Large Hadron Collider (LHC) worked since 10 September 2008 till 14 February 2013.

Tevatron worked since 1 December 1970, till 30 September 2011. Enormous resources

were spent, but any essentially new results wasn’t received. Neither superpartners, nor

additional dimensions, neither gravitons, nor black holes. neither dark matter, nor dark

energy etc., etc. weren’t found. As for the Higgs, the assertion that the boson found in the

125 - 126 GeV, is this particle, is highly doubtful –

The Higgs field permeates the vacuum of space, which means the mass of the boson and

the stability of the vacuum are closely intertwined. Theory predicted that if the Higgs boson

is heavier than about 129 GeV, the universe should be on safe footing. The much celebrated

particle has a mass of about 126 GeV - light enough to raise fears of instability. Higgs boson

could have destroyed the cosmos shortly after it was born, causing the universe to collapse

just after the Big Bang. The experiments that detected the Higgs boson revealed it had a

mass of 125 billion electron-volts, or more than 130 times the mass of the proton. However,

this discovery led to a mystery at that mass, the Higgs boson should have destroyed the

universe just after the Big Bang. This is because Higgs particles attract each other at high

energies. For this to happen, the energies must be extraordinarily high, ”at least a million

times higher than the LHC can reach,

Right after the Big Bang, however, there was easily enough energy to make Higgs

bosons attract each other. This could have led the early universe to contract instead of

expand, snuffing it out shortly after its birth. The Standard Model of particle physics, which

scientists use to explain elementary particles and their interactions, has so far not provided

an answer to why the universe did not collapse following the Big Bang,

All well-known elementary bosons (photons, W and Z bosons, gluons) are gauge. Apparently,

the found by LHC 125-126 particle represents some hadron multiplet.

On the other hand already in 2006 - 2007 the logic analysis of these subjects described in

[1], [2] has shown that all physical events are interpreted by well-known particles (leptons,

quarks, and gauge bosons).

That is within last several decades many theoretical physicists investigated what isn’t

present in the Nature. It is the Superstrings Theory, the Higgs theory, the Dark Energy and

the Dark Matter hypotheses, etc.

”Final Book” contains development and continuation of ideas of these books.

Chapter 1 gives convenient updating of the Gentzen Natural Logic [3], a logic explanation

of space-time relations, and logical foundations of the Probability Theory. The reader

who isn’t interested in these topics, can pass this part and begin readings with Chapter 2.

Chapter 2 receives notions and statements of Quantum Theory from properties of probvabilities of physical events.

In Chapter 3 Electroweak Theory, Quarks-Gluon Theory and Gravity Theory are explained

from these properties.

For understanding of the maintenance of this book elementary knowledge in the field

of linear algebra and the mathematical analysis is sufficient.

In this edition of this book I added the subsections ”Dimension of physical space” and

”Chrome of Baryons”, and the comment to results of work the LHC.

Contents

Introduction v

1 Time, space, and probability 1

1.1. Classical propositional logic . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2. Recorders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.3. Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.4. Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.5. Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.6. Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

1.6.1. Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

1.6.2. B-functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

1.6.3. Independent tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

1.6.4. The logic probability function . . . . . . . . . . . . . . . . . . . . 53

1.6.5. Conditional probability . . . . . . . . . . . . . . . . . . . . . . . . 54

1.6.6. Classical probability . . . . . . . . . . . . . . . . . . . . . . . . . 55

1.6.7. Probability and logic . . . . . . . . . . . . . . . . . . . . . . . . . 55

2 Quants 57

2.1. Physical events and equation of moving . . . . . . . . . . . . . . . . . . . 57

2.2. Double-Slit Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

2.3. Lepton Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

2.4. Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

2.5. One-Mass State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

2.6. Creating and Annihilation Operators . . . . . . . . . . . . . . . . . . . . . 97

2.7. Particles and Antiparticles . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3 Fields 105

3.1. Electroweak Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

3.1.1. The Bi-mass State . . . . . . . . . . . . . . . . . . . . . . . . . . 106

3.1.2. Neutrino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

3.1.3. Electroweak Transformations . . . . . . . . . . . . . . . . . . . . 128

3.1.4. Dimension of physical space . . . . . . . . . . . . . . . . . . . . . 142

3.2. Quarks and Gluons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

3.3. Asymptoiic Freedom, Confinement, Gravitation . . . . . . . . . . . . . . . 159

3.3.1. Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

3.3.2. Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

3.3.3. Baryon Chrome . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Conclusion 183

Epilogue 187

References 189

Index

Conclusion

Fundamental Theoretical Physics contains sequences of theories, each of which is explained

