On the Correct Formulation of the Starting Point of Classical Mechanics

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1 Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Volue 4, Issue 6, 27, PP -22 ISSN No. (Online) On the Coect oulation of the Stating Point of Classical echanics Teu Z. Kalanov Hoe of Physical Pobles, Yozuvchila (Pisatelskaya) 6a, 2 Tashkent, Uzbekistan *Coesponding utho: Teu Z. Kalanov, Hoe of Physical Pobles, Yozuvchila (Pisatelskaya) 6a, 2 Tashkent, Uzbekistan bstact: The coect scientific and citical analysis of the geneally accepted foundations of classical echanics is poposed. The ethodological basis fo the analysis is the unity of foal logic and of ational dialectics. The ain esults of the analysis ae as follows: () the coect stating point of kineatics is foulated: the infoational definition of the concept of tie; definitions of the concepts of otion, speed, and acceleation of ateial point in the etic syste of coodinates; the pinciple of otion of quantu paticle (photon); poof of the atheatical, physical, and foal-logical eoneousness (fallaciousness) of oentz tansfoations; (2) the coect stating point of dynaics is foulated: the definition of foce as a physical popety of the stuctue of the syste of the inteacting objects; (3) the coect stating point of the theoy of gavitation is foulated: the condition of existence of the gavitational inteaction which epesents the condition of existence of the egion of ovelap (supeposition, intesection) of the gavitational fields of the ateial objects; (4) the coect foulation of the law of gavitation within the faewok of the syste appoach is given (the foulation epesents the syste of the popotions); (5) it is poved that the foulation of Newton s epiical law of gavitation epesents the foal-logical and dialectical eos. Keywods: geneal physics, special elativity, quantu echanics, classical echanics, foaliss in classical echanics, Newtonian echanics, post-newtonian appoxiation, gavity, philosophy of science, histoy of science. PCS:.55.+b,.65.+g,.7.+w, 2.9.+p, 3.3.+p, w, 4.25.Nx, x, d, INTROUCTION Recently, the pogess of sciences, engineeing, and technology has given ise to a new poble: the poble of ationalization of the fundaental sciences (fo exaple, theoetical physics and atheatics). Rationalization of sciences is ipossible without ationalization of thinking and citical analysis of the foundations of sciences within the faewok of the coect ethodological basis: the unity of foal logic and of ational dialectics. Theefoe, one should call achieveents of classics of sciences in question within the faewok of the coect ethodological basis. s has been shown in woks [-99], the foundations of theoetical physics, of atheatics, and of philosophy contain foal-logical and dialectical eos. This signifies that any geneally accepted theoy can be efuted if it contadicts to the foal-logical and dialectical laws. s is known [98-], classical echanics as a banch of physics aose fo the needs of sciences and pactice and has a long histoy of developent. The ipotant significance of classical echanics is deteined by the contibution of the poinent scientists of past tie: J. Keple, alileo alilei, I. Newton, J.. agange, W. R. Hailton, and othes. Since the end of the 2th centuy, the place of classical echanics in physics has been no longe that of an independent theoy. Instead, classical echanics is now consideed an appoxiate theoy to the oe geneal quantu echanics. Classical echanics is a theoy useful fo the study of the otion of non-quantu echanical, lowenegy paticles in weak gavitational fields. In the 2st centuy classical echanics has been extended into the coplex doain and coplex classical echanics exhibits behavios vey siila to quantu echanics. Howeve, the eakable achieveents of the poinent scientists do not signify that the poble of validity of classical echanics is now copletely solved o the foundations of classical echanics ae not in need of analysis within the faewok of the coect ethodological basis: the unity of foal Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page

2 On the Coect oulation of the Stating Point of Classical echanics logic and of ational dialectics. In y opinion, classical echanics can be consideed as a coect theoy (scientific tuth) if and only if it elies on the coect ethodological basis. ut thee is no foal-logical and dialectical substantiation of classical echanics in the scientific liteatue (fo exaple, [98-]). In y opinion, the foundations of classical echanics ae not fee fo scientific objection. The pupose of this wok is to popose the citical analysis of the stating point of classical echanics. The ethodological basis fo the analysis is the unity of foal logic and of ational dialectics. 2. ETHOOOIC SIS s is known, coect ethodological basis of sciences is the unity of foal logic and of ational dialectics. Use the coect ethodological basis is a necessay condition fo coect analysis to ake distinction between tuth and falsehood. Howeve, this fact is ignoed by ajoity of scientists until now. Theefoe, the ain stateents of foal logic and of ateialistic dialectics which ae used in the pesent wok ust be stated.. The syste is a set of eleents that ae in elations and connections with each othe, foing cetain integity, unity. 2. The syste pinciple eads as follows: the popeties of the syste ae not a consequence of the popeties of its eleents; the syste deteines the popeties of the eleents; and the popeties of the eleents chaacteize the syste; 3. The stuctue (constuction, aangeent, ode) is a set of stable connections (bonds) in object, which ensues its integity and qualitative self-identity (i.e., which ensues the consevation of the basic popeties) unde diffeent extenal and intenal changes; 4. The syste analysis of ateial syste epesents a task of finding the states of the ateial syste. This task can be educed to the task of finding quantitative (tabula o analytical) elationships between the chaacteistics of the eleents of the ateial syste unde the condition of consevation of the stuctue (i.e., qualitative deteinacy) of the syste. The coect solution of the task should be based on the following pactical opeations (steps): (a) one chooses the eleent which ust be subjected to a quantitative change (i.e., to a oveent); the selected eleent undegoes the quantitative change without changing in the qualitative deteinacy of the syste; (b) one finds quantitative changes in othe eleents unde changing in the selected eleent; these changes should not lead to a change in the stuctue of the syste (i.e., to a change in the qualitative deteinacy of the syste); (c) one finds the boundaies of quantitative changes within which the syste eains identical to itself; (d) one finds the eleents which ae not changed; (e) one finds a quantitative (tabula o analytic) elationships between the values and diensions of the vaiables quantities which chaacteize eleents. Howeve, it should be ephasized that one can obtain an analytical solution of the task only in case of a siple stateent of the poble o in the case of siple systes. In these cases, an analytical solution epesents a popotion. The popotion epesents linea elationship between the elative inceents of the quantities descibing the diffeent eleents. 5. Popety is a philosophical categoy that designates such aspect of ateial object, which deteines diffeence o coonality between othe objects. Popety is one of the aspects of the given object o phenoenon. Soe popeties expess the qualitative deteinacy of the object, othes expess the quantitative deteinacy of the object; 6. Enegy is a geneal quantitative easue of the quantitative and qualitative changes unde inteactions of ateial objects. Enegy does not eege (appea, sping up) fo nothing and does not vanish (disappea; exteinate). It can only changes fo one values and fos to anothe. Vaious (diffeent) fos of enegy ae as follows: echanical, intenal, electoagnetic, cheical, nuclea and othe fos. The law of consevation of enegy eads as follows: the enegy of an isolated syste is conseved: E ( isolated syste) const. 7. Enegy is an inheent (inalienable) physical popety of ateial objects, which chaacteizes changes in the states of the ateial objects unde inteactions of ateial objects. Enegy epesents a physical quantity. Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 2

