Relativity defines the locally available share of total energy

Transcription

1 Physical Interpretations of Relativity Theory X, Iperial College, London Relativity defines the locally available share of total energy Tuoo Suntola Suntola Consulting Ltd., Finland The Dynaic Universe odel introduced in previous PIRT conferences is based on a zero energy balance of otion and gravitation in spherically closed space. Such an approach explains the rest energy of atter as the energy of otion ass in space possesses due to the otion of space, and allows the study of space as a closed energy syste. Due to the spherical syetry, a universal reference at rest in space is a state with zero velocity in space directions, directions perpendicular to the otion of space along the 4-radius of the spherical structure. Following the zero energy principle all local energy systes in space becoe related to the universal rest frae. Conservation of the total energy relates local velocities in space to the velocity of space and local gravitation in space to the gravitation of whole space thus replacing observer oriented reference fraes to energy syste oriented reference fraes like intrinsically applied in therodynaics, quantu echanics, and celestial echanics or any echanical syste. A zero energy balance eans that the energy of otion is obtained against release of potential energy, the principle first tie introduced by Gottfried Wilhel Leibniz in late 7 th century using the ters vis viva, living force obtained against release of vis ortua dead force. Such an approach fixes a local frae of reference to the local energy syste instead of fixing it to an inertial observer as allowed by Newton s laws of otion and the Galilean relativity, the forerunners of physical thinking for the upcoing centuries. In the Dynaic Universe fraework the conservation of energy in space is anifested through a chain of cascaded energy fraes which extend the zero energy balance of whole space to local reference fraes. As a fundaental difference to Einsteinian relativity, which relies on relativity principle and locally odified coordinate quantities, relativity in the DU defines the locally available share of the total energy conserving the absolute nature of the coordinate quantities and aking relativity an integral part of quantu echanics, electroagnetis, echanics, and therodynaics. In the Dynaic Universe fraework, the expressions of the rest energy of atter, the energy of a quantu, and the energy of electroagnetic radiation obtain a unified for, which deonstrates the abstract nature of ass as the substance for the expression of energy and the priary role of the conservation laws. Based on very few assuptions, the Dynaic Universe odel gives a coherent description of the structure of space and atter and produces precise predictions to physical phenoena throughout the scale fro icrostructures to cosological distances. Introduction The Dynaic Universe [,,3] gives a holistic view of the observable physical reality. Starting fro the overall structure and zero-energy dynaics of space, the dynaic universe approach allows a unifying analysis of the conservation of energy at all scales and shows the essence of relativity as an energetic coupling of local energy fraes to the energy frae of whole space. Energy fraes in the dynaic universe can be characterized as a chain of inbuilt Hailtonian fraes with potential energy and the energy of otion in balance. In the DU, space is described as a three diensional zero-energy surface in a fourdiensional universe. The iniu volue of a closed 3-surface has the shape of the surface of a 4-sphere, the shape space was widely assued to posses before Friedan generalized the interpretation of space-tie in general relativity. In the DU, the local geoetry of space is

2 Physical Interpretations of Relativity Theory X, Iperial College, London derived fro the conservation of total energy in ass center buildup. The dynaic approach links the rest energy of atter to the energy of otion ass has due to the otion of space in the fourth diension, the direction of the 4-radius of the spherically closed structure. The velocity of light in space becoes linked to the velocity of space, and the fourth diension, although not accessible fro space, obtains a direct geoetrical eaning allowing tie to be treated as a universal scalar. By converting the Einsteinian spacetie in dynaic coordinates into dynaic space in absolute coordinates, the Dynaic Universe perspective provides a unifying view on physical phenoena in a solid linkage to the cosological structure and the developent of space and the universe. The Dynaic Universe odel is priarily an analysis of energy balances in space starting fro whole space as an energy frae for interactions of otion and gravitation in cosological scale and ending to eleentary particles as icroscopic energy objects in their parent fraes. Such an approach is possible only in structured space and it leads to a holistic view of the physical reality. Energy available to local phenoena is linked to the energetic state of whole space through a syste of cascaded energy fraes. Such a linkage akes the laws of nature coon to all phenoena and allows the use of universal coordinate quantities, absolute tie and distance. Relativity in the Dynaic Universe results fro the conservation of total energy in space relativity is not related to observer or observation but to the energetic state of the object observed. The laws of nature coon to all energy fraes obviate the need for the relativity and equivalence principles.. The priary energy buildup The zero energy balance In the early 9 s when the theory of relativity was forulated the view of the structure of space was quite liited. The expansion of space had not been detected and the galactic structures were unknown. It was natural to think space as static entity without a specific center or a universal reference at rest. When Einstein in 97 published his view of the cosological structure of space as the surface of a 4-sphere, he needed the faous cosological constant to prevent a collapse of space into singularity [4]. In static space the interpretation of the observed constancy of the velocity of light led to a spacetie concept with a tie-like fourth diension and variable distance and tie coordinates characterized as proper tie and proper distance. Dilated tie was explained as a consequence of the velocity the object relative to the observer, and through a curved spacetie, a property of the spacetie geoetry. If spherically closed space is allowed to contract and expand in a zero-energy balance of otion and gravitation, the Einsteinian tie-like fourth diension becoes replaced by a purely etric diension in the direction of the otion of space along the 4-radius of the structure. The center of syetry and the reference at rest for the expansion and contraction of spherically closed space is in the center of the 4-sphere. Expansion of spherically closed space does not create otion within space; the oentu of the expansion appears only in the direction of the 4-radius perpendicular to all space directions. The related energy of otion appears as the rest energy of atter in space. A hoogeneous expansion of the 4-sphere is observed as recession of objects in space at a velocity proportional to their distances fro the observer. In spherically closed space a natural solution is not static space but space subject to contraction and expansion. Dynaics based on a zero-energy principle shows the rest energy of atter as the energy of otion ass has due to the contraction or expansion of space in the fourth diension, in the direction of the 4-radius. As a consequence of the conservation of the priary energy created in the contraction-expansion process, the velocity of space in the fourth diension sets the upper liit to velocities obtainable in space. The great ystery of the

