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**Abstract**

This post introduces a holistic approach to the description of the physical reality. The solution, referred to as the Dynamic Universe (DU) [1], is based on a zero-energy balance of motion and gravitation in spherically closed space. The Dynamic Universe allows the derivation of all of the physical and cosmological predictions of the theory of relativity in a closed mathematical form, and shows relativity as a consequence of the conservation of total energy in interactions in spherically closed space – not in terms of modified coordinate quantities, time and distance, as in the theory of relativity but in terms of locally available rest energy.

As a basic postulate, space is described as the 3-dimensional “surface” of a 4-dimensional sphere – the view originally expressed in the early works of Riemann and Mach. Space as the 3-surface of a 4-sphere was also the original idea introduced by Einstein in 1917 as the cosmological appearance of general relativity, but in search for a static solution he added the famous cosmological constant just to prevent the downfall of spherically closed space [2]. Accepting dynamics, spherically closed space allows a zero-energy balance between motion and gravitation of contracting or expanding space – a solution that most probably would have been realized if the findings by Edwin Hubble had been made before the advent of the theory of relativity.

The rest energy of matter in dynamic space appears as the energy of motion mass possesses due to the motion of space in the fourth dimension. The velocity of light in space is linked to the velocity of space in the fourth dimension.

Assuming conservation of total energy in interactions in space, the locally available rest energy of mass objects can be linked to the rest energy the object would have at rest in hypothetical homogeneous space, which serves as the universal frame of reference of all local frames in space. Clocks in fast motion or close to a local mass center in space do not lose time because of slower flow of time but because they use part of their total energy for motion and local gravitation in space.

The Dynamic Universe theory relies on only a very few postulates. It leads to relatively simple mathematics allowing the derivation of most predictions for physical phenomena and cosmological observations in a closed mathematical form without experimental parameters. For local phenomena, including near space, the DU predictions are essentially the same as the predictions given by the special and general theories of relativity. At extremes, at cosmological distances and in the vicinity of local singularities, black holes, the DU predictions work better than the corresponding predictions of the Friedman-Lemaître-Robertson-Walker (FLRW) cosmology and the GR based Schwarzschild metric.

The DU approach unties well-known knots in the prevailing theories and offers a useful platform to the unification of relativity, quantum mechanics, and cosmology – adding the bonus of an intelligible picture of reality.

**Introduction**

*Zero-energy balance and the finiteness of space*

Newtonian physics is local by its nature. No local frame is in a special position in space. There are no overall limits to space or to physical quantities. Newtonian space is Euclidean out to infinity, and velocities in Newtonian space grow linearly as long as there is constant force acting on an object.

Observations of the propagation of light in late 19th century showed a contradiction with the unlimited, linear Newtonian space. Relativity theory broke the linearity and the Euclidean appearance of Newtonian space by redefining the coordinate quantities, time and distance. In the redefined coordinates, the growth of velocities is limited to the velocity of light, which was defined as a natural constant. The local nature of Newtonian physics is retained in relativistic space, justified by the relativity principle claiming the same formulation of the laws of nature for any observer.

Description of finiteness by de-linearization of coordinate quantities can be seen as a mathematical rather than as a physical approach to explain observed physical reality. In the holistic perspective of spherically closed space, the finiteness of velocities appears a consequence of the finiteness of total energy in space. Starting from finite total energy in space allows universal coordinate quantities, time and distance, and links the velocity of light to the energetic state of the universe. In spite of the totally different postulates and the different picture of reality in the two approaches, the predictions for local physical phenomena are essentially the same. Differences arise at the extremes, at cosmological distances and in the vicinity of local singularities in space. Global relativity links the sizes of gravitationally bound systems to the expansion of space, which explains the observed Euclidean appearance of galactic space. Magnitude observations of supernovas are explained with high accuracy – without accelerating expansion, dark energy, or any other additional parameter. As a major difference to the GR based Schwarzschild metric, local singularities in DU space have stable orbits down to the critical radius – able to host the mass maintaining the singularity. The fast periods observed at Sagittarius A at the center of the Milky Way are in complete agreement with the DU predictions [3].