3 On the Coect oulation of the Stating Point of Classical echanics 8. The ateial object is a body, a field, a paticle, as well as a syste of bodies, of fields, of paticles. 9. Physical quantity is the unity of qualitative deteinacy and of quantitative deteinacy of a ateial object. atheatics descibes the change in the quantitative deteinacy of a ateial object (physical quantity). In tes of foal logic, atheatics does not descibe changes in qualitative deteinacy of an object.. atheatics studies the quantitative deteinacy belonging to the qualitative deteinacy of the object. In accodance with foal logic, the left-hand side and ight-hand side of the atheatical expession descibing the popety of a syste should be elate and belong to the qualitative deteinacy of this syste, i.e., (The qualitative deteinacy of the syste) = (The qualitative deteinacy of the syste). The left-hand side and ight-hand side of the atheatical expession descibing the popety of the eleent should be elate and belong to the qualitative deteinacy of this eleent, i.e. (The qualitative deteinacy of the eleent) = (The qualitative deteinacy of the eleent).. oth the quantitative and qualitative deteinacy of the object ust obey logical laws. Theefoe, accoding to the logical law of identity, the left-hand and ight-hand sides of the atheatical equation ust belong to the sae physical object (i.e. to the sae popety of the physical object o the physical odel of the object). nd, accoding to the logical law of lack (absence) of contadiction, the left-hand and ight-hand sides of the atheatical equation ust not belong to diffeent physical objects (i.e., to diffeent popeties, odels). 2. The esult of atheatical opeations on physical quantities ust have a physical eaning. Such atheatical opeations ae called adissible opeations. 3. THE STRTIN POINT O THE CORRECT OUNTION O CSSIC ECHNICS echanics is the science of the echanical oveent and inteactions of ateial bodies. The echanical inteactions epesent such actions of bodies on each othe, which lead to a change in speeds of these bodies, defoations o attactions of these bodies. Classical echanics is based on thee of Newton s laws which constitute the basis of echanics. The following questions aise: What is the cause (souce) oveent (as a change)? What ae the essential featues of the oveent as the popety of the inteaction between the ateial objects? 3.. Kineatics s is known, kineatics is the pat of echanics, devoted to the study of the geoetical popeties of the otion of ateial bodies without taking into consideation of thei asses and foces acting on the. In othe wods, kineatics studies otion of ateial bodies without taking into consideation of causes of the otion. The ain task of kineatics is the establishent (deteination) of ethods of epesentation of the otion of the ateial points o of bodies and the deteination of the elevant kineatic chaacteistics of the otions (i.e., tajectoy, speed, and acceleation of oving points; the angula velocity and the angula acceleation of the otating bodies, etc.). The otion of the ateial point can be given (epesented) by one of thee utually copleentay ways: vecto, coodinate, and tajectoy (natual) ways. The coodinate way (coodinate epesentation) is that the position of the point elative to the coodinate syste (efeence fae) is deteined by cetain thee coodinates x, y, z (i.e., by the Catesian coodinates x, y, z ) and the law of otion is given by thee equations (i.e., by x xt, y yt, z zt). If one eliinates vaiable t fo the equations, one can find the tajectoy (i.e., line in the coodinate syste) of the oving point. The tajectoy (natual) way of descibing is used if the tajectoy of the oving point elative to the coodinate syste (efeence fae) is known. The position of the given point is deteined by the distance between the efeence point selected on the tajectoy and the given point on the tajectoy (the distance is easued along the tajectoy). The law of otion is given by the equation expessing dependence of the taveled (tavesed) distance on tie: l l t. The basic kineatic chaacteistics of a oving point ae the speed and acceleation of the point. Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 3

