Universe without Big Bang
Topic of discussion
The JWST telescope has shown that extremely distant galaxies have features that require a longer evolution than their age in the Big Bang theory. Images of the galaxy GN-z11 have revealed a massive black hole at its center that could not have gained its mass in the time since the Big Bang [1]There are reports of the presence in the spectra of distant galaxies of lines of heavy elements that could not have formed from hydrogen in a chain of thermonuclear reactions, etc.
There is no explanation for this within the standard model. Let's try to look for an explanation outside this framework.
Let's start from afar – do tachyons exist?
The possibility of the existence of tachyons – hypothetical particles moving in a vacuum at a speed vgreater than the speed of light With– does not in itself contradict the special theory of relativity (STR), which prohibits only the transitions of the “light barrier”. But the question of their properties, including their exceptional undetectableness, remains open, despite the many publications on this topic.
In 1993, an article appeared in the UFJ [2]in which the problem of superluminal travel was considered from a special angle. More precisely, from the angle in which it should have been considered with a consistent application of STR. Since we will need the results of the consideration later, we will have to briefly reproduce the course of this consideration here, so that these results do not cause natural mistrust.
By consistent application of the STR we will understand only extrapolation to the superluminal region v > c the postulate of the equality of all inertial systems, in particular, in the sense of describing any physical phenomena in three-dimensional space and with one-dimensional time and interval invariance. In Minkowski's Euclidean space-time, spatial coordinates are expressed by real numbers, and temporal coordinates by imaginary ones: such coordinates are often more convenient than the coordinates of pseudo-Euclidean space-time.
Let in some inertial frame of reference (hereinafter referred to as the fixed frame) the coordinates of two events be equal, respectively, {icT, X} And {ic(T+dT), X + dX}, i.e. square of interval idS between these events in Minkowski space-time is equal
In a frame of reference moving relative to the first with constant speed v in the direction of the axis X1 (hereinafter referred to as the moving system), the square of the same interval, according to the STR, is expressed as follows:
Here dX1, dX'1 – projections of the interval onto the direction of movement of the moving system in the fixed and moving reference systems, respectively, dX2 = dX'2dX3 = dX'3 – projections of the interval onto mutually orthogonal directions, orthogonal to the direction of motion of the moving system; ic dT' – projection of the interval onto the time axis of a moving system.
In both reference systems, the interval has one time-like projection, expressed in (1) and (2) by an imaginary number, and three space-like projections, expressed in (1) and (2) by real numbers. The two real projections, perpendicular to the direction of relative displacement, are not subject to transformation, and the real projection, parallel to the direction of relative displacement, and the imaginary (time-like) are transformed during the transition from a stationary system to a moving one according to Lorentz.
Moving on to the case of superluminal speeds that interests us, we find that in the right-hand side of (2) when substituting | v | > With (when (1 – v2/c2)1/2 becomes imaginary) three projections of the interval remain real (icdT', dX'2 And dX'3 ), and there is still one imaginary (dX'1 ). Based on the equality of inertial systems, we believe that in “superluminal” reference systems the interval has three space-like projections measured in real units of length, two of which, perpendicular to the direction of motion, are not transformed: dX'2 = dX2 And dX'3 = dX3 and one timelike projection measured in imaginary units of length. The third spacelike projection dX1''parallel to the direction of relative displacement, it is necessary that the only remaining real quantity iсdT' = (dX1 – dT s2 / v) (1 – With2 / v2)1/2and the only timelike projection icdT” it turns out that there is only one imaginary quantity dX'1 = – is(dT + dX1/v)/(1 – c2/v2)1/2. The coordinate transformations in the “superluminal” case turn out to be identical to the usual Lorentz transformations up to the sign of the timelike projection and subject to the replacement v → With2/v.
Poincare [3] was the first to point out the identity of the Lorentz transformations with an imaginary time coordinate and the transformations of rotation in the plane of the axes icT And X1 by an imaginary angle φ'determined by the relations:
Newly obtained for the case | v | > c coordinate transformations turn out to be a special case of rotation transformations for a four-dimensional rotation by a complex angle φ'the real part of which is equal to an odd number π/2:
with inversion or time (for odd n), or coordinates in the direction of movement (for even n ).
The limiting special cases of relative rest of the primed reference system are curious:
A) v = 0 (φ' = 0):
iсdT' = icdT cos 0 + dX1 sin 0 = icdT (coincidence of time axes)
dX'1 = dX1 cos 0 – icdT sin 0 = dX1 (coincidence of axes X1)
b) v → ∞, n = 1 (φ' → π/2):
iсdT' ≡ dX1“ = icdT cos π/2 + dX1 sin π/2 = dX1 (coincidence of axes X1)
dX'1 ≡ icdT” = dX1 cos π/2 – icdT sin π/2 = – icdT (time axis inversion)
If the rotation transformation b) is repeated, then the rotation angle φ' the axes of the new reference system relative to the unprimed system will be equal to π:
iсdT' ≡ icdT” = icdT cos π + dX1 sin π = – icdT (time axis inversion)
dX'1 ≡ dX1“ = dX1 cos π – icdT sin π = – dX1 (mirroring of axes X1)
Finally, if transformation b) is repeated one more time, then the rotation angle φ' the axes of the new reference system relative to the unprimed system will be equal to 3π/2:
iсdT' ≡ dX1“ = icdT cos 3π/2 + dX1 3×3π/2 = – dX1 (mirroring of axes X1)
dX'1 ≡ icdT” = dX1 cos 3π/2 – icdT sin 3π/2 = icdT (coincidence of time axes)
Another such rotation will not lead to anything new; we will return to the original unprimed reference system, rotated by 2π.
