Aleksandr Maltsev
"Two 4-dimensional worlds create 3-dimensional and 5-dimensional." as you say.
I can consider the 4-dimentionnal space as the inertial time of a corpuscle so we get in all five dimension (4 space and 1 time). Let's continue and we can say "Two 5-dimensional worlds create 4-dimensional and 6-dimensional." but the question what is the significance of the 5-space dimension ? we built theories like this and we haven't any issue to prove it experimentally. It is like string theory which I had never beleive in it because there is no issue for experimental data or procedure to do it.

      About dark energy we should thrust in maths. The first time when scientists speak about vacuum energy is Planck book 1911 "Theory of heat radiation" -. Planck conclude that when an oscillator is in its fundamental state its energy is not equal to zero ( he take the mean energy of an oscillator when it is in quantum state n and in quantum n+1 so for n=0 the energy of the oscillator is not equal to zero). The Planck constant h is the area of the space phase of the oscillator between the level n and the level n+1. At n=0 the area between n=0 and the origin of the space phase is equal to zero so vacuum energy is also zero according to Planck model of the black body radiation but Planck take another way in considering the mean energy of the oscillator and he conclude that atoms are filled with energy.
      In fact we can get the same Planck conclusion by considering Shrodinger equation to get the energy of an osciilator and by applying Bohr priniple of correspondance in quantum mechanics. The area between the level n=0 and the origin of phase space of the oscillator will not equal to zero: it is equal to h/2 and so there is vacuum energy because all the oscillators when temeprature tends to zero will lies in this area. This is the power of maths and principles.

        Alaya Kouki Dear KhakiHeron
        Footnote "Can the real world be n-dimensional?" from a philosophical article. Mathematics shows that the Universe (matter, space, time, energy) arose as a result of a double dual decay. with cross join.
        I apologize for the google translate.
        MV - matter TE - physical vacuum. Phenomena of Nature: mass, volume, energy. time.
        The disintegration and unification of components can be explained by applying the concept of potential. The total potential of the Proto-nature is equal to zero. Let: τ = (-3); V=(-1); E=1; M=3. Potential of Proto-Vacuum τ V and Protomatter EM is respectively equal to (-4) and (+4) or duality is equal to 8.
        Further decay into dual pairs ( τ - V) and (E - M) creates the possibility for the formation of different variants of connections between them. The EV and MT variants describe systems that are neutral in potential and do not interact with each other. This is a variant of the dead nature.
        The variant МV=3—1=2 and τ Е= (-3) +1=-2 creates a new dual pair with a low degree of opposition relative to the pair "protomatter - protovacuum". The result of such a connection will be a decrease in the "confrontation" between the dual components and an increase in the stability of new systems. The unification of parts of different dual pairs created matter MV and ether τ E. Double decay and subsequent synthesis restored the unity of Proto-nature, at a new qualitative level

        1. The emergence of Natural Phenomena from Proto-Nature indicates the equivalence of the Natural Phenomena. Equivalence is achieved when:
        2. equality. Equality creates stagnation - a variant of dead Nature (explanation of the adoption by unequal potentials of the Phenomena of Nature τ = (-3); V= (-1); E=1; M=3);
        3. activities in different areas, with mutual communication. Variant of dynamic Nature.
        4. Interaction arises when it is possible to create multivariate states between points characterizing Phenomena. On the plane, the first multivariant (flexible) system is a quadrilateral (in our case, M, V, τ, E). Consequently, in the absence of defects in the Phenomena of Nature, the world would be flat. Proto-nature, divided into complex parts, matter MV and physical vacuum TE, further manifests its duality by the defects of the Natural Phenomena. Defects (movement) made the world three-dimensional. And vice versa. The volume allowed defects to occur.
        5. Dual disintegration breaks the unity of the original system. Duality is described by a line. To maintain unity, the line must close. The line closes faster in a plane than in a volume. Consequently, the division of the Phenomena of Nature into perpendicular planes is the most advantageous variant of preserving the dual world in unity.

        Experimental verification - excess radiation of energy by the Moon. The effect is proportional to the square of the mass and Jupiter is better, but farther away.
        Thank you for attention

          Aleksandr Maltsev
          Observations of the cosmos shows that vacuum energy=1E-9 Joule/m3 which correspond to a frequency of the fundamental state of the electromagnetic field v=1E12 Hz: I do a model for this which is:

          Consider that Universe is a black body. Take the Planck model of the black body radiation. When the temperature tends to zero than all the oscillators tends to the area of space phase equal to h/2.
          The mean energy of an oscillator is as follows:
          -Replace in Planck formulae of mean energy hv by hv/2.
          -Replace in Planck formulae kT by hv0/2 where v0 is the mean frequency of oscillator in Boltzmann model
          -Integrate for all frequencies the density of energy--> you get a law proportionnel to the forth power of v0--> so you can deduce v0 from General Relativity.
          v0 is declared as universal constant.
          Integrate the new ideas in Quantum mechanics-->you can deduce the Newton potential from quantum mechanics when you consider space as a collection of an infinite oscillators.

