Eos in Nobel ize fo hysics (3) Conseation of Enegy Leads to obability Conseation of aity, Momentum and so on Fu Yuhua (CNOOC Reseach Institute, E-mail:fuyh945@sina.com) Abstact: One of the easons fo 957 Nobel ize fo physics is fo thei penetating inestigation of the so-called paity laws which has led to impotant discoeies egading the elementay paticles. While the concepts of paity laws (law of conseation of paity and law of nonconseation of paity) ae questionable. Fo the expeiment of Chien-Shiung Wu et al in 957, the coect way of saying should be that the pobability of conseation of paity is 7% and the pobability of nonconseation of paity is only 9%. The essential eason fo the phenomena of nonconseation (including nonconseation of paity, momentum, angula momentum and the like) is that so fa only the law of conseation of enegy can be consideed as the unique tuth in physics. As fo othe laws, they ae coect only in the cases that they ae not contadicted with law of conseation of enegy o they can be deied by law of conseation of enegy; othewise thei pobability of coectness should be detemined by law of conseation of enegy o expeiment (cuently fo the most cases the coectness can only be detemined by expeiment). Conclusion: besides law of conseation of enegy, all othe laws of conseation in physics may not be coect (o thei pobabilities of coectness ae all less than %). Discussing the examples that law of conseation of momentum and law of conseation of angula momentum ae not coect (thei esults ae contadicted with law of conseation of enegy). In addition, the essential shotcomings of special elatiity and geneal elatiity ae caused fom the eason that law of conseation of enegy was not consideed at the established time of these two theoies; theefoe thei esults will appea the examples contadicted with law of conseation of enegy, and in the aea of geneal elatiity the attempt to deie the coect expession of enegy will nee be success. Finally the examples deiing the impoed Newton's second law and impoed law of gaity accoding to law of conseation of enegy ae discussed, which show the geat potentiality of law of conseation of enegy, and giing full play to the ole of law of conseation of enegy will completely change the situation of physics. Key wods: Weak inteaction, conseation of paity, nonconseation of paity, nonconseation of momentum, nonconseation of angula momentum, pobability, law of conseation of enegy, unique tuth, expession of enegy, impoed Newton's second law, impoed law of gaity Intoduction The impotance of law of conseation of enegy is fa fom being fully undestood, and its geat potentiality is fa fom being fully ealized.
One of the easons fo 957 Nobel ize fo physics is fo thei penetating inestigation of the so-called paity laws which has led to impotant discoeies egading the elementay paticles. Why is the paity nonconseation? The essential eason fo this is that so fa only the "law of conseation of enegy" will be qualified to become the unique tuth in physics. Not only we cannot poe that "law of conseation of paity" is not contadicted with law of conseation of enegy, but also cannot poe that "law of conseation of paity" can be deied fom law of conseation of enegy, so the so-called "law of conseation of paity" is not coect. Similaly, the so-called law of conseation of momentum and law of conseation of angula momentum ae not coect (o thei pobabilities of coectness ae less than %). By extension, all the physical laws that cannot be deied fom law of conseation of enegy ae pobably not coect (o thei pobabilities of coectness ae less than %). Fo example, the special elatiity and geneal elatiity ae not coect (o thei pobabilities of coectness ae less than %) fo the eason that law of conseation of enegy was not consideed at the established time of these two theoies. Othewise, all laws that can be deied fom law of conseation of enegy ae coect. Fo example, the impoed Newton's second law and impoed law of gaity can be deied fom law of conseation of enegy. Detemine the pobabilities of conseation of paity and nonconseation of paity accoding to the expeiment of Chien-Shiung Wu et al in 957 In the expeiment of Chien-Shiung Wu et al in 957, they found that the numbe of the electons that exiting angle θ>9 is 4% moe than that of θ<9. Fo this esult, we cannot simply say that paity is conseation o nonconseation. The coect way of saying should be that the pobability of conseation of paity is 7% and the pobability of nonconseation of paity is only 9%. Similaly, the pobabilities of coectness fo othe laws of conseation should be detemined by law of conseation of enegy o expeiment (cuently fo the most cases the coectness can only be detemined by expeiment). Examples that the law of conseation of momentum and law of conseation of angula momentum ae not coect In efeence [], an example is pesented in which the law of conseation of momentum and law of conseation of angula momentum ae not coect (the esults ae diectly contadicted with law of conseation of enegy). Hee we pesent the eason that the law of conseation of momentum and law of conseation of angula momentum ae not coect in anothe way. As well-known, in many cases, the law of conseation of momentum and law of conseation of angula momentum can be deied accoding to the oiginal Newton's second law. Howee, in efeences [] and [3], we hae pointed out that in some cases the oiginal Newton's second law is not coect, and the impoed Newton's second law F ma is needed to be applied. In this case, the law of