of previous ones by rules of the classical logic. For example, optics is absorbed by theory of

electromagnetism, classical mechanics - by special theory of relativity and quantum theory,

the theory of electromagnetism and weak interactions - by theory of electroweak interactions

of Sheldon Glashow and so on. That means that basic notions and statements of every

subsequent theory are more logical than basic notions and axioms of the preceding one.

When these basic elements of the theory become absolutely logical, i.e. when they

become notions and rules of classical logic, theoretical physics will come to an end, it will

rather be logic than physics.

—————————————————-

Any subjects, connected with an information is called informational objects. For example,

it can be a physics device, or computer disks and gramophone records, or people,

carrying memory on events of their lifes, or trees, on cuts which annual rings tell on past

climatic and ecological changes, or stones with imprints of long ago extincted plants and

bestials, or minerals, telling on geological cataclysms, or celestial bodies, carrying an information

on a remote distant past Universe, etc., etc.

It is clearly that an information, received from such information object, can be expressed

by a text which made of sentences.

A set of sentences, expressing an information of some informational object, is called

recorder of this object (p.15).

Obviously, the following conditions are satisfied:

I. A recorder does not kept logically hereafter refers to the classical propositional logic

inconsistent sentence.

II. If a recorder contains some sentence then one contains all propositional consequences

of that sentence.

+III. If recorder a contains sentence ”recorder b contains sentence A” then recorder a

contains sentence A.

For example, if recorder a contains sentence ”recorder b contains sentence ”Big Theorem

is proved” ” then recorder a contains sentence ”Big Theorem is proved”.

Some recorders systems form structures like clocks. The following results come from

the logical properties of a set of recorders (p.16)

First, all such clocks have the same direction, i.e. if an event expressed by sentence A

precedes an event expressed by sentence B according to one of such clocks then the same

for others as well (p.18).

Secondly, time, according to this clock, is irreversible, i.e. there’s no recorde which canreceive information about an event that has happened until this event really happens. Thus,

nobody can come back in past or receive information from future (p.32).

Thirdly, a set of recorders are naturally embedded into a metrical space, i.e. all four

axioms of metrical space are received from logical properties of the set of recorders (p.23).

Fourthly, if this metrical space is Euclidean, then the corresponding ”space and time”

of recorders obeys to transformations of the complete Poincare group. In this case Special

Theory of Relativity follows the logical properties of information. If this metric space is not

Euclidean then suitable non-linear geometry may be built on this space. And an appropriate

version of the General Relativity Theory can be implemented in that space-time (pp.29–48).

Therefore, basic properties of time - unidirectionality and irreversibility, metrical properties

of space and principles of the theory of relativity derive from logical properties of

the set of recorders. Thus, if you have some set of objects, dealing with information, then

”time” and ”space” are inevitable. And it doesn’t matter whether this set is included in our

world or some other worlds, which don’t have a space-time structure initially.

Such ”Time–Space” is called ”Informational Time–Space”.

Because we receive our time with our informational system then all other our times’

notions (thermodynamical time, cosmological time, psychological time, quantum time etc.)

should be defined by that Informational Time.

————————————————-

As it is well known, classical propositional logic can be formulated on the basis of the

properties of Boolean function. If the range of this function will be extended to the interval

[0, 1] of the real number axes then we shall obtain the function which has all properties

of the function of probability. Logical analogue of Law of Large Numbers in form of

Bernoulli is derived for this function. So, probability theory is a generalization of classical

propositional logic and, therefore, it is also propositional logic (pp.48–56).

—————————————————-

I consider the events, each of which can bound to a certain point in space-time. Such

events are called dot events[45]. Combinations (sums, products, supplements) of such

events are events, called physical events.

The probability density of dot events in space-time is invariant under Lorentz transformations.

