1 The length measurement unit in two difference space-time structures

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1 On the origin of gravitationa fore Zhi Cheng (9 Bairong st. Baiyun Distrit, Guangzhou, China Abstrat: Equivaene rinie is the basement of genera reativity theory. It oints out that the gravitationa fore is equivaent to the inertia fore. However, the genera reativity theory does not give the reason. In this aer, we assume the sae is a kind of easti media. The energy an take ressure on the sae. It wi make the sae urved. The urved sae-time rodues gravitationa fore. This aer gives the mathematia auation based on eastiity theory to show that this assumtion is true. It aso gives the aurate reationshi between mass and gravitationa fore. The reationshi is in ine with the onusion of genera reativity. Key words: Gravitationa fore; urved sae time; urvature 0 Introdution In 01, Cheng assumed that there is a three dimensiona time us one dimensiona sae struture of sae-time besides the we-known three dimensiona sae us one dimensiona time [1]. And then he onstruted the new Mawe equations whih had high symmetri harateristi in sae and time [1-]. The two sae-time struture an be distinguished by the veoity of arties. It aso affets the ength measurement unit. We wi anayze the ength measurement differene between these two sae-time strutures. And then we wi anayze how the mass omress the sae. 1 The ength measurement unit in two differene sae-time strutures m ΔX Figure 1. The moving distane of artie m in three dimensiona sae We assume a artie m moves in the referene frame of three dimensiona sae. The 1

2 distane it moved is ΔX as shown in figure 1. Then it wi be ΔY in three dimensiona time sae-time struture unit. There is the funtion shown beow. Y f( (1 Sine the two sae-time strutures are symmetri, then we have X f( ( Then f( f( ( So Xf( f( Const. Sine X f( f( We have ΔX ΔY (4 Where is the onstant. It is the same for time unit. Δt Δt y (5 The veoity reationshis between two differene sae-time strutures By differentiating with reset to time in formua (4, we have d ΔX ΔY 0 That is v ΔY 0 (6 d t Where v is the artie s veoity in three dimensiona sae referene frame. By onsidering formua (4 and (5, we an have v d t (7

3 v ( y ty ty Where ω is the artie s veoity measured in three dimensiona time s unit. So we have v t If the artie is doing uniform motion, we an aways find a referene frame to make v t If the artie is doing aeerated motion, we an aways find a oaized inertia referene frame aording to genera reativity [4]. So we an use the same method to study the veoity reationshis between two sae-time strutures. Therefore v (8 Formua (8 refets the veoities measured in two differene sae-time strutures units. It is onsistent with the onusions drawn from aer [1-]. That means the two sae-time strutures anayzed in this aer is same as the two sae-time strutures assumed in aer [1,]. The assumtion of easti sae-time strutures For totay sheriay symmetri sae-time struture, we an auate the resuts by searating the sae and time aording to the theory of genera reativity [4]. Therefore, we ony need to assume that the three dimensiona sae is made of easti media. For a sheria she whih has the inner radius a, and the outer radius b, the inner ressure is i, and outer ressure is o. We an auate the stress rodue by the ressures aording to the knowedge of eastiity theory [5]. However, we ony need to onsider the ondition that b aroahes infinity and 0 equas zero. So we have a kr (9 R R ia

4 a kt (10 R t ia The unit of k R and k t is m - in formua (9and(10, whih is same as the urvature of three dimensiona sae. By omaring formua (9 (10 with the urvature tension of sheriay symmetri sae that auated by theory of genera reativity [4], we have GM a (11 It shows that the arameter a reresents the radius of a sae hoe rodued by the mass. The hoe wi take ressure on the sae to turn the fat sae into the urved sae. The auation is onsistent with the theory of genera reativity. We wi anayze the dee meaning of a in setion 4. 4 How mass take ressure on sae The stati and motion are reativey in two sae-time struture. The so aed energy in three dimensiona sae is refer to the motion energy in generay. This motion energy is rodued by the virtua hotons aording to aer [,]. The stati energy is referring to mass. However, the stati mass in three dimensiona sae annot be stati in three dimensiona time struture aording to the anaysis in setion 1 and in this aer. So we an assume that the mass in one sae-time struture is the motion energy or virtua hoton energy in other sae-time struture. So we an use the virtua hoton s wave ength to reresent the vaue of mass instead of Comton wave ength. For a artie m, the orresondent virtua hoton s energy in three dimensiona time an be eressed as beow. m r y 4 (1 Where r y is the waveength radius of three dimensiona time. We an use formua (4 to onvert it to the ength unit of three dimensiona sae. That is r y (1 a We an obtain formua (14 by entering formua (1 into formua (1. m a (14 By entering formua (11 into formua (14, we an obtain G (15 Obviousy, formua (15 is the auation formua of Pank ength [6,7]. However formua (15

5 has no seia demands of the mass. It rovides strong theories and eeriments suort for this aer. We an find the meaning of arameter a from formua (14 now. Formua (9(10(11 show that the hoe radius a is the waveength of a mass in other sae-time struture (three dimensiona time. After onverting it into the unit of three dimensiona sae, we an find that it roortiona to the mass. 5 Conusion So we an make the onusion from formua (9(10(11(14(15. The onusion is that the matter (inuding one or many arties wi form a sae hoe. The hoe s radius is roortiona to the mass. The hoe wi take ressure on the sae, and make it urved. The urved sae wi rodue gravitationa fore aording to the theory of genera reativity. Referene [1] 程智. 时空对称结构的麦克斯韦方程组. 北京 : 中国科技论文在线. htt:// [Retrieved on ] [] Cheng, Z. Hyer-Symmetri Mawe Equations and Its Aiations. htt://vira.org/abs/ [Retrieved on ] [] 程智. 波函数的电磁波诠释. 北京 : 中国科技论文在线. htt:// [Retrieved on ] [4] 俞允强. 广义相对论引论 ( 第二版 (An Introdution to Genera Reativity. 北京 : 北京大学出版社,000: 44,79,107 [5] Timoshenko and Goodier, SP Timoshenko, JN Goodier. Theory of Eastiity. MGraw-Hi, New York ( [6] Padmanabhan T. Physia signifiane of Pank ength. Annas of Physis, 1985, 165(1: [7] Padmanabhan T. Pank ength as the ower bound to a hysia ength saes. Genera reativity and gravitation, 1985, 17(: