Physical and mathematical postulates behind relativity

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1 Physial and mathematial postulates behind relativity Tuomo Suntola Physis Foundations Soiety, Finland, In this presentation we look for answers to questions: What was the problem solved with the relativity theory, and, did the theory solve the right problem? Newtonian physis is loal by its nature. No loal frame is in a speial position in spae. There are no overall limits to spae or to physial quantities. Newtonian spae is Eulidean until infinity, and veloities in Newtonian spae grow linearly as long as there is onstant fore ating on an objet. Observations on the properties of the propagation of light in late 9th entury showed ontradition with the unlimited, linear Newtonian spae. Relativity theory broke the linearity and the Eulidean appearane of Newtonian spae by redefining the oordinate quantities, time and distane. In the redefined oordinates, the growth of veloities is limited to the veloity of light, whih was defined as a natural onstant. The loal nature of Newtonian physis remains in relativisti spae, justified by the relativity priniple laiming the same formulation of the laws of nature for any observer. In a holisti perspetive, the finiteness of veloities an be seen as a onsequene of the finiteness of total energy in spae. In suh an approah relativity appears primarily as relativity of the loal to the whole, and is expressed in terms of the loally available share of total energy. Postulation of the finiteness of the total energy in spae allows universal oordinate quantities, time and distane, and links the veloity of light to the energeti state of the universe. In spite of the totally different postulates and the different piture of reality in the two approahes, the preditions for loal physial phenomena are essentially the same. Differenes arise at the extremes, at osmologial distanes and in the viinity of loal singularities in spae. Global relativity links the sizes of gravitationally bound systems to the expansion of spae, whih explains the observed Eulidean appearane of galati spae. Magnitude observations of supernovas are explained with high auray without aelerating expansion, dark energy, or any other additional parameter. Global relativity based on finite total energy in spae is analyzed in detail in the Dynami Universe model []. From Newtonian spae to relativisti spae Newtonian physis is loal by its nature. No loal frame is in a speial position in spae. There are no overall limits to spae or to physial quantities. Newtonian spae is Eulidean until infinity, and veloities in spae grow linearly as long as there is onstant fore ating on an objet. Finiteness of physial quantities was first observed about years ago as finiteness of veloities. As onluded from the experiments by Mihelson and Morley in late 8 s, the veloity of an observer did not add to the phase veloity of light. The speial theory of relativity introdued a mathematial struture for the desription of the finiteness of veloities by modifying the oordinate quantities, time and distane in suh a way that veloities in spae never exeed the veloity of light, whih was postulated to be a natural onstant. In modified oordinates, the finiteness of the veloity obtainable by aelerating a mass objet was illustrated as an inrease of the mass of the objet aelerated, Figure. Extension of the saturation of veloities to the veloity obtained in free fall in gravitational field led to the generalization of the theory of relativity. Modifiation of the oordinate quantities is expressed in terms of a 4-dimensional spaetime system, where modifiation of time and distane is determined by mass density distribution in loal spae. In the viinity of a loal point-like mass enter, spaetime is urved 9 degrees at a ritial radius, whih turns the veloity of free fall in the diretion of non-urved spae to zero (for an observer far from the mass enter) as expressed in the Shwarzshild solution of general relativity, Figure. The Shwarzshild solution does not, however, affet the Newtonian orbital veloity, whih exeeds the Shwarzshild veloity of free fall at the distane of three times the ritial radius thus leading to unstable orbits below that limit [].

2 time time veloity veloity (a) t t v a F F t (b) v 3 dt dt t m m F m dt ' dt dx ' dx dt v Figure. a) In Newtonian spae the veloity of an objet inreases linearly as long as there is onstant fore ating on the objet. b) In relativisti spae the inrease of the veloity of an objet saturates to the veloity of light, whih is defined as a onstant and the maximum veloity obtainable in spae. In speial relativity (SR), the saturation of the veloity is obtained by re-defining the oordinate quantities, time and distane. Saturation of retilinear motion is illustrated in the figure. (a) Newtonian veloity of free fall v ff Newton GM ff Newton r stable orbits ff Newton orb Shwarzshild v ff Shwarzshild (b) Proper distane and proper time in Shwarzshild spae dr ' dr dt ' dt Shwarzshild veloity of free fall GM dr ' dr r GM dt ' dt r 4 rr DU 3 ff Newton dt dt ' M ff Shwarzshild ff Shwarzshild v ff Shwarzshild GM GM r r r GM Shwd Figure. (a) The veloity of free fall in Newtonian spae, ff(newton), approahes infinity when distane to a point-like mass enter approahes zero. In Shwarzshild spae, based on the general theory of relativity, the veloity of free fall goes to zero at ritial radius r, where loal spaetime is urved 9 degrees. The predited orbital veloity at irular orbits in Shwarzshild spae exeeds the veloity of free fall at 3r, whih exludes stable orbits beyond that limit. (b) Proper distane in Shwarzshild spae is obtained by substituting the veloity term of SR proper distane by Newtonian veloity of free fall, and the proper time by adding the Newtonian veloity of free fall as an orthogonal omponent to veloity in the SR expression of proper time.

3 Like in Newtonian physis, no loal frame, or inertial observer, is in a speial position in spae. Aording to the speial and general theories of relativity there is no universal frame of referene in spae; veloities and spaetime strutures are studied relative to an observer in a loal frame of referene. In the prevailing theory, the osmologial appearane of relativisti spae is expressed in terms of the Friedman-Lemaître-Robertson-Walker metri [3]. The FLRW metri desribes spae as an expanding, gravitationally bound system as a whole but ignores the linkage of the expansion to gravitationally bound subsystems like galaxies or planetary systems in spae []. Obtaining finiteness by modifying oordinate quantities may ahieve a orret desription of observations and in many ases it does but it does not tell the physial reasons for finiteness, e.g. why is the veloity of light the maximum veloity in spae? Physial basis of finiteness in spae In fat, there are many physial signs of finiteness in spae. For example, the spetral distribution and power density of the Cosmi Mirowave Bakground radiation (CMB) is, with high auray, equal to the spetral distribution and power density of radiation density within a blak body soure. Perhaps the most signifiant sign of finite and losed spae omes from the equality of total rest energy and gravitational energy in spae; In his letures on gravitation in early 96 s Rihard Feynman [4] stated: If now we ompare the total gravitational energy E g = GM tot/r to the total rest energy of the universe, E rest = M tot, lo and behold, we get the amazing result that GM tot/r = M tot, so that the total energy of the universe is zero. It is exiting to think that it osts nothing to reate a new partile, sine we an reate it at the enter of the universe where it will have a negative gravitational energy equal to M. Why this should be so is one of the great mysteries and therefore one of the important questions of physis. After all, what would be the use of studying physis if the mysteries were not the most important things to investigate. Feynman pondered also the geometry of spae [5]:...One intriguing suggestion is that the universe has a struture analogous to that of a spherial surfae. If we move in any diretion on suh a surfae, we never meet a boundary or end, yet the surfae is bounded and finite. It might be that our three-dimensional spae is suh a thing, a tridimensional surfae of a four sphere. The arrangement and distribution of galaxies in the world that we see would then be something analogous to a distribution of spots on a spherial ball. Spae as the surfae of a 4-sphere is quite an old onept of desribing spae as a losed but endless entity. Spherially losed spae was outlined in the 9 th entury by Ludwig Shläfli, Bernhard Riemann and Ernst Mah. Spae as the 3-dimensional surfae of a four sphere was also Einstein s original view of the osmologial piture of general relativity in 97 [6]. The problem, however, was that Einstein was looking for a stati solution it was just to prevent the dynamis of spherially losed spae that made Einstein to add the osmologial onstant to the theory. In fat, another problem arose from the spaetime onept established in the relativity theory. In fat, losing of three-dimensional spae requires a fourth dimension of a metri nature, whih infringes on the spaetime onept and aordingly on the basis of Einsteinian relativity. Obviously, this was also the reason Feynman did not take into onsideration the possibility of a dynami solution to the great mystery of the equality of the rest energy and the gravitational energy in spae. As soon as we neglet the spaetime onept and assume a fourth dimension of a metri nature, spae an be losed as a 3-dimensional surfae of 4-dimensional sphere with the radius in the fourth dimension. In suh a struture Feynman s great mystery obtains a dynami solution spherially losed spae appears as a spherial pendulum in the fourth dimension: In a ontration phase spae gets motion from the gravitation of the struture onverting the energy of gravitation into the energy of motion. The ontration turns into expansion by passing singularity in the expansion phase the energy of motion gained in the ontration is paid bak to gravitation. As in a pendulum, the sum of the energies of motion and gravitation are equal throughout the proess. With the initial ondition of rest at infinity, the sum of the energies of motion and gravitation is zero throughout the ontration expansion proess, Figure 3. 3