The observed speed of motion of a moving frame of reference for an arbitrary φ' is defined as follows:
a) an elementary interval is considered that has in the moving system only one projection that is not equal to zero, namely, a time-like projection (the proper time interval);
b) using rotation transformations φ' (3) timelike projection is defined icdT and projection dX1 on direction of relative displacements in a fixed frame of reference;
c) observed speed w is found as a spacelike projection relation dX1 to the elementary time interval dT.
In case | v | > With we have
From (5) it follows that in a sequential STR with an invariant interval for | v | > With 3-vector v loses the meaning of the observed relative velocity, retaining the role (according to Poincaré's interpretation) of one of the parameters determining the mutual orientation of the coordinate axes of two inertial reference systems that have imaginary time axes. The observed relative velocity w turns out to be less than the speed of light as in | v | < with, and at | v | > s. It can also be said that for particles at | v | > c the group and phase velocities change roles: v becomes the phase velocity.
Unusual symmetry in the world of elementary particles
Applying the above approach to the transformations of the 4-density of energy-momentum, 4-density of electric current and 4-density of angular momentum, we can obtain the conclusion that any particle with rest mass has mcharge q and torque Jyzin addition to this state (let's designate this state as number 1) there are three more “superluminal” states:
state with rest mass mcharge –q and the moment of rotation –Jyz (state 2);
state with rest mass –mcharge q and torque Jyz (state 3);
state with rest mass –mcharge –q and the moment of rotation –Jyz (state 4).
The particle in states 2, 3 has the sign of the ratio q/mopposite to the sign of this relation in states 1, 4, and in different states with the same sign of the relation q/m it is observed with opposite moments of rotation Jyz. For example, an electron in state 2 is a positron. A neutrino in state 2 corresponds to a particle with a mass equal to the neutrino mass and with an antiparallel spin. That is, particles in state 2 are classical antiparticles in relation to particles in state 1. It is important that they fall on matter (on bodies of particles in state 1) in the same way as particles in state 1, since their gravitational masses have the same signs.
Another matter is particles with states 3, 4. Particles of states 3 and 4 interact with each other in the same way as “particle-antiparticle” pairs: they are attracted to each other and annihilate. But bodies of particles in states 3, 4 are gravitationally repelled from bodies of particles in states 1, 2! But why – this should be dealt with separately.
The nuances of the theory of gravity
Cosmology without the Big Bang is consistent with some theory of gravitation based on STR, in which the transformations of the 4-dimensional rotation of particle wave functions (Lorentz transformations) are supplemented by a scale transformation and a reflection transformation. We briefly describe this modification in the weak field limit in the same Euclidean coordinate system with an imaginary time axis x0 ≡ ictWhere c – the speed of light, which will allow us to unify the indices of the tensor components. And we will check whether this theory satisfies the basic requirements for the theory of gravity, whether it corresponds to the results of experiments.
The scale transformation is chosen so that as the particle approaches the gravitating bodies:
its inertia increased, in accordance with Mach's principle, which is not the case in the general theory of relativity (GTR);
its total energy was decreasing, in accordance with classical ideas.
In the special case of a static field we have:
Where:
– H – a scale factor that has the physical meaning of the modulus of the total Newtonian potential of the Universe at a certain point, normalized to the square of the speed of light; at the beginning of the count, the calibration is taken H = 1 and the speed of light is taken to be equal to c;
– ki – wave 4-vector of a particle in a static potential Hfrom the point of view of an observer at the origin, who is, by definition, in H = 1;
– k'i – the wave 4-vector of the same particle, from the point of view of a local observer located in the potential H;
– ν' And ν – the corresponding frequencies of the particle's wave function.
At H > 1 ν < ν'that is, the gravitational redshift and the decrease in energy with an increase in the modulus of the potential are taken into account in this modification of the theory.
For the distant speed of light (with the local speed, by definition, equal to c) we get:
From the origin with a unit scale factor, the local speed of light in the region with H > 1 seems smaller.
From (6), taking into account the phase invariance, the coordinate transformations follow:
Having introduced the notations:
– we obtain transformations in the form:
In the new coordinates, the scale factor is introduced uniformly for all projections of each of the 4-vectors.