3 Physical Interpretations of Relativity Theory X, Iperial College, London equality of the rest energy and the gravitational energy of all ass in space is a direct indication of the zero-energy balance of otion and gravitation in space [5]. In contraction, started fro a state of rest at infinity in the past, otion is gained against release of gravitational energy. In expansion, otion works against gravitation resulting in gradual deceleration of expansion until rest at infinity (see Figure -). A detailed analysis of the intrinsic fors of the energies of otion and gravitation in a hoogeneous 4-sphere allows the expression of the zero energy condition as GM ΣM " Mc Σ 4 = (:) R 4 where G is the gravitational constant, c is the velocity in the direction of the radius R 4 of the 4- sphere, and M = I g M Σ is the ass equivalence of the total ass M Σ in space. The factor I g =.776 coes fro the integration of the gravitational energy of a 4-sphere. Equation (:) links the velocity of the contraction or expansion along the 4-radius R 4 to the gravitational constant, the total ass in space, and the 4-radius as c 4 GM " GI gm Σ =± =± (:) R R 4 4 Applying a ass density ρ.55 ρ c, where ρ c is the Friedann critical ass density, 4- radius R 4 = 4 9 light years (= the present estiate of the Hubble radius), and the gravitational constant G = 6.7 [N /kg ] equation (:) gives c = 3 k/s which is equal to the present velocity of light. Conservation of energy in interactions in space requires that the axiu velocity obtainable in space is equal to the expansion velocity c 4, which confirs the interpretation of c = c 4 as the velocity of light in hypothetical hoogeneous space. It also confirs the interpretation of the rest energy as the energy of otion ass has due to the otion of space in the direction of the 4-radius. Energy of otion tie contraction expansion Energy of gravitation FIGURE -. Energy buildup and release in spherical space. In the contraction phase, the velocity of space in the direction of the 4-radius increases due to the energy gained against loss of gravitation. In the expansion phase, the velocity gradually decreases, when the energy of otion gained in contraction is returned to gravity. 3

4 Physical Interpretations of Relativity Theory X, Iperial College, London Tie t fro singularity can be expressed as t R 3 c 4 = (:3) which eans that for a Hubble radius of 4 billion light years [corresponding to Hubble constant H = 7 [(k/s)/mpc], the age of the expanding universe since singularity is 9.3 billion years. When solved for tie t since singularity in expanding space, the expansion velocity and the velocity of light in hoogeneous space obtain the for c /3 dr4 3 = = GM" t (:4) dt 3 While working against the gravitation of the structure, the velocity of expansion and, accordingly, the velocity of light in space slow down gradually. At present the deceleration is dc/c 3.6 /year. The rest energy of atter is built up against release of the gravitational energy of the structure in a contraction and expansion process in the fourth diension. The expression of the rest energy of ass eans excitation of the energy of otion against the gravitational energy of whole space (see FIG. -). (t ) Energy of otion E = c E E g Expansion tie Singularity Energy of gravitation GM " Eg = R 4 FIGURE -. The dualistic expression of the rest energy of atter. In the expansion of space the rest energy gained in a pre-singularity contraction phase is gradually released back to the gravitational energy. The zero-energy linkage of the copleentary expressions of energy links any localized ass object to the rest of space. There is no need to assue antiatter in zero energy balanced space. The negative counterpart of the positive rest energy of atter is the gravitational energy due to all other ass in space. By its nature, the energy of gravitation is non-localized, contrast to the localized nature of the rest energy. Closed spherical space gives an essentially ore ordered picture of our universe and the prevailing laws of nature than do the standard cosology odel and the relativity theory behind it. Instead of a sudden appearance in a big bang, the buildup and release of the energy of atter in space can be described as a continuous process fro infinity in the past through singularity to infinity in the future. Following the zero energy principle, any expression of energy in space becoes related to the energetic state of whole space through a chain of cascaded systes. 4