4 Contration Expansion Energy of motion E p m m GM " Eg m R 4 time Energy of gravitation Figure 3. Energy buildup and release in spherial spae. In the ontration phase, the veloity of motion inreases due to the energy gained from the release of gravitational energy. In the expansion phase, the veloity of motion gradually dereases, while the energy of motion gained in ontration is returned to the energy of gravitation. Obviously, the energy of motion mass in spae possesses due to the motion in the fourth dimension is observed as the rest energy of matter in spae. It an be shown, that for maintaining the zero-energy ondition in spae, the veloity of spae in the fourth dimension appears as the maximum veloity obtainable in spae. The onlusion is that the veloity of light is not a physial onstant but determined by the veloity spae has in the fourth dimension. The zero-energy balane of motion and gravitation in spherially losed spae binds the total rest energy of matter to the size, and aordingly to the state of expanding spae. The expansion of spae works against the gravitation of the struture, whih means that the veloity of expansion, and aordingly, the veloity of light in spae dereases in the ourse of the expansion. Many physial proesses, like planetary motions and harateristi osillation frequenies of atomi loks are linked to the expansion veloity of spae, whih means that the veloity of light in most measurements is observed as being a onstant. The dynami zero-energy balane of motion and gravitation means that the total energy (the absolute value of the positive rest energy and negative gravitational energy), at any time, is finite and speifially determined by the state of the expansion. The postulates needed are:. Spae is spherially losed through a fourth dimension of a metri nature.. Time is a universal salar. 3. Total mass, inluding the mass equivalene of eletromagneti energy, in spae is a primary onservable throughout the development of spae. 4. The zero-energy balane of motion and gravitation prevails in spae. Adopting the postulates above we have to rejet two of prevailing postulates:. The onstany of the veloity of light.. The spae-time onept. 4

5 Global relativity in zero-energy spae It an be shown that. Relativity of observations within spae, at any time, an be seen as a onsequene of the finiteness of total energy in spae.. Relativity in zero-energy spae is not loal relativity between an observer and an objet, but global relativity between the loal and the whole. In order to derive the properties of global relativity we need to add one more postulate, whih ompletes the list of postulates:. Spae is spherially losed through a fourth dimension of a metri nature.. Time is a universal salar. 3. Total mass, inluding the mass equivalene of eletromagneti energy, in spae is the primary onservable throughout the development of spae. 4. The zero-energy balane of motion and gravitation prevails in spae. 5. Total energy is onserved in all interations in spae. Adopting the postulate of onserving the total energy, we rejet three more postulates behind Einsteinian relativity. The list of rejeted postulates beomes:. The onstany of the veloity of light.. The spae-time onept. 3. The relativity priniple. 4. The equivalene priniple. 5. The Lorentz transformation. A full analysis of the properties of matter, eletromagneti radiation, relativity, elestial mehanis, and the osmologial appearane of zero-energy spae is presented as the Dynami Universe theory (DU) []. Hypothetial homogeneous spae In zero-energy spae the primary energy buildup reates the rest energy of matter as momentum and the energy of motion due to the motion of spae in the fourth dimension. As the initial ondition, in hypothetial homogeneous spae, all mass is assumed to be uniformly distributed in spherially losed spae forming an ideal, fully symmetri 3-dimensional surfae of a fourdimensional sphere. There is no motion within spae, i.e. the only momentum of mass in spae ours in the diretion of the 4-radius of the struture. The gravitational fore, as the gradient of gravitational energy, appears in the diretion of the 4-radius only. Loally, suh a situation an be desribed as equal energies of motion and gravitation in the opposite diretions in the diretion of the 4-radius, the loal fourth dimension, whih is onveniently desribed as the imaginary diretion. Loal spae Conservation of the zero-energy balane of motion and gravitation in mass enter buildup appears as a loal bending of spae in the fourth dimension. DU spae has veloity in the diretion of the 4-radius R. Bending of spae means that loally, in bended spae, the veloity of spae and, aordingly, the loal veloity of light are redued by the osine of the bending angle. The situation is not muh different from loally bended spaetime in the Shwarzshild solution of general relativity, however, there are remarkable onsequenes from that differene. 5