The dependence of the speed of light on the potential modulus leads to a delay in the radar signal on the way “there and back” when locating planets closer to the Sun from Earth:
Where:
– With(N) – the radar pulse velocity observed from Earth, With(N) = c/H2;
– H2 ~ (1+Φ)2 ~ 1+2Φ – the square of the sum of the background gravitational potential at the origin (always normalized) and the Newtonian addition from the Sun Φ = γM/(R(l)c2) <<1; γ – gravitational constant, M – the mass of the Sun, R(l) – the distance from the signal trajectory point to the center of the Sun;
– dl – an element of the trajectory in units of the origin of the observer's system located on Earth.
The delay values (11) for the location of Mercury and Venus coincide with those measured experimentally; the calculation details can be seen, for example, in [4].
The general form of the Lorentz-covariant equation of motion of a particle in such a gravitational field:
Where:
– Pi – 4-momentum of the particle;
– τ – proper time of the particle; – Wj – 4-particle speed;
– gm – 4-vector of the gravitational charge of a particle, associated with its wave 4-vector:
Where ν – frequency of the particle wave function, k0 – timelike projection of the wave 4-vector, kμ – projections of the wave 3-vector of the particle, h – Planck's constant; – Hij – 4-potential of the gravitational field in general form, taking into account the movement of the field sources.
The most characteristic special cases of equation (12) can be noted.
In the particular case of a static field of a spherically symmetric body with mass M and particles with their own mass mat rest at the initial moment of time, where
from (12) we obtain:
or, for 3-speed:
In the particular case of tangential motion of a relativistic particle near a non-rotating spherically symmetric source of a static field, we have, at
or, for 3-speed:
what if v2 → c leads to a doubling of the deviation compared to classical predictions. The theory meets the requirement of predicting a double deviation of photons in the solar field, and the same result is obtained when representing light as a plane wave whose phase velocity is c/H2 [4].
From (12) also follow formulas for inertial forces in non-inertial reference frames, including centrifugal and Coriolis forces [5]These forces are similar to electromagnetic ones caused by the 4-coordinate dependence of the vector potential of the electromagnetic field.
The equation of motion (12) is invariant with respect to the simultaneous inversion of charge signs gm ~ m and potential Hijthat is, to the total replacement in the Universe of particles in states 1, 2 with particles in states 3, 4. This means that gravitational phenomena in areas of predominance of negative and positive gravitational masses are identical to each other.
When the sign of only one of the quantities is inverted gm ~ m or Hijthe sign of the rate of change of the 4-momentum changes, which means that gravitational attraction is replaced by gravitational repulsion. That is, particles in states 3, 4 must be pushed out of the region of predominance of matter from particles in states 1, 2. A symmetrical picture will be observed in the region with predominance of particles in states 3, 4: there is no place for particles in states 1, 2 there.
Thus, if the total gravitational potential is dominated by contributions of any sign, electrically neutral groups of particles with positive gravitational masses will be formed and accumulated in the region with a predominance of particles in states 1 and 2, and electrically neutral groups of particles with negative gravitational masses will be formed and accumulated in the region with a predominance of particles in states 3 and 4.
Now, if we imagine the distant past of the Universe as a mixture of particles in all the listed states, then even without complex calculations we can see that after annihilations and the appearance of electrically neutral forms, we will receive background electromagnetic radiation and growing clusters of particles in states 1, 2, mutually avoiding growing clusters of particles in states 3, 4.
It makes sense to talk about the nature of the red shift, which depends on the distance to the radiation source, another time.
A universe without beginning or end?
Self-sustaining gravitational polarization of the Universe gives it a chance to be eternal in time and infinite in space. It is possible to roughly model the development of the Universe in a certain period of time by representing its unstable initial state as a lattice, in small neighborhoods of whose nodes clusters of particles in states 1, 2 and clusters of particles in states 3, 4 are located randomly, but alternately. One of the polarization phases of such a “Universe”, very similar to the actually observed picture, is shown in Fig. 1, where clusters of different types are depicted as red and green dots.
The alternating contributions of clusters 1, 2 and clusters 3, 4 ensures the convergence of the gravitational potential in any region of the infinite Universe, thereby eliminating the Seeliger paradox.
The age of the galaxies observed by JWST in the proposed Unstable Lattice model, an alternative to the Big Bang model, is not limited to hundreds of millions of years, as in the standard cosmological model, giving them time to form their complex structures and elemental composition. It is worth noting that the solution is proposed within the framework of classical physics and special relativity, without involving any unnecessary entities.
LITERATURE
1. Maiolino R., Scholtz J., Witstok J. et al. A small and vigorous black hole in the early Universe. Nature – 2024.
2. Telezhko G. M. On symmetry with respect to the light barrier. Ufa Physics Journal. — 1993. — Vol. 38, No. 2. — P. 183–189.
3. Poincaré H. Sur la dynamique de l'électron // Compt.Rend.Hebd.Seances Acad.Sci. – 1905 – 140 – P. 1504 – 1508.
4. Bowler M. Gravity and Relativity. Mir, M. – 1979. 215 p.
5. Telezhko G. M. Some particular consequences of the theory of gravity with scale-rotation-reflection transformations. In the collection: Science. Research. Practice. Collection of articles from the international scientific conference. St. Petersburg – 2022. – P. 69-72.
