Dynamical 3-Space: neo-Lorentz Relativity

The major extant relativity theories - Galileo's Relativity (GaR), Lorentz's Relativity (LR) and Einstein's Special Relativity (SR), with the latter much celebrated, while the LR is essentially ignored. Indeed it is often incorrectly claimed that SR and LR are experimentally indistinguishable. Here we show that (i) SR and LR are experimentally distinguishable, (ii) that comparison of gas-mode Michelson interferometer experiments with spacecraft earth-flyby Doppler shift data demonstrate that it is LR that is consistent with the data, while SR is in conflict with the data, (iii) SR is exactly derivable from GaR by means of a mere linear change of space and time coordinates that mixes the Galilean space and time coordinates. So it is GaR and SR that are equivalent. Hence the well-known SR relativistic effects are purely coordinate effects, and cannot correspond to the observed relativistic effects. The connections between these three relativity theories has become apparent following the discovery that space is an observable dynamical textured system, and that space and time are distinct phenomena, leading to a neo-Lorentz Relativity (nLR). The observed relativistic effects are dynamical consequences of nLR and 3-space. In particular a proper derivation of the Dirac equation from nLR is given, which entails the derivation of the rest mass energy mc^2


Introduction
Physics has failed, from the early days of Galileo and Newton, to consider the existence of space as a structured, detectable and dynamical system, and one that underpins all phenomena, until 2002 when it was discovered that the Michelson-Morley experiment was not null [1,2], and indeed confirmed Lorentz's Relativity Theory 1 . Essentially the last 400 years of physics has been one of much confusion because the key phenomenon of space had been missed, and indeed Minkowski and Einstein had even denied its existence, claiming instead the actual existence of spacetime, a geometrical amalgam of the geometrical models of space and time [3]. Subsequent to the above discovery the dynamics of space has been determined and subjected to many experimental and observational tests, from laboratory experiments to the discovery of the uniformly expanding universe [4,5,6,7,8,9,10,11]. The discovery of dynamical space changes all of physics. It is now possible to sort out the confusion over which relativity principle is confirmed by experiment, and for the 1st time we get a clear picture of the nature of reality.
A "Relativity Principle" (RP) specifies how observations by ing connected S n 's shown embedded, at a coarse grain level, in an an emergent E 3 . The quantum foam is fractal, so this connectivity is repeated at all scales [4]. Right: Representation of the fractal 3-space velocity field v@r; tA as determined by experiment [11]. This detected space structure is passing the earth at $500km/s, with the velocity slightly different within each cell. This data implies that dynamical space has a fractal texture. different observers are related. In doing so the RP reflects fundamental aspects of realty, and any proposed RP is subject to ongoing experimental challenge. There have been three major relativity theories: Galileo's Relativity (GaR), Lorentz's Relativity (LR) and Einstein's Special Relativity (SR), with the later much celebrated 2 , while the LR is essentially ignored. Yet it is often claimed that they are experimentally indistinguishable. Here we show that (i) they are experimentally distinguishable, (ii) that comparison of gas-mode Michelson interferometer experiments with spacecraft earth-flyby Doppler shift data [10,12] demonstrate that it is LR that is consistent with the data, while SR is in conflict with the same data, (iii) SR is exactly derivable from Galilean Relativity by means of change of space and time coordinates, so that the well-known SR relativistic effects are purely coordinate effects, and cannot correspond to the observed dynamical relativistic effects. The connections between these three relativity theories has become apparent following the discovery that space is a dynamical and observable system, and that space and time are distinct phenomena.
We give a non-historical presentation, because historical presentations were always confused by the lack of realisation that a dynamical space existed, although serious consideration was given to Lorentz Relativity [13,14,15].
But 1st a warning: a common error when discussing the physics of space and time is to confuse space and time coordinates with the actual phenomenon of space and time, and also to confuse space intervals, as measured by a ruler or round trip light speed measurements, and time measured by an actual clock, with actual intrinsic measures of space and time phenomena: coordinates are arbitrary, whereas the intrinsic measures are set by the dynamics of space.

Quantum Foam Dynamical Space
Our understanding of reality evolves through ongoing iterations of theory and experiments/observations. For the discussions herein we, as always, need an explicit paradigm, otherwise the words "space" and "time" lack meaning. To that end we note that a deeper Quantum Homotopy Field Theory model of space arises from a stochastic non-quantum information-theoretic account [4]: this involves an emergent wave-functional ©::; ; ::; t where the configuration space is that of homotopic mappings between closed compact networks: X S 3 S , see Fig1 -these are the Nambu-Goldstone modes of the informationtheoretic system. ©t evolves in time according to a stochastic functional Schrödinger equation, and generates a quantum foam structure. This wave-functional has an approximate embedability in E 3 , permitting the use of E 3 coordinates r a fx; y; zg. This E 3 is an emergent coarse-grained property of the quantum foam, and not a separate entity. So we are not dealing with a dual system. The model also has an absolute/universal time index t. This cosmic time is observable, but which however is not, in general, given by "clock time". Quantum matter is described by wave-functional components having topological properties -essentially Skyrmionic solitons. A classical description of this quantum foam is given by a velocity field v@r; tA, with the dynamics determined by phenomenological arguments, see Sect.7, where the velocity is defined relative to a network of observers, using an E 3 to label space points. Experiment and observations have revealed that the space dynamics is at least a 3-parameter system: G -Newton's gravitational constant, -the fine structure constant, which determines a space self-interaction effect, and -having the dimensions of length, describing another self-interaction effect, and which appears to be a very small Planck-like length [8]. The fractal structure of the textured space at the macroscopic level has been detected by experiments [11], see

Galilean Relativity
We give here a modern statement of Galilean Relativity from the point of view of the paradigm in Sect.2. The assumptions in GaR are (i) space exists, but is not observable and not dynamical, and is modelled as a Euclidean 3-space (E 3 ), which entails the notion that space is without structure, (ii) observers measure space and time intervals using rods and clocks, whose respective lengths and time intervals are not affected by their motion through space, (iii) velocities are measured relative to observers, where different observers, O and O H , relate their space and time coordinates by t H a t; x H a x V t; y H a y; z H a z: (1) where V is the relative speed of the observers (in their common x-direction, for simplicity). The speed w of an object or waveform (in the x direction) according to each observer, is related by w H a w V (2) Eqns (1) and (2) form the Galilean Relativity Transformation, and the underlying assumptions define Galilean Relativity (GaR). Newton based his dynamics on Galilean Relativity, in particular his theory of gravity, to which General Relativity reduces in the limit of low mass densities and low speeds.

