Errors in Nobel Prize for Physics (7) Improper Schrodinger Equation and Dirac Equation

Transcription

1 Errors n Nobel Prze for Physcs (7) Improper Schrodnger Equaton and Drac Equaton u Yuhua (CNOOC Research Insttute, E-mal:fuyh945@sna.com) Abstract: One of the reasons for 933 Nobel Prze for physcs s for the dscovery of new productve forms of atomc theory (namely Schrodnger equaton and Drac equaton). hle, ths paper ponts out that Schrodnger equaton and Drac equaton are mproper. Accordng to Neutrosophy, Schrodnger equaton and Drac equaton have three stuatons of truth, falsehood and ndetermnacy respectvely. Three reasons lead to Schrodnger equaton and Drac equaton are mproper: frstly, they are not derved by the prncple of conservaton of energy; secondly, the random (stochastc) concept could lead to absurd results; thrdly, they cannot solve many problems such as gravtaton. Applyng "partal and temporary unfed theory of natural scence so far" ncludng all the equatons of natural scence so far (n whch, the theory of everythng to express all of natural laws, descrbed by Hawkng that a sngle equaton could be wrtten on a T -shrt, s partally and temporarly realzed n the form of "partal and temporary unfed varatonal prncple of natural scence so far"), ths paper presents "partal and temporary unfed theory of quantum mechancs so far", ths unfed theory can be used to make Schrodnger equaton and Drac equaton tend to be proper (makng Schrodnger equaton and Drac equaton are restrcted (or constraned) by prncple of conservaton of energy, and thus they can satsfy the prncple of conservaton of energy; also makng they are restrcted (or constraned) by a certan gravtatonal theory, and establsh "partal and temporary unfed theory of quantum-gravtaton so far"). Key words: Schrodnger equaton, Drac equaton, mproper, prncple of conservaton of energy, partal and temporary unfed theory of natural scence so far, partal and temporary unfed theory of quantum mechancs so far, partal and temporary unfed theory of quantum-gravtaton so far Introducton In quantum mechancs, Schrodnger equaton and Drac equaton are two very mportant basc equatons. One of the reasons for 933 Nobel Prze for physcs s for the dscovery of new productve forms of atomc theory (namely Schrodnger equaton and Drac equaton). hle, ths paper ponts out that Schrodnger equaton and Drac equaton are mproper. Accordng to Neutrosophy (more nformaton about Neutrosophy may be found n references [, ]), all propostons (ncludng Schrodnger equaton and Drac equaton) have three stuatons of truth, falsehood and ndetermnacy respectvely. In whch the stuatons of falsehood and ndetermnacy lead to that Schrodnger equaton and Drac equaton are mproper. Applyng "partal and temporary unfed theory of natural scence so far" ncludng all the equatons of natural scence so far (n whch, the theory of everythng to express all of natural laws, descrbed by Hawkng that a sngle equaton could be wrtten on a T-shrt, s

2 partally and temporarly realzed n the form of "partal and temporary unfed varatonal prncple of natural scence so far"), we can make Schrodnger equaton and Drac equaton tend to be proper. Schrodnger equaton and Drac equaton are mproper rstly, Schrodnger equaton and Drac equaton are not derved by the prncple of conservaton of energy. As well-known, Schrodnger Equaton s actually a basc assumpton of quantum mechancs, people can only rely on experments to test ts correctness. hle n physcs the prncples, laws, equatons and the lke that do not consder the prncple of conservaton of energy wll be nvald n some cases. In some aspect, the functon of Schrodnger Equaton s equvalent to Newton s second law. However n reference [3], through the example of free fallng body, we derve the orgnal Newton's second law by usng the law of conservaton of energy, and prove that there s not the contradcton between the orgnal law of gravty and the law of conservaton of energy; and through the example of a small ball rolls along the nclned plane (belongng to the problem cannot be solved by general relatvty that a body s forced to move n flat space), derve mproved Newton's second law and mproved law of gravty by usng law of conservaton of energy. How to derve Schrodnger Equaton wth the law of conservaton of energy, s a topc for further research. or the reason that the Drac equaton s complyng wth the prncples of specal relatvty and quantum mechancs smultaneously, and t s the Lorentz covarant form of Schrodnger Equaton; therefore, the Drac equaton s not derved by the prncple of conservaton of energy also. In addton, we already pont out the shortcomngs of specal relatvty n reference [4], so the Drac equaton nevtably has the defects caused by specal relatvty. Secondly, the random (stochastc) concept could lead to absurd results. The random (stochastc) results gven by Schrodnger equaton and Drac equaton have been opposed and crtczed by many scholars. Here we present some absurd results caused by the random (stochastc) concept of Schrodnger equaton and Drac equaton. Accordng to the Schrodnger equaton and Drac equaton, when the partcle s n a certan state, ts mechancal quanttes (such as coordnates, momentum, angular momentum, energy, etc) generally do not have a defnte value, and have a seres of possble values, each possble value s appeared wth a certan probablty. In accordance wth ths random (stochastc) concept, the mass of mcroscopc partcle such as electron, proton and neutron, should also generally do not have a defnte value! And the number of electron, proton and neutron contaned by the atom of each element should also generally do not have a defnte value! Partcularly, the rato of proton mass to electron mass should also generally do not have a defnte value (nstead of )! Thrdly, they cannot solve many problems such as gravtaton. Not only Schrodnger equaton and Drac equaton cannot be used to solve the gravtatonal problem, but also they cannot be used to solve many problems of

3 mcroscopc partcles. or example, they cannot gve that the rato of proton mass to electron mass s equal to Another example s that they cannot gve the sheldng dstance n plasma problem, the Debye dstance formula must be appled. Makng Schrodnger equaton and Drac equaton tend to be proper. Partal and temporary unfed varatonal prncple of natural scence so far In reference [], for any feld, least square method can be used to establsh ths feld s "partal and temporary unfed theory so far" (the correspondng expresson s "partal and temporary unfed varatonal prncple so far"). equatons Supposng that for a certan doman Ω, we already establsh the followng general (, n) () On boundary V, the boundary condtons are as follows B (, m) () Applyng least square method, for ths feld and the domans and boundary condtons the "partal and temporary unfed theory so far" can be expressed n the followng form of "partal and temporary unfed varatonal prncple so far" n d m ' B dv mn (3) V where: mn was ntroduced n reference [5], ndcatng the mnmum and ts value should be equal to zero. and ' are sutable postve weghted constants; for the smplest cases, all of these weghted constants can be taken as. If only a certan equaton s consdered, we can only make ts correspondng weghted constant s equal to and the other weghted constants are all equal to. By usng ths method, we already establshed the "partal and temporary unfed water gravty wave theory so far" and the correspondng "partal and temporary unfed water gravty wave varatonal prncple so far", n reference [6]; and establshed the "partal and temporary unfed theory of flud mechancs so far" and the correspondng "partal and temporary unfed varatonal prncple of flud mechancs so far" n reference [7]. Some scholars may sad, ths s smply the applcaton of least square method, our answer s that: the smplest way may be the most effectve way. It should be noted that, n past tme, due to we cannot realze that the strct "unfed theory" cannot be exsted, therefore n references [6] and [7], the wrong deas that "unfed water gravty wave theory", "unfed water gravty wave varatonal prncple", "unfed theory of flud mechancs" and "unfed varatonal prncple of flud mechancs" were appeared. Now we correct these mstakes n ths paper. It should also be noted that, Eq.() can be ncluded n Eq.(), therefore we wll only dscuss Eq.(), rather than dscuss Eq.().

