Physics Essays volume 16, number 3, 2003

Transcription

1 Physis Essays olume 6, number 3, 003 Calulation of So-Called General Relatiisti Phenomena by Adaning Newton s Theory of Graitation, Maintaining Classial Coneptions of Spae and Relatiity Reiner Georg Ziefle Abstrat With the example of the motion of Merury around the Sun it is shown how Newton s theory of graitation should be adaned by taking into onsideration the finite eloity of graitational expansion and the present onept of transferene of fores by partiles to be able to alulate so-alled general relatiisti phenomena suh as the additional motion of Merury s perihelion, the urature of a light beam at the surfae of the Sun, and the phenomena obsered at the binary pulsar PSR 93+6, maintaining lassial oneptions of a Eulidean spae and the Galilean priniple of relatiity. Key words: perihelion, Merury, relatiity, GRT, pulsar, PSR 93+6, graitation, Paul Gerber, Newton, Einstein. INTRODUCTION Newton s theory of graitation has, in ontrast to Einstein s theory of general relatiity, the defiieny that ertain phenomena annot be predited by it. An example is the problem of the motion of Merury s perihelion. In the 9th entury sientists searhed for a further planet in our solar system in order to be able to orretly explain the motion of Merury s perihelion on the basis of Newton s theory of graitation. But the planet they alled Volano was neer found. Howeer, Einstein s theory of general relatiity was later able to explain this phenomenon as well as others. Newton assumed that graitational fore has an instantaneous effet, that is, a graitational expansion with infinite speed. Today we know that graitational expansion annot be infinitely fast. One of the first sientists who tried to deelop Newton s theory of graitation further by onsidering the finite eloity of graitational transferene and by assuming that the graitational transferene might probably hae the alue of the eloity of light was Paul Gerber, a German shool teaher, whose publiation in the year 97 is disussed later. () But, as far as I know, there does not exist a sientifi publiation on the attempt to deelop Newton s theory of graitation further by onsidering the present onept of transferene of fores by partiles. In a omprehensie sientifi iew, this is an inomplete and onsequently unsatisfatory matter.. ADVANCING NEWTON S THEORY OF GRAVITATION To be able to explain the so-alled general relatiisti phenomena by adaning Newton s theory of graitation we hae to go bak to the imagination of Newton about spae and relatiity, the way it used to be in the physiists imagination until the beginning of the 0th entury, before Einstein himself deeloped his ideas. While Newton s theory of graitation takes plae in a Eulidean spae, Einstein s spae is a non-eulidean, or a so-alled ured, spae. While Newton belieed in the Galilean priniple of relatiity, Einstein established a ompletely new kind of priniple a relatiisti one. For a paradigm it is shown with the example of the motion of Merury how Newton s theory of graitation an be deeloped further if we postulate the following, of whih the first and seond points, to present-day physiists, sound, of ourse, ery strange: () We lie in an Eulidean spae. () The Galilean priniple of relatiity is alid. (3) The speed of graitational extension has the same speed as light, i.e., about km/s. (4) The graitational fore is transferred by partiles alled graitons. From this we get the fol- 375

2 Calulation of So-Called General Relatiisti Phenomena by Adaning Newton s Theory of Graitation lowing deriation: Graitons, whih are emitted by matter, respetiely a mass, shall moe from this matter in all diretions by the speed of light in a Eulidean spae. Next we want to go from the assumption that Merury is in a resting position with respet to the Sun. In this ase a ertain number of graitons emitted by the Sun will run aross Merury. The relatie frequeny with whih the graitons emitted by the Sun meet Merury depends on the eloity with whih the graitons moe with respet to Merury. If Merury did not moe, the graiton s eloity with respet to Merury would hae the speed of light (), whose relatie alue is. In this ase the relatie alue of the frequeny with whih the graitons emitted by the Sun meet Merury is also. If Merury moes around the Sun, whih is the ase in reality, with the