Lorentz and Neo-Lorentz Relativity
When Maxwell formulated his unification of electric and magnetic fields 3 the speed of EM waves came out to be the constant c a I= p 0 0 for any observer, and so independent of the motion of the observers wrt one another or to space. This overtly contradicted GaR, in (2). Hertz in 1890 [16] pointed out the obvious fix-up, namely that Maxwell had mistakenly not used the then-known Euler constituent derivative @=@t C v ¡ r, in place of @=@t, where v is the velocity of some structure to space relative to an observer, in which case Maxwell's equations would only be valid in the local rest frame defined by this structure. In that era a dual model was then considered, namely with a Euclidean space E 3 and an extended all-filling aether substance, so that the velocity v was the velocity of the aether relative to an observer. To be explicit let us consider the case of electromagnetic waves, as described by the vector potential A@r; tA satisfying the wave equation (in absence of charges and currents), but using the Euler constituent derivative, as suggested by Hertz: @ @t C v@r; tA¡r 2 A@r; tA a c 2 r 2 A@r; tA: Here r a f @ @x ; @ @y ; @ @z g. In Lorentz Relativity there is a static aether in addition to an actual Euclidean space, so v is independent of r and t; whereas in neo-Lorentz Relativity v@r; tA describes a dynamical space, with r and t describing a cosmic embedding space and a cosmic time. We find plane-wave solutions only for the case where the space flow velocity, relative to an observer, is locally time and space independent, viz uniform, A@r; tA a A 0 sin@k ¡ r !tA with !@k; vA a cjkj C v ¡ k. The EM wave group velocity is then v g ar k !@k; vA a c k C v and we see that the wave has velocity v g relative to the observer, with the space flowing at velocity v also relative to the observer, and so the EM speed is c in direction k relative to the aether (LR) or space (nLR). In searching for experimental evidence for the existence of this aether, or more generally a Preferred Frame of Reference (PFR), Michelson conceived of his interferometer, see Appendix A. Unknown to Michelson was that his design had an intrinsic fatal flaw: if operated in vacuum mode it was incapable of detecting the PFR effect, while with air present, as operated by Michelson and Morley in 1887, it was extremely insensitive [1,2]. The problem was that Michelson had used Newtonian physics, viz GaR, in calibrating the interferometer, Sect. 6.2. Michelson and Morley detected fringe shifts, but they were smaller than expected, and were interpreted as a null effect: there was no aether or PFR effect. However Lorentz [17,18] and Fitzgerald [19] offered an alternative explanation: physical objects, such as the arms supporting the interferometer optical elements, undergo a contraction in the direction of movement through the aether, or more generally relative to the PFR: the length becoming L a L 0 p I v 2 R =c 2 , where L 0 is the physical length when at rest wrt the PFR, and v R is the speed relative to the PFR. It must be noted that this is not the Lorentz contraction effect predicted by SR, as discussed later, as that involves L a L 0 p I v 2 O =c 2 , where v O is the speed of the arm or any space interval relative to the observer. The difference between these two predictions is stark, and has been observed experimentally, and the SR prediction is proven wrong, see Sects. 6.3 and 6.4.
Next consider two observers, O and O H , in relative motion.
Then the actual intrinsic or physical time and space coordinates of each are, in both LR and nLR, related by the Galilean transformation, and here we consider only a uniform v: these coordinates are not the directly measured distances/time intervalsthey require corrections to give the intrinsic values. We have taken the simplest case where V is the intrinsic relative speed of the two observers in their common x directions. Then from (1) the derivatives are related by @ @t a @ @t H V @ @x H ; @ @x a @ @x H ; @ @y a @ @y H ; @ @z a @ @z H : In the general case space rotations may be made.Then (3) becomes for the 2nd observer, with v H a v V , @ @t H C v H ¡r H 2 A H @r H ; t H A a c 2 r H2 A H @r H ; t H A: (4) with A H @r H ; t H A a A@r; tA. If the flow velocity v@r; tA is not uniform then we obtain refraction effects for the EM waves, capable of producing gravitational lensing. Only for an observer at rest in a time independent and uniform aether (LR) or space (nLR) does v H disappear from (4).