6 (a) SR&GR: Distane in spae-time: ds dt dt ' dr (b) DU: Motion of spae in dt + distane in spae dr dt dt dr dt v dt v dt es es dt dt ' E rest E g v ff Shwarzshild spae DU spae M M Figure 4. Spaetime geometry and the redution of the time differential in the viinity of a mass enter in Shwarzshild spae based on general relativity, and the motion of spae and redution of the veloity of spae in the loal fourth dimension in DU spae. In Shwarzshild spae, in the distane differential dt, time is vetor quantity and is a salar. In DU spae, as a veloity, is a vetor quantity and the time differential dt is a salar operating equally in spae diretions and in the fourth dimension. In Shwarzshild spae based on general relativity, bending of spaetime in the viinity of a mass enter in spae results in a redution in the time differential dt and an inrease of the distane differential dr, Figure 4(a). In DU spae, bending of spae in the viinity of a mass enter results in a redution in the veloity of spae in the loal fourth dimension. The redution of the loal veloity of spae reates a veloity of free fall as an orthogonal omponent of the veloity of spae in the loal fourth dimension in bended spae, Figure 4(b). The motion of spae in time differential dt an be expressed as the vetor sum of the loal 4-veloity of spae and the esape veloity opposite to the veloity of free fall. As a property of the universal salar time in the DU, time is used equally in spae and in the fourth dimension, whih is essential for understanding the nature of the rest energy of matter as the energy of motion, the produt of veloity of spae and the momentum in the fourth dimension E p m () rest where is the veloity of spae in hypothetial homogeneous spae, and is the veloity of spae in the loal fourth dimension. In the Earth gravitational frame the loal veloity of light = an be estimated to be on the order of parts per million (ppm) lower than the veloity of spae in hypothetial homogeneous spae. Celestial mehanis in GR spae and in DU spae In GR based Shwarzshild spae, in the time-like distane differential dt, time is a vetor quantity and is a salar. In DU spae, as a veloity, is a vetor quantity and time is a salar operating equally in spae diretions and in the fourth dimension. An important onsequene of the differene appears in elestial mehanis near a loal singularity in spae. As illustrated in Figure, the orbital veloity in Shwarzshild spae exeeds the veloity of free fall near the ritial radius thus disabling stable orbits. In DU spae, orbital veloities remain below the veloity of free fall down to the ritial radius, prediting slow orbits in the range of < r < r essential for hosting the mass of the loal singularity, Figure 5. Preditions for perihelion advane, Shapiro delay, and the bending of light near mass enters are essentially the same in Shwarzshild spae and in DU spae. 6

7 stable orbits ff Newton ff Newton orb Shwarzshild ff DU ff Shwarzshild orb DU 4 rr DU 3 (a) Figure 5. Veloities of free fall and orbital motion at irular orbits in (a) Shwarzshild spae, and (b) in DU spae. The horizontal sale is drawn in units of the ritial radius in DU spae, where the ritial radius is half of the ritial radius in Shwarzshild spae. The veloity of free fall in Newton spae is used as a referene in both harts. 4 rr DU 3 (b) Global relativity In DU spae, relativity appears as a redution of the rest energy due to loal gravitation and motion in spae. As illustrated in Figure 4, loal mass enters reate a dent in the surrounding homogeneous spae. In bended spae in a dent, the veloity of spae in the loal fourth dimension and, aordingly, the loal veloity of light are redued. The loal veloity of light an be expressed in terms of the tilting angle and the global gravitational energy arising from all mass in spherially losed spae Eg GM os () Eg r Loal momentum in the fourth dimension is affeted by both the gravitational state through the gravitational fator and the loal veloity in spae. The effet of loal veloity on the rest mass available in the moving objet an be expressed as mrest m In equation (3) the square root fator has nothing to do with the Lorentz transformation although it is formally idential with the Lorentz fator. In the DU, the square root term an be derived from the onservation of total energy, both in the ase of free fall and in the ase the veloity is obtained via insertion of additional mass like the mass equivalene of Coulomb energy in an aelerator, Figure 6. Combining the effets of motion and gravitation on the loally available rest energy we get E rest E (4), rest Kineti energy obtains a general form E E p mm (5) kin m (3) E E rest rest Im E rest p Re E m kin Re Figure 6. Redution of the rest mass available in an objet moving at veloity v= in spae. The inrease of mass m is obtained from the mass equivalene of Coulomb energy qq EC Ekin mc r r r 7

