (Ψ), we shall use the following equation:

Below we calculate the

Compared with the Earth example, the value:

The term “Ψ” extends the calculation of mass (kg) to a mass-matter value as a function of variables that allow to typify space-time curvature and provide the energy quantity value correlated to chronotope.

We can summarize by stating that:

In a certain meaning, we apply a transformation of a quantitative scalar parameter in a composite qualitative complex.

Finally, we can define the energy equation.

Whereas:

it follows that:

The Equation (3) seems to show that mass-matter energy is generated by a time discrepancy.

In this first phase of the model exposure, we think to concentrate the focus on the conceptual appearance, which even in its simple description covers the physical world reality to a higher complexity than the standard model vision.

Time difference which arises between the matter intended as chronotope and the next space around [

The energy equation seems to detect precisely this elastic tension which is determined in function of matter density that resides there. The calculation is also applicable to atomic elements.

The model fully expresses the direct correlation present between the inertial and gravitational mass.

It is evident that the matter is simultaneously cause and phenomenon of the same dynamic. To this effect, a direct correlation exists between inertial and gravitational mass, so the gravitational mass value acquires an objective value defined as a 0)>.

Depending on the model, we can calculate the gravitational acceleration by placing the value of mass-matter [Ψ] as numerator and the denominator value (lagtime) in seconds:

g: gravity

r: radius

G: gravitational constant

In the example of calculation applied to the Earth, we shall have a value of:

Time curvature defines the value of the specific attraction capacity of a body (A_{0}):

The expression of equivalent^{19} coincident terms establishes the precise physical correlation.

With this correlation, we conclude the first stage of the “Vacuum-matter interaction through hyper-dimensional time-space shifting” model.

We analyzed the correlation existing between on the assumption that the interaction is determined by physical, and not necessarily relativistic, quantities.

The mathematical correlations were analysed by using the algebra of quaternions, taking the centre of the hypersphere as a real component. The diagram is placed on a hyperplane described as the “Timespace quadrant” which allows you to overlay the various components, and real and imaginary coordinates.

The TS quadrant shows a photogram of the dynamics of time-curvature as a function of the mass, the complex variables of precursive time were analysed in a stationary context without introducing the dynamics of motion and movement.

You should be aware that:

1) In motion dynamics, a body becomes equal to a hypersphere in movement on timelines, as evidenced by the quadrant TS.

2) The interaction between bodies or particles to be analyzed under interaction logics between hypersphere of their respective masses, as in the case of the gravitational force intended as a mutual attraction force.

3) Finally, we consider that the hypersphere is a precursive space-time area. Therefore, the interactions between bodies are precursive (assets) when in a propagative shape than the particle motion.

The assumptions of the “h-d-t-s-s” model suggest a method for combining relativistic theories and quantum discontinuities, giving coordinate time on a different dimensional plane, and conferring on it the role of mediator between matter and space.

The model that is proposed is an extension of the standard model, introducing a few new variables and correlations regarding the causal dynamics of the phenomena, opening a search path towards unification of the hitherto highlighted ideas.

René Burri, (2016) Vacuum-Matter Interaction through Hyper-Dimensional Time-Space Shifting. Journal of High Energy Physics, Gravitation and Cosmology,02,432-446. doi: 10.4236/jhepgc.2016.23037

With reference to what has been discussed, the “precursive time” is auto defined as a complex variable of time, this allows the determination of space-time via quantum correlations.

From Equations (1)-(4) it is in fact possible to calculate the mass of a body, the force of gravitational attraction and the total energy, operating with quantum variables.

The paper is intentionally “dry” as it has no practical or application connotations since the study is still in progress, in this first publication step is described a theoretical hypothesis of interpretation which places at the root of the problem the space-matter interaction, a question that reflects on some significant conflicts in modern Physics, with that I am referring to entanglement, wave-particle duality, gravitation, etc.

The “hdtss” hypothesis introduces some variables that until now have not been considered for the calculation of mass, like: temperature, the coefficient of quantum compensation spacetime, or the Boltzmann constant; moreover, it states that matter’s energy is “contained” within the temporal variation that generates (Dq_{t}).

The demonstration of this thesis is described by the correlations (1)-(4).

The equations are applicable either to large masses or to individual protons (!).

The precursive time (Ψ) introduces a theoretical hypothesis which allows us to operate an inversion of perspective in the dynamics of interaction between matter and space in a transformation that transfers the origin of the space time curvature to the complex time variable.

In the hypothesis used in the study regarding QCD particles, if we apply the correlation (Ψ) it leads us to the conclusion that some sub-particles may be generated only at the very moment of the collision of the respective temporal discrepancies

As evidence for this, we can only produce some calculations and verify that the unity of total mass, eV and Ψ are consistent with the hypothesis.

As far as gravitational waves are concerned, a new chapter shall be written with reference to the interactions between bodies and the concept of propagation according to the logic of the “TS” quadrants.

In this first work I have decided to limit the conclusions to the gravitational mass because, for the motion dynamics, the theory describes a moving body which can be compared to or represented by a hypersphere that moves in space.

The study of this behaviour leads to the generation of a wave dynamics of gravitational propagation (see hyper- sphere geometry) while the “propagation” effect can be generalized via a matrix of temporal precursive areas, expressed as Hopf vibrations from

(The first contains the last, because the last is more precursive with respect to the first, that is to say it is anticipated).

This description of motion dynamics can explain many phenomenologies, like propagation energy, entanglement and unexplained theories like the “Pilot wave theory of Bohm ? De Broglie”.

A last consideration with regard to the general characteristic: the “hdtss” model is based on the complex interaction typical of networks or neuronal structures.

The single event cannot be analyzed according to an adiabatic concept, but has to be put in the context of a global system, this because precursive spaces interact in advance with respect to particle motions (Ref. “b” p. 19).

The study that has been carried out is proposed as a hypothesis for a theoretical investigation in order to evaluate new concepts that could explain the conflicts apparent in the present physical reality.

Hydrogen atomic mass = 1.00794 u = 7.69 ´ 10^{−20} “Planck Mass”

Equation

The equation has been developed starting from the Rydberg constant, and it is being studied at the moment.

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