Special Relativity from Galilean Relativity
The above uses physically intrinsic choices for the time and space coordinates, which are experimentally accessible. However we could choose to use a new class of time and space coordinates, indicated by upper-case symbols T; X, Y , Z, that mixes the above time and space coordinates. We begin by showing that Special Relativity (SR), with its putative spacetime as the foundation of reality, is nothing more than Galilean Relativity (GaR) written in terms of these mixed space and time coordinates. The failure to discover this, until 2008 [20] reveals one of the most fundamental blunders in physics. One class of such mixed coordinates for O is 4 T a @vA @I v 2 c 2 At C vx c 2 ; X a @vAx; Y a y; Z a z (5) where v is the uniform speed of space (in the x direction), and where @vA a I= p I v 2 =c 2 . Note that this is not a Lorentz transformation. If an object has speed w, x a wt, wrt to O, then it has speed W , X a W T , using the mixed coordinates, Similarly for O H using v H , w H and W H . In particular (6) gives for Using the above we may now express the Galilean speed transformation (2) in terms of W H ; W and V for the mixed coordinates, giving which is the usual SR transformation for speeds, but here derived exactly from the Galilean transformation. Note that c enters here purely because of the definitions in (5), which is designed to ensure that wrt the mixed space-time coordinates the speed of light is invariant: c. To see this note that from (5) the transformations for the derivatives are found to be @ @t a @vA I v 2 c 2 @ @T ; @ @x a @vA v c 2 @ @T C @ @X ; @ @y a @ @Y ; @ @z a @ @Z : (9) r a f @ @X ; @ @Y ; @ @Z g. Then we have from (3) X H a @V A@X V T A; Y H a Y; Z H a Z; (10) 4 It is important to use different notation for the GaR coordinates and the SR coordinates: often the same notation is used, illustrating the confusion in this subject.
Here is derivation of SR length contraction from Galilean Relativity using coordinates introduced in (5) Confusing a space and time coordinate system with actual space and time phenomena has confounded physics for more than 100 years, with this illustrated above by the recently discovered exact relationship between Galilean Relativity and Einstein Relativity. In mainstream physics it is claimed that Special Relativity reduces to Galilean Relativity only in the limit of speeds small compared to c. But the various so-called "relativistic effects" ascribed to Special Relativity are nothing more than coordinate effects -they are not real. It was Lorentz who first gave a possible dynamical account of relativistic effects, namely that they are caused by absolute motion of objects relative to the aether (LR) or, now, dynamical space (nLR), which according to the evidence discussed above, is absolute motion relative to a dynamical and structured quantum foam substratum: space. In Lorentz Relativity relativistic effects are genuine dynamical effects and must be derived from some dynamical theory. This has yet to be done, and for the length contraction effect would involve the quantum theory of matter.
Finally we note in Fig.2 that the so-called length contraction effect in SR is exactly derivable from GaR -and so it is purely a coordinate effect, and so has no physical meaning. Known dynamics: G; ; . % I=IQU from grav. expts. and absolute time.

Detecting Lorentz Relativistic Effects
We now show how only Lorentz Relativity gives a valid account of the experimental results dealing with light speed anisotropy.
To that end we consider the differing predictions made by the relativity theories for the length contraction effect, and we use data from Michelson interferometer experiments, which being a 2nd order in v=c detector requires length contraction effects to be included, when relevant. These contradictory predictions are compared with detailed data from the NASAspacecraft earth-fly Doppler shifts, which in LR and nLR do not involve any length contraction, as no objects/supporting arms are involved. The flyby Doppler shifts have been also confirmed by laboratory 1st order v=c experiments by DeWitte and Cahill, see [11], and so not requiring 2nd order v=c length contraction effects to be considered. So we have a critical and decisive test of the relativity theories. In all cases we parametrise the calibration theory for the Michelson interferometer travel time difference between the two arms according to ¡t a k 2 L 0 v 2 p c 3 os@PA (12) where k 2 is the theory-dependent calibration constant. Here L 0 is the at-rest arm length, v P is the relevant velocity projected onto the plane of the interferometer, and is the angle between that projected velocity and one of the arms, see Fig.3.

Lorentz and neo-Lorentz Relativity Interferometer Calibration
In both LR and nLR the length contraction effect is a real dynamical effect caused by the absolute motion of an actual object wrt aether (LR) or dynamical space (nLR). In Appendix A we give a simple analysis that yields the calibration constant k 2 a @n 2 IA, when n % I is the refractive index of the gas present: for air n a I:HHHPW at STP, giving k 2 a H:HHHSV.
Some data from the Michelson-Morley and Miller experiments are shown in Fig.4, showing, together with other data, that this value of k 2 gives excellent agreement with the Doppler shift data, and different 1st order in v=c experiments [11]. The gasmode interferometer experiments and spacecraft Doppler shift data give v % SHHkm/s. Note that high-accuracy vacuum-mode Michelson interferometers will give a null result (n a I), as has been repeatedly observed.

