Projection Gravitation, a Projection Force from 5-dimensional Space-time into 4-dimensional Space-time

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1 Intenational Jounal of Physics, 17, Vol. 5, No. 5, Available online at Science and ducation Publishing DOI:1.1691/ijp Pojection Gavitation, a Pojection Foce fom 5-dimensional Space-time into 4-dimensional Space-time Xiao Lin Li * *oesponding autho: hidebain@hotmail.com Abstact A new gavity theoy. Gavity is a pojection foce fom 5-dimensional space-time into 4-dimensional space-time. The Loentz symmety is a pojection of paticle-wave symmety fom 5-dimensional space-time into 4- dimensional space-time. The gavity is an additional pojection foce of Loentz symmety. The new gavity is an extension to Loentz symmety. The new gavity can be seen as some kind of symmety. Gavity only exists in 4- dimensional space-time. In 5-dimensional space-time, thee not have gavity. quivalence pinciple is invalid in the new gavitation. In the new gavitation, thee does not have gavitational acceleation. In the new gavitation, thee only have inetial coodinates, not have non-inetial coodinates. In the new gavitation, the gavity souce is only the est mass, not enegy. The paticle can t be the gavity souce if the paticle not has est mass. The photon not has gavity. But any paticle can be affected by gavity. The photon is affected by gavity also. The gavitational mass is only equivalent to the est mass. Unde appoximate weak gavity and appoximate cicula obit condition, the new gavitation is equivalent to the Geneal Relativity. The fou classic expeimental tests, the deflection of light by the sun, the pecession of mecuy, the ed shift of light by the sun, the ada echo delay, ae expeimental tests to the new gavitation also. But even unde appoximate weak gavity condition, if the obit is not appoximate cicula, if the obit has highe eccenticity, thee exists obvious diffeence between the Geneal Relativity and the new gavitation. This diffeence can be a expeimental test to distinguish which one is moe ealistic. The space-time is flat in the new gavitation, not is cuved. In the new gavitation, the enegy is conseved. The new gavitation is simple than the Geneal Relativity. In the new gavitation, the photon s equivalent gavitational acceleation is twice of the acceleation in Newton Gavitation. In the new gavitation, thee not exists black hole, but exists empty hole, and not exists space-time singulaity and enegy singulaity. The new gavity has obvious scale effect. The new gavity has the scale facto. In gavity field, the scale facto detemines the quantization esults of paticle s motion. The new gavity pehaps is a foce that inhibits the uncetainty of macoscopic objects. The new gavitation can deive out the esult of the Planck negy. Keywods: new gavitation, 5-dimensional space-time, paticle-wave symmety, Loentz symmety, pojection gavity, est mass, gavitational mass, Geneal Relativity, equivalence pinciple, Newton Gavitation, flat space-time, inetial coodinates, appoximate weak gavity, appoximate cicula obit, eccenticity, deflection of light, pecession of mecuy, ed shift of light, ada echo delay, black hole, empty hole, gavitation quantization, scale effect, scale facto, Planck negy ite This Aticle: Xiao Lin Li, Pojection Gavitation, a Pojection Foce fom 5-dimensional Space-time into 4-dimensional Space-time. Intenational Jounal of Physics, vol. 5, no. 5 (17): doi: /ijp Intoduction Since Newton poposed the theoy of gavitation, the study of gavitation has become moe and moe deeply. Newton gavitation can't explain deflection of light and pecession of mecuy. In the ealy th centuy, instein poposed the Special Relativity, and futhe poposed Geneal Relativity. The Geneal Relativity theoy can explain these phenomena. Geneal elativity is moe pefect than Newton gavity theoy. In the th centuy, human find the quantum phenomena, and poposed the Quantum Mechanics, and poposed the Quantum Field Theoy. But, human find that, between Geneal Relativity and Quantum Mechanics, thee ae contadictions, and gavity cannot be quantized. The poblem of gavitation becomes moe and moe complicated and difficult. By now, humans have not solved the poblem of gavitational quantization. In the face of this situation, human has poposed a vaiety of new theoies of gavity. Based on the theoy of quantum mechanics, the autho puts fowad a new gavitational model in the flat space-time. Unde appoximate weak gavity and appoximate cicula obit condition, the new gavitational model is equivalent to the Geneal Relativity. Fo the gavitational quantization poblem, this new model may povide a new way to solve it.. Gavity is Pojection Foce fom 5-dimensional Space-time In the pevious two papes [1,], autho has poposed a new physical model, the paticle-wave symmety in 5-

2 18 Intenational Jounal of Physics dimensional space-time. Paticle wave is pesent in 5-dimensional space-time. The paticle wave goup velocity must be equal with its phase velocity, and the two speed value is invaiant, and the two speed value is the light speed. In this case, the 5-dimensional space-time is 4-dimensional space and 1-dimensional time. osmic space-time obseved by human is 3-dimensional space and 1-dimensional time. This likes Figue 1. Figue 1. Fom this simple model, we pojected the paticle-wave symmety into 4-dimensional space-time, so we can deive out the esult of the Loentz symmety, and we can deive out esult of the mass-enegy equation in the Special Relativity Theoy. So the Loentz symmety in 4-dimensional space-time is just a pojection of the paticle-wave symmety in 5-dimensional space-time actually. So the Loentz symmety is the effect of this pojection. Please eade ead the pevious two papes [1,] at fist, you will undestand the new paticle-wave symmety model. Autho is no longe to epeat the desciption in this pape. In this new model, thee exist two key concepts. Fistly, thee exists the paticle-wave symmety in the 5-dimensional space-time. Secondly, thee exists a pojection action fom 5-dimensional space-time into 4-dimensional space-time. The pojection action is like Figue. Figue. The new paticle-wave symmety model is based on the wave-paticle duality of quantum mechanics. Theefoe, it is natually in accodance with quantum mechanics, thee is no contadiction between quantum mechanics and the new paticle-wave symmety model. So the Loentz symmety becomes a deived out esult of quantum mechanics. The Loentz symmety is a global symmety. In a inetial coodinates, at evey space-time point, the symmety is same. So we can undestand it in such a way. The pojection action fom 5-dimensional space-time into 4-dimensional space-time have same pojection facto at evey space-time point. The pojection facto is 1. Please be caeful to undestand this. This is vey impotant. To Loentz symmety, the pojection facto is 1 at evey point. So we can ask a question. If the pojection facto is not same at evey point, but diffeent point have diffeent pojection facto, what will happen? This question will diect to a new gavity model. This is the key of new gavity theoy. We know, gavity follows the two equation (.1) and (.) in Newton gavitation. F GMm = (.1) GMm V =. (.) So the Newton gavity is a function of space actually. So the Newton gavity can be seen as a effect of space. Analogy Newton gavitation, if we take the pojection facto into a function fom simila to Newton gavity function, this will bing effect simila to the Newton gavity. So we will get exta gavity effect based on the Loentz symmety. So we build an association between Loentz symmety and gavity. So we can get a new gavitational theoy satisfying Loentz symmety. In physics, the Loentz symmety is manifested in mass-enegy equation (.3). 4 = P + m. (.3) Autho guess that the gavity will behaves as a additional facto of this equation (.3). So, autho poposed a new equation (.4). This equation is the new gavitational equation. GM P m 4 v = +. (.4) In this equation, v is the gavitational potential enegy. The gavitational potential enegy is negative. M is the est mass of gavitational souce. m is the est mass of the paticle affected by gavity. is the distance fom the paticle to the gavitational souce. P is the GM momentum of paticle. The pojection facto is. The gavity is some kind of pojection powe. So the gavity has elationship with 5-dimensional space-time. The gavitational souce is the paticle-wave symmety s pojection action fom 5-dimensional space-time into 4- dimensional space-time. So the new gavity can be seen as some kind of symmety. This symmety is extension of the Loentz symmety. This symmety is based on the Loentz symmety. Fo simplified instuctions, we fist thought that the gavitational souce and the paticle is point paticle, thei mass is concentated in a cental point. GM Why the pojection facto is? This is inspied by the analogy of Newton gavitation. The new gavity must be able to appoximate the esults of Newton's gavity. The new gavity must satisfy the Loentz symmety. And the new gavity must satisfy the law of synthesis of gavity. So we take the pojection facto fo this fom. This is a guessing esult. Whethe it is coect, ely on expeiments to test it. Does the 5th dimension eally exist? What is the pojection action s popety fom 5-dimensional space-time into 4-dimensional space-time? Why exist this pojection action? These questions ae a new physics subject that needs futhe study.

3 Intenational Jounal of Physics 183 Obviously, in the new gavitation, when the paticle s speed is small, its momentum is small, omit momentum item in (.4), we will get the esult of Newton gavitation appoximately. v GM GMm m Plus the enegy of the paticle itself, in a gavitational field, the motion equation of a paticle is equation (.5). This is the new gavitational equation. Whethe it is coect, ely on expeiments to test it. GM P m P m 4 4 = + +. (.5) In equation (.4), why the gavitational souce mass is only its est mass, why it not is its all enegy mass like the Geneal Relativity? This can be infeed fom the pojection action. We pojected he paticle-wave symmety in 5-dimensional space-time into 4-dimensional space-time, so we get the Loentz symmety. The effect of this action is that tansfe the 4th motion component of paticle into the est mass of paticle in 3-dimensional space. In this pojection action, the motion component of paticle in 3-dimensional space is not change. At othe wods, the pojection action only has elationship with est mass, not has elationship with all enegy of paticle. The gavity is only a additional effect of this pojection action. So the gavity pojection facto should have elationship with the est mass of the souce only, not should have elationship with all enegy of souce. So the gavitational mass of souce only is equal with its est mass. So, if a paticle does not have est mass, it can t act as a gavitational souce, it can t geneate gavity. The photon can t geneate gavity. The momentum can t geneate gavity. In mass-enegy equation, the inceased momentum, and the inceased enegy, can t geneate additional gavity. In mass-enegy equation, the equivalent mass of enegy can t geneate gavity. The mass and enegy which not have Loentz invaiance can t geneate gavity. Only the est mass with Loentz invaiance can geneate gavity, can act as gavitational souce. Fom equation (.4), we can get a esult. When a paticle move in gavity filed, the value of the gavity that the paticle accept have elationship with paticle s momentum. When a paticle move in gavity filed, the inetia mass of the paticle have elationship with paticle s est mass, and the inetia mass of the paticle have elationship with paticle s momentum also. The inetia mass of the paticle have this equation. P + m m = =. So, the inetia mass of the paticle is not equal with its est mass. In the new gavitation, the object which geneate gavity, and the object which eceive gavity, ae not in ecipocal oles. The momentum can t geneate gavity. But the momentum can affect the value of the gavity that the paticle accept. In the gavitational equation (.4), the pojection facto GM is. To a gavitational souce, this facto is a constant.. And this facto has scale popety. So we can define a new scale constant. So we get a new fomula (.6). This constant is an identifie constant of a gavitational souce. We can use this constant to simplify the fom of equations. GM =. (.6) Fom fomula (.6), we can find a popety of gavity. The gavity has scale effect. The popety of a gavitational souce is uniquely identified by its scale constant. To a gavitational souce, it has lage est mass, its scale constant is lage. This is also the embodiment of the pojection action. To a pojection action, it is bound to be elated to a scale facto. So, we can simplify the equation (.4) to equation (.7), and we can simplify the equation (.5) to equation (.8). 4 v = P + m (.7) 4 4 P m P m. = + + (.8) Because the gavity is additional pojection effect of Loentz symmety, so we can get this esult. In a gavity field, to a same obseve, evey space point is in the same inetial coodinates. To a same obseve, the space-time in the gavity field is flat space-time. The space-time in the gavity field is not cuved. This is vey diffeent fom the Geneal Relativity. The Loentz symmety is elated to the speed of the obseve's motion. In the gavity field, the obseve is affected by the gavity, so the obseve will move in the gavity field. The obseve move to anothe space point, the obseve s speed will change also. This pocess will bing a new Loentz tansfomation, and bing a new inetial coodinates. That means, to evey space point in the gavity field, thee exist one inetial coodinates coespondingly. Diffeent space point has diffeent inetial coodinates. Detemine a space point, will detemine a inetial coodinates. In this detemined inetial coodinates, the space-time is flat, not cuved. So, in the gavity field, the obseve at a space point do obseve, will get this esult. The evey space point is in the same inetial coodinates, and the time at evey space point is same. Diffeent space point has diffeent coodinate value only, not have diffeent local coodinates. Thee not exist coodinates tansfomation between diffeent space points. Fo example, when obseve the gavity field fom infinite distance, the evey space point is in the same inetial coodinates, the time at evey space point is same; thee not exist space-time bending effect; thee not exist clock delay. A paticle move in the gavity field, its movement popety is detemined by equation (.5). So, the space-time is flat in the new gavity, not is cuved. Thee not exist the local inetial coodinates. Thee only exist one global inetial coodinates. This is the geat diffeence between the new gavity and the Geneal Relativity. Fom the above discussion, we can find this esult. In the new gavity model, thee only exist inetial coodinates,

4 184 Intenational Jounal of Physics not exist non-inetial coodinates. The gavity can change the movement speed of paticle. The acceleation can change the movement speed of paticle also. The two have same effect. But the gavity and the acceleation ae diffeent. The gavity can change the movement speed of paticle, this is because diffeent space point have diffeent pojection facto, it is not because acceleation. In fact, thee is no acceleation of paticle motion in Newton mechanics in the new gavity model. Acceleation is only the concept of macoscopic classical physics, which cannot be bought into quantum theoy. In quantum theoy, thee only have the change of quantum state. The change of quantum state will show effect like the change of speed. In fact thee is no acceleation. The change of the quantum state is the tansition mutation, which cannot be equivalent to acceleation. If the acceleation is equivalent to acceleation, it is infinitely lage. The new gavity is only a additional pojection effect based on the Loentz symmety. The new gavity only changing the paticle state, not acceleate the paticle. Just a continuous state change bings an acceleated maco effect. But thee is no eal gavitational acceleation. The new gavity is vey simila to quantum theoy. Theefoe, in pinciple, the new gavity model can be econciled with the quantum theoy, do not poduce contadictions. The new gavity model may solve the poblem of gavitational quantization. The Loentz symmety, and the gavity, the two ae the pojection action fom paticle-wave symmety in 5-dimensional space-time. The paticle-wave symmety is one popety of quantum theoy. So, between the gavity and the quantum theoy, thee is some kind of deep connection that has not been evealed. The quantum theoy in 5-dimensional space-time is an aea that needs to be studied in depth. The 5th dimension, o the 4th space dimension, maybe it is eal. The motion equation of paticle in gavity field is equation (.8). It can be simplified to equation (.9). 4 = (1 ) P m (1 ) m. + = (.9) Fom equation (.9), we can get a esult. The motion equation of paticle in gavity field can satisfy the Loentz symmety. Fom equation (.4), we can get a esult. To the new gavity, its value has elationship with paticle s momentum. So, the new gavity is not a linea foce. The new gavity is a nonlinea foce. The gavity inceases the momentum of paticle. The inceased momentum convesely inceases the gavity accepted by paticle. This is a positive feedback loop pocess. Theefoe, the new gavity accepted by paticle is lage than the Newton gavity. So the new gavity is stonge than the Newton gavity. To two paticles, when the distance between two paticles eaches a value, the gavity foce between two paticles will exceed the oulomb foce. Because the new gavity equation (.4) is equation in flat space-time, the calculation method in the new gavitation is simila to the Newton gavitation. So, the accumulated calculation method in Newton gavitation can still be used in the new gavitation. This is a big advantage of the new gavitation. In the new gavitation, evey obseve is in one inetial coodinates. The inetial coodinates is in a flat space-time. The space-time is not cuved. So, the motion of paticle in the gavity field will keep the enegy consevation. So, the new gavitation does not destoy the consevation of enegy. This is anothe big advantage of the new gavitation. The new gavity is a cental foce also. This is same with the Newton gavity. So, the motion of paticle in the gavity field will keep the consevation of angula momentum. Fom equation (.8), we can find a popety. It can be easily quantized. So we can wite a wave function equation of paticle moving in gavity field. And the wave function equation can satisfy the Loentz symmety. This is a big advantage of the new gavitation. The aim that autho poposed the new gavity model, is ty to solve the poblem of gavitational quantization. In the equation (.9), thee have a popety which is simila to equivalence pinciple. If we take m as the inetia mass of the paticle, the equivalence pinciple is shown in the equation (.9), the gavity stength is equal the acceleation. But, this is fomal. The m is not the eal mass of paticle. The m is not a eal physical quantity. The m is only a fomal equivalence mass. The m does not have eal physical meaning. So, in the new gavitation, the equivalence pinciple in Newton gavitation is not eally set up. In the new gavitation, the eal physical quantity is the momentum P and the est mass m of paticle. The motion state of the paticle can be detemined by the two physical quantity. That is, the motion state of the paticle 4 be detemined by P + m. That is, the momentum P and the est mass m uniquely identify a motion state. The two physical quantity have diffeent value, this is a diffeent motion state. In the equation (.9), in the gavity field, at a space point, the gavitational foce facto is not has elationship with the motion state. In the gavity field, at a space point, to any paticle, and to any motion state, has the same gavitational foce facto. This can be undestood as the equivalence pinciple in the new gavitation. Howeve, the equivalent pinciple in the new gavitation is based on the motion state of the paticle, is not based on the acceleation of the paticle. The new equivalent pinciple can be undestood as a boade equivalent pinciple. But this undestanding, elatively eluctantly, does not have clea physical meaning, easy to poduce conceptual confusion. The autho tends to conclude that, in the new gavity, the equivalence pinciple is not set up. This can avoid conceptual confusion. The equivalence pinciple in Newton gavitation is only a esult in appoximate weak gavity, is not stictly set up. In the new gavitation, because the equivalence pinciple in Newton gavitation is not stictly set up, so the concept of acceleation actually no longe exists in the new gavitation. The new gavity does not acceleate a paticle. The new gavity is change a state of paticle. Thee's a big diffeence between the two statements. The font statement is not applicable to quantum theoy. But the behind statement is applicable to quantum theoy. Because thee only exist state changing in quantum theoy, not exist acceleation pocess. The gavity effect is changing the paticle s motion state A to state B, not acceleate the paticle. The fomula in Newton Mechanics, F= ma, is not set up in the new gavity. If eplace the

5 Intenational Jounal of Physics 185 m with m, can keep this fomula. But the m is a equivalent mass, is not a eally mass. In the late chaptes, we can find that, even if we use the concept of equivalent mass, and use the fomula to calculate the motion obit, we can t get the coect obit esult also, it will lead to lage eos. This equivalent pocessing method does not compute the coect obit esults. Thee not exist acceleation in the new gavity, and thee not exist acceleation in quantum theoy. The concept of acceleation only exists in Newton Mechanics. Theefoe, the non-inetial coodinates will disappea. So the non-inetial coodinates does not exists. This is the geat diffeence between the new gavitation and the Geneal Relativity. The new gavity can emain consistent with the Quantum Mechanics. But the new gavity is completely diffeent with the Geneal Relativity. The moe impotant distinction between the new gavity and the Geneal Relativity is that, how to undestand the Loentz symmety? The Geneal Relativity is based on the Special Relativity. In the Special Relativity, the Loentz symmety is undestood as space-time symmety, the Loentz tansfomation is space-time tansfomation. But the new gavity is based on the paticle-wave symmety in the 5-dimensional space-time. The paticle-wave symmety is a popety of paticle wave, is not a popety of space-time. We pojected the paticle-wave symmety into 4-dimensional space-time, so we get the Loentz symmety in 4-dimensional space-time. So the Loentz symmety is a popety of paticle wave also, is not a popety of space-time. In this pojection pocess, we add anothe additional pojection facto. So we can get the gavity effect in 4-dimensional space-time. The gavity is the additional pojection effect. So, the new gavity and the Loentz symmety, the two ae pojection effect, the two ae not space-time effect. The physics space-time is the 5-dimensional space-time. The 4-dimensional space-time obseved by human is just a pojection of 5-dimensional space-time. In the 4-dimensional space-time, thee miss a dimension of space. These magical effects in elativity theoy, like the time delay and expansion, actually comes fom the missing of dimension of space. These magical effects ae just obsevation effect, ae not eally physics esult. In the 5-dimensional space-time, these magical effects will disappea, not exist. The gavity only exists in 4-dimensional space-time. In 5-dimensional space-time, the gavity will disappea. In the new gavitation, the gavity only has elationship with the est mass of the gavitational souce, and the gavity not has elationship with the momentum of the gavitational souce. But, the gavity has elationship with the momentum of the paticle which accepts the gavity. Theefoe, the new gavity does not follow the Newton's Thid Law. This is a vey obvious esult. Fo example, the photon can accept gavity, but the photon can t geneate gavity. So, the gavity between a photon and a electonics does not satisfy the Newton's Thid Law, and the total momentum of the two paticles is not conseved, pehaps the total angula momentum of the two paticles is not conseved also. The new gavity is just additional pojection effect of Loentz symmety, thee not have eaction of gavity inevitably. We can think about it in anothe way. The gavity has elationship with the 5-dimensional space-time. Theefoe, in the 4-dimensional space-time, the two paticles ae not an independent closed-system actually. So the new gavity does not follow the Newton's Thid Law. This poblem needs futhe study. The new gavitation has many new popeties. It needs to be futhe studied. 3. The New Gavitational xpeimental Veification By actual calculation, we can get a esult. In the case of weak gavitational field appoximation and nea-cicula obit appoximation, the obital equation obtained by the new gavity and the obital equation obtained by the Geneal Relativity ae exactly the same. In the case of weakly gavitational field appoximation and nea-cicula obit appoximation, the two theoy ae completely equivalent. Theefoe, the expeimental veification of the Geneal Relativity unde the weak gavitational field appoximation can also pove the validity of the new gavity. Theefoe, the expeimental veification unde the appoximation of the weak gavitational field does not distinguish whethe the Geneal Relativity is coect o the new gavity is coect. But the new gavity theoy is a theoy in the flat space-time. The new gavity theoy is much simple than the Geneal Relativity. By actual calculation, we can get a esult. ven unde the appoximation of the weak gavitational field, thee ae obvious diffeences between the new gavity and the Geneal Relativity. Only in the weak gavitational field and the nea-cicula obit, when two conditions ae satisfied simultaneously, the two theoy ae completely equivalent. When only the weak gavitational field appoximation is satisfied, the esults of the two theoy calculations will be significantly diffeent fo the non nea-cicula obits with lage eccenticity. This diffeence can be used fo expeimental testing, which theoy is moe accuate, which is moe in line with the actual physical pocesses The Pecession of Mecuy Unde the foce of the Sun gavity, efe to the method of calculating the obit of mecuy in Newton Gavitation, and efe to the method of calculating the obit of mecuy in the Geneal Relativity. The following calculations can be pefomed on the obit pecession of mecuy. The mecuy moves in the sun gavity field. Its motion equation is the equation (.8). The est mass of the mecuy is m. The est mass of the sun is M. Please note that. The momentum P of the mecuy is also the function of. Its value vaies with. So we can get equation (3.1.1). 4 = (1 ) ( P + m ). (3.1.1) Unde the appoximation of the weak gavitational field, the appoximate momentum of the mecuy is fomula (3.1.). P= mv. (3.1.)

6 186 Intenational Jounal of Physics So get 4 (1 ) ( mv m ) In pola coodinates = + (3.1.3) (1 ) ( V ). m = + (3.1.4) d dθ V = ( ) + ( ). (3.1.5) dt dt The angula momentum of the mecuy is dθ L= m. dt Fo simplifying fomula, we take the angula momentum of the unit est mass. So get So get θ d L =. dt dθ L = dt 1 d d dθ 1 d d( ) = = L( ) = L. dt dθ dt dθ dθ Put this into fomula (3.1.5), so get d( 1 ) L V L ( ). dθ = + (3.1.6) Put this into fomula (3.1.4), so get d( 1 ) 1 = (1 ) L (( ) + ) + (1 ). (3.1.7) dθ m 1 We set u =, put this into fomula (3.1.7), so get du (1 u ) L(( ) u ) (1 u ). m = dθ + + (3.1.8) On both sides of the equation, do diffeential calculation by θ, so we get a complex equation. To du ( ) dθ d u du L(1 u + u ) L (1 u )( ) dθ d θ + (3.1.9) 3 Lu 3 Lu + ( L + ) u =. d u dθ item, the u and item, the u is small, omit it. 3 u ae small, omit it. To L u 3 Lu = Lu (u 3), u is small, omit it. To u item, GM GM L V, GM GM = =, so, the is small, omit it. So, the equation (3.1.9) is simplified to, d u du L L( ) 3Lu Lu dθ dθ + = d u du u 3 u ( ) dθ + = L + + dθ u 3 u ( ). θ + = + + d (3.1.1) d u GM GM GM du d L θ The (3.1.1) is the motion equation of mecuy moving in the sun gavity field. The font thee items is the esult in Newton Gavitation. The next two items is the coection of the new gavity. This coection will get the esult of the pecession of mecuy s obit. The Geneal Relativity get this equation, d u GM GM u 3 u. dθ + = L + (3.1.11) The esult in the new gavity, and the esult in the Geneal Relativity, we compae the two esults. The font fou items is same exactly. GM But, in the new gavity, thee add a item ( du dθ ). 1 du d( ) 1 d 1 d dt = = = dθ dθ dθ dt dθ 1 d 1 1 d V V = = = = u. dt L L dt V V θ θ Put into fomula (3.1.1), so get d u GM GM V 3 GM u u u. dθ + = L + + Vθ (3.1.1) Theefoe, in the new gavity, when the adial motion speed is fa less than the lateal motion speed, the 5th item is small item. If we omit the 5th item, so we can get the same esult in the Geneal Relativity. The mecuy obit meets this condition appoximately. So the 5th item can be omitted. To mecuy obit, the new gavity can get the same esult in the Geneal Relativity. The new gavity theoy can explain the pecession of mecuy. We compae the two equations, (3.1.1) and (3.1.11). We can found that. ven unde the appoximation of the weak gavitational field, thee ae obvious diffeences between the new gavity and the Geneal Relativity. Only in nea-cicula obit, the condition that the adial motion speed is fa less than the lateal motion speed can be satisfied. The 5th item can be omitted. The esult of the new gavity can be same with the esult of the Geneal Relativity. When only the weak gavitational field

7 Intenational Jounal of Physics 187 appoximation is satisfied, but the obit is non nea-cicula obit with lage eccenticity, the esults of the two theoy calculations will be significantly diffeent. We measue the obits of stas with lage eccenticity. This can be an expeimental test. So we can distinguish that. Which theoy is moe accuate, which is moe in line with the actual physical pocesses. Remind eades. In the new gavity, to the calculation of obit pecession, can t use the method of calculation to d acceleation. If we use ma = F = - v to compute obit d like in the Newton gavitation, we can t get the coect esult. This is because the equivalence pinciple is set up appoximately in the new gavity. The equivalence pinciple is only a esult in appoximate weak gavity, is not stictly set up. Thee not exists the gavity acceleation stictly. So we can t use the acceleation method to compute obit coection. The acceleation method will lead to lage eos. We must calculate diectly fom the equation (.8), we can get the desied obit coection esult. This also poves that. In the new gavity, the concept of acceleation in Newton gavity is invalid. The acceleation is only a appoximate method, can t be used in stict calculation. 3.. The deflection of light by the sun Fom the equation (.8), we can get a esult. The photon has no the est mass, so it can t act as the gavitational souce, it can t geneate gavity. But the photon has the momentum, so its motion can be affected by the gavity. The est mass of the photon is zeo. So the equation (3.1.1) change to equation (3..1). 1 Set u =, so get = (1 ) P (3..1) = (1 ). (3..) u P Now we must convet P to a fomula of V, we can compute its motion obit. So, to the photon, we define a fomula (3..3), the m is a equivalent mass of the photon. So get P= mv. (3..3) = (1 ). (3..4) u mv Simila to the calculation of mecuy s obit, in pola coodinates d dθ V = ( ) + ( ). (3..5) dt dt take the angula momentum of the unit equivalent mass So get dθ L =. dt du (1 u ) L(( ) u ). m = dθ + (3..6) On both sides of the equation, do diffeential calculation by θ, so we get To du ( ) dθ d u du L(1 u + u ) L (1 u )( ) dθ d θ + (3..7) 3 Lu 3Lu + Lu=. d u dθ item, the u and item, the u is small, omit it. 3 u is small, omit it. To L u 3 Lu = Lu (u 3), u is small, omit it. So the equation (3..7) is simplified to d u du L L( ) 3Lu Lu dθ dθ + = du u 3 u ( ) θ + = + dθ d u d u 3 u ( ). θ + = + d (3..8) d u GM GM du d θ The (3..8) is the motion equation of photon moving in the sun gavity field. We compae it with the esult in the Geneal Relativity. The font thee items is same exactly. GM But, in the new gavity, thee add a item ( du dθ ). Simila to the calculation of mecuy s obit. 1 du d( ) 1 d 1 d dt = = = dθ dθ dθ dt dθ 1 d 1 1 d V V = = = = u. dt L L dt V V θ θ Theefoe, in the new gavity, when the adial motion speed is fa less than the lateal motion speed, the 4th item is small item. If we omit the 4th item, so we can get the same esult in the Geneal Relativity. To the question of the deflection of light by the sun, it meets this condition appoximately. We can omit the 4th item. So the new gavity can get the same esult in the Geneal Relativity. The new gavity theoy can explain the deflection of light by the sun. Simila to the calculation of mecuy s obit. To the motion of photon in the gavity field, thee ae obvious diffeences between the new gavity and the Geneal Relativity. Only the condition that the adial motion speed is fa less than the lateal motion speed be satisfied, the 4th item can be omitted. The esult of the new gavity can be same with the esult of the Geneal Relativity. When the motion of photon is not a sideways sweep of stas, the

8 188 Intenational Jounal of Physics photon has a lage adial motion speed, the esults of the two theoy calculations will be significantly diffeent. We measue vaious type of photon. This can be an expeimental test. So we can distinguish that. Which theoy is moe accuate, which is moe in line with the actual physical pocesses. Fom the equation (3..1), we can get the esult. The speed of photon moving in the gavity is the light speed. The gavity does not change the speed value of photon, but change the momentum of photon, and change the motion obit of photon. This is a vey obvious conclusion. Because the new gavitation is based on the Loentz symmety, so it should not take a esult conflict with the Loentz symmety. Although the photon move with the speed in the gavity, but the gavity will change the momentum of photon, and will change the motion obit of photon. The photon move between two space points, compaed with the movement in the vacuum, movement in the gavity field will take moe time. This is equivalent to the slow motion speed of the photon in the gavity field, o can be consideed equivalent to a time delay. But this is an equivalent way of thinking. It is not tue. In fact, the photon s moving speed in the gavity field maintains the light speed, is not changed. And thee not exist time delay in the gavity. The new gavitational space-time is flat. In some special case, to the motion of photon in the new gavity, thee have an equivalent method. In the Newton gavitation, the movement of paticle affected by the gavity, will geneate acceleation. d ma = F = v. (3..9) d The new gavitational foce is the equation (.4). The est mass of photon is zeo. The photon only has the momentum. So the equation (.4) change to, F GM GMP v = P = (3..1) d GMP GM dp d d = v = ( ) (3..11) On the condition that the adial motion speed is fa less than the lateal motion speed, thee exists this fomula appoximately. L = P Because consevation of angula momentum, so So get dl = dl d = ( P+ dp ) d =. dt d dt d dt Put into (3..11), get dp P =. d dv GMP GM P GMP F = = ( ( )) =. (3..1) d Simila to Newton Mechanics, we define an equivalent mass of the photon. So get Put into (3..1), so get The acceleation is P = mv = m. F GMm =. (3..13) a GM =. (3..14) The photon s equivalent gavitational acceleation is twice of the acceleation of the paticle which has est mass, and is twice of the acceleation in Newton Gavitation. But the acceleation does not incease speed of photon. The acceleation decease speed of photon. This is a supising esult. Theefoe, if we compute the motion of photon by the method of Newton gavitation, the acceleation of the photon must be twice of the acceleation in Newton Gavitation. But this is a appoximate esult. This is coect only on the special condition that the adial motion speed is fa less than the lateal motion speed. To odinay case, this no longe is coect. The motion of photon in the gavity is vey special. The photon has no est mass, so it is vey diffeent with the odinay paticles which have est mass. To odinay paticles, we can daw on Newton gavitation, using foce and acceleation to see the gavitational phenomenon. Howeve, the motion of photon can no longe be viewed in tems of gavitational foces and acceleations. Fo photons, the gavitational view as a space-time pojection effect, thus affecting the photon, in this pespective to see the poblem, moe easily undestood. This is simila to the Geneal Relativity. But the space-time pojection effect of the new gavity is diffeent fom the space-time effect of the Geneal Relativity. The new gavitational space-time is flat, not is cuved The Red Shift of Light by the Sun In the new gavity, the space-time is flat, not is cuved. vey obseve is in an inetial coodinates. So, in the new gavity field, the motion of photon keeps the enegy consevation. So the question of the ed shift of light by the sun is vey simple. In the new gavity, the motion equation of photon is (.8). The est mass of photon is zeo. So, get = (1 ) P. (3.3.1) The photon is emitted fom space point 1, its momentum is P1. The enegy 1 is 1 = (1 ) P 1. The photon move to space point, its momentum change to P. The enegy is 1

9 Intenational Jounal of Physics 189 = (1 ) P. The enegy is conseve. 1=. So get (1 ) (1 ) P 1 P = 1 (3.3.) Not include the gavitational enegy, the enegy of the photon itself meet this fomula. So get = P = hν. (3.3.3) (1 ) (1 ). ν ν hν1 = hν (3.3.4) ( ) = =. ( 1 ) 1 1 The ed shift of light is defined as ν (3.3.5) ν = 1 1 (3.3.6) ν 1( ) ( 1) ν = 1 = ( ) ( ) 1 1 ( 1) 1 1 ( ). 1 1 Hee, we do a appoximate pocessing, 1 1. To the question of the ed shift of light by the sun, the gavity is an appoximate weak gavity, so we can do this appoximation. So the ed shift of light by the sun is 1 1 GM ν = ( ). (3.3.7) 1 This esult is same with the Geneal Relativity. And this esult is same with the Newton gavitation. Fom the above desciption, we can find that. In the new gavity, to one obseve, the calculation of the deflection of light by the sun, and the calculation of the ed shift of light by the sun, ae follow the same gavitational equation, ae in the same inetial coodinates, ae in the same flat space-time. Thee not exist effect of cuved space-time. Thee not exist time delay. Thee not exist coodinates tansfom. The method in the new gavity has consistent logic. In the Geneal Relativity, the calculation of the deflection of light by the sun is based on the motion equation. But the calculation of the ed shift of light by the sun must use the method of time delay, can t use the method of the motion equation. The two calculation must use diffeent method, does not have consistent logic. This is also a aspect being doubted to the Geneal Relativity The Rada cho Delay by the Sun The calculation of the ada echo delay by the sun is simila to the calculation of the deflection of light by the sun. Fom the above desciption of the calculation of the deflection of light by the sun, the motion equation of photon is d u u 3 GM u GM ( du ). dθ + = + dθ (3.4.1) In the Geneal Relativity, the calculation of the ada echo delay by the sun is based on the equation (3.4.). d u GM u 3 u. dθ + = (3.4.) Simila to the calculation of the deflection of light by the sun, if we only take the font thee items of the equation (3.4.1), the two equations is same exactly. So the new gavity can take same esult with the Geneal Relativity. So the new gavity can explain the ada echo delay by the sun. Simila to the calculation of the deflection of light by the sun, thee must meet a condition that the adial motion speed is fa less than the lateal motion speed, the esult is coect. We can get the same esult with the Geneal Relativity. If the condition can t meet, the adial motion speed can t be omitted. So thee have obvious diffeences between the new gavity and the Geneal Relativity. So, if we measue the esult of the ada echo delay in vaious situations, we can distinguish that. Which theoy is moe accuate, which is moe in line with the actual physical pocesses. We study the equation (3.3.1) again. This equation is the motion equation of photon in the gavity. We can found that. It can be seen equivalently as that the light speed is deceased by the gavity. But, please distinguish it caefully. This just is an equivalent pocessing method. The light speed is not deceased in fact. In the new gavity, we define an equivalent speed of light. g = (1 ). So the equation (3.3.1) will have a same fom with the photon in the vacuum. = P g. This is equivalent with the time delay in the Geneal Relativity. In the Geneal Relativity, in the appoximate weak gavity field, the time delay is GM GM tgt 1 (1 ) t (1 ) t. This effect is completely equivalent with the speed deceased of light. The deceased facto is 1. But, please note. This equivalence can be set up only in the appoximate weak gavity field. In the new gavity, whethe the gavity is stong o weak, the deceased facto is same, it is 1. But in the Geneal Relativity, when the gavity is stong, the facto is

10 19 Intenational Jounal of Physics GM =. So, in stong gavity, the esult of the new gavity is not same with the esult of the Geneal Relativity. 4. The mpty Hole in the New Gavitation In the new gavity, the motion equation of paticle is equation (.8). Fom this equation, we can stictly calculate the paticle s elational function between the motion speed and the space point. Fom equation (.8), get 4 = (1 ) P + m. (4..1) The is the enegy of paticle in the gavity field. Because the enegy is conseved, so the enegy is the initial enegy. This enegy will emain unchanged. It is a constant. To a paticle which has the est mass, in the gavity, it meets the Loentz symmety. So get So get P = mv = m. 1 V m m = mv = V. (1 ) V 1 Afte a complex calculation, the final esult is V (4..) 4 = m 1 (1 ). (4..3) The equation (4..3) is the elational function between the motion speed and the space point in the gavity field. But this equation is coect to the paticle which has the est mass. To the paticles which not have est mass, it is not coect. The speed of paticles which not have est mass will keep the speed of light, like photon. Fom equation (4..), as long as we know paticle s the est mass and its initial enegy, so we can calculate its motion speed at any space point.. We fist discuss the aea In this aea, when paticle move in the gavity field, with the decease of the distance, the speed V of the paticle will incease continuously. The speed will close to, but neve each. This is simila to the velocity vaiation in the Loentz symmety, whee V is constantly inceasing, close to, but can neve each. In othe wods, paticles can only be infinitely close to, but can t achieved. Fom (4..3), we find that. Thee exists a vey special position. At =, at this special sphee, the speed of paticle will each. To any paticles, if it achieves this special position, its speed must be. But we view the equation (4..1) again. If the paticle achieves the position, its enegy must be zeo. Because enegy is conseved, so, if a paticle can achieve the position, its initial enegy must be zeo. But we view the equation (4..1) again. If a paticle s initial enegy is zeo, only the paticle s initial position is. As long as the paticle s initial position is not, its initial enegy can t be zeo. So we pove that, the paticle can t achieve the position. Fom the equation (4..1), we can find that. As long as the paticles appea in the aea <, its enegy must be negative. But the enegy is conseved. So the paticles in the outside aea, can t move into the inne aea. The paticles can appea in the inne egion, only the paticles ae excited diectly in the inne aea. Does the paticles can be excited in the inne aea? This question need futhe eseach. Fom above discuss, we can seen the scale facto of the new gavity as the black hole adius. The black hole adius of the new gavity only be half of the Geneal Relativity, and only be half of the Newton gavitation also. But, the concept of the black hole in the new gavity is diffeent with the Geneal Relativity. In the new gavitation, the paticles in the outside aea of black hole can t move into the inne aea of black hole. The new gavitation not have a special coodinates which paticles can move into inne aea fom outside aea. Obseve in any space point and in any coodinates, we will take the same equation. So, in the new gavitation, the esult applies to all coodinates. In the new gavity, because the gavity foce, to the two paticles, as long as one has the est mass, it must have the black hole adius. So, the distance between the two paticles only can be infinitely close to the black hole adius, can t each the black hole adius, can t be less than the black hole adius. Theefoe, the concept of the black hole in the new gavitation is vey diffeent. In fact, the black hole is a empty hole, in the new gavitation. It is a empty hole which pohibits the enty of outside paticles. This is simila a no-fly zone. The empty hole of the new gavity does not suck in paticles, but pohibits paticles into this aea. The empty hole of the new gavity is simila to the wind eye of huicanes and typhoons. So, in the new gavity, thee not have the space-time singulaity and the enegy singulaity. In above discuss, we put all the est mass of the gavitational souce at a cental point, and we see the gavitational souce as a point paticle. But, in fact, a gavity souce is collection by a lage numbe of paticles, is not a point paticle. To the sun, if we obseve it in the outside of the sun, we can calculate a empty hole adius of the sun. But, if we obseve it in the inside of the sun, the inne est mass of the sun is deceasing. The moe you ente the sun's coe, the smalle the inne est mass of the sun. Until the sun has been educed to a quantized point paticle, this pocess can be inteupted. That is, the moe you ente the sun's coe, the smalle the empty hole of adius of the sun. So, the question of the sun s empty hole is vey complex. We cannot simply assume that, paticles cannot ente into the

11 Intenational Jounal of Physics 191 inne aea of the empty hole of the sun. This question needs futhe eseach. In fact, this is a manifestation of the gavitational scale effect. The adius of the empty hole depends on the total est mass of the gavitational souce. But, the total est mass of the gavitational souce is changing with the the obseved distance. The moe you ente the gavitational souce s coe, the smalle the total est mass of the gavitational souce. Unless the gavitational souce is a quantized point paticle, its total est mass does not change. Only the gavitational souce is a quantized point paticle, its adius of the empty hole does not change with the obseved distance, can keep a constant. So, to the gavitational souce which is not a quantized point paticle, its adius of the empty hole will change with the obseved distance. The empty hole has a scale effect. So the empty hole o black hole may not be eal. About the empty hole o black hole, it needs futhe eseach. 5. Quantization in the New Gavity The motion equation of the paticle in the new gavity field is (.8). Fom (.8), can get 4 (1 ) P (1 ) m. = + (5.1) This equation is simila to the Klein-Godon equation. It meets the Loentz symmety. The equation is vey easy to be quantized. So we can tun the motion equation into a quantum wave function equation. The motion of a paticle in a gavity field can be descibed as quantized. And the quantum wave function equation meets the Loentz symmety. This is the emakable advantage of new gavity. Follow the standad quantization method, tun enegy into an opeato and tun momentum into an opeato, so we can get a quantum wave function equation. Ψ 4 (1 ) (1 ) m. (5.) = Ψ+ Ψ t We define the stationay state wave function Ψ= e it/ φ. (5.3) So we can get the stationay state wave function equation. 4 φ = (1 ) (1 ) m. φ + φ (5.4) The new gavity is the cente foce field. So we can efe to the calculation method of wave equation of the hydogen atom. Afte complex pocessing, we get the adial equation (5.5) finally. To solve this adial equation, we can calculate the quantized enegy of the paticle moving in the gavity field. 4 d u m ll ( + 1) +. u = (5.5) d (1 ) In geneal, the solution of this equation is too difficult. The autho only makes a simplified calculation to two special cases, and discusses some special popeties of the quantization of the new gavity. In geneal computing, inteested eades can study this topic in depth, evealing the quantum popeties of the new gavity in geneal situations Quantization in the Appoximate Weak Gavity In the appoximate weak gavity, <<, so 1 (1 + ) (1 ) So the (5.5) can be simplified to 4 ll ( + 1) d u m + + u =. (5.6) d This equation is simila to the adial equation of the hydogen atom. So we solve this equation efeing to the hydogen atom. We define a new quantum numbe of angula momentum. Then define ' ' l( l+ 1) = ll ( + 1). (5.7) ' = (5.8) n n l The n is the quantum numbe of enegy of the paticle. The n is the adial quantum numbe. So can get 4 m 1 = ( ). 4n So we get the fomula of the quantized enegy. 4 4m n = + n ( 1 1). (5.9) (5.1) This is only a simplified esult. Because the n have elationship with, so the equation of the is a quatic equation. Its calculation is vey complex. Hee we only make simplified calculation and make simple appoximate discussion. So the following discussion is only a efeence. It pehaps has eo. Because we get the equation (5.9) and (5.1) only in the appoximate weak gavity, the esult (5.1) has actual physical meaning when the n is big. That is the long distance motion. To the nea distance motion, o the n is small, the esult (5.1) does not have actual physical meaning. Please note this. We obseve the fomula (5.7) caefully. Thee exists a limit on enegy actually. If the enegy does not meet