It has been known for several decades that the rest energy of all matter in space is essentially equal to the total gravitational energy in space.

In his lectures on gravitation in early 1960’s Richard Feynman [4] stated:

*“...One intriguing suggestion is that the universe has a structure analogous to that of a spherical surface. If we move in any direction on such a surface, we never meet a boundary or end, yet the surface is bounded and finite. It might be that our three-dimensional space is such a thing, a tridimensional surface 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 spherical ball.”*

In the same lectures [5] Feynman also pondered the equality of the rest energy and gravitational energy in space:

*“If now we compare the total gravitational energy E*

_{g}= GM_{tot}^{2}/R to the total rest energy of the universe, E_{rest}= M_{tot}c^{2}, lo and behold, we get the amazing result that GM_{tot}^{2}/R = M_{tot}c^{2}, so that the total energy of the universe is zero. — It is exciting to think that it costs nothing to create a new particle, since we can create it at the center of the universe where it will have a negative gravitational energy equal to M_{tot}c^{2}. — Why this should be so is one of the great mysteries — and therefore one of the important questions of physics. After all, what would be the use of studying physics if the mysteries were not the most important things to investigate.”The Dynamic Universe approach means just combining of Feynman’s intriguing suggestion of spherically closed space to the great mystery of the equality of the total rest energy and gravitational energy. Obviously, Feynman did not take into consideration the possibility of a dynamic solution – in fact, such a solution does not work in the framework of the theory of relativity, which is based on time as the fourth dimension. In the DU approach time is a universal scalar allowing the definition of velocity and momentum equally in space directions and in the fourth dimension. Momentum due to the motion of space in the fourth dimension and momentum within space combine to form a momentum four-vector and the related energy-momentum four-vector.

*Global relativity and a unified expression of energy*

In a detailed analysis of the zero-energy balance of motion and gravitation in spherically closed space, we can identify following basic concepts [1]:

The rest energy of a mass m can be written as

[tex]{E_{rest\left( {\beta ,\delta } \right)}} = {E_{rest\left( {0,0} \right)}}\prod\limits_{i = 0}^n {\left( {1 - {\delta _i}} \right)\sqrt {1 - \beta _i^2} } = {c_0}mc[/tex] (1)

where

*c*

_{0}is the velocity of light in hypothetical homogeneous space, equal to the velocity of space in the direction of the 4-radius, and

*m*is a locally available rest mass

[tex]m = {m_{rest\left( \beta \right)}} = {m_{rest\left( 0 \right)}}\prod\limits_{i = 0}^n {\sqrt {1 - \beta _i^2} } [/tex] (2)

where velocities [tex]{\beta _i} = {{{v_i}} \mathord{\left/ {\vphantom {{{v_i}} {{c_i}}}} \right.

\kern-\nulldelimiterspace} {{c_i}}}[/tex] are the velocities mass object

*m*is subject to in the local frame and in all the parent frames (like the Earth gravitational frame, the solar frame, the Milky Way frame, etc. out to hypothetical homogeneous space). The local velocity of light

*c*is

[tex]c = {c_\gamma } = {c_0}\prod\limits_{i = 0}^n {\left( {1 - {\delta _i}} \right)} [/tex] (3)

where the gravitational factors [tex]{\delta _i} = {{G{M_i}} \mathord{\left/

{\vphantom {{G{M_i}} {{r_i}{c^2}}}} \right.

\kern-\nulldelimiterspace} {{r_i}{c^2}}}[/tex] are the gravitational factors of object

*m*’s locations in the local gravitational frame and in all the parent frames.

The concepts of “locally available rest mass,

*m*” and “local velocity of light,

*c*” can be seen as the DU replacements of the concepts of proper time and proper distance in the theory of relativity. The derivation of

*m*and

*c*are fully based on the conservation of total energy, and does not rely on the relativity principle, the equivalence principle, or the Lorentz transformation as the concepts of proper time and proper distance do. Equation (1) illustrates the global relativity characteristic to the DU – any local energy state is related to an energy state in hypothetical homogeneous space serving as the global frame of reference.