8 whih in the ase of mass insertion obtains the form E E, E m kin DU total total Equation (6) is essentially equal to the expression derived in speial relativity E rest m, SR Equations (4) and (6) are derived solely from the onservation of total energy in spae. The derivation has nothing to do with the Lorentz transformation, spaetime, the relativity priniple, or the equivalene priniple. The relativisti mass m m rest is not a onsequene of the veloity in spae but it is the mass ontribution needed to build up the veloity of a mass objet at onstant gravitational potential. In a omplete form, the rest energy in DU spae omprises all the veloities a loal objet is subjet to in spae, e.g. in the Earth gravitational frame we are subjet to, the rotational motion and gravitation of the Earth, the orbital veloity and the gravitational state of the Earth in the solar frame, the veloity and the gravitational state of the solar frame in the Milky way frame, the veloity and the gravitational state of the Milky way in the loal galaxy group, et. until we have hypothetial homogeneous spae as our referene n E E m i rest n rest i (8) i Unified expression of energy In DU spae, the veloity of light hanges with time. It is also a funtion of the loal gravitational environment. For a preise analysis of the onservation of energy it is useful to apply the unified expressions of energies given in Figure 7. (6) (7) Coulomb energy e h E C NN NN NNmC r r i i Energy of a yle of eletromagneti radiation E p N m N m N Rest energy of a loalized energy objet h E p m k rest m 4 m m i Figure 7. Unified expressions for the Coulomb energy, the energy of a yle of eletromagneti radiation, and the rest energy of a loalized mass objet. 8

9 There are several important findings in the unified expressions of energies in Figure 7. In DU spae moving at veloity in the fourth dimension, a point emitter of eletromagneti radiation an be regarded as a one-wavelength dipole in the fourth dimension. Solved from Maxwell s equations, the energy emitted by a dipole of length z, in one yle of osillation of N unit harges in the dipole is P Nez 6 f z z E N e f N.49h f f f 3 3 where 3 h.49 e h () showing that the veloity of light is a hidden fator in the Plank onstant h. Removal of from the Plank onstant reveals the intrinsi Plank onstant h = h/ with dimensions [kgm]. The intrinsi Plank onstant shows the mass equivalene of a yle of eletromagneti radiation as h kg () m N N k where k = / and = h /. With a single transition of a unit harge (N = ) in a point emitter we get a quantum of radiation h p () E k m We also find that by applying the Plank onstant in (), the fine struture onstant appears as a purely numerial fator without any onnetion to physial onstants e e 3 3 h.49 e The breakdown of the Plank onstant into its onstituents, and the identifiation of the intrinsi Plank onstant is an exeedingly important step for the unified expression of energies and for understanding the wave-like nature of mass as the substane for all expressions of energy. Applying the intrinsi Plank onstant, mass an be expressed in terms of a wavelength equivalene or wave number equivalene. A mass objet moving at veloity = v/ in spae an be desribed in terms of a wave struture in four dimensions by rewriting the energy-momentum four-vetor E m p (4) into the form k k k (5) and further mm mm m k k k (6) mm mm m or as a omplex wave struture * k k i k (7) mm mm m where (*) is used as the notation for a omplex funtion. Equations (4) to (7) have a major impat on the piture of reality and the physial interpretation of quantum mehanis. (9) (3) 9

