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THE INSOLVENCY OF THE THEORY OF ELECTROMAGNETICISM AND THE EXIT FROM THE COMPLETED DROP.

"SPECIAL" THEORY OF RELATIVITY
(SRT * - new edition, SOTO and Quaternary Universe)

To the 100th anniversary of the theory of relativity

Physics. Discoveries in physics.

V.M. Myasnikov

Welcome to the forum

"SPECIAL GENERAL" THEORY OF RELATIVITY (SOTO)

Such a cumbersome and awkward name is due to the fact that there is no better yet, on the other hand, it very accurately reflects the essence of the proposed theory: many (maybe all!) Known results of the general theory of relativity in its approximation can be obtained by methods and mathematical apparatus of the special theory of relativity Weak gravitational field.

Unlike the new SRT * , which has a direct predecessor in the person of Einstein's STR , the proposed theory of SOTO does not have such predecessors. Neither the general theory of relativity nor any of the other theories of gravity that are known to us prompt the idea of ​​creating SOTO (of course, after the creation of SOTO , "retroactively," such ideas can be found, for example, in GRT). Moreover, the very concept of gravity is not necessary for the creation of SOTO . The theory admits a gravitational interpretation, but does not require it with necessity.

Meanwhile, the main idea is very simple. If the idea of ​​an inseparable connection between time and space, thanks to SRT , has taken root in physics quite firmly, then the idea of ​​such an inseparable connection between mass and space is less obvious, although GRT has done a lot in this direction. We believe that the reason for this is that there was no adequate mathematical apparatus, simple and transparent , in the sense of its possible use in physics. We created such an apparatus - this is the mathematical apparatus of quater. And now for the construction of CTO, it is enough to add one single addition to the scheme for constructing SRT * (see above) - the physical reference point must have mass.

Let - a material point (a real body, the dimensions of which can be neglected) of the mass (The point and its mass are denoted by one letter).

The geometric reference system of Minkowski is a reference frame with a geometric reference point Without taking into account its mass and the chosen direction (ray) from the reference point. Geometric space-time (without taking into account the mass of the reference point) is called a quaternion space-time , Defined in the geometric Minkowski reference frame with the selected direction given by the unit vector ,

. (29)

The physical reference system of Minkowski is the frame of reference with the material reference point M taking into account its mass and the same chosen direction (ray) from the reference point. We call such a frame of reference the space-mass ( see Chapter IV ).

. (thirty)

Transformations from the geometric to the physical reference system are carried out by Lorentz transformations, which are defined as a spinor hyperbolic rotation, and the rotation spinor Is determined by the normalization of the space-mass quater at the corresponding point

those. , Where Is determined from , a - the unit of the selected direction.

The physical space-time (taking into account the mass of the reference point) is called the quaternion space-time , Defined in the physical reference system of Minkowski.

. (31)

In real practice, all measurements are made, as a rule, without taking into account the mass of the reference body, so we believe that we are able to make such measurements, i.e. Know the geometric space-time . The physical space-time ( 31 ) is determined by means of Lorentz formulas (transformations), bearing in mind their covariance in this case ( Chapter III ).

. (32)

After doing all the calculations and writing the result in a Cartesian coordinate system whose Ox axis is directed along the selected ray, for and - respectively, we obtain

. (33)

Further, setting the events and Simultaneous (see (5) and (6)), we find

, , , (34)

Where

or . (35)

Note that in all real physical situations (For the Earth and ), So we can assume

, , ( ). (36)

Thus, taking , With the "inclusion" of the body weight of the reference, the time slows down, the length (in the radial direction) increases, the mass of the test body increases.

Finally, as in SRT * (see (23)) , the transformations ( 34 ) are interpreted as transformations of the standards of time, length, and mass

, , (37)

With their subsequent use in the relativistic theory of dimension.

SOME CONSEQUENCES

Newtons potential . The main parameter is written in the form

, (38)

Where - the Newtonian gravitational potential (more precisely - the potential modulus) created by the body on distance From its center, or Is the normalized Newtonian potential. We rewrite ( 35 ), taking into account the smallness of the parameter (36)

, . (39)

We draw attention to the fact that it is the possibility of a gravitational interpretation of the main parameter that allows one to gravitationally interpret all the results formally obtained within the framework of the SOTO and to identify the physical space-mass with the gravitational field.

Gravitational redshift. All known formulas for the gravitational red (violet) shift of spectral lines, gravitational frequency shift formulas, and so on. Are a direct consequence of time dilation and increase in length, if they are interpreted as the frequencies and lengths of electromagnetic waves. For example, denoting - some spectral line from the light source in physical space (gravitational field) and - the same line in the reference spectrum (from the source in the geometric space, that is, in the absence of the gravitational field), from (34), under condition (39), we have - the gravitational red shift of this spectral line. Here - the relative gravitational potential in the place where the light source is located. The formula for the gravitational redshift is also written for the relative displacements in the form

. (40)

Thus, all such formulas formally (without involving the concept of gravity) follow directly from the theory, on the other hand, their gravitational interpretation is confirmed in experiments. Therefore, we consider such experiments as a direct confirmation of our theory.