4 On the Coect oulation of the Stating Point of Classical echanics 2. Clock C (i.e., a ateial device ceated by an) deteines tie t ; tie t chaacteizes clock C ; tie t is a popety of clock C. Tie t is the univesal infoational (i.e., non-physical) vaiable quantity [6, 3, 2, 38, 48, 49]. Theefoe, tie is not a popety of natual ateial objects. The diension of tie is second (s). If t and t ae the values of the vaiable t ae cetain points of tie), then the diffeence t t t quantity t (i.e., t and epesents the fixed inceent of the value of the vaiable quantity t fo the value t to the value t t t is the vaiable inceent of the value of the quantity t fo t. The diffeence the value t to soe othe value at that t. 3. The Catesian etic coodinate syste XOY is the etic ateial syste foed by the identical ateial scales OX and OY on the plane [5, 73, 77-8, 89, 9-94]. Scales OX and OY have the diension of ete (). The ateial point on the plane XOY epesents a ateial object. The set of possible positions (i.e., the geoetical states) of the object in the syste XOY is called geoetic space of the states of the object. (esciption of the positions of the ateial object in the syste XOY is called geoetical epesentation (coodinate epesentation) of the object ). The ateial object and the ateial syste XOY ae the independent pats of the whole. Clock C as a ateial object can be and ove in the syste XOY. The ateial object C and the ateial syste XOY ae the independent pats of the whole. ut tie t (as the popety of clock C ) does not exist in the syste XOY : t does not epesent a geoetical (ateial) object. Scale of tie does not belong to the syste XOY and does not epesent an extension of the syste XOY because tie has no diension of ete (). The quantity which has no diension of ete () cannot be gaphically epesented in the syste XOY [9-94]. In othe wods, the quantity which has no the diension of ete () does not exist in the coodinate syste XOY. 4. The positions of the ateial point (i.e., the ateial object) on the plane XOY is deteined by the coodinates (i.e., by the ateial pojections, the segents of the scales) x and y which have the diension of ete (). (Coodinate is the geoetic concept which designates cetain segent of the scale. esciption of the positions of the ateial point in the syste XOY is called geoetic epesentation (coodinate epesentation) of point ). ateial point exists in the syste XOY if and only if the coodinates of point exists in the syste XOY. Thee ae no coodinates in geneal, but thee exist only the coodinates of the ateial point. The concepts positions of ateial point on plane XOY and coodinates of ateial point on plane XOY ae identical ones. If point ove on plane XOY, then the coodinates of point ae functions of tie: x x t y y t., 5. If clock C is in syste XOY and ateial object has no effect on the clock echanis, then popety of clock C (i.e., tiet ) does not depend on the existence of object. If popety of clock C does not depend on clock positions in syste XOY, then tie t does not depend on ate of change in positions of the oving clock C in syste XOY. utheoe, tie t does not depend on the length of the path taveled by oving clock C in syste XOY. 6. If point is oved on plane XOY, then the positions of the point chaacteize the tajectoy of the point : the path (i.e., the ateial line on plane XOY ) is the locus of the positions of point. The length of the path (i.e., the length of the segent of line) taveled by point ove (fo) tie t is l t. The concepts of segent and length of line segent ae not identical ones: the segent of the line is a ateial object, and the length of the segent of the line is a denoinate (diensional) nube (i.e., popety, the quantitative deteinacy of the ateial object). The line segent exists on plane XOY, but the path length (as length of segent) do not exist on the plane XOY. In othe wods, thee ae only geoetical (i.e., ateial) objects on plane XOY : ateial points, ateial lines, and ateial figues on plane XOY. The path length Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 4

5 On the Coect oulation of the Stating Point of Classical echanics (i.e., the quantitative deteinacy of the line segent) is easued by the use of a device; easueent esults ae denoinate (diensional) nubes. In othe wods, the path length exists as a set of denoinate (diensional) nubes. The length l of the line segent has the diension of ete (), but the quantity l has no a gaphical epesentation because l is not the ateial segent of the line on plane XOY. Theefoe, the concepts length of path of point and coodinates of point ae non-identical concepts. 7. The atheatical (i.e., quantitative) quantity l has the popeties of additivity and ultiplicativity, but it is not chaacteized by the popety of diectivity on the plane XOY. The popety of additivity l l2 is geoetically (i.e., pactically) intepeted as follows: two segents of staight line having lengths l and l 2 ae coincided with the scale X ; oigin of the fist segent is coincided with the zeo point of the scale X ; the end of the fist segent is connected with the oigin of the second segent; the length of the connected segents is l l2. The popety of ultiplicativity l l2 is pactically intepeted as follows: the fist segent of staight line having length l is coincided with the scale X ; oigin of the fist segent is coincided with the zeo point of the scale X ; the second segent of staight line having length l 2 is coincided with the scale Y ; oigin of the second segent is coincided with the zeo point of the scale Y ; the aea of the ectangle constucted on these segents is l l2 ; the quantity of the aea does not exist in the syste XOY because the quantity of the aea has no the diension of ete (). 8. easue of ateial object epesents the unity of qualitative and quantitative deteinacy of object. The easue of the ateial object is invaiant unde tansfoation of coodinates. The length of path (i.e., popety of line segent, easue of line segent) is invaiant unde tansfoation of coodinates. In othe wods, the length of path is independent of choice of coodinate syste. The concepts of diection, diection of otion, and vecto in syste XOY epesent the physical concepts (i.e., qualitative deteinacy) and cannot be defined atheatically (i.e., in tes of quantity) in the syste XOY [65-68, 7-75]. In physical point of view, thee exists a diection of otion. ut, in geoetic and atheatical points of view, thee ae only line segents and nubes. The length of the line segent (length of tajectoy) is not chaacteized by a diection of otion, and the diection of otion does not deteine the length of path. (Explanation is that the atheatical foalis does not contain otion as change in geneal. Changes ae ade by an. Vecto is an illustation of diection). Thus, the path length is independent of the diection of the otion of point. 9. The quantity l t l is called inceent of the length of the path of point ove (fo) t tie t t t whee t, t is the initial tie. The quantity l t l t t Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 5 v t is ate of change in the quantity l. In othe wods, speed of otion of point is ate of change in quantity l t. (oveent is change in geneal). y definition, the speed of the otion of point is the aveage speed ove tie t. Thee is no instantaneous speed (i.e., speed at point of tie t ) [6]. The speed of the otion is the essential featue (popety, chaacteistic) of otion: speed is the ate of the change in nube. The ate of the change in the quantity l t has no a gaphical epesentation in syste XOY because the quantity of the ate has no the diension of ete (). The ate of the change in the quantity l t is not defined and is not chaacteized by any diection because the quantity l t is not defined and is not chaacteized by a diection of the otion of the point in the syste XOY. Thus, the ate of the change in the path length is independent of a diection of the otion of the point.