            "To unify quantum and classical physics, consider temperature."
            Temperature in classical physics is the mean kinetic energy of a gaz in a given volume.
            In quantum mechanics temperature tranduce the entropy of an oscillator of a black body i.e. it transduce irreversibility or chaotic mouvement. If the vibration of the oscillators of a black body are perfect than there is no entropy and the potentiel energy of an oscillator is transformed periodically to its kinetic energy without any loss.
            If the vibrations are chaotic than there is entropy and the mean energy of an oscillator depends of its frequency and the temperature of the medium.
            Consider now cosmos, its temperature tends theoritically to zero so there is no radiation but cosmos is expanding due to vacuum energy or constant lambda of General Relativity. Vacuum energy can be considered as the density of energy of the fundamental state of the electromgnetic field so we should need a new universal constant to modelise the mean energy of an oscillator in the classical case (Boltzmann case) as hv0/2 so we can deduce the value of v0.
            Combinig this constant with Planck constant and speed of light we get the unique abslute system of unities in which all interactions are unified in one interaction: the case when considering the space as a comosed of an inifinite number of oscillators lead to the Newton gravitationnel field.

              Alaya Kouki The definition "Temperature in classical physics is the mean kinetic energy of a gaz in a given volume" does not allow one to unify quantum and classical physics. To emit a photon, an electron, in a classical molecule, reduces its energy.

                  Aleksandr Maltsev
                  OK. I don't say this. Quatum mechanics and classical physics are unified by Bhor Principle of Correspondance. Bhor consider this principle as a quantum principle and it is valid for any quatum level. Fot high quatum levels quatum mechanics is the same as classical physics. For low quantum levels Bhor consider that there is a classical measuring which correspond to the level, that's why he consider the principle as general. I use it to found that vacuum have an energy.

                      Alaya Kouki I start with Newton. I use the Lorentz invariance, the characteristics of a moving body, to describe matter as a unity of mass and volume MV (Newton did not take into account the volume). Further algebra, geometry and differentiation.

                        5 days later

                        The answer to the question "What binds
                        matter into stable neutrons, protons, photons, neutrinos and an electron?" practically not
                        considered.

                        while reading around rotations , a bug (german red kitchen roach) entered the left corner of the new laptop a place that i previously saw insects (lenovo ideapad3) this made me ponder (made free creative associacions) about conscioussness and roatation aliens communicating from the future 🙂

                        what is this thing called rotatie (ro), drehen (de)

                        an other potentially weird idea i thought last year what if the atomic number of elements by witch they are classified has something to do with objects that have a topological dimensional shape related to that number for example something like a bunch of rods glued with the same elemental material to have an axes origin , for example for the helium witch is two or three ( depending how you start counting the elements ) it supposed to make a two perpendicular lines of material three like the corner of a cube, with carbon six or seven
                        when arriving at the last element it should have a number that the the sight cannot percieve because it would luk like a round spiky thing, maybe with with longer arms somebody experimentalist try to check properties about 3+1spacetime maybe li or be are the elements witch can say something about

                        also there might be other kinds of (feed)backs , (and forwards lateral sideways etc), comparing the positive negative with past and future maybe there are narry groups generalisations there is an article an invitation to n arry science i think is worth mentioning.

                        In the end of this FQXI competition I would to add more pages to my article because the main important ideas I had sad them in comments. Those ideas comes from the articles in this competition and I think that If I add new pages it is possible to made a new paradigm in physical science but the rules of FQXI team don't permit this option.

                          Alaya Kouki

                          Hear you, Khaki Heron, I also gained so much valuable input that I will definitely amend my essay afterwards! Someone already suggested to join forces and publish essays together in some journal afterwards. We should do that (irrespective of winning awards here in the competition) and then we can insert the input we got here, too. 🙂

                          Cheers,
                          Beige Bandicoot.

                              I agree. Contact me after the end of this competition and I will send you my new text to be a chapter for a common book. All writers in this Competition are wellcome.

                              I swell that ChatGPT or any other AI can't be more intelligent than all the participants in this Competition. Ask him what is 4-vector identity: he can't get any consistent response.

                              Response of chatGPT now ( I create now an account in chat GPT):
                              "In physics, a 4-vector identity refers to an equation or relation involving 4-vectors, which are mathematical objects used to describe certain quantities in spacetime. 4-vectors consist of four components, typically representing the three spatial dimensions and time.

                              One common 4-vector identity is the Minkowski metric, also known as the spacetime interval or the metric tensor. It is a mathematical construct that relates the spacetime distance between two events to the components of a 4-vector. The Minkowski metric is often denoted by the symbol η, and it has the following form:

                              η = diag(-1, 1, 1, 1)

                              Here, "diag" represents the diagonal elements of a matrix, and the values -1, 1, 1, 1 are placed on the diagonal in the order of (time, x-axis, y-axis, z-axis). This metric allows us to calculate the spacetime interval between two events using the equation:

                              ds2 = ημν dxμ dxν

                              In this equation, dxμ and dxν represent the components of the 4-vector describing the displacement between two events, and μ, ν take values from 0 to 3, corresponding to the four components of the vector.

                              The Minkowski metric is a fundamental tool in special relativity, as it provides a way to define the invariant spacetime interval, which remains the same for all observers regardless of their relative motion."

                              It is a very general response . It resolves nothing and can't improve science.

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