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2. Coincidence of oppositions – oppositions must exist at the same time in the same place. And not according to some physicists, including Boltzman and Einstein, who have thought that matter with inverse direction of time can exist in some distant regions of our space. The absolute coincidence of two universes means the identity of coordinates of any particles in one universe to coordinates of its mirror image. It is clear that here all velocities must change their sign. Ancient thinkers did not see oppositions to be identical – there must be some degree of imperfection. According to this principle of imperfection there must be a difference in these coordinates. These imperfections will be calculated. Their dynamics turns out to be identical with quantum mechanics. If we assume for any particle a possibility of going from one world to another, the trajectory would take the form of a cloud (see Figs. 1, 2). Actually, I have in mind a small point-like ensemble.
Any such cloud is present in all four worlds in the form of four ensembles. Now the most important step: I assume as some relations between four worlds a relations (or correlation ) between those four ensembles ( four parts of a cloud ). These correlation can be completely determined by the third principle:
3. The universe as a whole and any particle (in the absence of external forces) must be stable and self-supporting. I have in mind a simple thing: the above dynamical cloud can generate electromagnetic waves. After scattering on other such clouds in the universe the waves can return (through the world with inverse arrow of time) to their source and can ensure the stability of dynamics of this source. Supposing the identity of all sources (or all ground states for the clouds of trajectories) we shall rewrite the condition of self-supportance as the equation that will determine the form of the ground state. This simple (in outward appearance) equation contains all out physics! We have here the usual case of symmetry breaking, the ground state is a part of collective modes, the condition of self-supportance is the usual condition of self-concordance in the mean field method of calculating the result of phase transitions. Here all equations usually have the unique solution. This fact is very important because with the above principles we have now all physics without any need in experiments.
4. Some results of symmetry breaking must in some aspects ensure our existence. In this chapter I use only one such aspect: stability of the ground state of electron. But in the next chapters I shall take more general initial dynamics inside any of the four worlds and some additional demands “from below” will be needed. They are needed to construct the translation of new physics (or its part) into our today’s language. Then we would have: 1. demands from above (ideals of different spheres of culture); 2. symmetry breaking that generates lower dynamics; 3. demands from below (conditions of our existence); 4. construction of covering (as in mathematics or mysticism, but now with new device that uses the effects of this new physics). That is the key to the universe. Now I proceed to more detailed description of the four cosmological models that form four worlds.
2. Four perfect cosmological models
Before the mentioned above symmetry breaking (or a number of symmetry breakings) we can have the dynamics that is completely different from our mundane world. But I shall take cosmological models that are near to existing ones – only the signs of the arrow of time and the arrow of causality will be different. Then I can not obtain as a result of the symmetry breaking any possible world. But this “clogging” of higher level by some notion from lower level greatly simplified the problem of derivation of new physics. I hope to throw out these unwanted notions from lower level in the future. I shall assume metrics to have the form:
For the scaling factor b
in the conventional theory we have the Friedman equation for matter in the
form of rarefied gas (k – gravitational constant,
e – density of energy,
Because here I assume the Freedman equation to be derived from initial basic interactions (it will be done below) and because here we have no scale, km must depend on scales according to their dimensions. It will be shown later that
where R is a constant.
Equations (2-3) imply
where a is a constant. The two signs obviously refer to two worlds
that correspond to an expanding and contracting universe respectively. Now we have two cosmological models with all particles at rest but with the scales depending on t according to (5).
3. Rules for choosing the proper solution in the four worlds
As a dynamics inside every world I take the Maxwell classical electrodynamics with zero mass electrons. There is an essential
point here: I shall start from Maxwell equations in a medium and not in
vacuum. The medium is described by Boltzman kinetics and I shall assume
that as the result of proper derivation of this kinetics we must obtain
two forms of statistics: usual (causal) and anticausal (“anti-Boltzman”
equations: different sign before
From this expression for the field in our universe we can obtain the expressions for the field in other worlds changing (6) (together with metrics), through the same transformations that generate Table 1. We have (see Fig. 3):
Fig. 3. Four solutions to Maxwell equations in a chaotic medium. The numbers are indices in Table 1.