6 On the Coect oulation of the Stating Point of Classical echanics. The vaiable quantity v t takes on the values v t, v 2 t 2, 3 t 3 t v unde t, t2, t3, espectively. If the inteval (duation) of tie is the vaiable quantity t t, then the quantity v of the speed is a function of the aguent t t t t. The conventional concept of speed at point of tie (at instant of tie) t (o at point of plane XOY ) has no scientific and pactical sense because the speed of the otion is deteined by two (diffeent) positions of the oving point on plane XOY and by two (diffeent) points of tie: oveent is change in geneal; but thee is no change in position at point of tie t (o at point of plane XOY ).. If the speed of the otion of point depends on tie, then the quantity v t v t a is called acceleation of the point on the path length t l t t l whee v is cetain value of speed, which is expeientally t deteined. cceleation chaacteizes the otion of the point : acceleation is the essential featue (popety, chaacteistic) of the otion of point. The quantity of the acceleation of the point has no gaphical epesentation in the syste XOY because the quantity of the acceleation has no diension of ete (). The quantities l t and a ae connected by the following elationship: l t l t a 2. t 2. Coodinate systes XOY and X OY epesent the identical and utually independent systes (igue ) if: (a) the unity of qualitative and quantitative deteinacy of the syste XOY is identical with the unity of qualitative and quantitative deteinacy of the syste X OY ; (b) connection between the systes XOY and X OY is only infoation ones. In othe wods, the coodinate systes XOY and X OY ae the identical and utually independent ones if: (a) XOY and X O Y ae the inetial systes; (b) the scales X, Y and X, Y ae identical ones; (c) the chaacteistics of the clocks C and C ae identical ones; d) thee is no physical inteaction between XOY and X OY. If coodinate systes XOY and X OY ae identical ones, then the syste XOY is called esting syste, and the syste X OY is called oving syste (igue ). igue. Coodinate epesentation of oving ateial points, and O ' in the inetial systes XOY and X OY. Systes XOY and X OY epesent esting and oving systes, espectively; x ae coodinates of points. Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 6

7 On the Coect oulation of the Stating Point of Classical echanics Syste X OY is in syste XOY. In the case of one-diensional otion, syste X OY oves along the scale X. If soe ateial object is in syste X OY, then this ateial object is also in syste XOY. 3. If the identical systes XOY and X OY does not contain ateial objects, then the popeties of the clocks C and C ae identical ones: C C, t t. In this case, the points O and O ' can coincide at t t. If C C and the points O and O ' coincide at t, then t can take the value t. ut, in this case, t t unde t. If syste XOY contains ateial objects but these ateial objects have no effect on the clock C, then these ateial objects have no effect on the clock C as well: C C, t t. If ateial objects have an effect on the clock C only, then t t unde t. In this case, the systes XOY and X OY ae non-identical ones. ut this contadicts to the condition of identity of the systes XOY and X OY. Thus, the condition of identity of the systes XOY and X OY leads to the following equieent: C C, t t. This equieent epesents the equieent of siultaneity of a cetain event in the systes XOY and X OY. 4. It follows fo igue that (ength of line segent x ) = (ength of line segent O ' x ) + (ength of line segent x ' ) Whee valid: x, O ' x and x ' ae functions of tie t. In this case, the following elationships ae (ength of line segent segent x ' )/t, x l v )/t = (ength of line segent l O' V O ' v l v O ', l t l t l t, v, O ' x )/ t + (ength of line whee v is the speed of the object in the syste XOY ; v is the speed of the object in the O ' syste X OY ; V V is the speed of the elative otion of the systes XOY and X OY ; V O ' V is also the speed of the elative otion of the object in the systes XOY and X OY. These elationships epesent the coect foulation of the alilean pinciple of elativity, i.e., the pinciple of elative otion of the classical (acoscopic) objects. These O ' elationships do not ipose estictions on the values of the speeds v, v and V V. The alilean pinciple of elativity in the coodinate epesentation has the following fo: Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 7 v V O ' t x t V t x ; This elationship is called alilean tansfoation. 5. The otion of the quantu (icoscopic) objects diffes essentially fo the otion of the classical (acoscopic) objects. The pinciple of elative otion of the quantu (icoscopic) object is foulated as follows [3-7, 2, 34, 48, 49]: the tanslational otion of a fee quantu paticle is the absolute otion, i.e., the speed of the otion of a fee quantu paticle does not depend on the choice of efeence syste because a fee quantu paticle cannot be at est. In the case of light (i.e., a set of photons), this pinciple is foulated as follows: the speed of the light does not depend on the speed of the otion of the souce o eceive of the light. 6. If the systes XOY and X OY contain the utually independent physical objects and (igue ) oving with diffeent speeds, then a desciption of the otion (kineatics) of the object in the systes XOY and X OY is siila to the desciption of otion (kineatics) v V V O ' O ' V O ' V.