Galilean Relativity Interferometer Calibration
In Galilean Relativity there is no length contraction effect, and repeating the analysis in Appendix A, without that effect, we obtain k 2 a n 3 (% I for air). This is the calibration constant used by Michelson-Morley in 1887. Using this to analyse their data they found that v P IHkm/s. This is in stark conflict with the speed of v % SHHkm/s from spacecraft earth-flyby Doppler shift and 1st order in v=c experiments. So Galilean Relativity is ruled out.

A: Einstein Relativity Interferometer Calibration
There are two routes to k 2 from Einstein Relativity, depending on which choice of space and time variables is used. Here we use the Galilean space and time coordinates, as we have shown that they are the physical coordinates that underly SR, in which case k 2 a n 3 , giving v P IHkm/s as in Sect. 6.2, and so again is in stark disagreement with experimental data.

B: Einstein Relativity Interferometer Calibration
In this approach we use the mixed space and time coordinates conventionally used in SR calculations. Then the speed of light is c=n -invariant wrt to these coordinates, but there is no length contraction effect, because the arms are at rest wrt the observer.
Then again we find that k 2 a n 3 % I, and in disagreement with the experimental data.

Dynamical 3-Space and Neo-Lorentzian Relativity
We briefly outline the dynamical modelling of 3-space. It involves the space velocity field v@r; tA, defined relative to an observer's frame of reference, and using intrinsic space and time coordinates, r¡ @v @t C@v¡rA v C V @trDA 2 tr@DA 2 C :: a RG (13) r ¢ v a 0 and D ij a @v i =@x j . The velocity field v describes classically the time evolution of the substratum quantum foam. The bore hole g anomaly data has revealed a I=IQU, the fine structure constant. The matter acceleration is found by determining the trajectory of a quantum matter wavepacket [22].
where v R @r o @tA; tA a v o @tA v@r o @tA; tA; is the velocity of the wave packet, at position r 0 @tA, wrt the local space -a neo-Lorentzian Relativity effect. This ensures that quantum waves propagating along neighbouring paths are in phase, and so interfere constructively. This proper time expression, which entails that the maximum speed wrt space is c, is derived in Appendix B. There it follows from the dynamical length contraction, which is yet to be derived. This maximisation gives the quantum matter geodesic equation for r 0 @tA [4].
C::: (15) with g dv o =dt a d 2 r o =dt 2 . The 1st term in g is the Euler space acceleration a, the 2nd term explains the Lense-Thirring effect, when the vorticity is non-zero, and the last term explains the precession of orbits. The above reveals gravity to be an emergent phenomenon where quantum matter waves are refracted by the time dependent and inhomogeneous 3-space velocity field. The -term in (13) explains the so-called "dark matter" effects: if 3 H and v R =c 3 H we derive Newtonian gravity, for then r ¡ g a RG [4]. Note that the relativistic term in (15) arises from the quantum matter dynamics -not from the space dynamics, which does not involve c. Dynamical 3-space theory has been tested in laboratory light speed anisotropy measurements, G measurement anomalies, bore hole g anomaly, spacecraft earth-flyby Doppler shifts, spiral galaxy flat rotation curves, galactic black holes, galactic black hole -star motion correlations, galactic light lensing, universe expansion dynamics, universe cosmic textures and filaments, and gravitational wave detection experiments. The dynamics of space necessarily involves a Frame of Reference (FoR), by which an observer codifies the location r and time t of an event. There is a natural and fundamental choice for these, although in principle any non-degenerate choice is possible. The natural choice is an absolute FoR defined by (i) spatial separations jr 1 r 2 j correspond to the intrinsic distance between elements of space, and (ii) time intervals t 2 t 1 are absolute cosmic time intervals. Such a FoR is used in (13). Absolute cosmic time is now observable -it is the time steps defined by a clock that is at rest wrt the local space, so that the clock suffers no dynamical slowing effect. This merely requires a light speed anisotropy detector: the measured space speed permits the compensation of a clock moving wrt space. Of course these coordinates are subject to the usual arbitrariness in choices of units, such as meter and second. Globally the embedding space may be an E 3 , as in (13), or an S 3 , requiring a generalisation of (13), etc. At a deeper level the dynamics of space and quantum matter appears to emerge in a self-organising process from the information-theoretic Process Physics [4], with the classical physics dynamics in (13) arising from a derivative expansion, of the underlying Quantum Homotopic Field Theory. This information-theoretic model is a stochastic pattern formation and recognition system, with the stochasticity representing a limitation to self-referencing (SRN -Self Referential Noise), and from which space emerges, leading to the phenomenon of' "locality" and "local dynamics", but is intrinsically non-local and highly interconnected.