5 Physical Interpretations of Relativity Theory X, Iperial College, London In historical context there is an obvious connection between the zero energy principle in the Dynaic Universe and the Leibniz s idea of vis viva obtained against the release of vis ortua, i.e. kinetic energy, the living force is obtained against the release of potential energy, the dead force. Leibniz had a clear intuitive view of nature as a highly balanced syste of copleentary actions [6]. As an additional link to Leibniz s ideas, localized energy objects in the Dynaic Universe look like having soething characteristic to Leibniz s onads. Like a Leibniz s onad, a localized energy object in the DU is a reflection of the rest of the universe it can be equally described in ters of the rest energy of the localized object or the non-localized gravitational energy of the sae due to all other ass in space. A localized ass object exists as an excited state based on an energy loan to be paid back with the copletion of the cycle of physical existence. The energy of otion in space The Dynaic Universe relies on very few assuptions. The key assuptions are the closed spherical geoetry of space and a zero-energy balance of otion and gravitation. Instead of postulating gravitational and inertial forces, the Dynaic Universe postulates inherent gravitational energy and inherent oentu as they would appear at rest in hypothetical hoogeneous environent. Force is defined as the negative of the gradient of energy. The laws of otion, the relationship between force and acceleration, are not postulated but derived fro the conservation of the total energy in space. As a part of that derivation, the axiu velocity obtainable in space is shown to be equal to the velocity of space in the fourth diension. Mass in the Dynaic Universe is the substance for the expression of the energies of otion and gravitation. The total ass in space, denoted as M Σ, is a fundaental constant conserved throughout the energy buildup and release. The energies of gravitation and otion are based on the inherent fors of the energies defined in hypothetical epty environent at rest as and E () gi () () i i GM = (:5) r E = v p = v v (:6) respectively. Quantity p = v in equation (:6) is referred to as the inherent oentu of ass in otion at velocity v. The contraction and expansion of spherically closed space in the direction of the 4-radius is assued to take place in environent at rest authorizing the use of the expression of the inherent energy of otion. The energy of otion due to the expansion of space at velocity c 4 in the fourth diension is the rest energy of ass in space. For ass at rest in hoogeneous space the rest energy is expressed in for E = c p = c (:7) rest which is forally identical to the expression of the energy of electroagnetic radiation, E = c p, propagating at velocity c in space. Unlike the oentu of radiation propagating in space, the rest oentu p 4 in equation (:7) appears in the fourth diension perpendicular to the three space directions p4 = c4 For an object oving in space, the total oentu can now be expressed as the orthogonal su of the oentu in space, in one of the three space directions, and oentu in the fourth diension due to the otion of space as (:8) 5

6 Physical Interpretations of Relativity Theory X, Iperial College, London ptot = p+ p 4 (:9) Motion in space is not otion in environent at rest but in environent oving at velocity c 4 in the fourth diension. The total energy of otion becoes E = c p = c p + p = c c + tot 4 tot 4 4 p (:) which is essentially equal to the well known expression of the total energy introduced by the theory of special relativity through a copletely different reasoning. Velocity c in equation (:) refers to the velocity of light in hoogeneous space which is equal to velocity c 4. Kinetic energy, through a change in the total oentu, describes the local work done, or potential energy lost, in obtaining a velocity in space. A general expression of the kinetic energy obtains the for E = c Δ p = c Δ c+ cδ kin E = c p = c eff c E = c p = c c ( ) (:) In the fraework of relativity theory, built on the constancy of the velocity of light, only the second ter in equation (:) is relevant. As shown in [], in the DU fraework the ter Δc in equation (:) applies to kinetic energy obtained in free fall in a local gravitational frae where the velocity of local space is changed through tilting of space, and the second ter cδ in the case of otion obtained through acceleration at a constant gravitational potential in space. In the DU fraework, the locally observed total energy of otion obtains a generalized for tot (:) where c is the velocity of light in hypothetical hoogeneous space equal to the velocity of the expansion of space in the fourth diension, eff is the effective ass to be derived fro the velocity of ass in a local energy frae and the velocities of the local frae as energy object in its parent fraes in a syste of cascaded energy fraes. Velocity c is the local velocity of light deterined by the local gravitational state through the local tilting of space in the local gravitational frae and in the parent fraes in the syste of cascaded energy fraes. The locally available rest energy of atter obtains a generalized for rest 4 (:3) where the locally available rest ass and the local velocity of light are deterined by the conservation of the rest energy obtained in through the contraction and expansion of space and expressed in equation (:7). Relativity in Dynaic Universe relates the local energy of otion and gravitation to the corresponding energies in hypothetical hoogeneous space.. Buildup of kinetic energy through free fall in space In real space ass is accuulated into ass centers, aterial structures oving in local energy systes in space. The basic echanis of conserving the total energies of otion and gravitation in ass center buildup can be illustrated as a process of free fall where the velocity and oentu in space are obtained as orthogonal coponents of the velocity and oentu in the fourth diension through tilting of local space. The conservation of the total oentu can be expressed with equation p " + p ' = p esc " where p is the oentu in the local fourth diension, p esc is the escape oentu back to hoogeneous space, and p is the oentu in fourth diension in hoogeneous space. (:) 6

7 Physical Interpretations of Relativity Theory X, Iperial College, London Assuing ass to be conserved in the process, the conservation equation (:) can be written for corresponding velocities as c " + v ' = c esc " (see FIG. -). Figure - applies coplex coordinates with the iaginary axis in the fourth diension. In tilted space the direction of the local fourth diension is I and in hoogeneous space I.. The tilting angle φ of the local iaginary axis can be expressed in ters of the escape velocity and the iaginary velocities of space as sinφ v c (:) = = (:3) v c where v is the escape velocity in the direction of the local space, the Re axis, and v the escape velocity in the direction of hoogeneous space, the Re -axis. The local velocity of light in the -state is the local iaginary velocity of space and the local rest energy obtains the for c = c= c cosφ (:4) Erest = c p " = c c= E cosφ (:5) rest Free fall eans accuulation of ass into ass centers in space which eans breakage of the syetry used in calculating the gravitational energy in hoogeneous space. Mass M accuulated into a local ass center is no ore contributing to the gravitational energy of ass equivalence M in the center of syetry of spherically closed space. Mass M at distance r fro ass reoved fro the syetry reduces the gravitational energy of hoogeneous space as GM " GM E" g = = E" ( R )( g ) 4 r (:6) I I c " I c v v φ c " Re Re [r] FIGURE -. Escape velocity v in the direction of the Re axis is the velocity at which escape proceeds in the direction of the non-tilted space. Angle φ approaches zero and velocity v approaches velocity v when the escape approaches the non-tilted space. As illustrated in the figure, the oentu in equation (.4:) can be expressed as p ' = v r ˆ of ass object oving at velocity v in the local -frae (in the direction of the Re axis) or oentu p ' = v ' ˆ r of ass object frae (in the direction of the Re axis). = v /c = v /c = sinφ. ' = = cosφ oving at velocity v in hoogeneous space 7

