Model Explaining the Gravitational Force

Transcription

1 Model Explaining the Gravitational Force Clade Mercier eng., Agst nd, 015 Rev. October 17 th, 015 The niversal gravitation eqation of Newton is widely sed in the calclations in engineering and astrophysics becase it is simple to se and reqires little mathematical knowledge. It is a simple eqation that describes the gravitational phenomena at low speed and in weak gravitational fields. Althogh Einstein's general relativity largely spplants the niversal gravitation of Newton eqation in terms of accracy, this comes at the price of eqations asking a heavy mathematical paraphernalia. De to its amazing simplicity, the Newton's theory remains the first basic theory that is taght in most colleges and niversities. Several attempts have been ndertaken to nderstand the real basics of the phenomenon of gravitation, bt none answers all the following qestions: Do the laws of gravity are really the same everywhere? Does gravitation is de to a particle sch as the graviton? Does gravitation is transmitted at the speed of light, or is it instantaneos? Does gravitation wold apply otside of or niverse? Does or niverse will have, after an expansion phase, a contraction phase that will end p in a big crnch? This docment aims to show that it is possible to give a logical basis for the niversal gravitation of Newton. We will show that, in fact, the gravitational attraction is only a concept. The forces do not exist. We are in a hge bath of photons of different wavelength that hit s in every way and at all times. These repeated impacts create a radiation pressre that is not necessarily the same everywhere in the niverse. Jst as in a pool, the deeper we are immersed in the niverse, the higher the radiation pressre is intense. According to or theory, the objects are not attracted to each other, bt rather they are pshed over on each other by the radiation pressre srronding s. Using this concept, it is possible to calclate the acceleration transmitted to the objects. Circmscribing the experiences within a specific framework (macroscopic objects, moving at low speeds, the distances between objects are relatively small and the gravitational fields involved are weak) and making the concept of force existing, we get the eqation of the niversal gravitational force of Newton. KEY WORDS: Gravitation, Newton, Einstein, general relativity 1. INTRODUCTION In 1686, Isaac Newton presented for the first time an eqation describing the gravitational interactions between the different masses. It was not ntil the advent of Einstein to know that this theory was in fact valid only at low speed and with weak gravitational fields. Althogh his theory well describes the gravitational phenomena arond s, Newton has never issed any jstification as to the natre of the gravitational force. He noted its existence and described the theory of gravitation events, nothing more. This theory, however, had the great merit of

2 C. Mercier being simple to se. Even in or times, despite or crrent knowledge, we still commonly se the Newton's eqations becase of their simplicity. In 1915, Einstein presented his theory on the general relativity [14]. This is a relativistic theory of gravitation based on completely different gronds from those of Newton. It spersedes the theory of the latter in that it incldes the niversal Newtonian gravitation theory for low speeds (with respect to the speed of light in vacm) and the weak gravitational fields. It predicts the behavior of objects even at very high speeds approaching that of light [15]. Already Einstein considered that gravitation is not really a force. He conceived that gravitation as a manifestation of the crvatre of space-time that was prodced by the distribtion of energy in the form of mass or kinetic energy, which differs according to the observer's frame of reference. However, althogh none of the nmeros experimental tests carried ot was able to pt this theory falty p to now, this theory does not really explain why space-time is crved by the presence of energy. Althogh the nderlying principle in general relativity is simple, the mathematical arsenal that comes with is heavy and difficlt to nderstand for everyone. For this reason, when it comes time to be sed in practice, this theory often becomes the second choice. Bt it is essential in many applications sch as gravitational lenses, nderstanding of black holes, the behavior of satellites, the geostationary positioning system (GPS), etc. It is interesting to know that the general theory of relativity does not allow to find any new physical constant. The constants mst be measred and sed in calclations. For this reason, the general theory of relativity ses Newton's theory to "calibrate" itself at low speed.. DEVELOPEMENT.1. Forces do not Exist Let's start by making the following shocking statement: the gravitational and electrical forces do not exist. In fact, no force exists. In fact, the forces are concepts accompanied with practical mathematical tools to predict the interaction between different elements of matter. Bt these simply do not exist. In this article, we will focs on explaining the different forces and qantify them nder the form of eqations. As the concept of force is sefl and easy to nderstand, we will show that it is possible to display this concept as a mathematical reslt and not as an explanation.