We shall have analogous expressions for other fields and for particles (see Fig. 4).
Fig. 4. Four solutions to Newton equations in a chaotic field. The numbers are indices in Table 1.
Some notes
1. We actually have Boltzman kinetics after the interaction of four worlds is put on. But I am using it as initial dynamics inside worlds. This defect will be corrected in Chapter3. Actually, we have here many defects of this kind. I have developed a special technique for constructing the true dynamics inside any of the four worlds but the main problem is the relation of this inner dynamics to our mundane world. That is the topic of this chapter. I shall describe this relation (it is the task of all my life – the relation turns out to be non-trivial in many aspects) for some toy model of the four worlds – so we have here all our physics as one of the consequences. Then I will be able to improve this model and to repeat all derivation for any step along this improvement. On any such step I shall have a new and more advanced variant of physics. The main drowback of our culture (and our physics) is the absence of relations between different spheres of culture (and different sectors of physics). In this chapter I demonstrate an example of procedure for some new relations to be consciously derived – so in a very simple case. There are other problems that must be solved here – but they are secondary.
2. You could object: “Why solution depend on cosmic model if at small distances we have no cosmic or other matter.” But as will be shown below in this theory, the Green functions at small distances are constructed from those at all distances till the horizon – not as in today’s physics where physics of cosmic scales is derived from local physics.
3. The field of a moving charge can be obtained from
Coulomb field through the Lorentz transformation. But if we have L(v) for
Then we need an extension of special relativity. The four cases (7-10) can be rewritten in another form:
particles come to us from the past with positive temperature (11) particles come to us from the past with negative temperature (12) particles come to us from the future with negative temperature (13) particles come to us from the future with positive temperature (14)
Here, for negative temperature we have spectrum of energy limited from above. Here, for positive
temperature we have the usual Boltzman equation and for negative
temperature we have “anti-Boltzman” equation with different sign before
And in relation to Lorentz transformation we have for positive temperature the usual Lorentz matrix for coordinates and fields
and for negative temperature we have “anti-Lorentz matrix”
for the same system of reference. I introduce two types of vectors:
To ensure Lorentz-covariance we take as the rules for addition and multiplication:
for vectors of the same space:
(15) for vectors of different spaces:
This simple extension of special relativity theory has many consequences. It will be shown later
that all four types of vectors introduced above turn out to be tightly
connected. But if the connection of retarded Aret and advanced
Aadv (different signs of time) vectors has the form of simple
oppositions, the connection of causal
The beauty of complex numbers, the appearance of complex numbers in quantum mechanics – all those are the means to take into account the anticausal half of our world. The fields Aret and Aadv are connected through electromagnetic interaction with the universe as a whole. The fields
Then the appearance of complex numbers in quantum mechanics is the consequence of gravitation. The introduction of Aret and Aadv in physics gives us better logical structure of different part of physics. The introduction of
It turns out that matter is only a device to ensure equilibrium of causal and anticausal worlds. If we know this, we know the way to change the foundation of matter, we know the way of going out of slavery to matter. But up to now all that is as only a promise. To transform this promise into effective practice we must take the step that will be described in the next section.
4. The unique interaction between the four worlds
The main idea is that we can calculate strong connections (or correlations) of the four worlds (those connections generate all our physics) from an initial lagrangian where these four worlds do not interact. This phenomena is known in the theory of collective modes in many-particle systems. The initial very weak interaction can lead to symmetry breaking, where 1. the interaction becomes strong; 2. the form of resulting interaction practically does not depend on the form of the initial interaction. For our case of four worlds this independence is very important because here the initial interaction is not known. This independence is not universal but it takes place for all today’s experimental situation. There are many other situations where the initial interaction reveals itself – that is the new physics and we meet this physics on every step though we are not aware of this fact (see Chapter 3). The procedure of calculating this symmetry breaking appears in the case of two worlds as follows:
1. I start from usual lagrangian of classical electrodynamics (for zero mass electron):
The dynamics of two N-particle worlds is described by two lagrangians.