8 On the Coect oulation of the Stating Point of Classical echanics of the object unde the condition that the object is not a icoscopic object (fo exaple, photon). If the object epesents photon (quantu paticle, icoscopic object), then the utually independent objects (icoscopic object) and (acoscopic object) ae nonidentical ones: because these objects have diffeent qualitative deteinacy. ut this fact does not lead to violation of the condition of identity of the systes XOY and X OY because a photon has no effects on the scales X, Y, X, Y and on the echaniss of the clocks C, C. In othe wods, C C, t t also in the case of otion of photon in systes XOY and X OY. 7. The atheatical foulation of the pinciple of elative otion of photon in the systes XOY and X OY has the following fo: Whee v and v v ; v t v' t, v', v' V l l v' ae the speeds of the otion of photon in the systes XOY and X OY, espectively; l and l ae the lengths of the paths taveled by the photon in the systes XOY and X OY, espectively. These elationships have the following fo in the coodinate epesentation: x x, x v t, x v t ; v v', v' V v. Consequently, the coect foula of tansfoation of coodinates of photon in the systes XOY and X OY is as follows: x t t x. O ' The coect foula contains neithe V no t. Thus, the otion of photon (quantu paticle) obeys neithe the alilean elativity pinciple no the atheatical foulations of the oentz elativity pinciple. This eans that the oentz tansfoations epesent a logical eo [3-5,, 9, 2, 34, 38, 48, 49]. 8. s is known, the oentz tansfoations ae the esult of the following atheatical opeations: (a) Substitution of the alilean tansfoation (in standad notations), x t x t VO ' t, y y, z z ; VO ' V ; t t, Into the equation of the font of the light wave in the syste t y t z t c t X OY (in standad notations), x ; t t, Whee c is the speed of the light (photons) in the systes XOY and X OY ; (b) inding of the conditions unde which the equation of the font of the light wave in the syste X OY is tansfoed into the equation of the font of the light wave in the syste XOY, x y z c t. The founded conditions ae called oentz tansfoations and ead as follows: the equation x y z c t Is invaiant unde the oentz tansfoations. (The concept of invaiance signifies that the equation descibing the wave font has the identical fos in the systes XOY and X OY ). 9. atheatical, physical eanings and logical sense of the oentz tansfoations becoe appaent in the following siple case. If x t ct, x t ct ae the equations of the otion of the photon in the systes XOY and X OY, espectively, then the substitution of the alilean tansfoation, x t x t V t, V V O ', t t, into the equations of the otion of the photon eans that x t x t, x t x t. This substitution leads to the following standad elationships: Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 8

9 On the Coect oulation of the Stating Point of Classical echanics x V V x V t ct, ct V t ct, t t, t t. 2 c c ut, in y view [3-5,, 9, 2, 34, 38, 48, 49], the oentz tansfoations ae not fee fo the following objections. Objection., V ', t t is not In foal-logical point of view, the elationship x t x t V t V O the alilean tansfoation, x t x t V t, V V O ', because x t x t x t x t V t V, t t., V O ' Objection 2. Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 9, i.e., In atheatical point of view, the elationships (i.e., substitutions) x t x t x t x t, signify intesection of non-identical atheatical objects (i.e., equations) at any point of tie. In physical point of view, these elationships signify: (a) coincidence of the utually independent and non-identical ateial objects and (which ae oved at diffeent speeds!) at any point of tie; (b) foation of the syste (i.e., foation of bond, foation of connection, foation of the ateial unity of objects and ). In othe wods, the coincidence eans that the coincident (bonded, connected) objects and ae oved at diffeent speeds at any point of tie. ut this contadicts to actual pactice and, theefoe, foal logic. In addition, it is contay to the condition that the ateial objects and ae utually independent ones. Objection 3. y the condition, the systes XOY and X OY ae identical ones: t t. ut the substitution x t x t, x t x t, t t leads to the following elationship: V t t, t t. c This elationship contadicts to the condition of identity of the systes XOY and X OY : t t. Really, the elationship t t signifies connection of the independent ateial objects and. Thus, foal-logical eo is that the binding (connecting, conjunction) of the independent ateial objects and leads to the effect (action) on the clock C in the syste X OY and does not lead to the effect (action) on the clock C in the syste XOY. The above objections lead to the following conclusion: the standad atheatical foulation of the oentz pinciple of elativity (i.e., the oentz tansfoations) is atheatical, physical, and foal-logical eos. The only coect foulation of the pinciple of elative otion of light in the coodinate epesentation is as follows: x t x t, y t y t, z t z t, t t ; v v c. Thus, the oentz tansfoations the essence of the special theoy of elativity epesent the goss eo [3-5,, 9, 2, 34, 38, 48, 49]. Eliination of this eo leads inheently to the abolition of the special theoy of elativity ynaics s is known, dynaics is the pat of echanics devoted to the study of the otion of the bodies unde action of the foces applied to the. In othe wods, dynaics studies the otion of the ateial bodies, taking into consideation of the cause of the otion (i.e., inteaction between the bodies). The quantity of the inteaction between the bodies is easued by the use of a dynaoete. (ynaoete is the device fo easueent of foce, consisting of the foce link (elastic eleent) and easuing indicato). The basic concepts of dynaics ae ass and foce.. ass is the essential (fundaental) physical popety (essential featue) of a ateial object: ass is the aount of atte in the ateial object. The diension of the ass is kiloga (kg).