Substitution of (1) for the rest energy of an electron in Balmer’s equation gives the characteristic frequencies of atomic objects as

[tex]{f_{\left( {\beta ,\delta } \right)}} = {f_{\left( {0,0} \right)}}\prod\limits_{i = 0}^n {\left( {1 - {\delta _i}} \right)\sqrt {1 - \beta _i^2} } [/tex] (4)

where

*f*

_{(0,0)}is the reference frequency for the oscillator at rest in hypothetical homogeneous space. In a local frame, equation (4) reduces into

[tex]{f_{\left( {\delta ,\beta } \right)}} = {f_{\left( {0\delta ,0\beta } \right)}}\left( {1 - \delta } \right)\sqrt {1 - \beta _{}^2} [/tex] (5)

where [tex]{f_{\left( {0\delta ,0\beta } \right)}}[/tex] is the reference frequency of an oscillator at rest in the parent frame. In the Earth Centered Inertial frame (ECI frame) applicable to Earth satellite clocks, equation (5) equals, within 18 decimals, the proper time frequency prediction of general relativity. The DU predictions for perihelion advance, the Shapiro delay, and the bending of light near mass centers is essentially equal to the corresponding predictions of general relativity.

An important finding in the DU is the breakdown of Planck’s constant into primary electromagnetic constants: the elementary charge,

*e*, the vacuum permeability [tex]{\mu _0}[/tex], and the velocity of light

*c*[1,6]. Observing that the local velocity of light is not constant in the DU, and for the unification of the expressions of energy, it is useful to define the intrinsic Planck constant [tex]{h_0} \equiv {h \mathord{\left/ {\vphantom {h c}} \right. \kern-\nulldelimiterspace} c}[/tex]

[tex]{h_0} = \frac{h}{c} = \frac{{1.1049 \cdot 2{\pi ^3}{e^2}{\mu _0}c}}{c} = 1.1049 \cdot 2{\pi ^3}{e^2}{\mu _0}[/tex] (6)

The primary nature of the decomposition of the Planck constant is seen in the fine structure constant, which now appears as a purely numerical factor without any connections to other physical constants

[tex]\alpha = \frac{{{e^2}{\mu _0}}}{{2{h_0}}} = \frac{{{e^2}{\mu _0}}}{{2 \cdot 1.1049 \cdot 2{\pi ^3}{e^2}{\mu _0}}} = \frac{1}{{1.1049 \cdot 4{\pi ^3}}} \approx \frac{1}{{137.036}}[/tex] (7)

The intrinsic Planck constant allows uniform expressions of energy formally equal to the rest energy of a mass object

Coulomb energy: [tex]{E_C} = {N_1}{N_2}\frac{{{e^2}{\mu _0}}}{{2\pi r}}{c_0}c = {N_1}{N_2}\alpha \frac{{{h_0}}}{{2\pi r}}{c_0}c = {c_0} \cdot {m_C}c[/tex] (8)

Electromagnetic radiation: [tex]{E_{\lambda \left( N \right)}} = {c_0}\left| {\bf{p}} \right| = {c_0}\left| {\frac{{{h_0}}}{\lambda }{\bf{c}}} \right| = {c_0} \cdot {m_\lambda }c[/tex] (9)

where

*m*

_{C}and [tex]{m_\lambda }[/tex] are the mass equivalences of Coulomb energy and a cycle of electromagnetic radiation, respectively. The other way around, the rest energy of a mass object can be expressed in terms of its wavelength equivalence (the Compton wavelength) as

Mass object: [tex]{E_{\lambda \left( N \right)}} = {c_0}\left| {{{\bf{p}}_4}} \right| = {c_0} \cdot mc = {c_0}\frac{{{h_0}}}{{{\lambda _m}}}c[/tex] (10)

where [tex]{\lambda _m}[/tex] is referred to as the wavelength equivalence of mass

*m*. A mass object in the DU can be described as a standing wave structure with rest momentum in the fourth dimension.

