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

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1 An Expansion Theory Of The Universe Withot Dark atter And Dark Energy Chn-Xan. Jiang P. O. ox 394, eijing 854, P.. China Abstract In this paper we find a new gravitational formla: F = mc and establish an expansion theory of the 4 U niverse withot dark matter and dark energy.we obtain the expansion acceleration: ge = C PACS nmbers: e,. 5.-w. In the Universe there are two kinds of matter: () observable sblminal matter called tardyon and () nobservable sperlminal string matter called tachyons which coexist in motion.

2 We first define two-dimensional space and time ring [] x and j =. () can be written as Eler form ct t ct x z = = ct+ jx, () x ct are the tardyonic space and time coordinates, c is light velocity in vacm, z = ct e = ct (chθ + jsh θ ), () jθ is the tardyonic invariance, From () and () we have From (3) we have c θ tardyonic hyperbolical angle. ct = ct chθ, x = ct shθ (3) ct = ( ct). (4) x x θ = th = th. (5) ct c is the tardyonic velocity, chθ = The z denotes mathematics of the tardyonic theory. Using the morphism j : z jz, we have ( / c) and shθ = / c ( / c) jθ jz = x + jct = x e = x (chθ + j sh ), (6) θ x and t are the tachyonic space and time coordinates, x is tachyonic invariance, θ tachyonic hyperbolical angle. From (6) we have x = x chθ, ct = x shθ. (7). From (7) we have x ( x) ( ct ) c is the tachyonic velocity, =. (8) ct c θ = th = th. (9) x chθ = ( c/ ) and shθ = c/ ( c/ ).

3 The jz denotes mathematics of the tachyonic theory. oth the z and the jz form the entire world bt the jz world is nexploited and nstdied. Fig.. inkowskian spacetime diagram Figre shows the formlas ()-(9). j : z jz is that tardyon can be converted into tachyon, bt j : jz z is that tachyon can be converted into tardyon. = = c is the positive acceleration, bt = = c is the negative acceleration, which coexist. At the x axis we define the tachyonic string length t is the rest time. x = lim t = constant. t Since at rest the tachyonic time t = and system tachyonic motion as an action-at-a distance motion. Assme () =, we prove that the tachyon is nobservable. In rest θ = θ, from (5) and (9) we get the tardyonic and tachyonic coexistence principle [-3] Differentiating () by the time, we get d dt = c () c d =. () dt d d and can coexist in motion, bt their directions are opposite. dt dt We stdy the tardyonic and tachyonic rotating motions. In 673 Hygens discovered that the tardyonic rotation prodces centripetal acceleration 3

4 d dt =, (3) is rotating radis. Sbstitting (3) into () we have the tachyonic rotation prodces centrifgal acceleration d dt c =. (4) It is independent of tachyonic velocity and tardyonic velocity, only inversely proportional to radis. (3) and (4) are dal formlas, which have the same form. It is niqe and perfect. From (3) we get the tardyonic centrifgal force is the inertial mass. From (4) we get the tachyonic centripetal force, that is gravity F =, (5) mc F =, (6) m is the gravitational mass converted into by tachyonic mass m which is nobservable bt m is observable. Whether = or, all matter prodce the gravity. (5) and (6) are dal formlas, which have the same form. (6) is a new gravitational formla. This simple thoght made a deep impression on me. It impelled me toward a theory of gravitation. It is simplicity, elegance and mathematical beaty. It is the fondations of gravitational theory and cosmology. In the niverse there are two main forces: the tardyonic centrifgal force (5) and tachyonic centripetal force (6) which make strctre formation of the niverse. 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 is the Earth radis. We have the eqation of motion F mc =, (7) mc = g, (8) g is gravitational acceleration, is mass of freely falling body. From (8) we define the gravitational coefficient m g η = = = 6.9. (9) c 9 In 9 Eötvös experiment η ~5 and in 964 Dicke experiment η ~ [4]. Since the gravitational mass m can be transformed into the rest mass in freely falling body, we define Einstein s 4

5 gravitational mass = m and inertial mass i = [5]. We prove g i + g > i. () Therefore we prove that the principle of eqivalence is nonexistent. At the heart of the general theory of relativity is the principle of eqivalence[4]. Therefore the general theory of relativity and black holes conjectre cold all be wrong. Using (6) we stdy the expansion theory of the Universe. Figre shows a expansion model of the Universe. The rotation ω of body A emits tachyonic flow, which forms the tachyonic field. Tachyonic mass m acts on body, which prodces its rotation and gravitational force ω, revoltion mc F =, () 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 revoltion of the body arond body A prodces the centrifgal force F =, () Fig.. A expansion model of the Universe is the inertial mass of body, is the orbital velocity of body. At the point we assme O F + F. (3) = From ()-(3) we have the gravitational coefficient At the m η = =. (4) c O point the tachyonic mass m can be converted into the rest mass m in body, we have 3 5

6 F m =. (5) + Since F + F, centrifgal force is greater than gravitational force > F F, then the body expands otwards and its mass increases. This is a expansion mechanism of the Universe.From ()-(3) we have the expansion eqation of motion m F + F = = g From(6) we obtain the expansion acceleration e. (6) g e = m. (7) Sbstitting (4) into (7) we have the expansion acceleration g e = U 4 C. (8) 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 made a deep impression on me. It impelled me toward an expansion theory of the niverse with no dark matter and no dark energy. If the body A is the Sn and body is the planet. We calclate the gravitational coefficients η as shown in table. Table. Planet (km/sec) η ( ) ercry Vens Earth ars Jpiter Satrn Urans Neptne Plto

7 Since gravitational mass m can be transformed into the rest mass in body, we define Einstein s gravitational mass = m and inertial mass i = [5]. g i + We prove g > i. (9) Therefore we prove that the principle of eqivalence in the Solar system is nonexistent. The tachyonic mass m can be converted into electrons and positrons which are the basic bilding-blocks of elementary particles [6, 7]. In the niverse there are no Higgs particles which are not prodces at the Large Hadron Collider and other particle accelerators. This simple thoght made a deep impression on me. It impelled me toward a nification of gravitational theory and particle theory[3]. eferences. C. X. Jiang, Wli (Physics) (Chinese), 4, 9-5 (975).. C. X. Jiang, J. eijing Observatory (Chinese), 7, 3-38 (976). 3. C. X. Jiang, Hadronic J. 4, (). 4. C. W. isner, K. S. Thorne and J. A. Wheeler, Gravitation (Freeman, 973), P. 5, A. Einstein, The eaning of elativity (6th ed., Chapman and Hall, London, 967), p C. X. Jiang, Hadronic J. 3, 56-9 (979). 7. C. X. Jiang, Acta ath. Scientia, 8, (988). 7

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

Report and Opinion 2017;9(4s) 1.Mathematical Theory of Space-Time. Jiang Chunxuan athematical Theory Of Space-Time Jiang Chnxan Institte for asic esearch, Palm Harbor, FL3468-1577, USA And: P O ox 394, eijing 100854, P China jiangchnxan@sohcom, cxjiang@mailbcfnetcn, jcxan@sinacom, Jiangchnxan@vipsohcom,