10 On the Coect oulation of the Stating Point of Classical echanics ass is an additive physical quantity. The popety of additivity of ass of ateial object is expessed by the following elationship: 2 whee and 2 ae the asses of the pats of the object. ass is not a ultiplicative quantity: ass has no ultiplicative popety. Theefoe, the expession 2 has no physical eaning and is an inadissible expession in science. 2. ass of a acoscopic object does not depend on the positions of the object in the syste XOY. Theefoe, the ass of the acoscopic object is independent of the ate of change in the positions of the object in the syste XOY. The pinciple of independence of ass of acoscopic object on the speed of the object is foulated as follows: the ass and speed of the object ae utually independent physical quantities. Thee is no logical elation between the concepts of ass and speed of object : these concepts ae incopaable ones. Theefoe, the dependence of ass on the speed of the object in the special theoy of elativity (oentz tansfoations) epesents a foal-logical eo [3-5,, 9, 2, 34, 38, 48, 49]. 3. The poduct of ass and speed of the oving object epesents the essential physical popety (essential featue) of the oving ateial object: p t v t Whee the physical quantity p t is called oentu of object. The diension of the quantity of the oentu is law of identity: kg s. This definition of the oentu satisfies the foal-logical (Popety of the oving object ) = (Popety of the oving object ). In addition, the definition of the oentu satisfies the foal-logical law of lack (absence) of contadiction: (Popety of the oving object ) (Popety of the oving object non ) 4. The ate of change in the oentu of the oving object epesents the essential physical popety (essential featue) of the otion of the ateial object. The ate of change in the oentu of the oving object is defined as follows: p t p t v t v t t p Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page t t p t t Whee p t is a cetain value of the oentu, which is deteined expeientally. The diension of the quantity of the ate of change in the oentu is a, 2 kg s. The diension 2 kg s chaacteizes the qualitative deteinacy of the quantity of ate of change in the oentu. The definition of the ate of change in the oentu of the oving object satisfies the foal-logical law of identity: (Popety of the oving object ) = (Popety of the oving object ). In addition, the definition of the ate of change in the oentu satisfies the foal-logical law of lack (absence) of contadiction: (Popety of the oving object ) (Popety of the oving object non ) 5. The inteacting ateial objects epesent a syste. oce is the cause of changes in the syste. oce is an essential physical popety (essential featue, chaacteistics) of the ateial inteaction of the objects. oce is a physical popety of the stuctue (i.e., of the ateial connection of the eleents) of the syste. The qualitative deteinacy of the stuctue (i.e., of the ateial connection) is not identical with the qualitative deteinacy of the eleents of the syste.

11 On the Coect oulation of the Stating Point of Classical echanics Theefoe, the popety of the stuctue (i.e., the popety of the ateial connection) is not identical with the popety of any eleent of the syste. In othe wods, foce (as the popety of the ateial connection between of the inteacting objects) does not epesent a popety of the inteacting objects. The quantity of foce is easued by the use of a dynaoete and has the diension of kiloga-foce (kgf). The diension of kiloga-foce (kgf) chaacteizes the qualitative deteinacy of foce (i.e., of the stuctue of the syste). The diension of kilogafoce (kgf) is the univesal and independent diension of foce: this diension does not depend on the type of inteaction and cannot be educed to anothe diension. 6. If: (a) two ateial objects N, and ateial connection between objects N, (i.e., connects objects N and ) epesent the syste S N (whee the popety of the ateial connection is deteined (easued) by a dynaoete); (b) the objects N, inteact in such a way that the object N is the cause of the otion of the object at an acceleation a, then the elationship between the foce (which is easued by the use of a dynaoete) and acceleation Whee quantity a a epesents the following popotion: a a a is a cetain value of vaiable quantity a, i.e.,, a a, which is the eading of the dynaoete; the chaacteizes the stuctue of the syste and has the diension of kgf ; the quantity a chaacteizes the eleent of the syste and has diension of 2 kg s. The 2 diensions of kgf and kg s chaacteizing the stuctue and eleent of the syste have diffeent qualitative deteinacy and ae non-identical ones: (Qualitative deteinacy of foce) (Qualitative deteinacy of ate of change in oentu) Theefoe, the concept of foce does not epesent the syste of concepts of kiloga, ete, and squae second. In othe wods, the concept of foce and the concept of ate of change in oentu ae in conflict with each othe. 7. The coect elationships between quantity of foce and soe othe physical quantities (such as length, ass, speed of ateial object) epesent the popotions by quantity of foce and soe othe physical quantities: l l v v Thus, foce is a popety of the ateial stuctue of the syste of the ateial eleents (ateial objects). This popety of stuctue does not depend on the popeties of the eleents of the syste. 8. oce as a popety of the ateial connection of the eleents of the syste of the inteacting objects can be depicted as follows: l v,,. igue2. Illustation of the ateial stuctue of the syste of the inteacting ateial objects N and. The foce of the inteaction is a popety of the stuctue (i.e., the popety of the connection of the objects N and ). The aows depict the diections of the foce. Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page

12 On the Coect oulation of the Stating Point of Classical echanics The foce of the inteaction between two objects N and is depicted as staight-line segent with two aows at the endpoints. The two aows show (indicate) the diections of the foce. The endpoints of the segent epesent the two points of application (apposition) of the foce of the inteaction: one end shows (indicates) the point of application (apposition) of the foce to the object N, the othe end shows (indicates) the point of application (apposition) of the foce to the object. The segent with only one point of application (apposition) of foce and with only one aow does not epesent foce in geneal and the foce of the inteaction because such segent has no physical eaning: foce is always the foce of the inteaction. In othe wods, the inteaction foce is a single foce, N N ( int eaction ), (action) Which cannot be decoposed into two independent (opposite) coponents: the action foce ( counteact ion) and the counteaction foce. The action foce does not exist without the counteaction foce; the counteaction foce does not exist without the action foce. atheatical expession N N Signifies the coplete exteination (o absence) of the inteaction foce, i.e., ( inteaction ). Theefoe, the standad elationship ( action) ( counteact ion) Repesents an eo. 9. In the dialectical point of view, the foce of the inteaction of the ateial objects N and epesents the unity of opposite aspects: action and counteaction. The unity of opposites does not ean the identity of opposites because opposites have diffeent qualitative deteinacy.. In foal-logical point of view, the concepts of action and counteaction ae dissenting concepts. Thee ae no elation of identity, elation of subodination, and elation of patial coincidence between these concepts. The logical elation between the concepts of action and counteaction is the elation of disageeent: one concept eliinates anothe concept; both the concepts cannot be applied to the sae objects. (o exaple, the concept of action chaacteizes the active object N, the concept of counteaction chaacteizes counteacting object ). These concepts ae subodinate and contadictoy ones: the scopes (volues) of these two concepts ente into the scope of anothe oe geneal concept of inteaction as a unity of opposites. Theefoe, the concepts of action and counteaction ae connected by the foal-logical law of lack (absence) of contadiction: The elationship (ction) (Counteaction) N Satisfies the foal-logical law of identity: Consequently, the standad assetion that N ( inteaction) (Inteaction foce) = (inteaction foce). (ction foce) = (inteaction foce) Repesents violation of the foal-logical law of lack (absence) of contadiction. Thus, Newton's doctine of foce is incoect. Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 2