conseation of momentum and law of conseation of angula momentum ae no longe coect. Hee, because the impoed Newton's second law is deied accoding to the law of conseation of enegy expot, so we can say that based on the impoed Newton's second law, the esults of law of conseation of momentum and law of conseation of angula momentum ae indiectly contadicted with the law of conseation of enegy. 3 Example that elatiity theoy is contadicted with law of conseation of enegy The essential shotcomings of special elatiity and geneal elatiity ae caused fom the eason that law of conseation of enegy was not consideed at the established time of these two theoies; theefoe thei esults will appea the examples contadicted with law of conseation of enegy. Fo example, accoding to elatiity theoy, an object s speed cannot each the speed of light. Howee, based on law of conseation of enegy, when the speed of an object is close o equal to the speed of light, fo beaking the light baie, the speed of this object could be faste than light as it passes though the Sun s gaitational field. Figue. An object passes though the Sun's gaitational field at the speed of light As shown in Figue, an object passes though the Sun's gaitational field at the speed of light fom the infinite distance, assuming that its closest distance to the Sun is equal to, if the obit of this object will be tangent to the Sun, then is equal to the adius of the Sun. Ty to decide this object s maximum speed max as its distance to the Sun is equal to. Fo this poblem, in efeence [3], the impoed law of gaity eads.5 F () 4 Fo the eason that, as the object is located at the infinite distance, and the closest distance to the Sun, the enegies should be equal, so we hae
It gies mc. 5 mmax max c GM / 3 () Obiously this speed is faste than the speed of light, if the obit of this object will be tangent to the Sun, afte calculating it gies 6 ( 3.8 )c (A) max In addition, in the aea of geneal elatiity the attempt to deie the coect expession of enegy will nee be success. Einstein could not deie this expession of enegy, othe people also cannot deie it. 4 Deiing the impoed Newton's second law and impoed law of gaity accoding to law of conseation of enegy Now fo an example, we simultaneously deie the impoed Newton's second law and impoed law of gaity accoding to law of conseation of enegy, and it should be noted that they ae suitable fo this example only. Fistly, the aiational pinciples established by the law of conseation of enegy can be gien with least squaes method (LSM). Supposing that the initial total enegy of a closed system equals W (), and fo time t the total enegy equals W (t), then accoding to the law of conseation of enegy: W () = W (t) (3) This can be witten as: W( t) R W= W() (4) Accoding to LSM, fo the inteal [ t,t aiational pinciple: t ], we can wite the following R Wdt min (5) t whee: min denotes the minimum alue of functional Π and it should be equal to zeo. It should be noted that, in many cases W (t) is appoximate, and R W is not identically equal to zeo, theefoe Eq.(5) can be used to sole the poblem.
Besides the time coodinate, anothe one can also be used. Fo example, fo inteal [ x, x ], the following aiational pinciple can be gien accoding to the law of conseation of enegy: x x R W dx min (6) The aboe-mentioned pinciples ae established by using the law of conseation of enegy diectly. Sometimes, a cetain pinciple should be established by using the law of conseation of enegy indiectly. Fo example, a special physical quantity Q may be inteested,not only it can be calculated by using the law of conseation of enegy, but also can be calculated by using othe laws (fo this pape they ae the law of gaity, and Newton s second law). Fo distinguishing the alues, let s denote the alue gien by othe laws as Q,while denote the alue gien by the law of conseation of enegy as Q ',then the alue of R W can be edefined as follows: Q R W = Q' (7) Substituting Eq.(7)into Eqs.(5)and(6),as Q ' is the esult calculated with the law of conseation of enegy, it gies the aiational pinciple established by using the law of conseation of enegy indiectly. Othewise, it is clea that the extent of the alue of Q accods with Q '. Substituting the elated quantities into Eq.(5)o Eq.(6),the equations deied by the condition of an extemum can be witten as follows: a i k i (8) Afte soling these equations, the impoed law of gaity, and Newton s second law can be eached at once. Accoding to the alue of Π, the effect of the solution can be judged. The neae the alue of Π is to zeo, the bette the effect of the solution. It should be noted that besides of soling equations, optimum-seeking methods could also be used fo finding the minimum and the constants to be detemined. In fact, the optimum seeking method will be used in this pape. Now we sole an example. As shown in Fig., supposing that the small ball olls along a long incline fom A to B. Its initial elocity is zeo and the fiction and the otational enegy of small ball ae neglected. Fig. A small ball olls fom A to B Supposing that cicle O ' denotes the Eath, M denotes its mass; m denotes the mass of the small ball (teated as a mass point ), O A is a plumb
