According to studies on the precursive time quantum variable, this publication presents an in-depth analysis of the chapter on the correlation between the nuclear mass and electroweak force. This research shows that there is a close correlation between the nuclear mass and the energy of the orbitals which underlies the electroweak interaction.
The concept of the precursive time has been extensively exposed in previous publications both from a theoretical mathematical and topological point of view [
Time curvature has been indicated with the Greek symbol “τν” from the etymological initials from which the term “time” originated, namely: “tém-nein” (τεμ − νειν) Greek term which means “separate” split-up. In the concept of precursive time, there is in fact the original definition of time, understood as “quantity that quantifies what is separated”. It is essential to emphasize that the precursive time is a quantum variable, it is not a new relativistic reading of time, it is not a Lorentz transformation, and it is not a Wick rotation.
Precursive time is a concrete physical quantity, never characterized, expressed in quantum parameters that mediate the interaction between matter and spacetime.
Through the concept of precursive time that originates between the event’s instantaneous time and its imaginary projection in spacetime, it was possible to establish an important correlation property < mass – spacetime > defined in the following postulate:
Each event having mass |m > 0| implies a splitting of the events timeline of a quantity (Δτν) proportional to the corresponding mass.
We shall represent this concept in the following
Explanation:
We consider an event with |m0 > 0| (inertial state) at a precise instant on the normal timeline (denoted by time’s arrow).
The event (m0) is characterized by three space coordinates referred to a precise instantaneous time:
m 0 ( t 0 ) ( x 0 , y 0 , z 0 )
The assumption states that: event (m0) implies a splitting of the timeline events by a quantity |τν| proportional to its mass (m):
τ ν ⇒ ( e o − ) ( σ ω )
Theoretically, the splitting of the events time abscissa can be described as the projection of instantaneous time in a conjugate timeline coexistent and simultaneous at the time events.
σ ω ( x i , y j , z k )
Therefore, the real space(+) time coordinates will be related to a set of topologically hyperdimensional coordinates (ref.
∀ | m > 0 | ∈ ℝ ( x 0 , y 0 , z 0 ) ( t 0 ) ⊆ ℂ ( x i , y j , z k ) ( e o − )
Summing up, each event is characterized by:
m 0 ℝ ( x 0 , y 0 , z 0 ) ( t 0 ) , ℂ ( x i , y j , z k ) ( e o − )
(e0−) precursive time: is the conjugated imaginary time, coexisting and simultaneous with instantaneous time, is quantified in Joule/Planck time units (J/tp), it also returns a relationship in negative seconds since it is precursive with respect to the real time of the event (t0 ← e0−).
It should be noted that precursive time is different from the concept of time in advance since it is placed onto imaginary timeline.
(τν) indicate the time curvature: is the “time discrepancy” (∆τν) that originates between the event’s instantaneous time át0ñ and its imaginary projection in spacetime áe0−ñ, it’s a function of and proportional to its inertial mass. (τν) is energy quantified in Joule/second units (J/s).
It is very important to always keep in mind that: time curvature is a state condition of matter, regardless of it is motion and from observer’s frame of reference.
(σω) sigma point: hyperdimensional coordinates (xi, yj, zk), this characterizes and specifies the boundary of spacetime curvature.
The temporal splitting (τν) that is determined between the two-time abscissa (real + imaginary) is function of the mass and is quantified in (Joule/sec) as “time curvature”. The splitting of time is always true whatever |m > 0|.
The equation worked out to calculate this is as follows:
τ ν = 1 h m p c 2 F (1)
( τ ν ) time curvature J/s.
( m p ) m-> Planck mass.
(h) Planck constant.
(F) Fibonacci factor 1.618.
(F) Fibonacci factor: describes with accuracy the time curvature; it was obtained by spacetime torsion-contraction computer processing, drawing a centripetal cycloid “from the future towards the time event” with a Fibonacci progression ( t 0 ← e o − ).
The goal is to test the plausibility of the theory as applied to nuclear masses.
