понедельник, 22 ноября 2010 г.

Which Laws of Physics are Laws of Logic

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.

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I call any subjects, connected with an information as informational objects.For example, it can be a physics device, or an incunabulum with ancient texts,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.

I call a set of sentences, expressing an information of some informational object, a recorder of this object.

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 {Please, see details in  G. Quznetsov, Logical Foundation of Theoretical Physics, Nova Sci.
Publ., NY (2006), p.p.27-67}:

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.

Secondly, time, according to this clock, is irreversible, i.e. there's no recorde which can receive information about an event that has happened until this event really happens. Thus, nobody can come back in past or receive information from future.

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.

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.

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.

I call such "Time" Informational Time.

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.

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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 {Quznetsov, G. Logic and Probability,  Prespacetime Journal| September 2010 | Vol. 1 | Issue 6 | pp. 957-976} for this function. So, probability theory is a generalization of classical propositional logic and, therefore, it is also propositional logic.

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I consider the events, each of which can bound to a certain point in space-time. Such events are called pointlike events {H. Bergson, Creative Evolution. Greenwood press, Wesport, Conn., (1975). A. N. Whitehead,  Process and Reality. Ed. D. R. Griffin and D. W. Sherburne. The Free Press, N.Y. (1978). M. Capek, The Philosophical Impact  of Contemporary Physics. D. Van Nostrand, Princeton, N.J. (1961). M. Capek. Particles or events. in Physical Sciences and History of Physics. Ed. R. S. Cohen and M. W. Wartorsky. Reidel, Boston, Mass. (1984), p.1. E. C. Whipple jr. Nuovo Cimento A, 11, {\bf 92} (1986). J. Jeans, The New Background of Science. Macmillan, N. Y. (1933)}. Combinations (sums, products, supplements) of such events are events, called physical events.

The probability density of pointlike 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 pointlike 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 {Quznetsov G. It Is Not Higgs,  Prespacetime Journal| May 2010 | Vol. 1 | Issue 3 | Page 318-320}.

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 {Quznetsov G. It Is Not Higgs, Prespacetime Journal| May 2010 | Vol. 1 | Issue 3 | Page 333-336}. I call these five of anticommutive complex 4X4 matrices Clifford pentade. There exist only six Clifford pentads {Madelung, E., Die Mathematischen Hilfsmittel des Physikers. Springer Verlag, (1964), p.12..; G. Quznetsov, Progress in Physics, v2, (2009), pp.96-106}. 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 {Quznetsov, G. Logical Foundation of Theoretical Physics, Nova Sci. Publ., NY, pp.143-144} - these pentads are not needed yet.

It is proven {G. Quznetsov, Progress in Physics, v2, (2009), pp.96-106} 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 {Quznetsov G. It Is Not Higgs, Prespacetime Journal| May 2010 | Vol. 1 | Issue 3 | Page 333-336}. This equation is invariant under electroweak transformations. The Klein-Gordon type equation with nonzero mass is obtained for gauge fields $W$ and $Z$ {Quznetsov G. It Is Not Higgs, Prespacetime Journal| May 2010 | Vol. 1 | Issue 3 | Page 335-336}.

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" {G. Quznetsov, Progress in Physics, v2, (2009), pp.96-106}.And oscillations of color 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.

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 space-time so that here appears the discrepancy between quantity of the luminous matter in space structures and the traditional picture of gravitational interaction of stars in these structures {Quznetsov, G. Dark Matter and Dark Energy are Mirage, http://arxiv.org/abs/1004.4496; Prespacetime Journal| October 2010 | Vol. 1 | Issue 8 | pp. 1241-1248}.

If probability of a pointlike event is limited in space-time then density of that probability at certain instant of time is represented as a square of 4x1 complex matrix Planck's function which obeys an equation of Dirac's type.

Thus, concepts and statements of Quantum Theory are concepts and statements of the probability of pointlike events and their ensembles.

Elementary physical particles in vacuum behave as these probabilities. For example, in accordance with doubleslit experiment {Quznetsov, G. Double-Slit Experiment and Quantum Theory Event-Probability Interpretation, http://arxiv.org/abs/1002.3425}, if in vacuum partition with two slits is placed between a source of elementary particles and a detecting screen then here interference occurs. But if this system will be put in a cloud chamber, then  trajectories of particle will be clearly marked with drops of condensate and any interference will disappear. This situation is similar to that physical particle exists only in instants of time when any event occurs with one. And at other instants of time the particle does not exist, but there a probability of some event with this particle remains.

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 pointlike 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 awaited by all occures. And the wave function disappears without
any collapse in the moment when an event probability disappears after the event occurs.

Thus, the fundamental essence of nature are not particles and fields, but pointlike events and connecting them probability.

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