8 Physical Interpretations of Relativity Theory X, Iperial College, London E " = E ( )"cosφ v c c E ( ) " M E " g ( ) E" = E" cosφ g ( ) g( ) R 4 R " R cosφ = 4 M " =.776 M Σ FIGURE -. In tilted space ( M<<M and R <<R 4 ) the ass equivalence of hoogeneous space appear in the direction of the local fourth diension. where is the gravitational factor M R GM 4 = = (:7) r M" rc and, by cobining equations (:6) and (:7), the tilting angle φ can be expressed in ters of the gravitational factor (see FIG. -) E " cos = = (:8) g( ) φ ( ) E " g( ) Substitution of (:8) for cosφ in (:4) relates the local velocity of light to the local gravitational factor = = ( ) c c c The conservation of the total energy of otion in free fall can now expressed as tot = = p" " rest = p + v = + (:9) E E c c c c v (:) or by relating the local total energy to the escape velocity in the direction of hoogeneous space as v E = c tot ( c ) + (:) where the square root ter can be interpreted as the correction of escape velocity due to the tilting of space or an increase of an effective ass for the oentu in the direction of the real axis in hoogeneous space v p = v esc = = eff v (:) 8

9 Physical Interpretations of Relativity Theory X, Iperial College, London Kinetic energy and the Mach s principle Kinetic energy in space is the increase in the absolute value of the energy of otion { Δ E } = E E = E = c tot tot Δ ( c) = c( Δ c+ cδ) Mod rest kin In free fall, kinetic energy is obtained against a reduction in the local velocity of light and the ass is conserved. Acceleration of ass in space at constant gravitational potential eans conservation of the local velocity of light and the increase of kinetic energy is obtained through an increase in the ass of the object put in otion. For a detailed study of the coponents of oentu and the energy of otion it is useful to define a vector like energy equivalent of oentu E* = c p* = c p' + i c p" = E' + ie" or by using the scalar coponents in the real and iaginary directions as E* = c p' + i c p" = E' + i E" Figure 3- illustrates the energy equivalents of oenta for the rest energy, total energy and kinetic energy in the local coplex coordinate syste. It also illustrates the negative gravitational energy in the direction of negative iaginary axis. For an object at rest in a local energy frae in space the total energy otion has the iaginary coponent only, E* = E" = E rest [FIG. 3- (a)]. E* = i E" = i c p" = ic c (3:) (3:) (3:3) (3:4) When oentu p in a space direction is added, the total oentu obtains a coplex for cc E* = cp * = cp' + cic= ( sinφ+ icosφ tot φ ) (3:5) cosφ where the odulus can be written as the scalar su of the rest energy and kinetic energy as I I E rest E' kin E =E* rest ϕ Re E E I () E" kin E* kin φ E* rest Re E I (g) E" (g) ΔE" (g) = E" k (a) (c) FIGURE 3-. Energy equivalence of oenta for the rest energy, total energy and kinetic energy in local space. (a) For an object at rest in a local energy frae in space the total energy otion has the iaginary coponent only, E* = E" = E rest. (b) turn of rest oentu by angle φ = arc (sin ) results in a real coponent p = v by reducing the iaginary coponent by the factor. (c) the oentu in space required to result in the turn of total oentu by angle φ is p = c tanφ. Energy E* k is the coplex kinetic energy, the work done in space for changing the state of rest into the state of otion at velocity v in the local frae. The iaginary part of the kinetic energy is the work done in reducing the iaginary energy of gravitation E* k = ΔE" g. 9

10 Physical Interpretations of Relativity Theory X, Iperial College, London E* = cp * = cc cc ( sinφ i cosφ tot + + ) (3:6) cosφ Angle φ can be expressed in ters of the real part of the coplex rest oentu p ' v prest c φ rest = arc sin = arc sin = arc( sin ) Substitution of (3:7) transfors equation (3:5) into for E * tot ( ) which is the su of the coplex rest energy and the coplex kinetic energy ; v = (3:7) c v = c + ic (3:8) E * c v ic c rest = + (3:9) = + ( ) E* c v ic c kin The scalar value of the kinetic energy in equation (3:) is where (3:) E = E* = cc = c kin kin Δ c (3:) results in the buildup of effective ass Δ = = +Δ = eff (3:) (3:3) The coplex rest oentu p* rest() contributes to the real part of the total oentu, the oentu observed in space, and the corresponding energy equivalence as E' = c p' = c v rest rest As a consequence, the iaginary coponent of the rest energy is reduced to rest rest I (3:4) E" = c p" = c c = c (3:5) Motion in space does not change the iaginary velocity of space c, which eans that otion in space reduces the internal ass, I, available to contribute to the iaginary part of the rest oentu I = (3:6) The internal ass is the counterpart of effective ass; the buildup of kinetic energy in space reduces the energetic excitation of the oving object in the iaginary direction, and the zero energy balance in the iaginary for a oving object is