But probability density of such events in space at a certain instant of time is not

invariant under these transformations. I consider the dot events for which density of probability

in space at some instant of time is the null component of a 3+1-vector function which

is transformed by the Lorentz formulas (pp.58–59).

I call these probabilities the traceable probabilities.

It is known that Dirac’s equation contains four anticommutive complex 4X4 matrices.

And this equation is not invariant under electroweak transformations. But it turns out that

there is another such matrix anticommutive with all these four matrices. If additional mass

term with this matrix will be added to Dirac’s equation then the resulting equation shall

be invariant under these transformations I call these five of anticommutive complex 4X4

matrices Clifford pentade. There exist only six Clifford pentads I call one of them the light

pentad, three - the chromatic pentads, and two - the gustatory pentads.

The light pentad contains three matrices corresponding to the coordinates of 3-

dimensional space, and two matrices relevant to mass terms - one for the lepton and one for

the neutrino of this lepton.

Each chromatic pentad also contains three matrices corresponding to three coordinates

and two mass matrices - one for top quark and another - for bottom quark.

Each gustatory pentad contains one coordinate matrix and two pairs of mass matrices -

these pentads are not needed yet (pp.59–60).

Each vector of state has its own corresponing element of the Cayley-Dickson algebra

(pp.142–145). Properties of a state vector require that this algebra was a normalized division

algebra. By the Hurwitz and Frobenius theorems maximal dimension of such algebra is 8.

Consequently, a dimension of corresponding complex state vectors is 4, and a dimension

of the Clifford set elements is 4x4. Such set contains 5 matrics - among them - 3 diagonal.

Hence, a dimension of the dot events space is equal to 3+1.

It is proven (pp.65–68, 80–82) that any square-integrable 4x1-matrix function with

bounded domain (Planck’s function) obeys some generalization of Dirac’s equation with

additional gauge members. This generalization is the sum of products of the coordinate

matrices of the light pentad and covariant derivatives of the corresponding coordinates plus

product of all the eight mass matrices (two of light and six of chromatic) and the corresponding

mass numbers.

If this equation does not contain chromatic mass numbers then we obtain Dirac’s equation

for leptons with gauge members which are similar to electroweak fields obtained for

gauge fieldsW and Z (pp.83–89, 106–139).

If this equation does not contain lepton’s and neutrino’s mass terms then we obtain the

Dirac’s equation with gauge members similar to eight gluon’s fields (pp.141 –155). And

oscillations of chromatic states of this equation bend space-time. This bend gives rise to the

effects of redshift, confinement and asymptotic freedom, and Newtonian gravity turns out

to be a continuation of subnucleonic forces (pp.155–157).

And it turns out that these oscillations bend space-time so that at large distance space

expands with acceleration according to Hubble’s law. And these oscillations bend spacetime

so that here appears the discrepancy between q uantity of the luminous matter in space

structures and the traditional picture of gravitational interaction of stars in these structures

(pp.157–162)

Thus, concepts and statements of Quantum Theory are concepts and statements of the

probability of dot events and their ensembles.

Elementary physical particles in vacuum behave as these probabilities. For example, in

accordance with doubleslit experiment.

Thus, if between event of the creating of a particle and event of the detecting of ones

here events do not occur then at this period of time this particle does not exist - here only

probability of this particle detecting in some point. But this probability, as we have seen,

obeys the equations of quantum theory, and we get the interference. But in a cloud chamber

events of condensation form a chain, meaning the trajectory of this particle. In this case the

interference disappears. But this trajectory is not continuous - each point of this line has a

neighbour point. And the effect of this particle moving arises from the fact that a wave of

probability propagates between these points.

Consequently, the elementary physical particle represents an ensemble of dot events

associated probabilities. And charge, mass, energy, momentum, spins, etc. represent parameters

of distribution of these probabilities. It explains all paradoxes of quantum physics.

Schrodinger’s cat lives easy without any superposition of states until the microevent awaitedby all occures. And the wave function disappears without any collapse in the moment when

an event probability disappears after the event occurs (pp.71–79).

Thus, the fundamental essence of nature are not particles and fields, but dot events and

connecting them probability.

————————————————–

Hence, the fundamental theoretical physics is one among of extensions of classical

propositional logic.