The speed of light in a gravitational field. We remind you that the term "speed of light" is used in two different senses. First, it is a scalar - the fundamental physical constant, which is the exact upper limit ( Supremum ) of physical velocities in the Universe and, as such, does not depend on anything . (The analogy with the third law of thermodynamics is the existence of absolute zero ( Infimum ) of temperatures). And secondly - the speed of light . For the convenience of speech, we will speak of the photon velocity and denote . It is believed that the speed of a photon in a vacuum gives a value , I.e. . By "emptiness" is meant space (environment), in which there is nothing that could affect the speed of the photon. In our theory, we assume that the geometric space-time (without regard to mass) is empty, and the physical space-time (gravitational field), as we shall now show, is non-empty.

So, let

(41)

- The speed of a photon in a vacuum (in geometric space-time). Here and - longitudinal and transverse (relative to the radius vector) components of the photon velocity. Similarly in physical space-time we have

,

Substituting (See (34)), we obtain

Finally, taking ( 39 ) into account, we have

, (42)

Thus The photon speed decreases in the gravitational field of the body .

We draw attention to the fact that only the transverse component of the photon velocity decreases. The longitudinal component of the velocity does not depend on the gravitational potential in the radiation region, therefore, the longitudinal component of the signal does not carry information about the gravitational potential (but it can carry other information, for example, about Doppler shift). All information about the gravitational potential in the radiation region is borne by the transverse component of the signal, and it determines the corresponding structure of the spectrum . The latter naturally explains, for example, certain features in the spectra of stars with allowance for their gravitational fields, such as the dependence of the gravitational redshift on the position of the radiating region on the solar disk, the noticeable broadening of the absorption lines in the spectra of White dwarfs, and the broadening of the emission lines in the spectra of elliptical galaxies, Allowing to estimate their weights, etc.

It seems to us that the very form of formula ( 42 ) qualitatively indicates the curvature of the light beam and the deceleration of the propagation time of the radar signal in the gravitational field of the sun, the perihelion displacement (in deriving ( 42 ), the condition It is not decisive and can be discarded; We assume that ( 42 ) does not occur only for a photon), etc. Quantitatively, all this is confirmed by calculations (for details, see [1] ).

The dependence ( 42 ) of the speed of light on the gravitational potential gives the deviation of light in the gravitational field of the Sun, which coincides with the Einstein value calculated in general relativity. The same method applied to the motion of the planet under the assumption that the velocity of the planet has a component that depends only on the gravitational potential of the Sun and does not depend on the initial conditions (the "first shock") gives a perihelion displacement equal to one third of Einstein's calculated in general relativity.

And a formula was found in the general relativity that gives the delay time for the radar signal in the gravitational field of the sun ( Shapiro II 1964 , see, for example, C.Misner, K.Torn, J. Wheeler , Gravity , Mir, 1977, 3, pp. 355 and sl. , Formula 40.14 ), an experiment confirming the theoretical lag was carried out. We have considered this problem and found the time-lag formula, and it differs from the Shapiro formula. The analysis of the Shapiro formula showed that the formula has a "divergence" (the farther the object is from the Sun, the longer the delay time, in the limit - infinity?!). If this is a defect in the Shapiro formula, then it is due to this dependence of the speed of light on the gravitational potential used in GR . (We consider this as a "small bell not in favor of general relativity"). Our formula does not have this drawback.

Mass in the gravitational field. Law of gravitation. The mass of the test body in the gravitational field of another material body increases (see ( 34 ) with allowance for ( 39 ))

. (43)

Here - mass free trial body, - the mass of this test body in the gravitational field of the central body of mass on distance From its center, - the normalized gravitational potential (potential modulus, see (38)) at the point where the test body is.

We rewrite (43), multiplying the left and right sides by ,

(44)

The amount Can be interpreted as the "own" potential energy of the body of the mass (Or, which is the same, the potential energy of the body In relation to the universe, see above ), i.e.

,

Where - gravitational radius of mass . And then formula ( 44 ) has a completely clear and natural meaning: the total potential energy of the body in the gravitational field ( ) Is equal to the sum of the intrinsic potential energy of the body ( ) And the potential energy of this body in the gravitational field of the central body ( ). In Chapter IX ( see [2] ) we formulated the virial theorem . Bearing in mind this theorem, we rewrite ( 44 ) once more, changing the signs on the left and right sides by opposite,

.

We do not call the additional mass in ( 43 ) "hidden mass", for the reason that the term "hidden mass" has a special meaning in cosmology (the term "hidden mass" refers to the so-called gravitational active mass, while the increased mass ( 43 ) refers to the gravitational passive mass).