3 Model Explaining the Gravitational Force 3.. The Photon is Maybe the Most Elementary Particle Let s sppose that, its most simple representation, all matter is made of confined photons. To convince orselves, Einstein fond the following eqation: E = m 0 c (1) Let s try to find the signification this eqation. It says that it is possible to convert a mass at rest m 0 into a certain amont of energy (photons) by the disintegration of matter. Bt, this eqation is not nilateral. It is also possible to take the same qantity of energy and to convert it in a mass. This eqation works on a bilateral way. If, in final, the photons are the reslt of the disintegration of matter, we conclde that some way, all particles are in reality made of confined photons. The electrons, protons and netrons are not the most elementary particles. Not even qarks. It looks like photons are maybe the most elementary existing particles..3. Model Representing the Thermodynamic Vacm The vacm, as we are sed to conceive it, is an absence of molecles and atoms. However, the vacm is not nothingness as its name cold lead s to believe it. The vacm is fll of photons. It is a tre bath of electromagnetic wavelengths from π L p (where L p is the Planck length) p to the vale of the apparent circmference of the niverse π R (where R is the apparent radis of crvatre of the lminos niverse). To avoid any misinterpretation with the term "vacm" which cold lead s to believe that it refers to a total absence of all, history shold maybe kept the original name of «ether» for the vacm. However, even if we do not like this name and that we try to avoid it, to keep the most recent and sed terms, we will keep the name «vacm». However, we warn the reader that, for s, the vacm is fll of photons that hit masses on all sides. The vacm is simply a void of matter. 3. THE GRAVITATIONAL FORCE In a firs step, let s try to find a model that explains the gravitational forces with the help of photons which hit the masses in relation.

4 4 C. Mercier 3.1. Behavior of Two Microscopic Bodies When we talk abot a microscopic body, we mean a mass that is so small that it is not heavy enogh to statistically average ot the impacts that it cold receive coming from the different photons which srrond it to keep, in average, its initial position. Let s define the mass of an object as being the sm of momentms p of the photons that it is made of, divided by their speed with respect to the a given observer. m = p v A momentm can be of two types: linear or anglar. According to this, if the object is at rest relative to the observer, only the rotations cont. Bt if the object is moving in a linear motion, an additional momentm will be added. The mass of an object is given by the total momentm divided by the speed (linear or anglar) perceived a given observer. Then we realize, by this definition, that the mass of an object may change depending on the selected observer. Let's assme that the elementary particles are made of different arrangements confined photons (their with anglar momentm). The actal dimension of the photons is of the order of the Planck length, that is to say abot m. In fact, what gives them a greater wavelength than this vale, it's their anglar speed of rotation. The qicker they trn on themselves the smaller the wavelength is. However, we do not go into the detail of how these photons are confined to form the varios bricks that make p matter. The key here is to say that all the photons actally have the same physical size, whether confined or not. Let's see them as small beads that are all the same size. To give an example, let's sppose two of sch beads in the presence of one another in a space where there is a complete absence of material, light and electromagnetic waves. Only those two little beads are in this space. In this experiment, the niverse does not exist. We avoid deliberately sing the term "vacm" which is commonly sed to describe the space that is presented here becase the vacm as we normally conceive it is actally filled with electromagnetic waves. The two beads, called A and B, will not sffer of any "attraction" becase gravitational forces do not exist. If no movement is instilled in these beads relative to one observer at rest, nothing will happen and nothing will move. ()

5 Model Explaining the Gravitational Force 5 B A Figre 1) The black beads A and B are confined photons that receive constant impacts from photons of the qantm vacm (thermodynamic radiation pressre). As the bodies A and B are microscopic, behaviors seem chaotic and npredictable. Let's sppose now (see Figre 1) that we pt them in a space where there is almost innmerable qantity of beads of the same size as the beads A and B. However, there is space between the balls. They are in motion and sometimes collide. They hit or beads A and B from all directions. Or beads A and B are then animated of disorderly movements, frit of random shocks they experience. In sch a sitation, it wold be interesting to predict the exact behavior of the beads, bt to do so, we wold have to take in accont a considerable set of initial factors. It is simply impossible to do it. Only statistics can handle this kind of problem. 3.. Behavior of Two Macroscopic Bodies Unlike the previos sitation, we will consider here macroscopic bodies, is to say sfficiently large masses so that they are capable of averaging the impacts they receive withot moving from their initial position or relative considered to an observer at rest.

6 6 C. Mercier C Figre ) In the clster C (represented by black beads groped together bt free to move), the impact of a single energetic photon (empty bead) on the clster wold reslt in the fragmentation of the beads clster in all directions, ths providing individal moves from low speed to all the beads, sch as the breakage in a billiard game. Let's now contine or reflection (see Figre ) by ptting a mltitde of beads near each other to create two clsters which we call C and D. Let's note that no force holds the beads in each clster. However, there are enogh beads in each clster so that the impact of a ball from the space arond can be absorbed, at least partially (see Figre ). Becase of the law on the conservation of momentm, the clash between the beads from space and one of the clsters will reslt in a slow movement of all of the affected clsters. Bt, as there are a plrality of beads moving in the space arond, there is statistically a chance that other impacts occr on the other side of the clster, which will conterbalance the amont of momentm transmitted previosly. If the niverse containing all the beads is sfficiently homogeneos, each clster will remain consolidated by the "pressre" exerted by the shock of the beads from the otside (see Figre 3). We will call this pressre a "thermodynamic radiation pressre". In fact, it consists only of electromagnetic waves. Both scenarios (behavior of microscopic and macroscopic bodies) that we analyzed react differently. For beads A and B, the individal movements of the beads appeared to be random. Bt this is not the case for clsters C and D. Indeed, the mass of each clster being larger, the impacts coming from the different directions tend to statistically average ot. So clsters tend to do not have disorderly movements. Bt a new phenomenon occrs. If the clsters C and D are sfficiently close to each other, they will tend to block the path of certain beads from otside.

7 Model Explaining the Gravitational Force 7 C Figre 3) When the clster C is in vacm, it is sbjected to a brst of photons from all directions. Even if only one impact (as in Figre ) wold soon have scatter the beads of the clster, here, the beads are held together by all the impacts from all sides and which conterbalance by statistically meaning impacts. The clster vibrates, bt its center of mass does not move with respect to an external observer. For example (see figre 3), a bead from space normally wold have hit the clster D. Bt on its way, it meets the beads clster C. Similarly, a ball that wold normally hit the clster C enconter on its way the beads clster D. It therefore creates, over time, a deficit of percssion in the axis linking clsters C and D. This deficiency is even greater if we move closer the agglomerations C and D together. This thermodynamic radiation pressre deficit cases ncompensated impacts sffered by clsters C and D reslting in the increase of the momentm over time along the axis between them. Clsters C and D appear to be "attracted" to each other. An external observer who does not see the microscopic beads traveling throgh space arond the clsters simply will feel that the clster C is accelerated towards the clster D and vice versa. From there, the concept of force. According to the concept of force, the prodct of mass and acceleration is eqal to the force experienced. The observer only observes the reslt: there seems to be an attraction between the agglomerates. He does not see that the clsters are actally pshed one over the other.

8 8 C. Mercier C D Figre 3) When two clsters C and D are broght into presence of each other, it creates a qantm vacm (no photons) between the centers of mass of these. The clsters are ths pshed on each other de to the thermodynamic radiation pressre from the photons of vacm. From the otside, an observer that wold not see the photons of space wold be inclined to think that both clsters are attracted towards each other by a "gravitational force". We mentioned previosly that the fact that all the beads (photons) are of the same size was important. Indeed, whatever the wavelength of the photons is, the "bead" which models it has the radis of the Planck length. If a bead were bigger than another, it wold more likely to be hit. As all the beads of or model are the same size, they all have the same chance of being hit by the beads from the srronding space Calclation of the Potential Energy Between Two Macroscopic Bodies To help simplifying the model (see Figre 4) that we seek to explain, let's assme that or masses are of macroscopic type even if the specific case that is drawn does not have a lot of balls and shold normally be treated as a microscopic body. This is jst a simple example that serves to facilitate the nderstanding. Then, let's sppose that in the clster C, there is only n 1 = beads (called C 1 and C ) and that in the clster D, there are n = 3 beads (named D 1, D and D 3 ). There is then 6 lines (n 1 n = 3 = 6) that we can draw from the following bead: C 1 and D 1, C 1 and D, C 1 and D 3, C, D 1, C and D, C and D 3.

9 Model Explaining the Gravitational Force 9 C 1 C D 1 D D 3 Figre 4) These are the six lines that we can trace between the beads of the agglomerates C and D. These lines represent qantm vacms (no photons). Using another langage, they represent the nmber of gravitons (virtal photon representing the photon deficit). Assming that the beads are actally made of confined photons, we nderstand that the nmber of photons reqired to constitte the mass of objects in relation is negligible compared to the nmber N of photons constitting the total apparent mass of the niverse. The nmber N is so large that, whatever the mass of objects in relation is, there will still be approximately N photons in the niverse that will be free to participate in collisions. Let's try to calclate the energy associated with the photons deficit that exists between the clsters C and D. We associate this deficit to virtal photons. Some give the name of "gravitons" to these virtal photons. In or model, it is clear that gravitons simply do not exist. They represent only the deficit of photons that exists between the different clster masses. From or point of view, it is inconceivable that an object can emit gravitons that wold be real photons since the objects wold eventally melt and see their energy being redced over time. Moreover, it is ridiclos that a real particle that wold hit other objects cold have the effect of making them coming closer together. Conversely, if we lanch the beads on an object, it forces it to move away nder the impact of the beads that we lanch on it. The concept of graviton as a real particle is nonsense. It is rather, as we claim it, a virtal photon representing a particle deficit. The only photons that can come into resonance between the clsters A and B are those that will have a wavelength eqal to π times the distance r between the center of mass of the clster C and the center of mass of the clster D. The energy E ph of each of these photons will be: h c E = ph π r (3)

10 10 C. Mercier According to the CODATA 010 [6], the vale of the Planck constant is abot h (9) J s These photons are trying to psh the clsters by their repeated impacts between them. However, the other side of the clsters, the rest of the niverse pshes both clsters together with N photons. The reslting potential energy E between the two clsters will necessarily be a portion of E ph : h c n n (4) E = 1 π r N The nmber N represents the maximm nmber of πr wavelength photons that it is possible to see in the niverse [13]. According to or calclations [9], this nmber is approximately (1) In fact, Dirac had foreseen this nmber, realizing that the reports of certain physical characteristics of same nits always gave some nmbers [10]. In fact, they all stem from the same nmber on which is applied a different fractional exponent. If we make the concept of force existing to explain a work, the binding energy between two bodies can be seen as the prodct of the force F on the distance r: h c n n (5) E = F r = 1 π r N Isolating the force F, we obtain: h c n n (6) F = 1 π r N In previos works [9], we have specifically evalated the vale of N: (7) m R 1 11 N = = = 6, (1) 10 m L α 57 ph p Here, m is the apparent mass of the niverse and m ph is the mass associated with a π R wavelength photon. Moreover, R is the apparent radis of crvatre of the niverse and L p is the Planck length. According CODATA 010 [6], the Planck length L p (97) m. According to or work [11], that nmber is more arond L p (53) m. Using the eqation (7) in the eqation (6), we obtain:

