expanding universe has lead to many problems, including, in part, the need to invent ..... and a future 'exponentially accelerating expansion'. stopped physics ...
Evidence for 3-Space as a Dynamical System Reginald T. Cahill School of Chemical and Physical Sciences, Flinders University, Adelaide 5001, Australia Abstract. We compare two generalisations from Newtonian gravity: (i) the Einstein-Hilbert route via curved spacetime, and (ii) dynamical 3-space, which introduced a velocity field formulation in place of the Newtonian acceleration field formulation. The dynamical 3-space is shown to give a parameter free account of the Hubble expansion supernova data, without the need for dark matter nor dark energy, and also resolves the Big Bang Nucleosynthesis - WMAP abundance inconsistencies.
Introduction Some 300 years after Newton [1] introduced the idea of an unchanging and unobservable space, and an acceleration field residing in that space to account for the phenomenon of gravity, there are many phenomena that confound the issue of space and gravity. The 1st major generalisation of Newtonian gravity was the 1916 Einstein-Hilbert spacetime formalism, but that has required the invention of dark matter to account for the rotation of spiral galaxies, and as well dark energy to fit the universe expansion supernovae magnitude-redshift data. However, recently a different generalisation of Newtonian gravity has been reported [2, 3, 4, 6] which appears to overcome many of the issues with space and gravity: space is observable [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18] by means of the detection of the anisotropy of light/EM radiation, and indeed was detected first by Michelson and Morley (MM) in 1887 [9], contrary to conventional wisdom, for it turned out that, taking account of relativistic effects, there is a subtle cancellation in the Michelson interferometer unless the light passes through a dielectric, a gas in the early experiments, and then the calibration constant k involves the factor k2 = n2 − 1 in place of the value k = 1 used by Michelson - here n is the refractive index of the dielectric. For air n = 1.00029, and so the MM experiment was nearly 2000 times less sensitive than assumed, and so the actual observed fringe shifts correspond to a anisotropy speed in excess of 300km/s. Various recent vacuum resonant cavity experiments [21] are essentially vacuum-mode Michelson interferometers, and as such are incapable of detecting EM anisotropy. The latest data analysis [18] using the very accurate doppler shifts observed in spacecraft earth-flybys [20] gives an absolute speed of some 486km/s in the direction RA = 4.3h , Dec = -75◦ , which is the same direction, to within 5◦ , determined by Miller [10] in 1925/26 using a gas-mode Michelson interferometer. There is also evidence that lunar laser-ranging off the moon can be used to measure light speed anisotropy, as well as the detection of gravitational waves [19]. The MM data is in agreement with this latest flyby determination, as shown in [18]. This solar system velocity is wrt the local 3-space and is very different from the CMB velocity (369 km/s in direction RA=11.2h , Dec=7.22◦ ), as they are different phenomena, though often confused. These developments completely change our understanding of reality: there is an observable and dynamical
3-space whose existence has only recently been understood. This is not to be confused with the old notion of an aether residing in the Newtonian unchanging space. Generalising Newtonian gravity by using a velocity field leads to a new account of a dynamical 3-space and the emergent phenomenon of gravity, which is discussed below. This new theory overcomes the many difficulties that have arisen with the Hilbert-Einstein theory of gravity.
Dynamical 3-Space Newton’s inverse square law of gravity [1] has the differential form ∇.g = −4πGρ, ∇ × g = 0,
(1)
for the matter acceleration field g(r,t). Application of this to spiral galaxies and the expanding universe has lead to many problems, including, in part, the need to invent dark energy and dark matter. However (1) has a unique generalisation that resolves these problems. In terms of a velocity field v(r,t) (1) has an equivalent form [2, 3] ∂v ∇. + (v.∇)v = −4πGρ, ∇ × v = 0, (2) ∂t where now
∂v + (v.∇)v, (3) ∂t is the well-known Galilean covariant Euler acceleration of the substratum that has velocity v(r,t). Because of the covariance of g under a change of the spatial coordinates only relative internal velocities have an ontological existence - the coordinates r then merely define a mathematical embedding space. We give a brief review of the concept and mathematical formalism of a dynamical flowing 3-space, as this is often confused with the older dualistic space and aether ideas, wherein some particulate aether is located and moving through an unchanging Euclidean space - here both the space and the aether were viewed as being ontologically real. The dynamical 3-space is different: here we have only a dynamical 3-space, which at a small scale is a quantum foam system without dimensions and described by fractal or nested homotopic mappings [2]. This quantum foam is not embedded in any space - the quantum foam is all there is and any metric properties are intrinsic properties solely of that quantum foam. At a macroscopic level the quantum foam is described by a velocity field v(r,t), where r is merely a [3]-coordinate within an embedding space. This embedding space has no ontological existence - it is merely used to (i) record that the quantum foam has, macroscopically, an effective dimension of 3, and (ii) to relate other phenomena also described by fields, at the same point in the quantum foam. The dynamics for this 3-space is easily determined by the requirement that observables be independent of the embedding choice, giving, for zero-vorticity dynamics and for a flat embedding space, and preserving the inverse square law outside of spherical masses, at g=
least in the usual cases, such as planets, ∂v α ∇. + (v.∇)v + (trD)2 − tr(D2 ) = −4πGρ, ∂t 8 1 ∂ vi ∂ v j ∇ × v = 0, Di j = + , 2 ∂ x j ∂ xi
(4)
where ρ(r,t) is the matter and EM energy densities, expressed as an effective matter density. Borehole g measurements and astrophysical blackhole data has shown that α ≈ 1/137 is the fine structure constant to within observational errors [2, 3, 5]. For a quantum system with mass m the Schrödinger equation is uniquely generalised [5] with the new terms required to maintain that the motion is intrinsically wrt the 3-space, and not wrt the embedding space, and that the time evolution is unitary ∂ ψ(r,t) h¯ 2 2 1 i¯h = − ∇ ψ(r,t) − i¯h v.∇ + ∇.v ψ(r,t). (5) ∂t 2m 2 The space and time coordinates {t, x, y, z} in (4) and (5) ensure that the separation of a deeper and unified process into different classes of phenomena - here a dynamical 3space (quantum foam) and a quantum matter system, is properly tracked and connected. As well the same coordinates may be used by an observer to also track the different phenomena. However it is important to realise that these coordinates have no ontological significance - they are not real. The velocities v have no ontological or absolute meaning relative to this coordinate system - that is in fact how one arrives at the form in (5), and so the “flow" is always relative to the internal dynamics of the 3-space. A quantum wave packet propagation analysis of (5) gives the acceleration induced by wave refraction to be [5] g=
∂v + (v.∇)v + (∇ × v) × vR , vR (ro (t),t) = vo (t) − v(ro (t),t), ∂t
(6)
where vR is the velocity of the wave packet relative to the 3-space, and where vo and ro are the velocity and position relative to the observer, and the last term in (6) generates the Lense-Thirring effect as a vorticity driven effect. Together (4) and (6) and amount to the derivation of gravity as a quantum effect, explaining both the equivalence principle (g in (6) is independent of m) and the Lense-Thirring effect. Overall we see, on ignoring vorticity effects, that ∇.g = −4πGρ −
α (trD)2 − tr(D2 ) , 8
(7)
which is Newtonian gravity but with the extra dynamical term whose strength is given by α. This new dynamical effect explains the spiral galaxy flat rotation curves (and so doing away with the need for “dark matter"), the bore hole g anomalies, and the black hole “mass spectrum". Eqn.(4), even when ρ = 0, has an expanding universe Hubble solution that fits the recent supernovae data in a parameter-free manner without requiring “dark matter" nor “dark energy", and without the accelerating expansion artifact [27]. However
(7) cannot be entirely expressed in terms of g because the fundamental dynamical variable is v. The role of (7) is to reveal that if we analyse gravitational phenomena we will usually find that the matter density ρ is insufficient to account for the observed g. Until recently this failure of Newtonian gravity has been explained away as being caused by some unknown and undetected “dark matter" density. Eqn.(7) shows that to the contrary it is a dynamical property of 3-space itself. Significantly the quantum matter 3-space-induced ‘gravitational’ acceleration in (6) also follows from maximising the elapsed proper time wrt the wave-packet trajectory ro (t), see [2], s Z v2R (ro (t),t) τ = dt 1 − , (8) c2 and then taking the limit vR /c → 0. This shows that (i) the matter ‘gravitational’ geodesic is a quantum wave refraction effect, with the trajectory determined by a Fermat maximised proper-time principle, and (ii) that quantum systems undergo a local time dilation effect. A full derivation of (8) requires the generalised Dirac equation, with the replacement ∂ /∂t → ∂ /∂t + v · ∇, as in (5). In differential form (8) becomes 1 (dr(t) − v(r(t),t)dt)2 , (9) c2 which introduces a curved spacetime metric gµν that emerges from (4). However this spacetime has no ontological significance - it is merely a mathematical artifact, and as such hides the underlying dynamical 3-space. This induced metric is not determined by the Einstein-Hilbert equations, which originated as a generalisation of Newtonian gravity, but without the knowledge that a dynamical 3-space had indeed been detected by Michelson and Morley in 1887 by detecting light speed anisotropy. In special circumstances, and with α = 0, they do yield the same effective spacetime metric. However the dynamics in (4) is more general, as noted above, and has passed more tests. dτ 2 = gµν dxµ dxν = dt 2 −
Hertz-Maxwell Electromagnetic Theory Hertz in 1890 [22] noted that Maxwell had overlooked the velocity field that accompanies time derivatives ∂ /∂t + v · ∇ when a dynamical system, here EM fields, propagates in a dynamical substratum, ∂ µ + v.∇ H = −∇ × E, ∂t ∂ ε + v.∇ E = +∇ × H, ∂t ∇.H = 0, ∇.E = 0, (10) with v(r,t) being the dynamical 3-space velocity field as measured by some observer using time and space coordinates {t, x, y, z}, although Hertz did not consider a time and space dependent v. For uniform and time-independent v (10) has plane wave solutions E(r,t) = E0 ei(k.r−ωt) ,
H(r,t) = H0 ei(k.r−ωt)
(11)
√ ω(k, v) = c|~k| + v.k where c = 1/ µε.
(12)
Then the EM group velocity is vEM = ~∇k ω(k, v) = ckˆ + v.
(13)
So the velocity of EM radiation vEM has magnitude c only with respect to the 3-space, and in general not with respect to the observer if the observer is moving through that 3space, as experiment has indicated again and again, as discussed above. Eqns.(10) give, for uniform v, 2 ∂ + v.∇ E = c2 ∇2 E, ∂t 2 ∂ + v.∇ H = c2 ∇2 H. (14) ∂t on using the identity ∇ × (∇ × E) = −∇2 E + ∇(∇.E) and ∇.E = 0, and similarly for the H field.
Deriving Lorentz Symmetry We could choose to use a new class of time and space coordinates, indicated by uppercase symbols T, X,Y, Z, that mixes the above time and space coordinates. One such new class of coordinates is [23] vx v2 T = γ(v) (1 − 2 )t + 2 , c c X = γ(v)x; Y = y; Z = z, (15) p where γ(v) = 1/ 1 − v2 /c2 . These turn out to be the Minkowski-Einstein spacetime coordinates. Note that this is not a Lorentz transformation. The transformations for the derivatives are then found to be ∂ v2 ∂ = γ(v)(1 − 2 ) , ∂t c ∂T ∂ v ∂ ∂ ∂ ∂ ∂ ∂ , = γ(v) 2 + = , = . ∂x c ∂T ∂X ∂ y ∂Y ∂ z ∂ Z
(16)
∂ We define ∇ = { ∂∂X , ∂Y , ∂∂Z }. Transforming to the Minkowski-Einstein T, X,Y, Z coordinates using (15) and (14) we obtain the form of the source-free “standard" Maxwell equations ∂ 2E ∂ 2H 2 2 2 = c ∇ E, = c2 ∇ H (17) 2 2 ∂T ∂T
which are now covariant under Lorentz transformation VX 0 T = γ(V ) T + 2 , c 0 X = γ(V )(X −V T ), Y 0 = Y, Z 0 = Z,
(18)
where we have taken the simplest case, and where V is a measure of the relative speed of the two observers in their common X directions, but is not their actual observable relative speed. It is important to emphasize that the transformation from the Galilean covariant Hertz-Maxwell equations (10) to the Lorentz covariant Maxwell equations (17) is exact. It is usually argued that the Galilean transformations are the non-relativistic limit of the Lorentz transformations (18). While this is technically so, as seen by taking the limit v/c → 0, this misses the key point that they are related by the new mapping in (15). Also we note that for the Galilean space-time class the speed of light is anisotropic, while it is isotropic for the Minkowski-Einstein space-time class. It is only experiment that can decide which of the two classes of coordinates is the more valid space-time coordinate system. As noted above, and since 1887, experiments have detected that the speed of light is indeed anisotropic. This is a remarkable result. In the new class of coordinates the dynamical equation no longer contains the flow velocity v - it has been mapped out of the dynamics. In (17) there is now no reference to the underlying flowing 3-space system - for an observer using this class of space and time coordinates the speed of light relative to the observer is always c and so invariant - there will be no light speed anisotropy. We could also introduce, following Minkowski, a “spacetime" construct with pseudo-Riemannian metric ds2 = c2 dτ 2 = c2 dT 2 − dR2 = ηµν dX µ dX ν ,
(19)
and light cones along which ds2 = 0. As well pairs of spacetime events could be classified into either time-like or space-like, with the time ordering of spacelike events not being uniquely defined. Based alone on this apparent Lorentz symmetry we could be lead to two principles (1) The principle of relativity: asserting the equivalence of inertial reference frames, that no observer is preferred in respect of the propagation of light waves, and (2) The principle of the constancy of the one-way speed of light: all inertial observers will measure the speed of light to be the same (i.e. invariant), and in particular the same in all directions, i.e. isotropic. However these principles are purely artifacts of the non-physical space and time coordinates introduced in (15). Of course by demanding that the two postulates be valid we are actually merely selecting a special class of space and time coordinates, and not asserting an actual observational property of light wave propagation. Hence the Minkowski-Einstein space-time coordinates are degenerate in that they map out the existence of the dynamical 3-space. So the development of 20th century physics has been misled by two immensely significant “accidents", 1st that Maxwell failed to include the velocity v, and the 2nd that the Michelson interferometer in gas-mode is some 2000 times less sensitive than Michelson had assumed, and that the observed fringe shifts actually indicate a large value for v in excess of 300km/s. These two accidents
Hubble diagram showing the supernovae data using several data sets, and the Gamma-Ray-Bursts data (with error bars). Upper curve is ΛCDM ‘dark energy’ only ΩΛ = 1, lower curve is ΛCDM matter only ΩM = 1. Two middle curves show best-fit of ΛCDM ‘dark energy’-‘dark-matter’ and dynamical 3-space prediction, and are essentially indistinguishable. We see that the best-fit ΛCDM ‘dark energy’-‘dark-matter’ curve essentially converges on the uniformly-expanding parameter-free dynamical 3-space prediction. The supernova data shows that the universe is undergoing a uniform expansion, although not reported as such in [28, 29, 30], wherein a fit to the FRW-GR expansion was forced, requiring ‘dark energy’, ‘dark matter’ and a future ‘exponentially accelerating expansion’. FIGURE 1.
stopped physics from discovering the existence of a dynamical 3-space, until recently, and that the dynamical 3-space displays wave effects. Also again this transformation between the two classes of space-time coordinates explicitly demonstrates that “Lorentz covariance" coexists with a preferred frame, contrary to the aims of the experiments in [21]. Furthermore vacuum-mode Michelson interferometers, such as the vacuum cavity resonators, cannot even detect the long-standing light speed anisotropy, even less so the wave effects that have been otherwise detected - these wave effects are usually known as “gravitational waves". We can apply the inverse mapping, from the Minkowski-Einstein class to the Galilean class of coordinates, but in doing so we have lost the value of the velocity field. In this sense the Minkowski-Einstein class is degenerate -it cannot be used to analyse light speed anisotropy experiments for example.
Expanding Universe from Dynamical 3-Space Let us now explore the expanding 3-space from (4). Critically, and unlike the FLRW-GR model, the 3-space expands even when the energy density is zero. Suppose that we have a radially symmetric effective density ρ(r,t), modelling normal matter and EM radiation, and that we look for a radially symmetric time-dependent flow v(r,t)= v(r,t)ˆr. Then ∂ v(r,t) v(r,t) satisfies the equation, with v0 = , ∂r ∂ 2v vv0 α v2 2vv0 0 00 0 2 + v + vv + 2 + (v ) + + = −4πGρ(r,t). (20) ∂t r r 4 r2 r Consider first the zero energy case ρ = 0. Then we have a Hubble solution v(r,t) = H(t)r, a centreless flow, determined by α 2 ˙ H + 1+ H = 0, (21) 4 dH . We also introduce in the usual manner the scale factor a(t) according to with H˙ = dt a˙ H(t) = . We then obtain the solution a 4/(4+α) t0 1 t = H0 ; a(t) = a0 H(t) = (22) α (1 + 4 )t t t0 where H0 = H(t0 ) and a0 = a(t0 ) = 1, with t0 the present age of the universe. Note that we obtain an expanding 3-space even where the energy density is zero - this is in sharp contrast to the FLRW-GR model for the expanding universe, as shown below. The solution (22) is unique - it has one free parameter - which is essentially the age of the universe t0 = tH = 1/H0 , and clearly this cannot be predicted by physics, as it is a purely contingent effect - the present age of the universe when it is observed by us. Below we include the small effect of ordinary matter and EM radiation, except in the very earliest epochs. We can write the Hubble function H(t) in terms of a(t) via the inverse function t(a), i.e. H(t(a)) and finally as H(z), where the redshift observed now, relative to the wavelengths at time t, is z = a0 /a − 1. Then we obtain H(z) = H0 (1 + z)1+α/4
(23)
To test this expansion we need to predict the relationship between the cosmological observables, namely the apparent photon energy-flux magnitudes and redshifts. This involves taking account of the reduction in photon count caused by the expanding 3space, as well as the accompanying reduction in photon energy. The result is that the dimensionless ‘energy-flux’ luminosity effective distance is then given by dL (z) = (1 + z)
Z z H0 dz0 0
H(z0 )
(24)
and the distance modulus is defined as usual by µ(z) = 5 log10 (dL (z)) + m.
(25)
Because all the selected supernova have the same absolute magnitude, m is a constant whose value is determined by fitting the low z data. Using the Hubble expansion (23) in (24) and (25) we obtain a middle curve in Fig.1, yielding an excellent agreement with the supernovae and GRB data. Note that because α/4 is so small it actually has negligible effect on these plots. But that is only the case for the homogeneous expansion - the α dynamics can result in large effects such as black holes and large spiral galaxy rotation effects when the 3-space is inhomogeneous, and particularly precocious galaxy formation. Hence the dynamical 3-space gives an immediate account of the universe expansion data, and does not require the introduction of a cosmological constant or ‘dark energy’ nor ‘dark matter’.
Expanding Universe - Matter and Radiation Only When the energy density is not zero we need to take account of the dependence of ρ(r,t) on the scale factor of the universe. In the usual manner we thus write ρm ρr ρ(r,t) = + , (26) 3 a(t) a(t)4 for ordinary matter and EM radiation. Then (20) becomes for a(t) 4πG ρm ρr a¨ α a˙2 + = − + , a 4 a2 3 a3 a4
(27)
giving 8πG ρm ρr α a˙ = + 2 − 3 a 2a 2 2
Z
a˙2 da + f , a
where f is the integration constant. In terms of a˙2 this has the solution 8πG ρm ρr 2 −α/2 a˙ = + + ba , 3 (1 − α2 )a (1 − α4 )2a2
(28)
(29)
which is easily checked by substitution into (28), and where b is the integration constant. We have written an overall factor of 8πG/3 even though b, in principle, is independent of G. This gives b convenient units of matter density, but which does not correspond to any actual energy. From now on we shall put α = 0. Finally we obtain from (29) Z a
t(a) = 0
da
r
. ρr + 2 +b a 2a
8πG ρ
(30)
m
3
When ρm = ρr = 0, (30) reproduces the expansion in (22), and so the density terms in (29) give the modifications to the dominant purely-spatial expansion, which we have
Shows the Big Bang nucleosynthesis (BBN) abundances for: the 4 He mass fraction (top), D and (middle) and 7 Li (bottom) relative to hydrogen vs ΩB h2 , as curves, from Coc et al. [25]. Horizontal bar-graphs show astrophysical abundance observations. The vertical bargraphs show the values ΩB h2 = 0.0224 ± 0.0009 from WMAP CMB fluctuations, while the bar-graph 0.009 < ΩB h2 < 0.013 shows the best-fit at 68% CL from the BBN for the observed abundances [25]. We see that the WMAP data is in significant disagreement with the BBN results for ΩB h2 , giving, in particular, the 7 Li abundance anomaly within the ΛCDM model. The dynamical 3-space model has a different and hotter thermal history in the radiation dominated epoch, and the corresponding BBN predictions are easily obtained by a re-scaling of the WMAP value ΩB h2 to ΩB h2 /2. The resultant ΩB h2 = 0.0112 ± 0.0005 values are shown by the vertical bar-graphs that center on the BBN 0.009 < ΩB h2 < 0.013 range, and which is now in remarkable agreement with BBN computations. So while the BBN - WMAP inconsistency indicates a failure of the Friedmann FRW-GR Big Bang model, it is another success for the new physics entailed in the dynamical 3-space model. Plots adapted from [25]. FIGURE 2.
3 He
noted above already gives an excellent account of the red-shift data. Having b 6= 0 simply asserts that the 3-space can expand even when the energy density is zero - an effect missing from FLRW-GR cosmology. From (29) we obtain (from now-on an ‘overline’ is used to denote the 3-space values. Note that H 0 ≡ H0 - the current observable value) Ωr (1 + z)4 + Ωs (1 + z)2 ), Ωm ≡ ρm /ρc , Ωr ≡ ρr /ρc , 2 (31) 1/2 1/2 ρr 8πG Ωr 8πG + Ωs = 1; H0 = (ρm + + b) ≡ ρc Ωs ≡ b/ρc , Ωm + 2 3 2 3 (32) which defines the usual critical energy density ρc , but which here is merely a form for H0 - it has no interpretation as an actual energy density, unlike in FRW-GR. Note the factor of 2 for Ωr , which is a key effect, and is not in FRW-GR. In the dynamical 3-space model these Ω’s do not correspond to the composition of the universe, rather to the relative dynamical effects of the matter and radiation on the intrinsic 3-space expansion dynamics. H0 = 73 km/s/Mpc with Ωm ≈ ΩB = 0.04 and Ωs = 0.96 gives an age for the universe of t0 = 12.6Gyrs, while (35) with ΩM = 0.27 and ΩΛ = 0.73 gives t0 = 13.3Gyrs. Ωr = Ωr = 8.24 × 10−5 . H(z)2 = H0 2 (Ωm (1 + z)3 +
Friedmann-GR Standard ΛCDM Cosmology Model We now discuss the strange feature of the ΛCDM standard model dynamics which requires a non-zero energy density for the universe to expand. The well known Friedmann equation is 2 a˙ 4πG ρM ρr = + +Λ , a 3 a3 a4
(33)
where now ρM = ρm + ρDM is the energy composition of the universe, and includes ordinary matter and dark matter, and Λ is the cosmological constant or dark energy, expressed in mass density units. The differences between (28) and (33) need to be noted: apart from the α term (33) has no integration constant which corresponds to a purely spatial expansion, and in compensation requires the ad hoc dark matter and dark energy terms, whose best-fit values are easily predicted; see below. It is worth noting how (33) arises from Newtonian gravity. For radially expanding homogeneous matter (1) gives for the total energy E of a test mass (a galaxy) of mass m 1 2 GmM(r) mv − = E, 2 r
(34)
where M(r) is the time-independent amount of matter within a sphere of radius r. With E = 0 and M(r) = 34 πr3 ρ(t) and ρ(t) ∼ 1/r(t)3 (34) has the Hubble form v = H(t)r. In terms of a(t) this gives (33) after an ad hoc and invalid inclusion of the radiation and dark energy terms, as for these terms M(r) is not independent of time, as assumed above.
These terms are usually included on the basis of the stress-energy tensor formalism within GR. Eqn.(33) leads to the analogue of (30), Z a
t(a) = 0
da r
8πG ρ 3
,
(35)
ρr 2 + 2 + Λa a a M
H(z)2 = H02 (ΩM (1+z)3 +Ωr (1+z)4 +ΩΛ ), ΩM ≡ ρM /ρc , Ωr ≡ ρr /ρc , ΩΛ ≡ Λ/ρc , (36) 1/2 1/2 8πG 8πG ΩM + Ωr + ΩΛ = 1; H0 = (ρM + ρr + Λ) ≡ ρc . (37) 3 3 This has the same value of ρc as in (32), but now interpreted as an actual energy density. Note that Ωr = Ωr , but that Ωm 6= ΩM , as ΩM includes the spurious ‘dark matter’.
Predicting the ΛCDM Parameters ΩΛ and ΩDM The ‘dark energy’ and ‘dark matter’ arise in the FLRW-GR cosmology because in that model space cannot expand unless there is an energy density present in the space, if that space is flat and the energy density is pressure-less. Then essentially fitting the Friedmann model µ(z) to the dynamical 3-space cosmology µ(z) we obtain ΩΛ = 0.73, and so ΩM = 1 − ΩΛ = 0.27. These values arise from a best fit for z ∈ {0, 14} [27]. The actual values for ΩΛ depend on the red-shift range used, as the Hubble functions for the FLRW-GR and dynamical 3-space have different functional dependence on z. These values are of course independent of the actual observed redshift data. Essentially the current standard model of cosmology ΛCDM is excluded from modelling a uniformly expanding dynamical 3-space, but by choice of the parameter ΩΛ the ΛCDM Hubble function H(z) can be made to best-fit the data. However H(z) has the wrong functional form; when applied to the future expansion of the universe the Friedmann dynamics produces a spurious exponentially expanding universe.
Dynamical 3-Space and Hotter Early Universe The observed abundances of 7 Li and 4 He are significantly inconsistent with the predictions from Big Bang Nucleosynthesis (BBN) when using the ΛCDM cosmological model together with the value for ΩB h2 = 0.0224 ± 0.0009 from WMAP CMB fluctuations [26], with the value from BBN required to fit observed abundances being 0.009 < ΩB h2 < 0.013. The 3-space dynamics and the ΛCDM dynamics give different accounts of the expansion of the universe and in particular of the thermal history during the radiation dominated epoch. ΛCDM gives in that epoch, the Friedmann q from p p √ equation (33), a(t) = 2H0t Ωr , while (30) gives a(t) = 2H0t Ωr /2. Because the CMB is thermal radiation its temperature varies as T (t) = (2.725 ± 0.001)/a(t) ◦ K, and so the 3-space dynamics predicts an early thermal history that is 20% hotter. This means that a re-analysis of the BBN is required [24]. However this is easily
√ achieved by a scaling analysis. Essentially we can do this by effectively using H0 / 2 in place of H0 in the radiation-dominated epoch, as this takes account of the Ωr /2 effect. In terms of ΩB h2 , which determines the BBN, this amounts to the re-scaling ΩB h2 → ΩB h2 /2. This immediately brings the WMAP ΩB h2 = 0.0224 ± 0.0009 down to, effectively, ΩB h2 = 0.0112 ± 0.0005, and into excellent agreement with the BBN value 0.009 < ΩB h2 < 0.013, as shown in Fig.2.
Conclusions These results amount to the discovery of new physics. This new physics has also explained (i) the borehole g anomaly, (ii) black hole mass spectrum, (iii) flat rotation curves in spiral galaxies, (iv) enhanced light bending by galaxies, (v) anomalies in laboratory measurements of G, (vi) light speed anisotropy experiments including the explanation of the Doppler shift anomalies in spacecraft earth-flybys, and (vii) the detection of socalled gravitational waves. As well because (4) is non-local it can overcome the horizon problem. The new physics unifies cosmology with laboratory based phenomena, indicating a new era of precision studies of the cosmos. It must be emphasised that the long-standing and repeated determinations of the anisotropy of vacuum EM radiation is not in itself in contradiction with the Special Relativity formalism - rather SR uses a different choice of space and time variables from those used herein, a choice which by construction mandates that the speed of EM radiation in vacuum be invariant wrt that choice of coordinates [23]. However that means that the SR formalism cannot be used to analyse EM radiation anisotropy data, and in particular the flyby doppler shift data. The discovery of absolute motion wrt a dynamical 3-space has profound implications for fundamental physics, particularly for our understanding of gravity and cosmology. It shows that clocks, and all oscillators, whether they be classical or quantum, exhibit a slowing phenomenon, determined by their absolute speed though the dynamical 3space. This “clock slowing" has been known as the “time dilation" effect - but now receives greater clarity. It shows that there is an absolute or cosmic time, and which can be measured by using any clock in conjunction with an absolute speed detector - many of which have been mentioned herein, and which permits the “clock slowing" effect to be compensated. This in turn implies that the universe is a far more coherent and nonlocally connected process than previously realised, although a model for this has been proposed [2]. It also shows that the now standard discussion of the limitations of simultaneity were really misleading - being based on the special space and time coordinates invoked in the SR formalism, and that simultaneity is a fact of the universe, albeit an astounding one. As well successful absolute motion experiments have always shown wave or turbulence phenomena, and at a significant scale. This is a new phenomena that is predicted by the dynamical theory of 3-space.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
22. 23. 24. 25. 26. 27. 28. 29. 30.
Newton, I. Philosophiae Naturalis Principia Mathematica, 1687. Cahill R.T. Process Physics: From Information Theory to Quantum Space and Matter, Nova Science Pub., New York, 2005. Cahill R.T. Dynamical 3-Space: A Review, in Ether Space-time and Cosmology: New Insights into a Key Physical Medium, Duffy M. and Lévy J., eds., Apeiron, 135-200, 2009. Cahill R.T. Dark Matter as a Quantum Foam In-Flow Effect, Trends in Dark Matter Research, ed. J. Val Blain, Nova Science Pub., 95-140, NY, 2005. Cahill R.T. Dynamical Fractal 3-Space and the Generalised Schrödinger Equation: Equivalence Principle and Vorticity Effects, Progress in Physics, 1, 27-34, 2006. Cahill R.T. 3-Space Inflow Theory of Gravity: Boreholes, Blackholes and the Fine Structure Constant, Progress in Physics, 2, 9-16, 2006. Cahill R.T. and Kitto K. Michelson-Morley Experiments Revisited, Apeiron, 10(2),104-117, 2003. Cahill R.T. The Michelson and Morley 1887 Experiment and the Discovery of Absolute Motion, Progress in Physics, 3, 25-29, 2005. Michelson A.A. and Morley E.W. Am. J. Sc. 34, 333-345, 1887. Miller D.C. Rev. Mod. Phys., 5, 203-242, 1933. Illingworth K.K. Phys. Rev. 3, 692-696, 1927. Joos G. Ann. d. Physik [5] 7, 385, 1930. Jaseja T.S. et al. Phys. Rev. A 133, 1221, 1964. Torr D.G. and Kolen P. in Precision Measurements and Fundamental Constants, Taylor, B.N. and Phillips, W.D. eds. Natl. Bur. Stand. (U.S.), Spec. Pub., 617, 675, 1984. Krisher T.P., Maleki L., Lutes G.F., Primas L.E., Logan R.T., Anderson J.D. and Will C.M. Test of the Isotropy of the One-Way Speed of Light using Hydrogen-Maser Frequency Standards, Phys Rev D, 42, 731-734, 1990. Cahill R.T. The Roland DeWitte 1991 Experiment, Progress in Physics, 3, 60-65, 2006. Munéra H.A., et al. in Proceedings of SPIE, vol 6664, K1- K8, 2007, eds. Roychoudhuri C. et al. Cahill R.T. Combining NASA/JPL One-Way Optical-Fiber Light-Speed Data with Spacecraft EarthFlyby Doppler-Shift Data to Characterise 3-Space Flow, Progress in Physics, 4, 50-64, 2009. Cahill R.T. Lunar Laser-ranging Detection of Light-Speed Anisotropy and Gravitational Waves, Progress in Physics, 2, 31-35, 2010. Anderson J.D., Campbell J.K., Ekelund J.E., Ellis J. and Jordan J.F. Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth, Phys. Rev. Lett., 100, 091102, 2008. Braxmaier C. et al. Phys. Rev. Lett., 88, 010401, 2002; Müller H. et al. Phys. Rev. D, 68, 116006-117, 2003; Müller H. et al. Phys. Rev. D67, 056006,2003; Wolf P. et al. Phys. Rev. D, 70, 051902-1-4, 2004; Wolf P. et al. Phys. Rev. Lett. , 90, no. 6, 060402, 2003; Lipa J.A., et al. Phys. Rev. Lett., 90, 060403, 2003. Hertz H. On the Fundamental Equations of Electro-Magnetics for Bodies in Motion, Wiedemann’s Ann. 41, 369, 1890; Electric Waves, Collection of Scientific Papers, Dover Pub., New York, 1962. Cahill R.T. Unravelling Lorentz Covariance and the Spacetime Formalism, Progress in Physics, 4, 19-24, 2008. Cahill R.T. Dynamical 3-Space Predicts Hotter Early Universe: Resolves CMB-BBN 7 Li and 4 He Abundance Anomalies, Progress in Physics, 1, 67-71, 2010. Coc A, Vangioni-Flam E., Descouvemont P., Adahchour A. and Angulo C. Updated Big Bang Nucleosynthesis Compared with WMAP Observations and Abundance of Elements, ApJ 600, 544552, 2004. Spergel D.N. et al. Astro-phys J.S. 148, 175, 2003. Cahill R.T. Unravelling the Dark Matter - Dark Energy Paradigm, Apeiron, 16, No. 3, 323-375, 2009. Riess, A.G.: et al. Astron. J. 116, 1009, 1998. Perlmutter. S., et al. Astrophys. J. 517, 565, 1999. Perlmutter, S. and Schmidt, B.P. Measuring Cosmology with Supernovae, in Supernovae and Gamma Ray Bursters, Weiler K, Ed., Springer, Lecture Notes in Physics, 598, 195-217, 2003.