eloity, the eloity of the graitons emitted by the Sun would run aross Merury with a faster eloity than before, so that the relatie alue of the graiton s eloity with respet to Merury should be greater than, whih is of ourse not possible in relatiisti physis. But we hae postulated that the Galilean priniple of relatiity should be alid, so that we want to assume, neertheless, that this is possible. If the relatie alue of the eloity of the graitons emitted by the Sun with respet to Merury is greater than, that is to say not but x (Fig. ), then the relatie alue of the frequeny with whih the graitons emitted by the Sun meet Merury inreases by the fator x. As Merury moes around the Sun with the eloity, howeer, the relatie alue of the eloity of the graitons emitted by Merury and running aross the Sun should be greater than, that is to say also x. In this ase the relatie alue of the frequeny with whih the graitons emitted by Merury meet the Sun also inreases by the fator x. The fator x we an alulate easily by the Pythagorean theorem, whih is, in spite of the ured planetary orbit of Merury, suffiiently orret if we regard ery small distanes. We then get the formula for x: 376 x = +. To get the formula for relatie alues we hae to diide the absolute alues of (eloity of the graitons) and (eloity of Merury around the Sun) by the absolute alue of, so that we get x = + = +. Figure. The relatie eloity of the emitted graitons related to the Sun and Merury. The fator x I am going to all the graitational fator of motion γ in the following: γ = +. Hereby the frequeny of the interation between the graitons emitted by the Sun and the mass m of Merury inreases by the fator γ. Beause the relatie frequeny with whih the graitons emitted by Merury meet the Sun also inreases by the fator γ, the frequeny of the interation between the graitons emitted by Merury and the mass M of the Sun also inreases by the fator γ. To get the whole fator of the inreasing of the graitational interation between the Sun and Merury, we therefore hae to square the fator γ. By this knowledge, Newton should hae had to multiply his formula for the fore of graitation by the fator (γ ), and the formula for the fore of graitation should hae been ( γ ) GMm F =, r where G stands for the Newtonian graitational onstant, M for the mass of the Sun, and m for the mass of a planet. This result an be interpreted to mean that G is not as onstant as Newton thought. Beause of the differing speed of Earth around the Sun during one year of km/s, G should therefore flutuate slightly. In the formula of Newton s kineti equation

3 Reiner Georg Ziefle for planets, whih is not pointed out here, the fator (γ ) would be presered in the numerator, although the mass m of a planet anels out in the numerator and denominator beause of the proportionality, respetiely equialene, of inert and heay mass. 3. CALCULATION OF SO-CALLED GENERAL RELATIVISTIC PHENOMENA But for our further onsiderations we don t een need the formula of Newton s kineti equation for planets. Without this it is possible to derie the differene of the motion of Merury s perihelion as opposed to Newton s theory of graitation. As graitation auses an aeleration of masses, the postulated additional graitational effet must ause an additional graitational aeleration of a mass suh as Merury, depending on the mass s eloity relatie to the Sun. The oneption of today s physiists goes from the assumption that graitational aeleration depends on the largeness of the masses and the distane between the enters of the masses. But what happens if two masses, whih are attrating eah other by graitational fore, are inreasing or if the distane between two masses is dereasing? If we go from imagining that graitational fore is transferred by graitons, an inreased mass will emit more graitons by the fator the mass has inreased and therefore the frequeny of the interation between these emitted graitons and another mass inreases by the same fator. If the distane between two masses dereases by a ertain fator, there are arriing at eah mass more graitons in the same time by the square of this fator, so that the frequeny of the graitational interation between the emitted graitons and the masses is also inreasing by the square of this fator. If these effets ause graitational aeleration, the additional graitational