*Cosmology*

The precise geometry of space in the DU and the linkage of the velocity of light to the velocity of the expansion of space in the fourth dimension allow very straightforward derivation of key predictions for cosmological observations. The optical distance obtains the form

[tex]D = \Delta {R_4} = {R_4}\frac{z}{{1 + z}} = {R_4}\left( {{e^\alpha } - 1} \right)[/tex] (11)

where

*z*is the redshift and [tex]\alpha [/tex] is the distance angle of the object seen from the 4-center of spherically closed space. The radii of gravitationally bound orbiting systems in DU space are linked to the 4-radius

*R*

_{4}. It means that unlike in FLRW cosmology, the radii of galaxies and quasars expand in direct proportion to the expansion of space. The angular diameter

*d*of an expanding object is

[tex]\theta = \frac{d}{D} = \frac{d}{{\left( {1 + z} \right)}}\frac{{\left( {1 + z} \right)}}{{{R_4}z}} = \frac{d}{{{R_4}}} \cdot \frac{1}{z}[/tex] (12)

which means Euclidean appearance of galaxies and quasars – in a complete agreement with observations. DU space does not support the reciprocity assumed in expanding space models based the theory of relativity [7].

The DU prediction for

*K*-corrected (in multichannel photometry) magnitudes of standard candles obtains the form

[tex]\mu = m - M = 5\log \frac{{{R_4}}}{{10{\rm{ pc}}}} + 2.5\log \left[ {{z^2}\left( {1 + z} \right)} \right][/tex] (13)

as the replacement for the corresponding FLRW prediction [8]

[tex]\mu = m - M = 5\log \frac{{{R_H}}}{{10{\rm{ pc}}}} + 5\;\log \left[ {\left( {1 + z} \right)\int_0^z {\frac{1}{{\sqrt {{{\left( {1 + z} \right)}^2}\left( {1 + {\Omega _m}z} \right) - z\left( {2 + z} \right){\Omega _\Lambda }} }}dz} } \right][/tex] (14)

The prediction (13) fits with recent supernova observations at least as well as (14) does with optimized mass and dark energy densities [1,9,10]. Unlike the FLRW prediction (14), the DU prediction (13) has no dark energy or other free parameters. The fit of (13) means that the expansion of space continues with a decelerating rate maintaining the zero-energy balance of motion and gravitation in space.

**Summary**

As a holistic approach to physical reality, the Dynamic Universe starts from the whole and devolves down to the local. It is primarily an analysis of the energy resources available for the manifestation of physical processes and structures in space. The Dynamic Universe relies on a zero-energy balance in absolute time and universal distances as the coordinate quantities essential for human conception. The Dynamic Universe means a major change in paradigm but offers a platform – with built-in relativity and a firm anchor to human conception – to doctrines like Maxwell’s equations and electromagnetism in general, thermodynamics, celestial mechanics, quantum mechanics, and to cosmological considerations.

**References**

1. T. Suntola, “The Dynamic Universe, Toward a unified picture of physical reality”, ISBN 978-952-67236-0-0, Physics Foundations Society, 334 pages, 2009.

List of downloadable papers on the DU: http://www.physicsfoundations.org/society/dynamic_universe.html" [Broken]

2. Einstein, A., Kosmologische Betrachtungen zur allgemeinen Relativitäts¬theorie, Sitzungsberichte der Preussischen Akad. d. Wissenschaften (1917)

3. Genzel, R, et al., Nature 425 (2003) 934

4. R. Feynman, W. Morinigo, and W. Wagner, Feynman Lectures on Gravitation (during the academic year 1962-63), Addison-Wesley Publishing Company, p. 164 (1995)

5. R. Feynman, W. Morinigo, and W. Wagner, Feynman Lectures on Gravitation (during the academic year 1962-63), Addison-Wesley Publishing Company, p. 10 (1995)

6. T. Suntola, “Photon - the minimum dose of electromagnetic radiation”, in “The Nature of light – What Is a Photon?”, Taylor & Francis Group, CRC Press, ISBN 978-1-4200-4424-9 (2008)

7. I.M.H. Etherington, Phil. Mag., 15, 761 (1933)

8. S. M. Carroll, W. H. Press, and E. L. Turner, ARA&A, 30, 499 (1992)

9. A. G. Riess, et al., Astrophys. J., 607, 665 (2004)

10. T. Suntola and R. Day, arXiv/astro-ph/0412701 (2004)

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