We rewrite everything again, substituting in the right-hand side of ( 43 ) the exact expression for ( See (35) )

We used the expression for the speed corresponding to the redshift ( 40 ) in the first term, . Thus, we obtain an expression for the total energy of the body of mass In the gravitational field of the body . But then this expression for the total energy can be considered as a Lagrangian

In the Lagrange equation (Euler)

.

Gives an impulse and Force. Substituting in the Lagrange equation and calculating the right-hand side, we obtain

, (45)

- the law of gravitation for the external space of a material point (See [1], Chapter IV , a, and [2]) . The latter, naturally, goes over into Newtonian

The hidden mass. The mass of the universe. If we evaluate the mass of cosmic objects as a measure of their gravitational influence on an external test body (ie, use a test body for "weighing" cosmic objects), it turns out that the mass of cosmic objects essentially depends on their hierarchical structure.

Suppose, for example, and - Two stars in a star cluster. Their gravitational connection can be described as the position of one of them ( ) In the gravitational field of the other ( ), I.e. Its mass is estimated by ( 43 ), and their total mass, in the reference frame of the star In the sense indicated above is equal to

. (46)

Here and below - module of relativistic potential energy.

In Chapter I , out of the most general philosophical considerations, we proposed the addition of masses in the megaworld to be called the "mass effect in the megaworld" ( ), As an alternative to "mass additivity in the macrocosm" ( ) And "mass defect in the microcosm" ( ). Now SOTO provides a theoretical basis for explaining the "mechanism" of the mass effect in the megaworld.

Continuing the reasoning for and , We find

,

Further, generalizing on 4, 5 ... stars and on the whole cluster, -

, (47)

Where The mass of the cluster in the sense indicated; As a measure of the gravitational impact of a cluster on external bodies, the first term on the right-hand side is the observed mass of the glowing substance in the cluster as the sum of the masses of the stars, the second is the not directly observed hidden mass. Assuming the proper motions of the stars inside the cluster are negligibly small, the mass Can be interpreted as the relativistic kinetic energy of the cluster (divided by ), On the other hand, by the virial theorem (see Chapter IX) . Taking all this into account, we have

, (48)

those. The star cluster, as a whole, acts gravitationally on external material objects as if its mass were equal to twice the mass of its constituent stars (the mass of the luminous substance of the cluster). But this is exactly how the mass of the star cluster in the Universe is interpreted, and it should be considered as the true mass of the cluster.

Further we make a grandiose extrapolation, assuming that the mass is doubled with each transition from one hierarchical structure to the next higher one. In the list of hierarchical stages of the distribution of matter in the universe, we noted five (four?) Such steps (star clusters, galaxies, clusters of galaxies, superclusters, Metagalaxy), i.e. The mass of the universe is 16-32 times larger than the mass of the luminous matter. Of course, this is nothing more than a scheme. However, the hidden mass exists, quite a lot of facts speak about it. The proposed theory explains, at least qualitatively (in the sense that the coefficient of increase in the cluster mass may not be equal to 2, but it is certainly greater than one), the nature of the hidden mass, and this theory was not created specifically for this case. As for quantitative assessments, modern ideas about the Universe confirm rather than disprove them.

For example, modern estimates of the average density of the luminous matter of the universe give the value of the relative density (referred to the Einstein critical density) . In our model of the universe ( [2] ), the relative density , I.e. 25 times greater than measured for a luminous substance. Is not it a very good coincidence with the number between 16 and 32 ?

As you know, all the existing theoretical and practical searches for the hidden mass in the universe have not been crowned with success. We believe that this is not an accident, tk. Is not looking for something, and not there . The hidden mass should be sought not so much as invisible particles of matter , but as invisible (unknown) interactions (see the physical definition of mass, Chapter X ).

USED ​​BOOKS

V.M. Butchers. Natural philosophy. (book, 400 pages, unpublished).

V.Myasnikov. Expansion of the universe => local physics. Proceedings of Congress-98 "Fundamental Problems of Natural Science". Volume II. Series "Problems of the Universe" vol. 22. St. Petersburg, 2000, p. 353-370

V.Myasnikov. Mathematical principles of modern natural philosophy. Proceedings of the Congress-2002 "Fundamental Problems of Natural Science and Technology." Part II. Series "Problems of the Universe" vol. 25. St.Petersburg, 2002, p. 135-167.

V.Myasnikov. Mathematical principles of modern natural philosophy. Abstracts of the report. Fundamental problems of science and technology. Program and theses of the reports of the Congress-2002. St. Petersburg. 2002, p.74

The article uses only the author's original ideas that do not require third-party information, so the list includes only the author's work.

See also the site of the author http://Quater1.narod.ru

print version
Author: V. M. Myasnikov
PS The material is protected.
Date of publication 13.01.2005гг