13 On the Coect oulation of the Stating Point of Classical echanics 3.3. The aw of avitational Inteaction If inteaction between ateial objects and epesents the gavitational inteaction, then one ust conside the coplete syste S (igue 3) within the faewok of the syste appoach (i.e., within the faewok of the unity of foal logic and of ational dialectics). igue3. The gavitational inteaction of the acoscopic objects and. ateial objects and ae the gavitational fields of the objects and ; ateial object (shaded egion) is the egion of the ovelap of the gavitational fields and. The syste analysis consists in the following steps: detection of the eleents of the syste; detection of the connections between the eleents; and finding of elationships between the physical quantities chaacteizing eleents and connections.. Physical quantities elating to igue 3 ae defined as follows: (a) The acoscopic ateial objects and syste S ; (b) is the distance between acoscopic objects and ; (c) The acoscopic ateial objects and, espectively; (d) and and ae the adii of the gavitational fields epesents the eleents of the coplete ae the gavitational fields of the objects and, espectively; (e) The elationship is a necessay condition fo the gavitational inteaction; (f) The acoscopic ateial object (i.e., the shaded egion) epesents the egion of the ovelap of the gavitational fields and ; (g) is the stuctue of the syste; (in othe wods, the objects and ); (h) is a caie of the gavitational inteaction (the foce inteaction); is the ateial eleent which connects (i) The foce of the inteaction is a popety of the stuctue. 2. The elationships between the physical quantities chaacteizing eleents and connections in the coplete syste S can be defined in the following heuistic way: a) The foce inteaction between the ateial objects and exist if foce inteaction between the ateial objects and do not exist if Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 3 ; ; the

14 On the Coect oulation of the Stating Point of Classical echanics b) ass is a popety (attibute) of the gavitational field; the gavitational fields chaacteized by the asses and ; and ae c) The asses and of the gavitational fields and the asses and of the objects and, espectively; d) The ass of the egion of ovelap of the gavitational fields popotional to the su : e) The ass ; inceases unde decease of the distance : exp. ae diectly popotional to and is diectly (Reak: Invese popotional function y x is not anifested (i.e., gaph does not exist) in the etical syste XOY because y has no diension of length ( ete ) if x have the diension of length ( ete ) [89-94]. In addition, y is an unbounded function which has no physical eaning); f) The foce of the gavitational inteaction is diectly popotional to the ass : 3. Within the faewok of the syste appoach, the heuistic assetions lead to the following syste of thee popotions: ; ; exp exp exp, Whee: is a cetain value of the foce of the gavitational inteaction; is a cetain value of the ass of the egion and of the gavitational inteaction; ae cetain values of the asses of the objects and, espectively; is a cetain value of the distance between the objects and ; and espectively. ae cetain values of the adii of the gavitational fields of the objects and Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 4

15 On the Coect oulation of the Stating Point of Classical echanics Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 5 These values of the physical quantities ae deteined expeientally. The syste of the popotions epesents a syste of utually copleentay elationships which satisfy the foal-logical and dialectical laws. 4. The syste of the popotions leads to the following syste of thee utually copleentay (utually additional) atheatical foulations of the law of gavitation:,, exp exp. The law of gavity can be expessed in the following equivalent fo:,, exp exp. (Reak: The syste of the popotions is analogous (but not identical) to the following diffeential fo: R d R d R d R, Whee, R ae the aguents of the function R,. The diffeence between the diffeential fo and the syste of the popotions is that the diffeential and integal calculus is a false theoy [52-55, 57, 6, 89, 9-94]). 5. s is well known, the epiical foulation of Newton s law of gavitation is as follows: 2