Let apply the time curvature equation to the standard nucleus’ mass
“The atomic radius is usually understood as the distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius”.
In this research, the atomic radius is a measure obtained from the space-time curvature specifically from the time curvature (τν) equation.
The equation calculates the extent of curvature up to up to the boundary of the domain space of the specific atom.
Therefore, we define this extent of atomic spacetime curvature as atomic radius curvature.
From the (τν) equation we find the following values (
m p → τ υ → t p → e 0 − → σ ω
The value obtained (25.31434 pm), partially differ from the Covalent radii in pm from analysis of the Cambridge Structural Database; however, it is surprising to find that the values obtained are significantly consistent.
The atomic radius curvature ⇔ nuclear mass correlation is true for all elements of the table.
As an example (
The diagram of
If the thesis is correct, it is possible to assume that:
The atomic radius curvature originated by the spacetime time-curvature generated by the mass of the nucleus understood as: < the distance between the nucleus and the domain boundary of the specific atom > is the phenomenon that determines the atomic radius.
| nucleus mass (u.) | Planck masses (mp) | τν time curvature (J/s) | e0− boundary time frame reference (tp) | σω boundary curvature (m) |
|---|---|---|---|---|
| 1.008 | 7.691 × 10−20 mp | 5.2244804 × 1015 | 2.8166000 × 10−28 | 2.5314338 × 10−11 |
(τν: time curvature); (e0−: precursive time, boundary’ time position); (σω: space time curvature boundary == atomic radius curvature (meters)).
| elements | H (1) | Li (3) | Na (11) | K (19) | Rb (37) | Cs (55) | Fr (87) |
|---|---|---|---|---|---|---|---|
| nuclear mass | 1.0079400E+00 | 6.9400000E+00 | 2.2989769E+01 | 3.9098300E+01 | 8.5467800E+01 | 1.3290545E+02 | 2.2300000E+02 |
| τν (J/s) | 5.2244804E+15 | 1.3709225E+16 | 2.4951389E+16 | 3.2539177E+16 | 4.8110186E+16 | 5.9992770E+16 | 7.7701981E+16 |
| atomic radius curvature | 25.314 | 66.427 | 120.901 | 157.669 | 233.110 | 290.693 | 376.498 |
| Covalent radius | 25.00 | 128.00 | 166.00 | 200.00 | 201.00 | 245.00 | 260.00 |
| Atomic radius CSD | 25.00 | 145.00 | 180.00 | 220.00 | 235.00 | 260.00 | - |
In quantum mechanics an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom.
In this research the “atomic orbital position” does not mean the electron location but the distance between its energy orbital level and the nucleus.
The energy orbital level (sn) is the sphere orbital plane in which the total energy of the electrons referred to the energy levels of the periodic table of elements is stored (electron shell 1 ¸ 7), each energy orbital level is isotropic with respect to position in the spacetime (t−n' Sn). (
( s n ) = t − n ( x n i , y n j , z n k )
The discrepancy time that arises between (t0 ⇒ t−n) is an energy
∇ τ ν = ( t 0 − t − n ) J / s (2)
The radius curvature and the mass of the nucleus are proportionally related; it then follows that the energy τν originate by the time curvature is the energy of the system (
The commutative energy diagram: {nucleus mass -> spacetime curv. -> energy} (
complex configuration in which nucleus and orbitals levels constitute a single energy entity:
τ υ → t p → ( e 0 − ↔ σ ω ) = GeV / s
It follows that the overall energy orbital levels are a function of the time curvature induced by the nuclear mass:
e = m c 2 = m p c ϖ = 1.503451 × 10 − 10 J ⋅ s = 0.9383 GeV / s (3)
(v) is a coefficient named “Quantum Compensation Spacetime” was developed by space-time torsion-contraction computer processing, it has a value of: (πF); it can be regarded as a four-dimensional time curvature moment.