line, coodinate x is othogonal to O A, coodinate y is othogonal to coodinate x (paallel to O A), BC is othogonal to O A. The lengths of OA, OB, BC, and AC ae all equal to H, and O C equals the adius R of the Eath. In this example, the alue of which is the squae of the elocity fo the ball located at point is inestigated. To distinguish the quantities, denote the alue gien by the impoed law of gaity and impoed Newton s second law as,while denotes the alue gien by the law of conseation of enegy,then ' Eq.(6)can be witten as H ( ' ) dx min (9) Supposing that the impoed law of gaity and impoed Newton s second law can be witten as the following constant dimension factal foms F () D F ma () whee: D and ae constants. Now we calculate the elated quantities accoding to the law of conseation of enegy. Fom Eq.(), the potential enegy of the small ball located at point is V () ( D) D O ' Accoding to the law of conseation of enegy, we can get ( D ) D O' A m' ( D ) D O ' (3) And theefoe GM ' [ ] (4) D D D ( R H) O' Now we calculate the elated quantities accoding to the impoed law of gaity and impoed Newton s second law. Supposing that the equation of olling line is y x H (5) Fo the ball located at point, d/ dt a (6) because dt ds dx theefoe d a dx (7)
Accoding to the impoed law of gaity, the foce along to the tangent is Fa (8) D O ' Accoding to the impoed Newton s second law, fo point, the acceleation along to the tangent is Fa GM a ( ) ( ) (9) m Fom Eq.(7), it gies / / D O ' GM / d { } dx () D/ [( H x) ( R H y) ] Substituting Eq.(5) into Eq.(), and fo the two sides, we un the integal opeation fom A to, it gies x GM / / { } ( ) dx D / [( H x) ( R x) ] () H then the alue can be calculated by a method of numeical integal. The gien data ae assumed to be: fo Eath, GM=3.99 4 m 3 /s ; the adius of the Eath R=6.37 6 m, H=R/, ty to sole the poblem shown in Fig., find the solution fo the alue of B,and deie the impoed law of gaity and the impoed Newton s second law. Fistly, accoding to the oiginal law of gaity, the oiginal Newton s second law (i.e., let D = in Eq.(), = in Eq.()) and the law of conseation of enegy, all the elated quantities can be calculated, then substitute them into Eq.(9), it gies =57.45 Hee, accoding to the law of conseation of enegy, it gies ' B =.767 7, while accoding to the oiginal law of gaity, and the oiginal Newton s second law, it gies B =.35 7,the diffeence is about 5.4 %. Fo the eason that the alue of Π is not equal to zeo, then the alues of D and can be decided by the optimum seeking method. At pesent all the optimum seeking methods can be diided into two types, one type may not depend on the initial alues which pogam may be complicated, and anothe type equies the bette initial alues which pogam is simple. One method of the second type, namely the seaching method will be used in this pape. Fistly, the alue of D is fixed so let D =,then seach the alue of,as =.46, the alue of Π eaches the minimum 39.349;then the alue of is fixed,and seach the alue of D,as D =.99989, the alue of Π eaches the minimum 37.338;then the alue of D is fixed,and seach the alue of,as =.458, the alue of Π eaches minimum 37.33. Because the last two esults ae highly close, the seaching can be stopped, and the final esults ae as follows D=.99989,ε=.458, =37.33 Hee the alue of Π is only 4% of Π. While accoding to the law of conseation of enegy, it gies ' B =.785 7,accoding to the impoed law of
gaity and the impoed Newton s second law, it gies B =.73 7, the diffeence is about.7 % only. The esults suitable fo this example with the constant dimension factal fom ae as follows The impoed law of gaity eads F ().99989 The impoed Newton s second law eads.458 F ma (3) The aboe mentioned esults hae been published on efeence []. Accoding to the esults fo the example shown in Fig., it can be said that we could not ely on any expeimental data, only apply the law of conseation of enegy to deie the impoed law of gaity, and impoed Newton's second law; and demonstate that the oiginal Newton s law of gaity and Newton's second law ae all tenable appoximately fo this example. So, can only apply the law of conseation of enegy to deie that these two oiginal laws o demonstate they ae tenable accuately in some cases? The answe is that in some cases we can indeed deie the oiginal Newton's second law and poe the oiginal Newton s law of gaity is tenable accuately. Now, in the case that a small ball fee falls (equialent to fee fall fom A to C in Fig. ), we deie the oiginal Newton's second law and poe the oiginal Newton s law of gaity is tenable accuately. Assuming that fo the oiginal law of gaity and Newton's second law, the elated exponents ae unknown, only know the foms of these two fomulas ae as D' follows: F, F ma ; whee: D and D ae undetemined constants. D As shown in Fig., supposing that a small ball fee falls fom point A to point C. Simila to the aboe deiation, when the small ball falls to point (point is not shown in Fig.), the alue of calculated by the undetemined Newton's second law and the law of gaity, as well as the alue of ' calculated by the law of conseation of enegy ae as follows: GM [ D D ( R H) ' D O' ] y p / D' ( GM ) ( R H y) D / D' dy ( GM ) / D ' { [( R H y) D / D' D / D' ] y p }
/ D' ( GM ) [ ( D / D' ) ( D / D') O' ( R H) ( D / D') ] Let, then we should hae: / D', and D ( D / D') ; these ' two equations all gie: D ', this means that fo fee fall poblem, by using the law of conseation of enegy, we stictly deie the oiginal Newton's second law F ma. Hee, although the oiginal law of gaity cannot be deied (the alue of D may be any constant, cetainly including the case that D=), we aleady poe that the oiginal law of gaity is not contadicted to the law of conseation of enegy, o the oiginal law of gaity is tenable accuately. Fo the example shown in Fig. that a small ball olls along the inclined plane, in ode to obtain the bette esults, we discuss the aiable dimension factal solution with Eq.(4) that is established by the law of conseation of enegy diectly. Supposing that the impoed Newton s second law and the impoed law of gaity with the fom of aiable dimension factal can be witten as follows: F ma, k u ; F /, k u ; whee: u is the hoizon distance that the small ball olls ( u x H ). With the simila seaching method, the alues of k, k can be detemined, and the esults ae as follows 8 3 8.85 u,.7 u The esults of aiable dimension factal ae much bette than that of constant 4 dimension factal. Fo example, the final Π 5.866, it is only.9% of Π (3.7). While accoding to the law of conseation of enegy, it gies ' B =.767 7, accoding to the impoed law of gaity and the impoed Newton s second law, it gies B =.777 7, the diffeence is about.93 % only. The esults suitable fo this example with the aiable dimension factal fom ae as follows The impoed law of gaity eads (4) F 3.7 u The impoed Newton s second law eads 8 8.85 u F ma (5) whee: u is the hoizon distance that the small ball olls ( u x H ) Thee is anothe poblem should also be discussed. That is the impoed kinetic enegy fomula. As well-known, the kinetic enegy fomula has been modified in the theoy of elatiity, now we impoe the kinetic enegy fomula with the law of conseation of enegy. Supposing that the impoed kinetic enegy fomula is m Ed,
k 3 u ;whee: u is the hoizon distance that the small ball olls ( u x H ). 3 With the simila seaching method, we can get: k 3 9.95, then the impoed kinetic enegy fomula with aiable dimension factal fom eads 3 9.95 u E d m Because the effect of impoement is ey small (the alue of Π is only impoed fom 5.866 4 into 5.8634 4 ), theefoe these esults should be fo efeence only. 5 Conclusions In this pape, we econside the poblems about conseation of paity and nonconseation of paity with a new iewpoint. Fo the expeiment of Chien-Shiung Wu et al in 957, the new conclusion is that the pobability of conseation of paity is 7% and the pobability of nonconseation of paity is only 9%. We point out that, besides law of conseation of enegy, all othe laws of conseation in physics may not be coect (o thei pobabilities of coectness ae all less than %). So fa, because only the law of conseation of enegy can be qualified to become the unique tuth in physics, theefoe fo all the theoies and laws in physics (including the elatiity theoy, law of gaity, Newton's second law, law of conseation of momentum, law of conseation angula momentum, so-called paity laws, and so on), we should e-examine thei elations with law of conseation of enegy. In fact, many theoies and laws (such as impoed Newton's second law and impoed law of gaity) can be deied accoding to law of conseation of enegy, which show the geat potentiality of law of conseation of enegy, and giing full play to the ole of law of conseation of enegy will completely change the situation of physics. In addition, in a moe wide ange, the law of conseation of enegy can be used to deal with all the poblems elated to enegy in physics, astonomy, mechanics, engineeing, chemisty, biology, and the like with a unified way. Refeences Fu Yuhua, Science of Conseation of Enegy. Jounal of Dezhou Uniesity. 4(6):-4 Fu Yuhua, Deiing Impoed Newton s Second Law and the Law of Gaity at One Time with Fom of Factal Fomula, Engineeing Science. 3,Vol.5,No.6,55-58 3 Fu Yuhua. Shotcomings and Applicable Scopes of Special and Geneal Relatiity. See: Unsoled oblems in Special and Geneal Relatiity. Edited by: Floentin Smaandache, Fu Yuhua and Zhao Fengjuan. Education ublishing, 3. 8-3