11 Model Explaining the Gravitational Force 11 m h n n (8) ph F = c R 1 π R c r m The mass m ph associated with a πr wavelength photons (apparent circmference of the niverse) is as follows: h (9) m = ph π R c According to or researches [1], the apparent radis of crvatre of the niverse is: r (10) c 1 6 R = = e = (68) 10 m H β α π α β R This reslt is confirmed by others [,3,17]. In the CODATA 010 [6], we find the following vales: - The speed of light in vacm c m - The classic radis of the electron r e (7) m - The fine strctre constant α (4) The Rydberg constant R (55) m -1 The vale of β is an irrational nmber. It expresses the ratio between the speed of expansion of the material niverse and the speed of light in vacm c [7]: β = (11) The inverse of the Hbble constant [1] represents the apparent age of the niverse [16]. The measrement of the Hbble constant H 0 is not very clear now. According Xiaofen Wang [8] and his team, the vale of the Hbbell constant wold be abot H 0 7,1 ± 0,9 km/(s MParsec). By cons, according to or research [9], it is: 19 (1) c α β H = 0 7, (46) km/ r e Using the eqation (9), the eqation (8) becomes: c R F = m m n ph 1 r m n ph ( s MParsec) (13)

12 1 C. Mercier When we determined the nmber of photons that made p the clsters C and D, we actally split the masses m 1 and m by the rest mass that we can associate to the energy of a π R wavelength photon (apparent circmference of the niverse): m m (14) n 1 1 = m and n = m ph ph This statement is tre in the case where the masses m 1 and m are stationary with respect to a stationary observer. However, in the case where the masses are moving, the respective energy levels wold be higher. Indeed, a moving mass sees it level of energy increasing de to addition of photons. The nmbers of photons n 1 and n wold therefore be higher. For the simple case of static masses or moving to relatively slow speeds with respect to the speed of light, the eqation (13) can be rewritten sing the eqations (14): (15) c R m m F = 1 m r The apparent radis of the niverse is given by the ratio of the crrent speed of light c in a vacm and the Hbble constant H 0 : c (16) R = H 0 Using the eqation (16) in the eqation (15), we obtain: 3 c m m (17) F = 1 m H 0 r The apparent mass of the niverse is given by the following eqation [4,5] : 3 (18) c m = G H 0 In this eqation, G is the niversal gravitational constant of Newton (taken over by Einstein in his eqations of the general relativity). Using the eqation (18) we can rewrite the eqation (17) like this: G m m (19) F = 1 r

13 Model Explaining the Gravitational Force 13 This eqation is that of niversal gravitation of Newton. Newton's eqation is the reslt of a statistical average of photon impacts on macroscopic type masses. Moreover, it can be shown that Newton's gravitation eqation can be obtained sing the Poisson statistical eqation. De to the fact that the impacts of the photons cold not be adeqately compensated on the "microscopic" masses, the Newton's eqation can not describe the behavior of these latter. Only the behavior of macroscopic masses at low speed can be described sing this eqation. 4. DARK ENERGY No one cold prove its existence and many sspect that there is a form of energy that wold not be visible by traditional methods, the "dark energy". According to NASA, it wold compose 73% of or niverse. As we mentioned, the vacm of or niverse is actally a bath filled with photons of different wavelengths. We believe that dark energy wold be composed of photons whose wavelengths are sch that we it is not possible for s to measre them. Indeed, to make it possible to detect an electromagnetic wave, it is necessary to bild an antenna having the size of abot a qarter of wavelength. Obviosly, we are more or less confined to the Earth and the dimensions allowed to bild large-sized antennas are rather limited compared to the range of wavelengths that it wold be interesting to catch. Althogh we were allowed to make an antenna the size of or galaxy, there wold be a wide range of wavelengths missing. Similarly, in the infinitely small, we are blind for a very wide range of wavelengths. We shold know that the fll range, from the infinitely small to the infinitely large, stretches from the Planck circmference that is πl p p to the apparent circmference of or niverse that is πr. Since we are not able to measre all wavelengths, we can still se the theory Gravitational Interaction Speed Let's make an experience. Let's take an object and let's position it in space. Let's sppose that we are a great magician and that we are able to instantly make appear an object in space near the first object. How the two objects will let "know" to the other their position and their presence? Withot having more than Newton's eqation, this phenomenon might seem instantaneos. By sing or new knowledge of gravitation, we know that the gravitational force does not exist

14 14 C. Mercier and is actally the frit of a photon radiation pressre. Therefore, the transmission in the vacm of the "gravitational force" is the speed of light. 5. CONCLUSION As or model leads to the eqation of the niversal gravitation of Newton, we conclde that it can be sed to better nderstand the phenomenon of gravitation. Althogh the reslting eqation of or model is not as accrate as that of general relativity, or model has the advantage of being a simple explanation to nderstand and to express it mathematically. Classical Newton's mechanics theory does not attempt to give any explanation of the root case of gravitation. Einstein, with his theory of the general relativity, explained gravitation by a change in the geometry of space in the presence of energy (mass). However, this explanation does not say how the masses make vary the geometry of space. It only qantifies it. We believe that it will be possible in the near ftre to explain the concepts of nclear forces by sing a development of the same model that was sed to explain the concept of gravitational and electrostatic forces [18]. 6. REFERENCES [1] Mercier, Clade, "Calclation of the Apparent Radis of Crvatre of the Universe", Pragtec, Baie-Comea, Qebec, Canada, Jne 9, 013, paper available on Internet at: [] Silberstein, Ldwik, "The Size of the Universe: Attempt at a Determination of the Crvatre Radis of Spacetime", Science, v. 7, November 1930, p

15 Model Explaining the Gravitational Force 15 [3] Seplveda, L. Eric, "Can We Already Estimate the Radis of the Universe", American Astronomical Society, 1993, p. 796, paragraph [4] Mercier, Clade, "Calclation of the Apparent Mass of the Universe", Pragtec, Baie-Comea, Qebec, Canada, May 5, 01, paper available on Internet at: [5] Carvalho, Joel C., "Derivation of the Mass of the Observable Universe", International Jornal of Theoretical Physics, v. 34, no 1, December 1995, p [6] "Latest (010) Vales of the Constants", NIST Standard Reference Database 11, last pdate: April 01, paper available on Internet at: [7] Mercier, Clade, "The Speed of Light May not be Constant", Pragtec, Baie-Comea, Qebec, Canada, October 8, 011, paper available on Internet at: [8] Wang, Xiaofeng and al., Determination of the Hbble Constant, the Intrinsic Scatter of Lminosities of Type Ia SNe, and Evidence for Non-Standard Dst in Other Galaxies, March 011, pp. 1-40, arxiv:astro-ph/060339v3 [9] Mercier, Clade, "Calclation of the Universal Gravitational Constant G", Pragtec, Baie- Comea, Qebec, Canada, March 13, 013, paper available on Internet at: [10] Dirac, P. A. M., "Cosmological Models and the Large Nmbers Hypothesis", Proceedings of the Royal Society, UK, 1974, pp [11] Mercier, Clade, "Calclations and Interpretations of the Different Planck Units", Pragtec, Baie-Comea, Qebec, Canada, October 1, 015, paper available on Internet at: [1] Hbble, E. and Hmason, M. L., "The Velocity-Distance Relation among Extra-Galactic Neblae", The Astrophysical Jornal, v. 74, 1931, p.43. [13] Mercier, Clade, "Large Nmbers Hypothesis of Dirac Leading to the Hbble Constant and to the Temperatre of the Cosmic Microwave Backgrond", Pragtec, Baie-Comea, Qebec, Canada, Febrary 4, 013, paper available on Internet at: [14] Einstein, Albert, La relativité, Petite Bibliothèqe Payot, v. 5, Parish, original 1956 edition from Gathier-Villar integrally resed for the 001 Payot & Rivages edition, p [15] Einstein, Albert, "On the Electrodynamics of Moving Bodies ", The Principle of Relativity (Dover Books on Physics), New York, pblications Dover, 195 (original paper from 1905), pp [16] Mercier, Clade, "Calclation of the Age of the Universe", Pragtec, Baie-Comea, Qebec, Canada, April 9, 01, paper available on Internet at: [17] Vargas, J. G. and D.G. Torr, "Gravitation and Cosmology: From the Hbble Radis to the Planck Scale", Springer, v. 16, 003, pp. 10. [18] Mercier, Clade, "Model Explaining the Electrostatic Force", Pragtec, Baie-Comea, Qebec, Canada, Agst, 015, paper available on Internet at: