Report and Opinion 2017;9(4s) 1.Mathematical Theory of Space-Time. Jiang Chunxuan

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1 athematical Theory Of Space-Time Jiang Chnxan Institte for asic esearch, Palm Harbor, FL , USA And: P O ox 394, eijing , P China jiangchnxan@sohcom, cxjiang@mailbcfnetcn, jcxan@sinacom, Jiangchnxan@vipsohcom, jcxxxx@163com Abstract: Using space-time ring we establish the mathematical theory of space-time Using two methods we dedce the new gravitational formla Tardyonic rotating motion prodces the centrifgal force,bt tachyonic rotating motion prodces the centripetal force, that is gravity Using it we establish the expansion theory of the niverse and sggest the new niverse model We prove that in the niverse there are no dark matter and no dark energy New gravitational formla changes all that ltiverse and gravitational waves do not exist [Jiang Chnxan athematical Theory Of Space-Time ep Opinion 017;9(4s):10-110] ISSN (print); ISSN (online) 17 doi:107537/marsroj0904s1717 Keywords: new gravitational formla, expansion theory of niverse, new niverse model PACS:0490+e,9880-k 1athematical Theory of Space-Time In the Universe there are two matters: (1) observable sblminal matter called tardyon(locality) and () nobservable sperlminal matter called tachyon(non-locality) which coexist in motion Tachyon can be converted into tardyon, and vice versa Tardyonic rotating motion prodces the centrifgal force, bt tachyonic rotating motion prodces the centripetal force, that is gravity Using tardyonic and tachyonic coexistence principle we dedce the new gravitational formla, For establishing the mathematical theory of space-time we first define space-time ring [1,10] ct x Z ct jx, x ct (1) 0 1 x and t are the tardyonic space and time coordinates, c j is light velocity in vacm, 1 0 (1) can be written as Eler form j Z ct e ct (ch j sh ), ct 0 From (1) and () we have ct 0 0 is the tardyonic invariance, tardyonic hyperbolical angle ct 0 ch, ct0 ( ct) x x ct 0 sh From (3) we have 1 x 1 th th ct c c is the tardyonic velocity Using the morphism j : z jz, we have j jz x jct x0e x0 (ch j sh ), x and t x are the tachyonic space and time coordinates, 0 hyperbolical angle () (3) (4) (5) (6) is tachyonic invariance, tachyonic 10

2 From (6) we have From (7) we have x x0 ch, ct x0 sh x 0 ( x) ( ct ) th 1 ct x c is the tachyonic velocity th 1 c (7) (8) (9) Fig 1 athematical theory of space-time j : z jz j : jz z Figre 1 shows the formlas (1)-(9) is that tardyon can be converted into tachyon, bt is that tachyon can be converted into tardyon 0 c is the positive acceleration, bt c is the negative acceleration, which coexist At the ct-axis =0 and x=0 we define the tardyonic rest time t At the x axis we define the tachyonic rest space X 0 lim t constant t 0 (10) Since at rest the tachyonic rest time t 0 and, we prove that tachyon is nobservable Fig1 and (10) are mathematical theory of space-time, which are the fondations of physics and cosmology Using it we prove that dark matter, dark energy, gravitational waves,black holes, qantm entanglement and qantm compters do not exist From Fig1 we dedce new gravitational formla New Gravitational Formla: Assme F, from (5) and (9) we get the tardyonic and tachyonic coexistence principle [1-4,10] c (11) Using the analytical method we dedce the new gravitational formla Differentiating (11) by the time, we get d dt c d dt (1) 103

3 d d dt and dt can coexist in motion, bt their directions are opposite We stdy the tardyonic and tachyonic rotating motions In 1673 Hygens discovered that the tardyonic rotation prodces centripetal acceleration d dt, (13) is rotating radis Sbstitting (13) into (1) we have the tachyonic centrifgal acceleration d c dt (13) and (14) have the same form From (13) we get the tardyonic centrifgal force F, (14) (15) is the inertial mass From (14) we get the tachyonic centripetal force, that is gravity F, (16) m is the gravitational mass converted into by tachyonic mass m (15) and (16) have the same form (16) is the new gravitational formla Using the geometrical method we dedce the new gravitational formla Figre shows that the rotation of body A emits tachyon mass m, which forms the tachyon and gravitation field and gives the body revoltions and d Fig On body the dt d and dt coexistence From Fig it follows 104

4 t (17) From (17) it follows the tardyon centripetal acceleration on the body [-4], d lim dt t t 0 0 (18) From Fig it follows t (19) From (19) and (11) it follows the tachyon centrifgal acceleration on the body [-4], d c lim dt t t 0 0 (0) d On body the dt d and dt coexistence From (18) it follows the tardyon centrifgal force on body [-4], F, (1) is body mass From (0) it follows the tachyon centripetal force on body, that is gravity [-4,10], F, () m is the gravitation mass converted into by tachyon mass m which is nobservable, bt m is observable () is the new gravitational formla In 1976[] this simple thoght made a deep impression on me It impelled me to establish the new gravitational theory On body the F and F coexistence Fig3 On body the F and F coexistence 105

5 From Fig 3, it follows From (1), () and (3) it follows F F 0 (3) m c (4) ody increases mass m and centrifgal force is greater than gravitation force, then body expands otward Dark matter which cases cosmic attraction is wrong From () it follows Newtonian gravitation formla The m is proportional to body A mass A, in (4) m is proportional to, is inversely proportional to the distance between body A and body It follows A m k, (5) k is constant Sbstitting (5) into () it follows the Newtonian gravitation formla [-4,10] A F G, (6) 8 3 G kc cm / g sec is gravitation constant Now we stdy the freely falling body Tachyonic mass m can be converted into tardyonic mass m, which acts on the freely falling body and prodces the gravitational force F, (7) is the Earth radis We have the eqation of motion g, (8) g is gravitational acceleration, is mass of freely falling body From (8) it follows the gravitational coefficient m g c (9) 9 11 Eötvös experiment ~ 510 and Dicke experiment ~ 10 Since the gravitational mass m can be transformed into the rest mass in freely falling body, we prove that the freely falling bodies fall with the same acceleration 3The expansion theory of the niverse Using new gravitational formla we stdy the expansion theory of the Universe[10] Figre 4 shows a expansion model of the Universe The rotation 1 of body A emits tachyonic flow, which forms the tachyonic field Tachyonic mass m acts on body, which prodces its rotation, revoltion and gravitational force F1, (30) denotes the distance between body A and body, m is gravitational mass converted into by tachyonic mass m which is nobservable bt m is observable The rotation of the body arond body A prodces the centrifgal force 106

6 F 1, (31) Fig 4 A expansion model of the Universe is the inertial mass of body, is the orbital velocity of body At the O point we assme F1 F1 0 (3) From (3) it follows that the coexistence of the gravitational force and centrifgal force From (30)-(3) it follows the gravitational coefficient m c (33) O At the 3 point the tachyonic mass m can be converted into the rest mass m in body, it follows m F (34) Since F F1 0, centrifgal force F is greater than gravitational force F 1, then the body expands otwards and its mass increases This is a expansion mechanism of the Universe From (31,3,34) we have (35) From (35) we obtain the expansion F acceleration F1 m ge g (36) e m Sbstitting (33) in (36) we obtain 4 ge c (37) If body A is the Earth, then body is the oon; if body A is the Sn, then body is the Earth; It can explain or accelerating niverse In the niverse there are no dark matter and no dark energy This simple thoght 107

7 made a deep impression on me It impelled me to establish a expansion theory of the niverse Dark energy responsible cosmic replsion is wrong If the body A is the Sn and body is the planet We calclate the gravitational coefficients as shown in table 1 Table 1: Vales of the gravitational coefficients Planet (km/sec) ( ) ercry Vens Earth ars Jpiter Satrn Urans Neptne Plto The gravitational field of the solar system is the origin of the planet mass From it the planet acqire mass 4The new niverse model From the tachyonic theory we sggest the new niverse model The niverse has no beginning and no end The niverse is infinite, bt it has a center consisting of the tachyonic matter which is strong gravitational field (SGF), which governs motion of the whole niverse Therefore the whole niverse is stable and harmonios In the sn there is a center consisting of the tachyonic matter with SGF, which governs motion of the solar system It is stable and harmonios In the earth there is a center consisting of the tachyonic matter with SGF, which governs motion of the earth and the moon It is stable and harmonios In the moon there is a center consisting of the tachyonic matter with SGF, which governs motion of the moonit is stable and harmonios In atomic ncles there is a center consisting of the tachyonic matter with SGF, which governs motion of the ncles Therefore atomic nclei are stable and harmonios The tachyonic theory governs the amazing harmony of the whole niverse from the smallest to the largest scales New gravitational formla changes all that In the Universe there are no dark matter, no dark energy and no gravitational waves ltiverse, inflation and primordial gravitational waves do not exist [5-7] 5Conclsion In smmary We dedce tardyonic and tachyonic coexistence principle Using it we dedce the centrifgal formla and new gravitational formla We establish the expansion theory of the niverse withot dark energy and sggest the new niverse model which is amazing harmony The new gravitational formla is fondations of particle physics and cosmology We prove that in the niverse no dark matter, no dark energy, no gravitational waves and no qantm gravity Where did we come from? Where are we going? What makes p the niverse? These qestions have occpied mankind for thosands of years Over the corse of history, or view of the world has been changed Theologians and philosophers, physicists and astronomers have given s very different answers Where did we come from? We answer this qestions this way m m, tachyons tardyons[1], that is tachyons can be converted into the electrons and positrons which are the basic bilding-blocks of the elementary particles[8-9]the tachyons are the origin of mass Where are we going? We answer this qestion this way m m, that is the tardyons prodce tachyons[1] The tardyons and tachyons make p the Universe F Note In 1976 Jiang fond a gravitational formla [] :, m is the tachyonic mass In 004 F Jiang stdied the Universe expansion and fond, m is gravitational mass converted into by tachyonic mass m [10] Newtonian gravity formla is based on empirical evidence He did not explain what is gravity? how it works? In general theory of relativity there is no gravitational formla[11] In modified gravity and modified Einstein gravity 108

there are no gravitational formla[1]there cannot be really gravity theory withot gravity formla A tachyonis instability appears as a field with a negative mass sqared which is wrong[1]the tachyons

8 there are no gravitational formla[1]there cannot be really gravity theory withot gravity formla A tachyonis instability appears as a field with a negative mass sqared which is wrong[1]the tachyons are stable It has no rest time and no rest mass[1] Acknowledgments The athor thanks professor Walter Lewin for his mails (1) From: Walter HG Lewin <lewin@spacemited> Date:Sn,10 Jn 01 ::1-0400(EDT) Sbject: e: Fwd To: 13jiangchnxan@gmailcom;lewin@mited Cc: lc@vanockenbe Pblish this in a refereed jornal and once it is accepted by yorself a first class ticket to Stockholm to pick p Nobel prize for physics ()From: Walter HG Lewin <lewin@spacemit ed> Date: Sn,17 Jn 01 06:19: (EDT) Sbject: e To: 13jiangchnxan@gmailcom Cc: lc@vanockenbe Dear Jiang Thank for yor I sggest yo sbmit yor theory to a refereed jornal If it is accepted, then by yorself a plane ticket to Stockholm to pick p a Nobel prize Greetings 109

9 eferences 1 Chn-Xan Jiang, A theory of morphisms between the tardyon and tachyon, physics (Chinese), 4 (1975) Chn-Xan Jiang, On natre for gravitation, J eijing observatory (Chinese), 7(1976) Chn-Xan Jiang, An approach on the natre of attractive force, Potential science (Chinese), 4 (198) Chn-Xan Jiang, A nified theory of the gravitational and strong interactions, Hadronic J, 4 (001) P A Ade et al (ICEP Collaboration), Detection of -mode polarization at degree anglar scales by ICEP, Phys ev Lett 11, 41101(014) 6 S Dodelson, How h can we learn abot the physics of inflation? Phys ev Lett, 11, (014) 7 J Caligiri and A Kosowsky, Inflationary tensor pertrbations after ICEP Phys ev Lett, 11, (014) 8 Chn-Xan Jiang, A simple approach to the comptation the total nmber of hadronic constitents in Santilli model, Hadronic J,3(1979) Chn-Xan Jiang, A mathematical model for particle classification, Acta ath Scien, 8(1988) Chn-Xan Jiang, New gravitational formla and expansion theory of the niverse In: new stdies of space-time theory (Chinese), Dizi press, pp54-59, A Einstein, The meaning of relativity, 5 th edn, (Princeton niversity press, Princeton, 1956) 1 Astin Joyce, hvenesh Jain, Jstin Khory, ark Trodden eyond the cosmological srandard model Physics eports 568(015)1-98 5/7/

An Expansion Theory Of The Universe Without Dark Matter And Dark Energy

An Expansion Theory Of The Universe Withot Dark atter And Dark Energy Chn-Xan. Jiang P. O. ox 394, eijing 854, P.. China jcxan@sina.com Abstract In this paper we find a new gravitational formla: F = mc