11 Physical Interpretations of Relativity Theory X, Iperial College, London ,, eff / I /,,4,6,8 FIGURE 3-. The developent of the effective ass eff and internal ass I with the increasing velocity = v/c in an energy frae. The product of the effective and internal asses, eff I =, reains constant conserving the geoetric ean of the two asses. E" rest = GM " I c = I R" (3:7) This also shows that the iaginary part of the kinetic energy is work done for reducing the gravitational energy due to all other ass in space ( ) GM " I Δ E" = = E" g kin = c ( I ) c (3:7) R" which gives a quantitative expression to Mach s principle. The reduction in the internal ass I is counterbalanced by the increase of the effective ass eff. By cobining equations (5:3) and (5:6) the product of the effective and internal ass can be expressed as = eff I (3:8) which shows that the geoetric ean of the effective and internal asses is equal to the rest ass of the ass object studied (see FIG. 3-). The internal ass I appears as the rest ass for otion built up in the local frae in the oving object (see FIG. 3-3). I A E* k (A) I B E I (A) E I (A) = E rest(b) E* k(b) E* rest(a) Re A E I(B) Re B E* rest(b) (a) (b) FIGURE 3-3. Kinetic energy (a) in frae A (the parent frae to frae BB ), and (b) in frae B oving in frae A. The internal energy E I(A) of ass in frae A appears as the rest energy ass has available in frae B. Accordingly, the kinetic energy E k(b) of ass in frae B is subject to the effects of otions both in frae B and the otion of frae B its parent frae A. 4. Buildup of ass centers in real space, cascaded energy fraes In real space ass is aggregated into ass centers in several steps. Hoogeneous space has curled into galactic structures inhabiting galaxies with nuerous stellar systes, stars and planetary systes, all in otion in their parent fraes (see FIG. 4-).

12 Physical Interpretations of Relativity Theory X, Iperial College, London I (A) I (B) M B M A R" (B) M" FIGURE 4-. Mass object rotating in the M B gravitational frae rotates with the M B -frae in the M A -frae. Each ass center creates a local dent in space. Each dent in space reduces the local velocity of light and the otion of each frae reduces the ass of an object in a local frae. Each ass center creates a dent in space in the fourth diension resulting in a tilt in the direction of the local iaginary axis. As a consequence, the local iaginary velocity of space, and accordingly the local velocity of light are reduced in each step. Further, each sub-frae is in otion in its parent frae, which results in a reduction in the internal ass in each sub-frae. By starting fro hypothetical hoogeneous space and by cobining the effects of gravitation and otion in each step, the rest energy of ass in the n:th of the cascaded fraes is Erest where the rest ass in the n:th frae is and the local velocity of light rest n = c c = = c= c = c ( n) ( (4:) n i (4:) i= n i ) i= (4:3) In each local frae, the rest energy can be related to the rest energy in the iediate parent frae as ( ) E = c c= c c = E (4:4) rest rest where is the gravitational state of the object in the local frae and is the velocity of the local frae in the parent frae. Subscript is generally used to refer to the parent frae of a local frae. In the chain of cascaded gravitational fraes the parent frae of the next sub-frae is referred to as apparent hoogeneous space to the sub-frae (see FIG. 4-). Space in the M A - frae in Figure 4- serves as apparent hoogeneous space for the local dent around ass center M B. B The syste of cascaded energy fraes is a central feature in the Dynaic Universe odel. The cascaded energy fraes create a link fro any local energy frae to hypothetical hoogeneous space, which serves as a universal reference to all energy states in space (see FIG. 4-3). The syste of cascaded energy fraes is a consequence of the zero-energy principle and the conservation of the energetic excitation built up in the priary energy build-up process.

13 Physical Interpretations of Relativity Theory X, Iperial College, London I Hoogeneous space of the M A frae Re A I Β(Α) =I B I Re B M B Apparent hoogeneous space of the M B frae M A FIGURE 4-. The apparent hoogeneous space of the M B -frae around ass center M B follows the direction of space in the M A -frae as it would be without the M B center. Hypothetical hoogeneous Extragalactic space E = E I XG I( XG) E = E I rest = cc XG Milky Way frae E = E I( XG)( MW ) I MW E rest ( XG ) MW E rest ( MW ) Solar frae E = E I( MW)( S) I S S E rest ( S ) Earth frae E = E I( S)( E ) I E E E rest ( E ) Accelerator frae E = E I A I E A E rest ( A ) Ion frae E = E I Ion I A Ion E rest ( Ion ) FIGURE 4-3. The rest energy of an object in a local frae is deterined by the internal energy of the local frae in its parent frae. The internal energy is the iaginary coponent of the rest energy. The syste of cascaded energy fraes relates the rest energy of an object in a local frae to the rest energy of the object in hypothetical hoogeneous space. As a consequence of the conservation of the total energy in space, otion and local gravitation of each parent frae reduce the rest energy available in the local frae. 3

14 Physical Interpretations of Relativity Theory X, Iperial College, London The local state of rest in an energy frae is established through the separation of the effective ass related to the otion of the local frae in its parent frae, and the copleentary internal ass available as rest ass in the local frae. Motion of a local frae, or energy object, in its parent frae, results in a central force reducing the gravitation of the ass equivalence M of whole space. When ass in the local frae is studied as effective ass eff oving at velocity in the parent frae, the effective gravitational force of ass M of whole space is reduced due to the central acceleration as F " F " ( ) eff = ( n ) = n When the sae ass is studied as the internal ass at rest in the local frae [n+] the effective gravitational force of ass M of whole space is reduced due to the reduction of the locally available rest ass in the frae [n+] oving at velocity n in the parent frae as F " [ ] [ ] [ ] n+ rest n+ I n = = = n F " The equality of equations (4:5) and (4:6) eans that the replaceent of the effective ass in otion in the parent frae with the internal ass at rest in the local frae results in no change in the balance of forces in the fourth diension (see FIG. 4-4). (4:5) (4:6) I F C eff v = i R" I (a) R" eff = v/c F" eff c = χ R" c I = χ i R" ( ) i (b) I c I F" = χ i R" R" M" M" FIGURE 4-4. (a) The gravitational force of ass equivalence M on ass eff oving at velocity v with a local frae is reduced by the central force F C, which akes it equal to the gravitational force of ass equivalence M on ass I at rest in the local frae as illustrated in figure (b). 5. The energy of a quantu and the characteristic frequencies of atos Quantu as the iniu dose of electroagnetic radiation The Dynaic Universe approach unifies the local expressions of energy by identifying ass as the substance and the priary conserving quantity for all fors of energy including electroagnetic energy and photons. As a hidden essage in Maxwell s equations, an intrinsic for of Planck s constant, h = h/c [kg ], shows the ass equivalence and the energy of a single cycle or a wavelength of electroagnetic radiation as h E = c = cc (5:) 4

15 Physical Interpretations of Relativity Theory X, Iperial College, London or in a generalized for h E = N cc = N cc = cc (5:) where N is the nuber of unit charges oscillating in a hypothetical dipole eitting N quanta of radiation in a cycle [7]. The energy conserving structure of space is reflected in the energy of a wavelength of radiation through quantities c and c, the velocity of light in hypothetical hoogeneous space and in local space, respectively. The local velocity of light is equal to the velocity of space in the direction of local fourth diension which deviates fro the direction of the 4-radius due local tilting of space related to ass center buildup. Applying the intrinsic Planck s constant, h, the oentu of a quantu of radiation is expressed as h p = c= c= h f (5:3) A essage of equation (5:3) is that the conservation of oentu is equivalent to conservation of frequency, which iplicitly eans absolute tie in space. The energy and oentu of radiation are conserved in changing gravitational potential (i.e. the energy and oentu of radiation are independent of the local velocity of light). The gravitational blue/redshift is observed as a shortening or increase in the wavelength against shortening or increase in the local velocity light. In the eission of electroagnetic radiation, on the other hand, the wavelength is independent but the frequency is directly proportional to the local velocity of light, i.e. radiation propagating in space conserves the energy content obtained in the eission. However, as eaningful at cosological distances, electroagnetic radiation is subject redshift due to the expansion of space. The interpretation of a quantu obtained fro Maxwell s equations shows quantu as the eleentary energy of one wavelength of electroagnetic radiation in a closed wave front, thus showing quantu a property of wave-like expression energy. Such a quantu property eans that an energetically balanced dose of radiation in a closed syste assues an integer nuber of wavelengths or cycles, which always is the case in closed radiation systes described in ters of standing waves. Extension of the wavelike description of energy objects ore generally to ass objects occurs by applying the debroglie wavelength just as done by Bohr in his historical solution of the basic quantu states of a hydrogen ato. In agreeent with the wave description of quantu continuu a localized expression of quantu has been derived fro Maxwell s equations by G. Hunter [8]. Hunter s quantu, called soliton, is an ellipsoid with the length of one wavelength in the direction of propagation and the diaeter of /π perpendicular to the propagation direction. The diaeter of Hunter s soliton is in perfect agreeent with the resolution of electron icroscopes and the easured penetration of circularly polarized icrowaves through holes in a etal ask. Also, the capturing area of an antenna with gain one is equal to /π, which can be interpreted as capturing of a quantu of radiation fro a plane wave into a detectable soliton. Characteristic eission and absorption of hydrogen like atos The effects of otion and gravitation are transferred to the energy states and characteristic absorption and eission frequencies of atos through the rest energy of electron. By applying equations (4:) to (4:3) for the rest energy of electron the standard solution of the energy states of hydrogen like atos can be expressed as E n α Z Z, n c n i= = and the corresponding characteristic frequencies as ( i) i (5:6) 5

16 Physical Interpretations of Relativity Theory X, Iperial College, London f (, n n n ) = = f ( ) n, n n, n i i hc i= ΔE (5:7) where f (n,n) is the frequency of the transition for an ato at rest in hypothetical hoogeneous space f α, = Z n n h ( n n ) e c (5:8) As an iplication of the cross-linkage of the effects of otion and gravitation, the local velocity of light is an attribute of the gravitational state of the object in the local frae and in the parent fraes, and the locally available rest ass is an attribute of the velocity of the local frae in its parent frae and the velocities of each parent frae in the grand parent frae. The wavelength of the characteristic eission and absorption of hydrogen like atos is n n n (, ) h = Z n n α e i= i (5:9) Applying the standard solution of the Bohr radius and equation (4:) for the rest ass, the radius of the hydrogen ato can be expressed as h = = πμeen a n i= a i (5:) where a () is the Bohr radius of an hydrogen ato at rest in hypothetical hoogeneous space a = h = h (5:) πμe πα e e The square root expression in equations (5:) and (5:) has the for of the Lorentz factor, however, it has nothing to do with Lorentz transforation. The square root expression shows the reduction in the internal energy of an object in otion in an energy frae. In the DU fraework, the factor can be derived as a consequence of the conservation of energy. Originally, Lorentz identified the sae factor as an experiental correction to Coulob s force between oving charges. The Coulog energy By applying the intrinsic Planck s constant and the fine structure constant, the Coulob energy obtains the for qq μ e μ h EEM = cc= NN cc= NNα cc= cemc (5:) 4πr πr πr where the quantity EM [kg] is the energy equivalence of Coulob energy for N and N eleentary charges at distance r fro other qqμ 4π r EM = (5:3) As shown by equation (5:3) Coulob energy releases ass when distance r between charged objects q and q is reduced. The ass released appears as buildup of effective ass in the charged object accelerated through the reduction of r. 6

17 Physical Interpretations of Relativity Theory X, Iperial College, London Resonator as an electroagnetic energy object Electroagnetic radiation localized in a resonator behaves like any other energy object. The effective ass equivalence created by the otion of the resonator frae in its parent frae becoes counterbalanced by the internal ass equivalence and internal wavelength within the oving resonator frae. Accordingly, waves with the internal wavelength in the resonator are observed as propagating at the velocity of light relative to the state of rest in resonator, an effect that was first observed by Michelson and Morley in their interferoetric easureents in late 8 s. The search for an explanation to the findings of Michelson and Morley led to the declaration of the velocity of light a physical invariant for the observer, the choice which becae the cornerstone of the theory of relativity. Propagation of electroagnetic radiation can be equally interpreted as taking place in a local frae or its parent frae. An observer at rest in local a frae, oving at velocity r in the direction of radiation propagating in the parent frae, observes the frequency of the radiation Doppler shifted f obs ( ) ( ) c c = f ( r ) = = r which he can equally interpret as radiation with wavelength /( ) and phase velocity c in the observer s frae or radiation with wavelength and phase velocity c( ) in the parent frae. The oentu of radiation with frequency f obs in equation (6:) is ( ) r = r = = ( r ) (6:) h h p c c f r c (6:) which shows that the conservation of oentu is equivalent to the conservation of frequency in frae to frae observations. The study of energy fraes and the local state of rest in Sections 6 and 7 was ade for ass objects as closed energy systes. It can be shown, that closed in a closed syste like in a resonator the ass equivalence of electroagnetic radiation behaves just like the ass of conventional ass objects. When a resonator is put into otion in its parent frae in space the ass equivalence of the standing wave in the resonator shows an increased effective ass equivalence relative to the parent frae and a reduced internal ass equivalence relative to the state of rest in the resonator frae. A resonator creates a closed energy object by capturing the radiation of two opposite plane waves between the reflectors at the opposite ends of the resonator cavity. As taught by classical wave echanics, a resonant superposition of waves in opposite directions produces a standing wave r A = Asinπ cosπ ft = Asinkr cosω t (6:3) with nodes at r = n /. The oenta in a resonator at rest have a zero vector su but a nonzero scalar su p = ½p + ½p = ; ½p + ½p = p = p (6:4) ( + ) ( ) ( + ) ( ) tot tot tot where p tot = p I (EM) is the internal oentu, the scalar su of the oenta of the waves in opposite directions. When a resonator is in otion in the direction of its longitudinal axis in its parent frae, the internal oenta and wavelengths of the waves sent by the end plates of the resonator are subject to Doppler shift when observed at rest in the parent frae of the resonator. The wavelength of the wave sent in the direction of the velocity of the resonator is Dopler shifted due to the otion of the resonator as 7

18 Physical Interpretations of Relativity Theory X, Iperial College, London and in the opposite direction as = ( ) = ( ) I (6:5) + = ( + ) = ( I + ) (6:6) The su of the oentus of the Doppler shifted waves in the parent frae now becoes h h p = ½p + ½p tot = + c (6:7) ( ) ( + ) Multiplication of the noinators and denoinators of the ters in parenthesis in equation (6:7) by the factor gives h h p = ½ ½ tot + ( ) c= c (6:8) or applying the ass equivalence of electroagnetic radiation as p = c= tot ( eff ) v Equations (6:8) and (6:9) show that otion of a resonator, as a closed electroagnetic energy object in its parent frae, creates oentu through the increase of the effective ass equivalence exactly in the sae way as any other ass object. As a part of the balance, the internal oentu in the resonator, the oentu in the resonator frae, is reduced due to the reduced internal ass equivalence of the radiation (see FIG. 8-) p = (½ ½ ) c= (6:) I I EM I EM In the resonator frae the reference at rest is the resonator body. Accordingly, for waves in both directions in the resonator the frequencies and wavelengths are the internal frequency and wavelength fi ( ) where refers to the velocity of the resonator in its parent frae. I ( ) (6:9) c = (6:) I I p =,eff c p I Re (a) (b) FIGURE 8-. (a) The oentu of an electroagnetic resonator can be expressed in ters of an internal oentu p I of the standing wave in the resonator frae and (b) the external oentu p of the resonator as an energy object oving at velocity v = c in the parent frae. 8