10 From time dilation to redued lok frequenies Applying equation (8) to Balmer s equation, the harateristi emission and absorption frequenies atomi objets beome funtions of the gravitational state and veloity of the emitting or absorbing atom E, n n n f n, n f, n, n i i (8) h i Using the frequeny f, at rest in apparent homogeneous spae of the loal frame as the referene, the loal harateristi frequeny an be expressed as f f f 8, 4 DU,, In general relativity, the ombined effet of motion and gravitation on the proper frequeny of atomi osillators in a loal (Shwarzshild) gravitational frame is given by equation 4 f, f, f, GR () 8 On Earth and in near spae onditions the differene in the frequenies given by equations (9) and () appears in the 8 th deimal or beyond, whih is too small a differene to be deteted. The DU preditions (8) and (8) do not rely on any assumptions of the relativity theory but are just onsequenes of the onservation of total energy in spherially losed spae. Momentum of radiation and a mass objet in a moving frame In the DU framework, the Doppler effet of eletromagneti radiation an be derived following the lassial proedure taking into aount both the veloity of the soure and the reeiver in a frame in ommon to the soure and the reeiver. Let s assume that the radiation soure A is at rest in a propagation frame and the reeiver B is moving at veloity v = in the diretion of the radiation reeived. The wavelength B of the radiation observed at B is inreased ompared to the wavelength and frequeny measured at rest in the propagation frame and the momentum of the radiation observed at B beomes h h p B p () B where h is the intrinsi Plank onstant defined in () and p is the momentum observed at rest in the propagation frame. The wavelength of the observed radiation is inreased and the frequeny of the observed radiation is redued by fator ( ) due Doppler effet. As the result, the phase veloity of radiation observed in frame B moving at veloity is B fbb f f () i.e. the phase veloity of radiation observed in the moving frame is equal to the phase veloity of radiation in the rest frame (propagation frame). The observer s veloity does not hange the veloity of the radiation in observer s frame; the momentum of the radiation is hanged as a onsequene of the hange in the frequeny due to the Doppler effet. If the soure is taken to the same moving frame with the reeiver, there is no hange in the momentum of radiation between the soure and the reeiver even if we think that the propagation of radiation ours in the underlying rest frame. (9)

11 When a mass objet with momentum p = mv in a rest frame is taken to a frame moving at veloity v B, (v v B ) momentum p, as observed in the moving frame, is redued by reeiver s veloity as v B pb p p B (3) v where B = v B /v. Comparison of () with (3) shows that the redution of momentum of radiation and a mass objet is equal, but: In the ase of a mass objet the hange in momentum is observed as hange in veloity. In the ase of radiation the hange in momentum is observed as a hange in the wavelength and frequeny. Cosmologial appearane of zero-energy spae The preise geometry, absolute time, and the linkage of the veloity of light to the veloity of the expansion of spae along the 4-radius allow a parameter-free derivation of primary osmologial quantities. Global relativity links loal gravitational systems to whole spae, whih means that gravitationally bound loal systems expand in diret proportion to the expansion of spae. As a onsequene, galati spae is observed in Eulidean geometry, i.e. the angular size dereases linearly with the inreased redshift. In FLRW osmology, due to the loal nature of general relativity, gravitationally bound systems onserve their size in expanding spae. The FLRW predition for the angular size versus redshift of galaxies and quasars is not linear but turns into inrease above redshifts z >, Figure 8. The preise geometry and the onservation of the zero-energy balane in spae produe a parameter free predition for the magnitudes of standard andles as funtion of redshift m M R z z (4) p 4 5log 5log.5log log(las) log(las)... z... z (a) DU-predition (Eulidean) (b) FLRW-predition m =, = (no dark energy) m =.7, =.73 (dark energy added) Figure 8. Dataset of observed Largest Angular Size (LAS) of quasars and galaxies in the redshift range. < z < 3. Open irles are galaxies, filled irles are quasars. (Data olletion [7]: K. Nilsson et al., Astrophys. J. 43, 453, 993). In (a) observations are ompared with the DU predition. In (b) observations are ompared with the FLRW predition with m = and = (solid urves), and m =.7 and =.73 (dashed urves).