16 On the Coect oulation of the Stating Point of Classical echanics Whee is the gavitational constant. ut Newton s foulation is not fee fo the following objections: does not epesents a popety (featue) of ateial object; in accodance with pactice, ass of an object is a additive (not ultiplicative) quantity; a) The quantity has no physical eaning because: the quantity b) Quantities and 2 ae not anifested (i.e., gaph does not exist) in the etical syste XOY [89-94] because these quantities have no diension of length ( ete ); quantity 2 is an aea of the suface of non-existent ateial object. (What is this ateial object?). ut the aea of a suface does not chaacteize a distance. Thus, Newton s law of gavitation is incoect because it does not satisfy the foal-logical and dialectical laws 4. ISCUSSION. s is known, foal logic is the geneal science of the laws of the coect thinking, thought. The laws of foal logic epesent the theoetical genealization and eflection of pactice in the huan consciousness. Consequently, foal logic exists in the huan consciousness and pactice. Pactice is a citeion of validity (tueness, tuth) of foal logic. 2. ialectical ateialis is the geneal science of the ost coon (geneal) kinds of connections and the laws of developent of natue, of huan society, and of thinking, thought. The laws of dialectics epesent the theoetical genealization and eflection of pactice in the huan consciousness. Consequently, dialectics exists in the huan consciousness and pactice. Pactice is a citeion of validity (tueness, tuth) of dialectics. 3. The only coect ethodological basis of sciences is the unity of foal logic and of ational dialectics. Theoetical physics and atheatics ae sciences if and only if its foundations ae foulated within the faewok of the coect ethodological basis. 4. s is well known, science oiginated in the ancient wold in connection with the equieents of social pactice and had quick developent since 6-7-th ages. In the couse of histoical developent, science changed into a poductive foce and into the ost ipotant social institution which has a significant ipact on all sphees of society. Today, science is a huge sphee of huan activity aied at obtaining new knowledge and theoetical systeatization of objective knowledge about eality. Su of objective knowledge undelies the scientific pictue of the wold. The scientific pictue of the wold plays an ipotant wold-outlook ole in the developent of the huan society. 5. Science is developed in the inductive way, i.e., in the way of negation of negation. Theefoe, the extensive and evolutionay peiods ae altenated in the developent of science. The scientific evolutions lead to a change in the stuctue of science, in the cognition pinciples, in the categoies and ethods, as well as in the fos of oganization of science. 6. Inevitability of the scientific evolutions fo the fist tie was ephasized by. Einstein: pogess of science will be the cause of evolution in its foundations. lso, the following stateent is tue: the citical eassessent of the standad foundations of science leads to the pogess of science. These aspects in developent of science ae chaacteized, fo exaple, by. Einstein s wods: Thee has been foed the notion that the foundations of physics wee finally established and the wok of a theoetical physicist should be to bing a theoy in coespondence with all the tie inceasing abundance of the investigated phenoena. Nobody thought that a need fo adical ebuilding of the foundations of all physics could aise. Ou notions of physical eality neve can be final ones. t pesent, the validity of Einstein s assetion is confied by the poo states of sciences. 7. In this connection, the poble of citical analysis of the foundations of theoetical physics and of atheatics within the faewok of the coect ethodological basis (i.e., the unity of foal logic and of ational dialectics) aises. This ethodological basis epesents the syste of logical Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 6

17 On the Coect oulation of the Stating Point of Classical echanics laws and of geneal-scientific ethods of cognition of eality: obsevation and expeient, analysis and synthesis, induction and deduction, analogy and hypothesis, logical and histoical aspects, abstaction and idealization, genealization and liitation, ascension fo concete concepts to abstact concepts, copaison, odeling, etc. 8. The necessity of application of geneal-scientific ethods fo the citical analysis of theoetical physics and of atheatics is also stipulated by the fact that the foundations of theoetical physics and of atheatics contain vagueness which cannot be clea copehend and foulated in the standad physical and atheatical tes because physics and atheatics do not contain any univesal (geneal-scientific, philosophical) concepts; oeove, oigin of vagueness is often anifestation of thoughtless use of atheatics (. oltzann). In this case, foal-logical eos exist and coe into atheatics and natual-scientific theoies so fa. In y opinion, the eos in theoetical physics and atheatics ae the inevitable consequence of the inductive ethod of cognition. This gives possibility to elicit, to eveal, to ecognize eos done by the geat scientists of the past tie. eletion of the eos leads to the abolishent (eliination) of a set of standad theoies. ut even the istakes done by the geat scientists contibute to pogess in science: false hypotheses often endeed oe sevices than the tue ones (H. Poincae) because istakes extend the consciousness of scientists. Such is the dialectics of tuth and of lie in science. Today this fact signifies that one should call the geat scientific achieveents in question within the faewok of the coect ethodological basis: the unity of foal logic and of ational dialectics. 5. CONCUSION Thus, the coect scientific analysis of the geneally accepted foundations of classical echanics is possible only within the faewok of the coect ethodological basis: the unity of foal logic and of ational dialectics. The esults of the scientific-citical analysis ae as follows.. The following coect stating point of kineatics is poposed: a) The concept of tie: tie does not epesent a physical o geoetical quantity; tie is the independent infoation quantity; a clock deteines tie; tie chaacteizes a clock; b) The concept of otion of the ateial point in the geoetical syste of coodinates: otion of the ateial point in the geoetical syste of coodinates is changes in the positions (states) of the ateial point in the geoetical syste of coodinates; the concepts of diection, diection of otion, and vecto epesent the physical concepts and cannot be defined atheatically o geoetically; c) The concept of speed of paticle in the geoetical syste of coodinates: the speed of the ateial point is the aveage ate of change in the length of the path taveled by ateial point fo a cetain inteval of tie; the speed at a cetain point of tie o at a cetain point of coodinate syste is an inadissible concept because thee is no otion of paticle at a cetain point of tie o at a cetain point of coodinate syste; d) The concept of acceleation of ateial point in the geoetical syste of coodinates: the acceleation of the ateial point is the aveage acceleation ove a cetain inteval of tie; e) The concept of inetial systes of coodinates: the inetial geoetical systes of coodinates ae the identical systes; ate of clocks in the identical systes does not depend on the speed of the elative otion of the systes of coodinates; f) The pinciple of otion of quantu paticle (photon): the otion of the quantu paticle (photon) is the absolute otion, i.e., the otion of the quantu paticle (photon) does not depend on the speed of the elative otion of systes of coodinates; the otion of the photon in the inetial geoetical systes does not obey the oentz pinciple of elativity; oentz tansfoations the essence of the special theoy of elativity epesent the atheatical, physical, and foal-logical eos. 2. The following coect stating point of dynaics is poposed: a) the pinciple of independence of the ass of the object on the acoscopic speed of the object: the ass of the acoscopic object does not depend on the positions of the object in the geoetical syste of coodinates; consequently, the ass of the acoscopic object is independent of the speed Intenational Jounal of dvanced Reseach in Physical Science (IJRPS) Page 7