effet, whih I deried aboe, must also ause graitational aeleration if as pointed out by the moement of Merury around the Sun the frequeny of the interation between the masses and the graitons emitted by the Sun and the planet is inreasing by the square of the fator γ. If an additional aeleration of Merury results, so that the aeleration inreases by the fator (γ ), the eloity of the planet must also inrease by the same fator. If the eloity is inreasing by the fator (γ ), in a ertain time a larger angle is also traersed by the radius of the elliptial orbit of Merury by the fator (γ ). Eah angular position φ therefore hanges by the fator (γ ), so that we get for the hanged angular position φ φ = ( γ ) φ, = + φ. For the differene φ = φ φ we get φ = φ φ = + φ φ = φ + φ φ = φ. The eloity dependene of eah angle of an elliptial orbit is gien by min ( e) ( φ) = +, e osφ where e is the eentriity of the elliptial orbit and min is the eloity at the aphelion position. The eentriity of the elliptial orbit of Merury is and the eloity of Merury at the aphelion position is km/s. The hange of angle φ at eah angular position an be alulated by ( + e) min φ = ( e os φ ) φ. To alulate the hange in the angular position for the whole moement of the planet on its elliptial orbit we hae to use the median eloity of Merury around the Sun, whih is km/s. (4) This is related to the speed of light by a relatie eloity of , so that we get the square of a graitational fator of motion γ ( γ ) = + = + ( ) =

4 Calulation of So-Called General Relatiisti Phenomena by Adaning Newton s Theory of Graitation As the median angular position of an elliptial planetary orbit is π, hereby results from the median angular position φ an altered angular position φ : 378 φ = ( γ ) φ ( γ ) = π = + π. For the median differene φ = φ φ we get φ = φ φ = ( ) γ φ φ = ( ) γ π π = π. As there results an alteration for eah angular position along the whole route of Merury s path from perihelion to perihelion, that is, π, we hae to multiply this differene by π so that we get for the alteration of the angular position per reolution around the Sun φ = π π = π π = = rad. We get the same result if we partially integrate the formula for φ and put in for the median eloity of Merury ( = km/s): π φ = φ 0 dφ π ( = φ ) 0 ( ) = π = π = rad. If we diide π by π, we get the median angular position π of the elliptial orbit, as mentioned aboe. Contrary to Newton s theory of graitation, we get an alteration of the angular position of Merury s perihelion per reolution around the Sun of rad, or degrees. The time Merury needs for one reolution around the Sun is days. (4) This is 4.5 reolutions around the Sun per year ( days: days). To get the oneniently ited alteration of the angular position of Merury s perihelion in degrees per hundred years we hae to multiply the alteration of the perihelion position per year by : φ = = Expressed in angular seonds this is 43. : φ = = 43.. Aording to Einstein s theory of general relatiity, the additional adane of the perihelion s position per hundred years is, as opposed to Newton s theory of graitation, angular seonds. (3) The obseration for the additional forward motion of Merury s perihelion is about 43. ± 0.45 per hundred years. (3) The same onlusions result by using Newton s formula for the whole energy of an elliptial planetary orbit. () Aording to Newton s mehanis, the whole energy of an elliptial planetary orbit is the same as that of a irular orbit with the diameter of the major axis of the ellipse or with a radius of the semimajor axis (a) and is gien by the formula m GMm GMm E = = r a The term (m /) stands for the kineti energy (E k ) and the term (GMm/r) stands for the potential energy of graitation (E g ), whih is defined as a negatie graitational potential. On the basis of our onsiderations we hae to postulate that the Newtonian graitational onstant depends on the speed of a planet or of any other objet with a graitational interation, respetiely, in our ase, with the speed of Merury. If by the motion of Merury the Newtonian graitational onstant inreased by the fator (γ ), the whole energy of the elliptial planetary orbit would derease by the fator (γ ), beause of its negatie algebrai sign, so that the whole energy of an elliptial planetary orbit would be smaller by the fator (γ ) than Newton expeted. Clas-.