To corroborate the thesis, for example,
Diagram exposition
The diagram
| elements | H (1) | Li (3) | Na (11) | K (19) | Rb (37) | Cs (55) | Fr (87) |
|---|---|---|---|---|---|---|---|
| nuclear mass (u) | 1.0079400E+00 | 6.9400000E+00 | 2.2989769E+01 | 3.9098300E+01 | 8.5467800E+01 | 1.3290545E+02 | 2.2300000E+02 |
| total orbital’s energy levels (MeV) | 0.5104115 | 1.5312345 | 5.6145265 | 9.6978185 | 18.8852255 | 28.0726325 | 44.4058005 |
masses and the overall energy of the electronic orbitals is proportionally correlated.
If the analysis is correct, it is plausible to assume that:
1) A nucleus and the energy of its orbital levels are intrinsically connected.
2) Time curvature is a real phenomenon.
This suggests that the electroweak force is not properly a “force”, but an energy component yielded by nucleus space-time curvature.
( e q + ¯ ; e q − ¯ ) denote an imaginary straight line2 < future to present > passing through the {t0}.
An imaginary observer placed inside the nucleus would see nothing but a strange phenomenon of alteration of spacetime around it. However, both frames of reference (t0, e0−) are always coexistent, simultaneous, and instantaneous with respect to the event time.
As elaborated on in this paper, the energy orbital level is understood as the
overall energy of a discrete area of the curvature of spacetime induced by the presence of the nucleus.
Therefore, the absence of electrons in particle form is not a shortcoming of the theory, since based on the theoretical assumptions set forth, sticking to the processed data, it is strongly presumable that there can be no electrons in the particle state in the atom, only an energy of orbital levels with different energies as a function of the time curvature caused by the nucleus mass.
In essence, the electroweak interaction is inferred to be an interaction between the nucleus and the spacetime it originates from. The “spread” ( t 0 ← e o − ) indicated as (τν), is the energy in the form of quantized energy levels from which the electroweak force draws.
This correlation indicates that the electron ( + e − ) ( − e − ) is given by a fluctuation of the orbital radius equivalent to the energy of an electron:
Δ τ v n = m e 4 8 ε 0 2 h 2 τ v n → ( ( + e − ) ( − e − ) ) (4)
The ponderability of electrons in the “particle e − ” form will be established by interaction among atoms, such as electrochemical reactions, or interference in electromagnetic interactions.
The transfer energy-to-mass is consequent to the hyperdimensional leap from | e e o − | to instantaneous event |te|: 〈 ℂ ( x i e , y j e , z k e ) ( e e o − ) 〉 ⇒ 〈 ℝ ( x e , y e , z e ) ( t e ) 〉 |from wave form into particle state|
The overall energy required for the jump state is provided by the (Δτνe), the energy-to-mass ratio remains unchanged according to the physics principle of the conservation of mass-energy.
| Δ τ ν | → | e − |
As already surmised by Max Born-Pascual Jordan [
On the basis of the theoretical assumptions presented, it is possible to establish a consistent interpretation of the Heisenberg uncertainty principle (the electron lives in its energy orbital level (just) only in the energy form) and this is the reason why there is no conflict between the negative charge of the electron and the positive charge of the nucleus, because it is the nucleus itself that generates the space-time variations that gives rise to the “energy orbital level”.
In summary, the thesis of this study is that the electroweak force is an interpretation conditioned by a notion of an atomic model limited by representations of three-dimensional space.
Clearly, the extension to the hyper-dimensional integrated model introduces greater degrees of complexity, but it opens new horizons both because it unifies quantum mechanics to classical theories and introduces consistency variables to Young’s Double-Slit experiment and consequently to the Complementarity and Superposition Principles.
This study, in reference to [
Regarding the dynamics related to the different dislocations of the energy orbital levels (s1 ¸ s7) it is reasonable to assume that there are mechanics related to the nucleus that is not yet understood.
The theory found no conflict with known phenomenologies.
The author declares no conflicts of interest regarding the publication of this paper.
Burri, R. (2023) Extending the Standard Model in Hyper-Dimensional Mechanics. Journal of Applied Mathematics and Physics, 11, 572-581. https://doi.org/10.4236/jamp.2023.112035