if you consider a hamiltonian and the LQG to unify the QM qith the GR, so you don t consider a covariant analysis and so you just take mathematical tools to differenciate the spactime and it is what permit the wheeler Dewitt equation, the problem is to solve the infi nite quantities. So the problem is really philosophical consider the structure of this said spacetime of this GR, it is there now that becomes relevant considering a vaccuum differently and from this DE and made of atoms like structure and in my model they are 3d spheres in a fluidity. the big difference is that they are not quantas of gravitational field but quantas of informations antigravitational...........

    It is really how we consider the structure of the spacetime, and also how we consider the philosophical origin of the universe. The problem is that actually the light and photons have taken all the minds like primary essence and with this SR and GR like the only one truth, so we try to unify G c and h , the QM and the GR without thinking beyond the box and without trying to consider a deeper philosophical logic for the informations and the origin of this QM and QFT. It is really how we consider the main infornmations, the vacuum , the main codes, the strucuture hidden of this spacetime and I d say even of these spacetimes, not only the spacetime of this GR.

    If this DE antigravitational is a fifth force and is the main chief orchestra and it encodes the photons and the CDM to create the standard model the QM and QFT, all is different and this QG also is different. I have difficulties to understand how it is possible that the majority of physicists don t think farer and deeper than just these photons and this GR and SR. Sometimes I tell me that it is odd because it is just probably due to photonic observations and limitations still in knowledges and technologies. Maybe also it is philosophical like problem considering the light and a kind of God, like if all were persuaded that god is the light but if this infinite eternal consciousness exists and is in 0D and is omnipotent and inside and beyond the physicality, it is not an infinite heat but a thing that we cannot define and if this thing has decided to create an universe in 3D , so we need this central main cosmological sphere the supermatter energy in 3D sending the series of spheres for the photons, DE and CDM in a fluidity. It is different than strings or the LQG in consideing only photons oscillating vibrating with strings or points in 1d at this planck scale connected with a 1D cosmic field of this GR and this SR in fact.

    The confusion comes probably from this light like primary essence.....the SR and GR seems to have enormous problems , if this DE is informational and the real thing massless and is antigravitational, that becomes clear if this DE encodes these photons and CDM to create the ordinary matter and its fields.....

    The paper of Wilczek of course is very relevant considering the idea about these gravitons, but if these gravitons don t really exist due to philosophical problems mainly, so the noise will not be found. The gravitational waves have been found yes and I understand the idea with the noise to detect the gravitons and quantize this quantum gravitation.The perturbation theory and einstein gravity with the helicity 2 particle massless is considered and so they search to unify G c and h like I said , the GR and QM in finding a road for the quantization of the gravitational field. But for this we must be sure that these gravitons are the quantas of these gravitational waves found with the detectors, it could be simply oscillations of photons, so that becomes confusing philosophically about the origin of this QG. It is always the same problem considering the GR and SR , the photons like primary essence. But I find the idea of Wilczek relevant for larger states potentially detectable.If I can I will repeat that we cannot affirm that these gravitons exist really and that this GR is the primary essence. Wilczek considers the deviation geodesic with free falling masses with a separation of masses and correlate with the Riemanm tensor by gauge invariant perturbations of the metric, it is of course a relevant still idea considering the GR and works of Einstein, it is this separation wich is interesting with the Hill equation , so in a sense they harmonise the gravitational waves by solving the einstein equations, I d say in adapting them with different sources, signals. The fact to consider the change of the equation for the quantization of the gravitational field is very very relevant considering the link made with the equation of motion for the geodesic deviation , so indeed the idea is interesting for the quantum field, it is mainly about the detection but we detect photons or gravitons, the question is there and these gravitational waves maybe must have a deeper newtonian logic changing all the philosophy of this SR and GR. That is the masses are important and how we consider the massless particles, if this DE is the only thing massless and is of negative pressure, that changes all and these gravitational waves also like their origin and even the structure of this spacetime , I d say the spacetimes even considering the real vacuum of this DE possessing the main codes and informations and having a structure made of atoms. There are so roads with the fourier modes and specific harmonical analysis to do with these deeper scalar fields and this deeper philosophy of origin than just this SR and GR. Harmonic oscillators are there but with sortings about the groups , subgroups.....the geometrical algebras can help with the tensors, vectors, scalars and specific partitions and the non commutativity and the dewitt wheeler equation also can be utilised for the derivations, differential analysis, it will permit to superimpose all the unknowns and a deeper philosophy about the particles, waves, fields, vectors, scalars, tensors....The quantizations being the keys, so we shall see if in sorting well and in superimposing well the fifth force appears antigravitonal and if this QG is a newtonian force between massive particles or gravitons quantas of these gravitational waves.The states, the modes....so are indeed essential and important, there the probabilities and statistics are there to help with the good partitions probably. The hamiltonian being considered and the works of Hilbert, so in superimposing the two other spacetimes and a deeper philosophical origin of the mass , the solutions could appear to better understand this Quantum mechanic and QFT.The gravitational modes in a sense shall be ranked and the vacuum of this DE informational and antigravitational can permit to see clear .

      a month later

      Steve Dufourny Here are some general ideas , if I have made some errors , sorry I try to do my best and I am not perfect and I do n t affrim my assumptions, I just give some roads .

      let s try to create the tool about the spherical geometrical topological algebras , the aim is not to give an unique equation because the parameters possible are numerous and the equations apllied are adapted in function of choices .But here is some ideas for the spheres. Let s suppose a serie of spheres in motion in a space with a position x_i, y_i, z_i, une velocity v_i, an accelefration a_i, an oscillation of frequence f_i and an amplitude A_i, we can consider also a specific topology determinated with equations of distance and curvature, so we can describe the motion of each sphere like a differential equation
      m_i * d²x_i/dt² = F_i(x_i, v_i, t)
      where m_i is the mass de la sphere, F_i the force applied in the sphere , these forces can be electric, gravitational, , pressure, or others.....
      We can now desxribe the oscillations of each sphere like differential euations too
      d²x_i/dt² + (ωi)2 * x_i = 0
      où ω
      i = 2πf_i is the frequece angular of this oscillation
      Now let s consider the topology with the distances and curvature , so with differentrial and algebric euqtions
      d_ij = sqrt((x_j - x_i)2 + (y_j - y_i)2 + (z_j - z_i)2)
      and this for the curvature
      κ = (dφ/ds)/(ds/dt)
      où φis the angle s the arc , et t time
      We can now try a recursive equation for the serie primary of spheres
      V_n = V_0 / (2n+1)3
      where V_n is the volume of the nth sphere in the series, V_0 is the volume of the central sphere, and n is the index of the sphere in the series.
      Now let s resume and let try to converge for the standard model and with the DE and DM like scalar fields considered and let s consider that this DE encodes the DM and photons to create the ordinary baryonic matter
      here's a possible general formalism for the ideas we've discussed:
      Series of Spheres
      We consider a series of spheres in motion in a space, with a position vector r_i, a velocity vector v_i, an acceleration vector a_i, an oscillation frequency f_i, and an oscillation amplitude A_i. We can describe the motion of each sphere by the following differential equation:
      m_i d2 r_i / dt2 = F_i(r_i, v_i, t)
      where m_i is the mass of the sphere, F_i is the force applied to the sphere, and t is time.
      Topology
      We consider a specific topology determined by equations of distance and curvature. The distance between two spheres i and j is given by:
      d_ij = sqrt((r_j - r_i)2)
      The curvature of the space is given by the following differential equation:
      κ = (d2 φ / ds2) / (ds / dt)2
      where φ is the angle, s is the arc length, and t is time.
      Dark Energy
      We consider the dark energy as an informational and antigravitational fifth force that encodes the photons and cold dark matter. We can describe the motion of the dark energy using the following Lagrangian:
      L_DE = 1/2 (dϕ/dt)2 - V(ϕ)
      where ϕ is the dark energy field, and V(ϕ) is the dark energy potential. The potential V(ϕ) is determined by the equation of state of the dark energy.
      Dark Matter
      We consider the cold dark matter as a particle with mass m_DM that interacts gravitationally with the spheres and the dark energy. We can describe the motion of the dark matter using the following Lagrangian:
      L_DM = 1/2 m_DM (d2 x_DM / dt2)2 - U(x_DM, r_i, ϕ)
      where x_DM is the position vector of the dark matter particle, U(x_DM, r_i, ϕ) is the dark matter potential that depends on the positions of the spheres and the dark energy field, and t is time.
      Standard Model
      We can connect the series of spheres, the dark energy, and the dark matter to the standard model of particle physics using a relativistic bridge. The bridge is described by the following Lagrangian:
      L_SM = L_EM + L_W + L_Z + L_H + L_F
      where L_EM is the Lagrangian for electromagnetism, L_W and L_Z are the Lagrangians for the weak force, L_H is the Lagrangian for the Higgs boson, and L_F is the Lagrangian for the fermions. The Lagrangians depend on the gauge fields and the particle fields of the standard model.
      By combining these equations, we can create a general formalism that describes the motion of the series of spheres, the dark energy, the dark matter, and their interactions with the standard model.
      But we need to consider the lagrangians of the DE and DM, For DE:
      Equation of state parameter w
      Energy density ρDE
      Pressure p_DE
      Scale factor a
      One possible Lagrangian for DE is:
      L_DE = -ρ
      DE a3 (1 + w)
      For DM:
      Density ρDM
      Velocity v_DM
      Mass m_DM
      Scale factor a
      One possible Lagrangian for DM is:
      L_DM = 1/2 m_DM (a v_DM)2 - ρ
      DM a3
      now we can superimpose the lagrangians of this DE and DM to the others and play with the properties of series
      Now we consider these series of spheres instead of points or strings in 1D and we consider 4 E8 Firstly, we can represent each particle as a sphere or a serie of spheres in a 4-dimensional space. The position of the center of each sphere would correspond to the particle's position in 3D space, and the size of the spheres would be proportional to specific properties chosen topologically. In this way, we can represent both massive particles and massless particles photons.
      Next, we can use the E8 symmetry to describe the interactions between these particles. The E8 group is a Lie group with 248 dimensions and is one of the largest exceptional simple groups. It contains the symmetries of the Standard Model, as well as gravity but we consider alsi thjis fifth force anitgravitationa due to scalar massless fields for this DE
      To describe the interactions, it becomes complex in function of series and volumes and that implies categories , groups and subgroups .so 4 E8 for photons, cold dark matter, dark energy, and ordinary matter. The interactions between particles would then be described by the group structure of these E8 groups. For example, the photons could be represented by a subset of the E8 group that describes electromagnetic interactions, while the cold dark matter could be represented by a subset that describes the massive particles with the higgs superimposed
      To describe the formation of ordinary matter from dark energy and cold dark matter, we would need to introduce a mechanism that allows for the transformation of particles between different E8 groups. This could be accomplished by introducing a scalar field that couples to the E8 groups and drives the transformation.
      Finally, we can use the equations of motion for the E8 groups to describe the behavior of the particles and their interactions. These equations would be highly complex and difficult to solve analytically, so numerical simulations and approximations would likely be required.
      Now let s consider my intuitive equation E=m(c²+Xl²)+Y=2 mc² where X is a parameter correlated with the cold dand thermo for the DM and l is their linear velocity, and Y is a parameter correlated with this DE antigravitational and informational. The aim now is to try to correlate all this reasoning with the Higgs mechanism in completing it with these massive and massless scalar fields of the DM and DE , that could permit to explain some deep unknowns like the missing mass and mainly also the generation of this mass . For the quantum gravitation, it can be also utilised in trying to think outside the box in considering a different logic than these gravitons being the quantas of these gravitational waves in this general relativity.