4 In reference [], for unfed dealng wth the problems of natural scence, applyng least square method, "partal and temporary unfed theory of natural scence so far" can be expressed n the followng form of "partal and temporary unfed varatonal prncple of natural scence so far" NATURE n d m ' S mn (4) where: the subscrpt NATURE denotes that the sutable scope s all of the problems of natural scence, all of the equatons denote so far dscovered (derved) all of the equatons related to natural scence, all of the equatons S denote so far dscovered (derved) all of the soltary equatons related to natural scence (for example, the coeffcent n the Coulomb's law can be wrtten as the followng soltary equaton: S, where, S k 9. 9 N m²/c²), and and ' are sutable postve weghted constants. In ths way, the theory of everythng to express all of natural laws, descrbed by Hawkng that a sngle equaton could be wrtten on a T-shrt, s partally and temporarly realzed n the form of "partal and temporary unfed varatonal prncple of natural scence so far".. Partal and temporary unfed theory of quantum mechancs so far Now we apply the unfed varatonal prncple to make Schrodnger equaton and Drac equaton tend to be proper. The Schrodnger equaton can be wrtten as follows H t (5) where, H s the Hamltonan operator, s the wave functon, and s the reduced Planck constant. The Drac equaton can be wrtten as follows m (6) Referrng to "partal and temporary unfed varatonal prncple of natural scence so far" (namely Eq.(4)), applyng least square method, "partal and temporary unfed theory of quantum mechancs so far" can be expressed n the followng form of "partal and temporary unfed varatonal prncple of quantum mechancs so far" n m QM d ' S mn (7) where: the subscrpt QM denotes that the sutable scope s all of the problems of

5 quantum mechancs, all of the equatons denote so far dscovered (derved) all of the equatons related to quantum mechancs, all of the equatons S denote so far dscovered (derved) all of the soltary equatons related to quantum mechancs (for example, the rato of proton mass to electron mass can be wrtten as the followng soltary equaton: S, where, S mp / me ), postve weghted constants, and and ' are sutable denote all the functonals establshed by the prncples, laws, formulas and the lke that are not ncluded n quantum mechancs (they can be ncluded n the felds of mathematcs, chemstry and the lke, and we wll establsh ths knd of functonals wth the prncple of conservaton of energy and some gravtatonal theores). or example, accordng to Schrodnger equaton, t can gve H (8) t Accordng to Drac equaton, t can gve m (9) As substtutng ths form of Drac equaton nto Eq.(7), we should refer to the manner to deal wth Maxwell s equatons for establshng "partal and temporary unfed electromagnetc theory so far" n reference []. It should be noted that, as dealng wth the equatons related to quantum mechancs n Eq.(7), If only Schrodnger equaton s appled, we can only make ts correspondng weghted constant, and the other weghted constants ; and f only Drac equaton s appled, we can only make ts correspondng weghted constant, and the other weghted constants. Now we establsh functonal wth prncple of conservaton of energy. The general form of prncple of conservaton of energy s as follows Or E( t) E() const E( t) E () () Accordng to above expresson, we can establsh the followng functonal

6 t Et () dt () E() t = w ( ) where, w s a postve weghted constant. Or another form of the functonal Et () E() = w( ) () Substtutng Eq.() or Eq.() nto Eq.(7), we wll make Schrodnger equaton and Drac equaton (and other equatons) are restrcted (or constraned) by prncple of conservaton of energy, and thus they can satsfy the prncple of conservaton of energy..3 Partal and temporary unfed theory of quantum-gravtaton so far As establshng "partal and temporary unfed theory of quantum-gravtaton so far", frstly we should establsh "partal and temporary unfed theory of quantum mechancs so far" (namely Eq.(7)) and "partal and temporary unfed gravtatonal theory so far" respectvely, then these two unfed theores can be combned together (t s equvalent that one unfed theory s restrcted (or constraned) by another unfed theory). In reference [], we already pont out that, applyng least square method, "partal and temporary unfed gravtatonal theory so far" can be expressed n the followng form of "partal and temporary unfed gravtatonal varatonal prncple so far". GRAVITY n d m ' S mn (3) where: the subscrpt GRAVITY denotes that the sutable scope s the gravty, all of the equatons denote so far dscovered (derved) all of the equatons related to gravty, all of the equatons S denote so far dscovered (derved) all of the soltary equatons related to gravty, and and ' are sutable postve weghted constants. Accordng to Eq.(7) and Eq.(3), and they should be restrcted (or constraned) by prncple of conservaton of energy, therefore "partal and temporary unfed theory of quantum-gravtaton so far" can be expressed n the followng form of "partal and temporary unfed varatonal prncple of quantum-gravtaton so far". QM-GRAVITY QM GRAVITY mn (4) where: accordng to Eq.(), t t Et () = w ( ) dt, the reason for addng ths E() functonal s also to consder that they should be restrcted (or constraned) by prncple of conservaton of energy. Now, accordng to Schroednger equaton and several theores of gravtaton, we wll present "the smplest partal and temporary unfed theory of quantum-gravtaton so far".