19 Physical Interpretations of Relativity Theory X, Iperial College, London When studied as a closed energy syste, oenta of the waves in opposite directions in a resonator result in radiation pressure at the reflectors. In a physical resonator, the recoil due to the radiation pressure at the opposite ends of the resonator is copensated through a tension and an excited state in the cheical bonds between atos in the resonator body. Such a closed energy syste is fully coparable to a gas container, a rotating centrifuge, or a particle accelerator where the reference at rest of the energy frae is the physical body of the syste or the internal zero oentu point. Lasers, asers and Michelson-Morley interferoeters define each their local energy frae and, accordingly, the local state of rest serving as the reference for the velocity of light in the frae. As shown by equations (5:9) and (5:) both the eission wavelength and the atoic radius are functions of the velocity of the ato in the local energy frae and the velocities of local frae and the parents fraes. It eans that the resonance condition and the nuber of nodes in a standing wave in a resonator are independent of the velocity of the resonator in the parent frae. The description of electroagnetic resonators as energy objects with localized diensions, and the buildup of effective and internal asses due to otion in the parent frae deonstrates the nature of localized energy structures as propagating waves packaged by the local potential energy structure. The Dynaic Universe concept does not recognize classical ass particles but energy objects as closed energy structures coprising the balance of the local potential energy and the energy of otion. 7. Conclusions The Dynaic Universe gives a highly order and balanced picture of space both at cosological scale and in localized energy structures. The copleentary expression of energy, through the syste of cascaded energy fraes in the Dynaic Universe, serve as the replaceent to ether concepts in classical physics, and to the geoetrized spacetie in the theory of relativity. An essential difference between the DU and the relativity theory coes also fro the holistic nature of the Dynaic Universe the study of the energy balances in the DU is started fro whole space and then, step by step, derived into localized structures. Such an approach fixes the local states of rest to local energy fraes like iplicitly done in therodynaic and quantu echanical systes and, as an iportant additional feature, links the local energy fraes to their parent fraes and finally to hypothetical hoogeneous space which serves as the universal reference to all local fraes in space. Local energy fraes in the Dynaic Universe have certain characteristics of classical ether, however, a decent description of the local energetic state as well as frae to frae observations require the syste of cascaded energy fraes, and thereby the co-existence of the parent fraes behind any local frae. While the classical ether can be characterized as global, static environent, the energy frae syste in the DU can be characterized as a ultilevel ether syste, with each of the coexisting fraes sensitive to their angle relative to the local fourth diension. The Newtonian approach was priarily guided by iediate observations, which is quite natural in such a pioneer s situation. Force, relative otion, and oentu fored the cornerstones in Newton s echanics. Energy, as a ore abstract concept, was added to classical echanics through several steps as the integrated force [9]. Newton s equations of otion were perhaps too excellent at their tie, aking otion ore or less independent of its origin. When cobined with Galilean relativity, Newtonian otion found its reference at the observer, an obvious isconception that was inherited to the theory of relativity. Relative velocity is well justified in kineatic sense as the rate of the change in the distance between an object and the observer. Relative velocity does not, however, tell the aount of effective ass and kinetic energy stored in a oving object; the buildup of effective ass and kinetic energy are related to the work done in obtaining the otion in the relevant energy frae. Classical ether was iplicitly fixed to the observer which ade Newton s laws of otion applicable to any observer as such. The observer oriented approach claiing for sae 9

20 Physical Interpretations of Relativity Theory X, Iperial College, London observations to any observer was reflected in the relativity principle, which was presented to justify the odification of the local ether environent so that observations looked the sae for any observer. The result was the Lorentz odified inertial fraes and spacetie odified gravitational fraes. The DU ultilevel ether is built up fro the syste of cascaded energy fraes. Motion gained fro potential energy in a local frae, is paid back in the sae frae. Energy bookkeeping actuates through the reduction of the rest energy in each frae, or ore precisely, through the rest oentu which also carries the inforation about the direction of the fourth diension relevant to the frae. In the DU fraework, there is an essential difference between velocity in kineatic sense and velocity as an expression of kinetic energy. In kineatic sense, velocity eans the rate of the change in the distance between two locations or velocity relative to a fixed or oving point in space. Galilean relativity and the Galilean transforation of velocities apply to kineatic velocity everywhere in space. When expressing kinetic energy, velocity appears as a square ter which cancels the vector nature of velocity and akes the concept of relative velocity irrelevant. Kinetic energy follows the structure of energy fraes as a part of the conservation of the total zero energy balance in space. References. Suntola, T., Theoretical Basis of the Dynaic Universe, Suntola Consulting Ltd., ISBN (4) 9 p, Suntola, T., PIRT-IX, "Physical Interpretations of Relativity Theory IX", London, Septeber 3-9, 4, p Suntola, T., PIRT, Moscow, July 4-7, 5, p Einstein, A.., Kosologische Betrachtungen zur allgeeinen Relativitätstheorie, Sitzungsberichte der Preussischen Akad. d. Wissenschaften (97) 5. R. Feynan, W. Morinigo, W. Wagner, Feynan Lectures on Gravitation (during the acadeic year 96-63), Addison-Wesley Publishing Copany, 995, p. 6. Leibniz, G.W., Mateatischer Naturwissenschaflicher und Technischer Briefwechsel, Suntola, T., Proc. SPIE Vol. 5866, p Hunter, G., Kowalski, M., Alexandrescu, C., Proc. SPIE Vol. 5866, p A.F. Antippa, Can. J. Phys. 78, (),