      Now let s generalise this, Electromagnetic force:
      The electromagnetic force is described by the equations of quantum electrodynamics (QED), which involve the exchange of photons between charged particles. The key equation is:
      Fμν = ∂μAν − ∂νAμ
      where Fμν is the electromagnetic field tensor, Aμ is the electromagnetic potential, and μ and ν are indices that run from 0 to 3. This equation relates the electromagnetic field to the electromagnetic potential.
      The probability amplitude for a charged particle to emit or absorb a photon is given by:
      Mfi = −ieψ2¯γμψ1 * (-gμν/q2)ieqν
      where Mfi is the probability amplitude for the process, ψ1 and ψ2 are the wavefunctions of the initial and final states of the particles, q is the four-momentum transfer, and γμ is a matrix that describes the spin of the particle.
      Weak force:
      The weak force is responsible for processes like nuclear decay. It is described by the equations of quantum field theory, which involve the exchange of W and Z bosons between particles. The key equations are:
      Mfi = −gW2/8mW2Jμ+J−μ
      Mfi = −gW2/8mW2Jμ3J−μ3
      where Mfi is the probability amplitude for the exchange of a W or Z boson between two particles, gW is the weak coupling constant, mW is the mass of the W boson, Jμ and Jμ3 are the currents associated with the particles, and the superscript ± and 3 denote the isospin of the particles.
      Strong force:
      The strong force is the force that holds atomic nuclei together. It is described by the equations of quantum chromodynamics (QCD), which involve the exchange of gluons between quarks. The key equation is:
      LQCD = −1/4FμνaFνμa + ψ¯(iγμDμ − m)ψ
      where LQCD is the Lagrangian density for QCD, Fμνa is the field strength tensor for gluons, ψ is the quark field, m is the mass of the quark, and Dμ is the covariant derivative.
      Higgs field:
      The Higgs field is responsible for giving mass to particles. The key equation is:
      LHiggs = (Dμφ)†(Dμφ) − V(φ)
      where LHiggs is the Lagrangian density for the Higgs field, Dμ is the covariant derivative, φ is the Higgs field, and V(φ) is the Higgs potential.
      These equations describe the probabilities of particle interactions and the forces that cause them in the Standard Model.
      Now here are the Einstein Field Equations:
      Gμν = 8πTμν/c4
      where Gμν is the Einstein tensor that describes the curvature of spacetime, Tμν is the stress-energy tensor that describes the distribution of matter and energy in spacetime, and c is the speed of light.
      The Einstein Field Equations are the cornerstone of General Relativity (GR), which is a theory of gravity that describes the interaction of matter and energy with spacetime. GR provides a geometric description of gravity, where the curvature of spacetime is related to the distribution of matter and energy in spacetime.
      So how to unify all this in considering deeper scalar vectors tensors fields of the DE and DM , so we could complete the EFE and GR
      it is possible to modify the Einstein field equations to include scalar fields that represent dark matter (DM) and dark energy (DE). One approach is to introduce an additional scalar field, called a quintessence field, to describe the behavior of DE.
      The modified Einstein field equations with a quintessence field can be written as:
      Gμν = 8πG(Tμν + TQμν)
      where Gμν is the Einstein tensor, G is the gravitational constant, Tμν is the stress-energy tensor of matter and radiation, and TQμν is the stress-energy tensor of the quintessence field.
      The stress-energy tensor of the quintessence field can be written as:
      TQμν = (ϕ,μϕ,ν - 1/2 gμνϕ,αϕ,α - V(ϕ))gμν
      where ϕ is the quintessence field, V(ϕ) is its potential energy, and gμν is the metric tensor.
      In addition to the quintessence field, scalar fields can also be used to describe the behavior of DM. One such model is the scalar field dark matter (SFDM) model, where DM is described by a Bose-Einstein condensate of scalar particles. In this model, the scalar field obeys the Klein-Gordon equation and its stress-energy tensor can be added to the right-hand side of the Einstein field equations.
      The modified Einstein field equations with both a quintessence field and a scalar field for DM can be written as:
      Gμν = 8πG(Tμν + TQμν + Tχμν)
      where Tχμν is the stress-energy tensor of the scalar field for DM.
      The stress-energy tensor of the scalar field for DM
      Tχμν = (ħ2/m2)(χ,μχ,ν - 1/2 gμνχ,αχ,α)gμν
      where χ is the scalar field for DM, m is the mass of the scalar particles, and ħ is the reduced Planck constant.
      The Lagrangian density for the modified Einstein field equations with a quintessence field and a scalar field for DM can be written as:
      L = (1/16πG)(R - 2Λ + 2gμνϕ,μϕ,ν - gμνV(ϕ) - 2gμνχ,μχ,ν)
      where R is the Ricci scalar, Λ is the cosmological constant, and the last term represents the scalar field for DM.
      This modified Lagrangian density can be used to derive the modified Einstein field equations with both a quintessence field and a scalar field for DM.
      a possible approach to unifying the equations could involve modifying the Einstein field equations to include a scalar field that represents dark energy and a tensor field that represents dark matter. This modified equation could also include a fifth force that is responsible for antigravity.
      The modified Einstein field equation could look like:
      Gμν = (8πG/c4)Tμν + Λgμν + Φμν + Ψμν + ΦSμν
      where Gμν is the Einstein tensor, Tμν is the stress-energy tensor for matter and radiation in the universe, Λ is the cosmological constant that represents dark energy, Φμν is the tensor field that represents dark matter, Ψμν is the tensor field that represents the fifth force, and ΦSμν is the scalar field that represents the interactions of dark energy.