7 Supposng thst a certan theory of gravtaton can be wrtten as follows GR (5) Accordng to Eq.(8), Eq.(5), ang Eq.(), we can establsh the followng general form of "the smplest partal and temporary unfed theory of quantum-gravtaton so far". (6) d d mn Q-G GR where, accordng to Schroednger equaton Eq.(8): H, accordng to t Eq.(): t Et () dt, and the expresson of GR E() t = w ( ) the appled theory of gravtaton. Now we wll dscuss several concrete theores of gravtaton. should be determned by Supposng that Newton s theory of gravty s appled, and t can be wrtten as follows GMm r It gves GMm GR (7) r Supposng that the mproved Newton's formula of unversal gravtaton presented n reference [] s appled (ths formula can gve the same results as gven by general relatvty for the problem of planetary advance of perhelon and the problem of gravtatonal defecton of a photon orbt around the Sun), and t can be wrtten as follows GMm r 3G M c r 4 mp It gves GMm 3G M mp r c r (8) GR 4 Supposng that the more accurate gravtatonal formula presented n reference [, 3] s appled (as solvng the problem of gravtatonal defecton of a photon orbt around the Sun wth ths formula, the result of deflecton angle s exactly the same as gven by precse astronomcal observaton, whle the results gven by general relatvty and the mproved Newton's formula of unversal gravtaton have stll slght devatons wth the precse astronomcal observaton), and t can be wrtten as follows GMm GMp wg M p ( ) r c r c r It gves GMm 3GMp wg M p ( ) (9) r c r c r GR 4 4

8 Supposng that Ensten's gravtatonal feld equatons s appled, and t can be wrtten as follows Rab Rgab Tab It gves GR Rab Rgab Tab () If other theory of gravtaton s appled, then other form of GR can be gven. 3 Conclusons Establshng "partal and temporary unfed theory of quantum mechancs so far" and "partal and temporary unfed theory of quantum-gravtaton so far", can make Schrodnger equaton and Drac equaton tend to be proper. urther topc of research should be the applcaton of these partal and temporary unfed theores so far. References lorentn Smarandache, A Unfyng eld n Logcs: Neutrosophc Logc. Neutrosophy, Neutrosophc Set, Neutrosophc Probablty and Statstcs, thrd edton, Xquan, Phoenx, 3 u Yuhua, Neutrosophc Examples n Physcs, Neutrosophc Sets and Systems, Vol., 3 3 u Yuhua, Expandng Newton Mechancs wth Neutrosophy and Quad-stage Method New Newton Mechancs Takng Law of Conservaton of Energy as Unque Source Law, Neutrosophc Sets and Systems, Vol.3, 4 4 u Yuhua. Shortcomngs and Applcable Scopes of Specal and General Relatvty. See: Unsolved Problems n Specal and General Relatvty. Edted by: lorentn Smarandache, u Yuhua and Zhao enguan. Educaton Publshng, u Yuhua. New soluton for problem of advance of Mercury's perhelon, Acta Astronomca Snca, No.4, u Yuhua, Unfed water gravty wave theory and mproved lnear wave, Chna Ocean Engneerng, 99,Vol.6, No., u Yuhua, A unfed varatonal prncple of flud mechancs and applcaton on soltary subdoman or pont, Chna Ocean Engneerng, 994, Vol.8, No.