12 where m is the apparent magnitude and M is the absolute magnitude of the referene soure at distane parse. R 4 is the 4-radius of spherially losed spae, whih orresponds to the Hubble radius in FLRW spae. The value used for R 4 is 4 billion light years orresponding to Hubble onstant H 7 [(km/s)/mp]. Equation (4) applies for the K-orreted distane modulus in multi-bandpass detetion used in reent supernova observations. Equation (4) is the DU replaement for the orresponding FLRW predition R z H mm 5log 5logz dz p z mzzz (5) where m is the assumed mass density and the assumed dark energy density in spae. Figure 9 shows a omparison of the preditions in (4) and (5) with Supernova Ia observations [8,9]. The differene between the two preditions is negligible in the redshift range < z < but beomes meaningful at higher redshifts. The key message of equation (4) and its omplete fit with observations is that there is no dark energy or aeleration of expansion. The expansion of spherially losed spae ontinues in a zeroenergy balane of motion and gravitation with a deelerating veloity due to the work the expansion does against the gravitation of the struture. 5 DU 45 FLRW ,.,., z z Figure 9. Distane modulus = m M, vs. redshift for Riess et al. high-onfidene dataset and the data from the HST, Riess [8]. The optimum fit for the FLRW predition (5) is based on m =.7 and =.73. The differene between the DU predition (4) and the predition of the standard model (5) is very small in the redshift range overed by observations, but beomes meaningful at redshifts above z > 3.

13 Summary Replaement of the mathematial postulates of modified oordinate quantities, time and distane in speial and general relativity, with the physial postulates of a spherially losed struture and zero-energy balane in the Dynami Universe, turns loal relativity between observer and objet into global relativity between the loal and the whole. Global relativity appears as the loally available share of total energy in spae loks in motion or in a loal gravitational field in the Dynami Universe do not lose time beause of slower flow of time but beause part of their energy is used for motion and loal gravitation in spae, thus leaving less energy to run the osillation. The Dynami Universe desribes the finiteness of physial resoures in spae as a onsequene finite total mass in spherially losed spae. Suh an approah onverts the infinite Newtonian spae and mathematially postulated Einsteinian relativity into a losed but edgeless spae and having a global relativity based on physial postulates. The Dynami Universe allows universal oordinate quantities, time and distane, essential for human oneption and a holisti piture of reality. There is no spae-time linkage in the Dynami Universe; time is universal and the fourth dimension is metri by its nature. The loal state of rest is linked through a hain of nested energy frames to the state of rest in hypothetial homogeneous spae spae as it would be without aumulation of mass into mass enters in spae. The linkage of the loal to the whole is a harateristi feature of the Dynami Universe. The whole in the Dynami Universe is not onsidered as the sum of elementary units the multipliity of elementary units in spae is onsidered as the result of diversifiation of whole. There are no independent objets in spae everything is linked to the rest of spae. Preditions for loal phenomena in DU spae are essentially the same as the orresponding preditions given by the speial and general theories of relativity. At extremes at osmologial distanes and in the viinity of loal singularities in spae differenes in the preditions beome meaningful. The reasons for the differenes an be traed bak to the differenes in the basi assumptions and in the strutures of the two approahes. The Dynami Universe is essentially based on the onservation of a zero-energy balane in spherially losed spae, whih shows relativity as a onsequene of finite resoures in spae thus replaing the mathematial postulates of Einsteinian relativity by postulates with purely physial nature. Aknowledgements I express my gratitude to Prof. Ari Lehto, Dr. Tarja Kallio-Tamminen, and Dr. Heikki Sipilä for many insightful disussions on the laws of nature and the philosophial basis and theoretial struture of the Dynami Universe. Referenes. Tuomo Suntola, The Dynami Universe, Towards a unified piture of physial reality, ISBN , Physis Foundations Soiety, Espoo (9), J. Foster, J. D. Nightingale, A Short Course in General Relativity, nd edition, Springer-Verlag, ISBN () 3. C.W. Misner., K. S. Thorne & J.A. Wheeler, Gravitation, W. H. Freeman & Co., New York (973) 4. R. Feynman, W. Morinigo, and W. Wagner, Feynman Letures on Gravitation (during the aademi year 96-63), Addison-Wesley Publishing Company, p. 64 (995) 5. R. Feynman, W. Morinigo, and W. Wagner, Feynman Letures on Gravitation (during the aademi year 96-63), Addison-Wesley Publishing Company, p. (995) 6. Einstein, A., Kosmologishe Betrahtungen zur allgemeinen Relativitätstheorie, Sitzungsberihte der Preussishen Akad. d. Wissenshaften (97) 7. K. Nilsson et al., Astrophys. J., 43, 453, (993) 8. A. G. Riess, et al., Astrophys. J., 67, 665 (4) 9. T. Suntola and R. Day, arxiv/astro-ph/47 (4) 3