5 Reiner Georg Ziefle sial mehanis predits that the orbiting eloity of a planet is larger if the energy E of an elliptial orbit is smaller. This means that, if the whole energy E of the elliptial planetary orbit is smaller by a ertain fator, the angle traersed by the radius in a ertain time must also be larger by this fator, so that the sidereal reolution of Merury around the Sun is finished before the perihelion position is reahed again, so that the perihelion position must adane by eah reolution around the Sun. If we regard the photons of a light beam as partiles (as Einstein did himself) with a graitational interation, in the ase of a light beam striking the surfae of the Sun, the square of the graitational fator of motion γ would be ( γ ) = + = + = + =. As we postulated that the Newtonian graitational onstant depends on the speed of any objet with a graitational interation by the motion of a light beam, respetiely a photon, the Newtonian graitational onstant should also in this ase inrease by the fator (γ ), so that the urature of a light beam at the surfae of the Sun should hae double the alue as is expeted by Newton s mehanis: GM 4GM φ = =. r r This is the orret alue, as is predited by Einstein s theory of general relatiity. (5) By simple onsiderations other so-alled general relatiisti phenomena an also be alulated. Aording to Kepler s seond law, in the same time the same area of an elliptial planetary orbit is always traersed by its radius. This means that the area ( A) traersed by the radius in a ertain time and the time ( t) the radius needs to traerse this area are proportional. Howeer, if the eloity inreases by the fator (γ ) in a ertain time, a larger angle is traersed by the radius of the elliptial orbit of Merury, also by the fator (γ ). And, if in a ertain time a larger angle ( φ) is traersed by the radius by a ertain fator, a larger part ( A) of the planetary orbit is traersed by the square of this fator, as an area is a square measure with respet to an angle. Aording to this, A is proportional to φ, so that we get, for the median differene A = A A, A = φ A = π A = [ ] A = A. Aording to Kepler s seond law, A and t are proportional, but if the radius traerses a larger part of the area of the planetary orbit in the same time, whih is larger by A, the time the radius needs to traerse this area is shorter by t, so that t must hae a negatie algebrai sign. Therefore we get t = t. Aording to our onsiderations, the time that Merury needs for one reolution around the Sun is less than Newton expeted by a fator of As Merury needs days ( t = s) for one reolution, Merury needs about s less per reolution around the Sun: t = t = s = s. Aording to this, the reolution of Merury or of another planet around the Sun must be faster than Newton would hae expeted and must get slightly faster and faster with time, so that the orbit of a planet loses energy. I reised my preditions for other so-alled general relatiisti phenomena, for example the phenomena obsered at the binary pulsar PSR (6,7) In this ase the alulation is a little bit more diffiult, as there are two stars, a pulsar and its unseen ompanion. The pulsar and its ompanion both follow eentri elliptial orbits around their ommon enter of mass. The eentriity of the pulsar s elliptial orbit is gien by e = The minimum separation is alled periastron and the maximum separation is alled apastron. The period of the orbital motion is 7.75 h and the stars are nearly equal in mass, about.4 solar masses (m p =.4, m =.4). Therefore in the following we go from the simplifying assumption that the parameters of the elliptial orbit of the pulsar are π 379

6 Calulation of So-Called General Relatiisti Phenomena by Adaning Newton s Theory of Graitation also alid for the orbit of the ompanion. During the moement on their orbits the stars moe more slowly when they are at the apastron than when they are at the periastron. The eloity of the stars aries from a minimum of 75 km/s to a maximum of 300 km/s. The median eloity of the stars is 87.5 km/s. As the two elliptial orbits hae an inlination (i) toward eah other of about angular degrees (os i = 0.933), the median eloity m with respet to the ommon enter of mass is 75 km/s: m = 87.5 km/s osi = 87.5 km/s = 75 km/s. This is Aording to our onsiderations, in this ase we expet the square of the graitational fator of motion γ to be ( γ ) = + = The semimajor axis of the elliptial orbit of the pulsar is gien by a. For the minimum distane of the pulsar on the major axis from its elliptial fous we get q = a ( e) = a With respet to the plane through the enter of mass and the two stars we get a minimum distane from the enter of mass at the periastron of q = a ( e) osi = a = a. And for the maximum distane of the pulsar on the major axis from its elliptial fous we get Q = a ( + e) = a.67. With respet to the plane through the enter of mass and the two stars we get a maximum distane from the enter of mass at the apastron of Q = a ( + e) os i = a =.509 a. As we an see, the distanes are smaller with respet to the elliptial orbit, whih is projeted on the plane through the enter of mass and the two stars, than the analog distanes on the major axis. This is the reason why we got a slower median eloity of 75 km/s instead of 87.5 km/s as the pulsar or its ompanion is moing around the smaller projeted orbit in the same time as on the larger elliptial orbit in the plane of the major axis. There is an important differene between the orbit of Merury where the Sun stays at the elliptial fous, so that the graitational effet of the Sun against Merury is unaltered and that of the two stars, whih are moing around their ommon enter of mass. The graitational effet of eah star with respet to the ommon enter of mass alters with the distane of eah star from the ommon enter of mass. From the data of distanes at the apastron and the periastron we an see that the relatie graitational effet, whih is aused in the ommon enter of mass by eah star at the periastron, is about 8 times stronger than at the apastron, where the relatie graitational effet is with respet to the graitational effet at the periastron. As the graitational effet is reiproal to the square of the distane, we get for the relatie graitational effet at the periastron ompared with the graitational effet at the apastron [ a ( + e) os i] ( + e).67 = = = [ a ( e) os i] ( e) For the median relatie graitational effet aused in the enter of mass by eah star we get = This means that the median graitational effet, whih is aused by eah star in the ommon enter of mass, is about 9.45 times stronger than in the ase of an elliptial orbit, so that the relatie graitational effet in the enter of mass is unaltered. If the median graitational effet aused by the ompanion in the ommon enter of mass is about 9.45 times stronger than in the ase of an elliptial orbit, the graitational effet is unaltered in the enter of mass, respetiely. Aording to our onsiderations aboe, the angle traersed by the radius of the elliptial orbit of the pulsar in a ertain time must be on aerage 9.45 times larger, so that the effet we deried aboe must be on aerage 9.45 times greater. To get the alteration of the angular position of the periastron, we therefore hae to multiply the effet we deried aboe for the alteration of Merury s perihelion position by 9.45, so that we expet 380

7 Reiner Georg Ziefle φ = π γ π π [( ) ] 9.45 π 9.45 = = π = rad 9.45 = rad. Aordingly, the alteration of the angular position of the pulsar (and its ompanion) at the periastron per reolution around the ommon enter of mass is about rad, whih is about angular degrees. The time the pulsar needs for one reolution around the ommon enter of mass is 7.75 h. This gies 3 reolutions per year, so that we get an alteration of the pulsar s position at the periastron per year of about 4. : φ = = 4.. This means that the periastron is adaning about 4 angular degrees per year, as is also predited by Einstein s theory of general relatiity. Depending on the method, the obsered alteration of the periastron s angular position is 4.0, respetiely 4., per year. (6,7) Aording to our onsiderations aboe, this also means that the area ( A ) of the elliptial orbit of the pulsar and of its ompanion, whih is traersed by the radius in a ertain time, is on aerage larger by the square of the fator 9.45 than the omplying part of an elliptial orbit, where the graitational effet in the enter of mass would be unaltered, respetiely, so that we get A = (9.45) A. And, as A and t are proportional, t = (9.45) t. For the relatie alteration of the time that the pulsar needs for one reolution we get t t = [( γ ) π π ] = π t [ π ] = t = t. When the position of the periastron is reahed depends on the arrial of both stars at their minimum separation, so that we hae to regard the elliptial orbit of the pulsar and its ompanion, and therefore hae to double this result, if we want to alulate the relatie alteration of the arrial of the pulsar and its ompanion at the periastron: t = t = t. Thus we get a relatie alteration of about.3 0. Einstein s theory of general relatiity predits an alteration of.4 0, while the obsered relatie alteration of time with respet to the arrial at the periastron is (.30 ± 0.) 0 per reolution. (7) As the pulsar and its ompanion need about 7.75 h ( t = 7907 s) per reolution around the ommon enter of mass, they therefore need s less per reolution to reah the position of the periastron: t = t = s = s. This is about s per year (3 reolutions). Aording to this, the reolution of the pulsar and its ompanion around the ommon enter of mass is faster than Newton would hae expeted and must get faster and faster with time, so that the system is losing energy, whih is explained by present-day physiists by graitational radiation. (6 8) 4. DISCUSSION Aording to my onsiderations, the postulated additional graitational effet must ause an additional graitational aeleration on a mass suh as Merury, depending on the mass s eloity relatie to the Sun. The oneption of today s physiists starts from the assumption that graitational aeleration depends on the size of the masses and the distane between the enters of the masses. If we go from the imagination, that graitational fore is transferred by graitons, an inreased mass will emit more graitons by the fator the mass has inreased and therefore the frequeny of the interation between these emitted graitons and another mass inreases by the same fator. If the distane between two masses dereases by a ertain fator, more graitons are arriing at eah mass in the 38

8 Calulation of So-Called General Relatiisti Phenomena by Adaning Newton s Theory of Graitation 38 same time by the square of this fator, so that the frequeny of the graitational interation between these emitted graitons and the masses is also inreasing by the square of this fator. If these effets ause an aeleration, the additional graitational effet, whih I deried aboe, must also ause an aeleration, if as pointed out by the motion of Merury or another planet around the Sun the frequeny of the interation between the graitons emitted by the Sun and the planet and their masses inreases by the square of the fator γ. As mentioned in the introdution, one of the first sientists who tried to deelop Newton s theory of graitation further by onsidering the finite eloity of graitational transferene and by assuming that the eloity of the graitational transferene might probably hae the alue of the eloity of light was Paul Gerber, a German shool teaher. () Gerber imagined that a mass auses a status of enforement in its surrounding spae, whih spreads by the eloity of light. He apprehended that by assuming a finite eloity for the graitational transferene the moement of masses should affet the graitational interation between masses. He went from the assumption that graitation is the result of a graitational potential, whih is aused in an attrated mass by the status of enforement spreading from an attrating mass. The graitational potential he defined as the positie work that has to be ahieed to moe an attrated mass, whih is at a ertain distane from an attrating mass, in an indefinitely far position from the attrating mass. If the eloity by whih this has to be ahieed is of no releane, it means that the eloity is approximately zero. If an attrating mass, for example Merury, has a ertain eloity with respet to the attrated mass, for example the Sun, the status of enforement would spread faster from Merury toward the Sun. Howeer, if Merury is moing with respet to the status of enforement spreading from the Sun in the diretion of Merury by a ertain eloity, the status of enforement and the eloity of the mass would pass eah other by the sum of their eloities. As Merury moes around the Sun, the potential that would be able to be deeloped in the mass of the Sun and the mass of Merury in the ase Merury is in a resting position with respet to the Sun therefore would not hae the time any more that the potential would need to deelop a ertain alue, so that the positie graitational potential should be lower than before. This means that by the motion of a mass against another mass the graitational interation between the masses would derease. Hereby, aording to Gerber, the kineti energy would relatiely inrease with respet to the dereasing positie graitational potential. Therefore the time Merury needs for one sidereal rotation around the Sun would derease, while the rotation of the radius with a ertain length of Merury s elliptial orbit would slow down, so that the perihelion would be reahed later than with respet to the sidereal period of reolution. After these onsiderations, Gerber applied Newton s kineti equations for planets to this deriation of an aeleration of the period of Merury s reolution. By this he ould also alulate the differene of the perihelion position of 43 angular seonds per hundred years against Newton s theory of graitation. Gerber starts from the assumption that graitation is the result of a graitational potential, whih is aused in an attrated mass by the status of enforement spreading from an attrating mass. This means that graitational energy is spreading from the attrating mass out to outer spae. If we regard the priniple of mass-energy onseration, in this ase the attrating mass should lose energy and therefore mass, so that we should be able to obsere a derease of masses gradually due to that loss. But as yet no obseration reports suh a derease of masses. By the moement of Merury around the Sun, aording to Gerber, the graitational interation is dereasing, while, aording to my onlusions, the graitational interation is inreasing. It s true that, aording to Gerber s onlusions, the kineti energy is relatiely inreasing with respet to the dereasing positie graitational potential. But let s again hae a look at Newton s formula for the whole energy of a planetary orbit: m GMm GMm E = = r a As mentioned aboe, the term (m /) stands for the kineti energy (E k ) and the term (GMm/r) stands for the potential energy of graitation (E g ), whih is here defined as a negatie graitational potential. If the graitational interation, respetiely the positie graitational potential, is dereasing, as Gerber postulated, the negatie graitational potential in the formula aboe is less negatie and therefore inreasing, so that there would result a higher energy of the elliptial orbit of Merury. Aording to lassial mehanis, a higher energy of an elliptial orbit results in a slower reolution around the Sun. This means that in this ase we hae to postulate a deeleration of the period of Merury s reolution around the Sun and not an aeleration as Gerber thought..

9 Reiner Georg Ziefle In 999 Paul Marmet (9) published another deriation of the additional adane of Merury s perihelion position, based on the assumption of the priniple of mass-energy onseration: Classial Desription of the Adane of the Perihelion of Merury. It is useful to ite parts of his publiation: Let us mention first that we beliee that the priniple of massenergy onseration is one of the most important fundamental priniples in physis. Energy always possesses mass and mass always possesses energy. The logial explanation implies that the atoms haing extra graitational energy on Earth hae a slightly larger mass than the atoms at a lower potential energy on Merury. The priniple of massenergy onseration requires that one Merurykilogram (at Merury-distane from the Sun) ontain slightly less mass than the Earth-kilogram (at Earthdistane from the Sun), een if the number of atoms is exatly the same (by definition). In the following Marmet points out that, using quantum mehanis, loks on Merury should funtion at a different rate and that lengths on Merury and Earth should also be different. Physial lengths an be expressed either in Earth-meters or in Merury-meters. The same orbit of Merury an also be measured using the shorter standard Earth-meter. Then, the number of Earth-meters to measure the same physial orbit of Merury is larger when it is measured using the shorter Earth-meter. We must notie that Newton s laws of physis deal with the numbers that are fed into the equations. Sine the number of meters to measure the same physial length (using the longer Merury-meters) is smaller than the number of Earth meters, we must not be surprised to find different physial results when Newton s laws use the orret loal (proper) number. [T]he Merury obserer, measuring a smaller number of loal meters to the Sun (with the longer loal meter), will alulate that the eloity of Merury must be larger (than the Earth obserer using the Earth-meter). [T]he absolute mass of the Sun does not hange beause it is measured with respet to the moing Merury-kilogram. Howeer, the number of Merury-kilograms that represents the Sun will be different. the number of Merury-kilograms in the Sun is larger than the number using Earthkilograms. We know that G is an absolute physial onstant. Howeer, sine the standard units existing on Merury are different from the standard units on Earth, different numbers will then express the same physial graitational onstant G. By using different numbers for the hanged Merury-units for G, for the mass of the Sun, and for the Merury-meters for the length of the radius of Merury s orbit (while the mass of Merury expressed in Merury-kilograms anels out in the numerator and denominator), Marmet is also able to alulate the orret alue of the adane of the perihelion of Merury. Beause of the loal smaller mass-unit of Merury, Marmet uses a larger numerial mass, and, beause of the larger Merury-meters of Merury, he uses a smaller numerial length in the formulas for Merury, so that there is a hange of Merury s orbit and also a stronger graitational attration between Merury and the Sun. Although Marmet s model suits lassial mehanis loally, that is to say, by his model it is possible to alulate the so-alled relatiisti phenomenon of the additional adaning of Merury s perihelion by using loal alues, his model doesn t represent a pure lassial physial theory, as it uses quantum mehanis to derie loal alues, respetiely units. Using alues in the lassial equations, whih are with respet to the loality of Merury remote alues, for example the alues used on Earth, by Marmet s model it is not possible to alulate the additional adane of Merury s perihelion. 5. CONCLUSIONS There exist at least four possible deriations by whih so-alled general relatiisti phenomena an be alulated, suh as the adane of Merury s perihelion. As pointed out aboe, Paul Gerber s deriation ontradits the priniple of energy-mass onseration and also lassial mehanis, while Paul Marmet s model doesn t represent a pure lassial physial theory, as his model uses quantum mehanis to derie loal alues. By Marmet s model it is only possible to alulate the additional adane of Merury s perihelion if we use loal alues in the lassial equations. Howeer, Einstein s theory of general relatiity needs a lot of additional assumptions, whih result in a ompletely new physial insight. As shown aboe, it is possible to adane Newton s theory of graitation only by taking into onsideration the finite eloity of graitational expansion and the present onept of transferene of fores by partiles to be able to alulate so-alled general relatiisti phenomena maintaining lassial oneptions of a Eulidean spae and the Galilean priniple of relatiity. By the theory introdued in this artile it is possible to predit soalled general relatiisti phenomena without using loal alues or relatiisti physis. By our postulation that motion auses an additional graitational effet, 383

10 Calulation of So-Called General Relatiisti Phenomena by Adaning Newton s Theory of Graitation we touh on Einstein s theory of general relatiity, as Einstein postulated an equialent effet of mass aused by motion. But our onlusions also mean that the eloity of graitational expansion is, with respet to different obserers, noninariant or nononstant. This is an antithesis to relatiisti physis, but no ontradition to the fat that we on Earth measure a (relatiely) onstant eloity of light. As there obiously exist more than one onsistent theory to explain and alulate so-alled general relatiisti phenomena, it is to be deided whih one omplies with reality. For this we should onsider Okham s razor. With respet to Okham s razor we hae to asertain that there annot be fewer additional assumptions in Newton s theory of graitation than in our deriation, that is to say, graitational interation is aused by something, as for example graitons, and the graitational interation is transferred by a ertain finite eloity, as for example the eloity of light. Without these two assumptions, Newton s theory of graitation is inomplete. Another question that arises is this: Is it also possible to explain and alulate so-alled speial relatiisti phenomena by adaning Newton s mehanis by alternatie oneptions about the traeling of light? In fat this is also possible! But this is to be disussed in another artile. Reeied 30 May 003. Résumé En utilisant l exemple du mouement de Merure autour du soleil, la néessité de déelopper la théorie de la graitation de Newton est démontrée en prenant en onsidération la itesse finie de l expansion graitationnelle ainsi que le onept atuel de transfert des fores par les partiules de manière à permettre le alul des phénomènes dits «de relatiité générale», tels que le mouement supplémentaire du périhélie de Merure, la ourbure des rayons lumineux à la surfae du soleil et les phénomènes obserés sur le pulsar binaire PSR 93+6 en onserant les onepts lassiques de l espae eulidien et le prinipe galiléen de la relatiité. Referenes. P. Gerber, Ann. Phys. 5, 45 (97).. A.P. Frenh, Newtonshe Mehanik (Walter de Gruyter Verlag, Berlin, 996). 3. M. Berry, Kosmologie und Graitation (Teubner Verlag, Stuttgart, 990). 4. J. Herrmann, Atlas zur Astronomie (Deutsher Tashenbuh Verlag, Münhen, 990). 5. R. Oloff, Geometrie der Raumzeit Eine mathematishe Einführung in die Relatiitätstheorie (Vieweg Verlag, Wiesbaden, 999). 6. J.H. Taylor and J.M. Weisberg, Astrophys. J. 53, 908 (98). 7. J.H. Taylor, R.A. Hulse, L.A. Fowler, G.E. Gullahorn, and J.M. Rankin, Astrophys. J. 06, L53 (976). 8. J.H. Taylor, L.A. Fowler, and J.M. Weisberg, Nature 77, 437 (979). 9. P. Marmet, Phys. Essays, 468 (999). Reiner Georg Ziefle Philosophishe Fakultät der FernUniersität Hagen Holzmühlstrasse Leutershausen, Federal Republi of Germany 384