The fields
2. I assume as a result of symmetry breaking the appearance of the ground state where electrons from different worlds are tightly interwoven together – though in (17‑18) we have no interaction.
As example, we can
assume that electron of the world 1 is moving (in an external field
where
For the electron of the world 2 we have the similar
And as the result of the same symmetry breaking we have a new interaction
I.e. we have here five unknown functions and two equations of motion. You could ask: “In what way the expanding and the contracting worlds can be sticking together?” The answer is: because for the contracting world we have different arrow of time. You could ask: “Then
after The answer is: yes, but rules for choosing the solutions are different in these worlds. You could ask: “Then why you do not take only one world?” The answer is: two worlds are identical only on cosmological scales. On the scales of 10-14 cm and smaller they are quite different and instead of the mirror symmetry we have here “the caduceus” symmetry: four clouds from different worlds are rotating around common center. You could ask: “You have taken this symmetry because it is popular in mysticism?” The answer is: no. It is the unique solution of the equations for unknown interaction of the four worlds.
3. Let all particles in
our universe besides a chosen two to be paired by the interaction (19).
The chosen pair will radiate fields We have for the chosen pair the lagrangian From this lagrangian we can derive equations of motion. Let the solution of these equations have the form: These three functions
are functionales on the three functions But all particles are identical, and because of that we must have the calculated ground state for the chosen pair to be identical to the ground state supposed for all other pairs in the universe, i.e. If we want to know the
ground state in an external field With four worlds we have
four lagrangians 1
® 3 with connection
3
® 1 with connection
2
® 4 with connection
4
® 2 with connection
Now we have four unknown
trajectories If we have four ensembles of trajectories in four worlds (or one ensemble for a trajectory that can pass from one world to another), we can construct for distributions (or one distribution) equations analogous to (20). Below I shall discuss
more complex case where the ground state is defined by five functions: two
trajectories of the centers of gravity, The considerations around (20) may seem to be abstract, but along the text they will be repeated on different concrete examples. The equations (20) and their analogues will be solved. Now I want only to give you a hint on a general idea of derivation of interaction of the different worlds. Now you must solve this functional equations and see the consequences of the resulting physics. Solutions turn out to be simple, but the number of consequences turns out to be unlimited. It is a wonderful procedure: You start from the simplest dynamics (16) and get from (20) such a complex and incomprehensible dynamics as quantum mechanics and general relativity theory. And correct magnitude of electron mass, Planck constant, constant of gravitation. And many new physical effects on the usual scales of space-time and energy. You can take instead of (16) any other dynamics – say, the dynamics of angelic emotions. And in the same manner you can see the consequences. Actually, we have here an algorithm of generating new physical worlds. You can put here some objections – they will be answered below and in the next chapters. This “everything from nothing” has two sources: 1. Incommensurability of the initial ± t symmetry and the world with only one arrow of time that is a result of symmetry breaking. 2. Loops in time. This incommensurability puts stringent demands on possible solutions of (20). The solution that I shall describe below turns out to be unique and very special. Loops in time are unknown in today’s physics. But all our experimental facts, all our enigmas, all our revelations are, actually, different aspects of loops in time. The factors that form these loops are depicted on Fig. 5 for two particles 1 and 2. Green functions for waves are taken from (17) for retarded wave and from (18) for advanced wave. Connections are taken from (19).
Fig. 5. Loop in time. Loop is formed by four dependencies:
Existence of these loops has many unexpected consequences. 1. Loops are quadratic in Green functions of internal dynamics of four worlds. Our observable dynamics is dynamics of these loops. Hence our usual Maxwell equations, Newton laws, Lorentz and Poincare transformations and so on are squares of some primordial true higher internal dynamics. Hence this “angelic” initial dynamics is square roots of our mundane observable dynamics. That is the explanation of effectiveness of the Dirac’s square root, spinors, supersymmetry. Hence we must expect that the correct form of initial dynamics inside the worlds must be not (16) but a square root of Maxwell dynamics. This square root has time derivative in first degree. Then in initial dynamics we have a definite solution of evolution in time and we do not have the problem of choosing the proper solution. This problem is a result of sticking together of two internal dynamics in the new dynamics of loops. The main feature of my approach can be described as a step to prephysics through splitting, decomposing of our today’s physics that is the result of the mentioned above sticking together f four opposing worlds In a sense I repeat the famous trick of Dirac.
2. Through these loops any particle can interact with any other particle in the universe – see Fig. 6.
Fig. 6. Connections through the loops. The contribution from a
loop connecting two particles at the distance r is proportional to
The total energy of
these loops turns out to be equal to
3. The relations (21) have for particle 1 (after averaging on all particles of the universe as a particle 2) autooscillating solution with the frequency that is near to the magnitude of Compton frequency.
4. The elasticity of this net of loops turns out to be equal to Einstein lagrangian of “free space” in general relativity theory. The magnitude of gravitational constant is close to its experimental value.
5. And even the usual Coulomb force is generated by the loop connecting two particles. It is not the force that we can expect from lagrangian (16).
6. These loops generate many new effects which have been completely unknown until now.
The selfaction depicted on Fig. 6 is the correct form of the selfaction which Lorentz tried to introduce into electrodynamics a hundred years ago.
1. We have four worlds instead of two and loops not only in dynamical time but also in statistical time (i.e. in direction of causality). Note: conditions for stability will be minimum of energy for causal worlds and maximum of energy for anticausal worlds.
2. Because of transitions of particles from one world to another (see Figs. 1-2) we must start not from (16) but from
I assume the change of sign of dynamical and statistical time to be simultaneous, hence
Here I assume that velocity of particle also changes sign, i.e. we have situations depicted on Fig. 7.
Fig. 7. Turning point on a trajectory: a, not b.
Now unknown connections
(19) depend on Actually, these
3. All the above
calculations of the results of the symmetry breaking are carried out on
the background of a supposed cosmological model C. But after derivation of
local physics (including general relativity) we can calculate the
cosmological dynamics
With this improvement of Einstein equations we have only one cosmological model and not a spectrum of models (open and closed models).
2. All calculations are
carried out on the background of statistics S that is the result
3. All local physics turns out to be the result of the response of the universe through the loops of Fig. 5. This response takes place only for some undumping frequencies that, in turn, depend on L in (20), on cosmology and statistics. This fact complicates all above conditions for self-concordance. You could ask: “Why such a complex procedure exists for so simple thing as, for example, quantum mechanics?” The answer is: “Quantum mechanics is only a small and not very interesting part of physics that we have from (20). Any condition for self-concordance generates completely new physical effects that are unknown now. Then you must rejoice at any new condition for self-concordance.” You must keep in mind that the above scheme is only the first step of the great liberation from time and matter. In the next chapters I hope to repeat this scheme for more general and more thrilling ideals of prephysics. You will have new language and new conditions for self-consistence, the above equations (20) (or their analogues) remain as a bridge connecting our mundane world to higher worlds of our future. That is the end of description of all ideas and all simplifying assumptions. Everything that follows will be pure mathematics. This mathematics – equations (20, 24-25) – are difficult and I begin once more from some assumptions but now not from assumptions about the nature of physics. The assumptions will be about possible solutions of (20, 24-25). I start from the simplest assumptions of this kind, then I shall see the consequences, then I shall proceed to more refined assumptions, and so on till all assumptions will be proved to obey (20, 24-25). |
)
along a trajectory
is
the position of the center of gravity.
.
.
(19)
,
these fields will be scattered on other pairs in the universe and will be
returned as the fields of response
,
,
.
,
,
(20)
,
we can take instead of this field the pair that generates this field and
to carry out the renormalization (20) for two pairs and for the
interaction between them.
,
four unknown connections and 8 equations analogous to (20).
and
of
moving around these centers, and one function 
.
Instead of (20) we would have the five conditions of self-concordance.