      Now let s consider the works of Bob Coecke and the ZX and ZW calculus , here is a wonderful work of professor Coecke, here is the generality if we consider your ZX calculus with the nodes for the quantum states and quantum operations , so I have understood the 2 main nodes for the qubits in the |0⟩ or |1⟩ state, while red nodes represent Hadamard gates, phase gates, or controlled-not gates. After the wires represent the flow of infornmations between these nodes with a geometrical connections horizontal or vertical
      So after the graphical notation represent the quantum circuits with the superimposing of these nodes and wires on a dimension like the 2d for example , and so you utilise specific symbols or colors .
      after so you consider rules for these graphical notations to manipulate if I understand well these quantum circuits like the F ruleto combine the nodes or to consider o to pi for example,
      The H rule is to convert the nodes of colors for example and with a gate like the hadamard one. The P rule is to add phases like for the angles and between 0 and 2 pi for example
      So it is indeed more than relevant for the simplification of circuits , now the relevance for me is to insert the relationships between quantum states for hidden symmetries or parameters in considering the ZW calculus now where the nodes are physical states or physical operations where we can rank the classical states and quantum states and their operations, so these nodes black and whites of color are relevant for the subgroups of physical states and the operations, all is a question of ranking. The wires of this ZW calculus for the flow of physical information between the nodes can be horizontal or vertical like for the ZX calculus for the connections and so it is the same technic than for the ZX calculus with the wires and nodes and operations for the graphical representations but the states are different , so to manipulate the physical systems and their operations . The F rule is like for the ZX calculus but the nodes are different and it is also between 0 and 2 pi, after the C rule to compose the nodes of same input or output and the Z rule to add or superimpose a physical phase for a black node for example, sothis ZW simplify the physical states at the difference of quantum states for the ZX calculus,
      Here is now an idea to reach a quantum universal computer, this idea if not from Bob Coecke, it is just an idea correlated with my theory So now if the spheres 3d are considered and if we rank all this with the spherical volumes and if we converge with the ZX and ZW calculus and in considering the densities , motions, oscillations, phases of these 3D finite primary series with the spherical topological geometrical algebras that I have invencted, we have road if we have the correct finite primary series to find the categories in quantum mechanics and in topology and we can find the quantum gravitation with deeepr scalar fields and a deeper philosophy
      With the ZX and ZW calculus and in simulating the correct philosophy of the universe and the foundamental objects with deeper scalar fields, it is more than revolutionary if the simulations and probabilities are well made because we reach the deepest unknowns and it becomes even intriguing

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