Deriving Generalised Dirac and Schrödinger Equations
Because Special Relativity is simply Galilean Relativity using mixed space-time change of coordinates, the well-known SR relativistic effects cannot be actual physical phenomena, as discussed above. This implies that the Dirac equation, which historically was constructed starting with SR, must in fact have a different origin. Here we derive the Dirac equation from neo-Lorentz Relativity, and which gives a generalised form that takes account of the existence of the dynamical space. The Schrödinger and Dirac wave equations model quantum matter as a wave phenomena, with the particulate aspect of matter, i.e. localised matter, accounted for by localised wave packets. The velocity of a wave packet is given by the group velocity v 0 a r k !@kAj K , wrt an inertial observer, where !@kA is the dispersion relation, and K is the dominant wave vector that characterises the wave packet.
@r; tA a Z d 3 kf@kAe i!(k)t+ik¡r ; (16) where f@kA is peaked about k a K.
Hence the task is to construct a free-fall wave function equation that gives the Galilean Relativity energy relation E a !@KA a mv 2 O =PCE 0 for a free wave packet, at low speeds, and which demands v R < c in the limit of high speeds, where v R is the speed relative to space, and so in accord with (14). Here E 0 is the energy of a wave packet at rest wrt to space, which emerges below from neo-Lorentz relativity. We begin with an ansatz for the time evolution of @r; tA: i @ @t a @b 2 Ca 2 @ i rA 2 AA n i v:r C I P r:v (17) where a and b are real numbers to be determined, along with the exponent n. The term v:r arises from introducing the Euler constituent time derivative, which ensures that it is motion wrt the dynamical space that produces dynamical effects. The last term, 1 2 r:v, is uniquely determined as the Euler derivative, by itself, does not lead to a hermitian operator on the RHS, needed to produce a unitary time evolution. For a uniform space flow v wrt an observer, moving uniformly through space, and for a plane wave solution a e i!(k)t+ik¡r , we obtain !@kA a @b 2 C a 2 2 k 2 A n C k ¡ v The velocity v 0 is then v o a r k !@kA a Pna 2 k@b 2 C a 2 2 k 2 A n 1 For large k v R has the limiting value c only if n a I=P and a a c. For small k we then obtain E a !@kA a b C 2 k 2 c 2 which produces the Galilean Relativity kinetic energy term p 2 =Pm (p a k) only if b a mc 2 . We thus obtain the restmass energy E 0 a mc 2 , when the wave packet is at rest wrt space, and not wrt the observer. Eqn. (17)  generalised to now account for the interaction of the wave function with the dynamical space which, as shown above, gives the emergent phenomenon of gravity. The rest mass energy is also present. Eqn. (21) for plane waves and uniform space flow gives E p a ! p R ¡ v a mc 2 where p R a k a mv R . The RHS is independent of the observer's speed through space, and so E p is an intrinsic measure of the energy of the particle. This implies that the nonrelativistic limit kinetic energy of a particle should be K a 1 2 mv 2 R , which is observer independent.
To include spin we follow the Dirac idea and generalise (17) by introducing matrices B and A i i @ @t a @B i Ã ¡ rA 2n i v:r C I P r:v For a uniform v and a plane wave , we have the eigenvalue equation for !@kA: To determine B and A we assume that the RHS matrix is a unit matrix, up to a scalar factor, and require that B 2 a b 2 1; A 2 i a a 2 1; A i A j a A j A i ; i j; BA i a A i B; (27) giving !@kA a @b 2 C a 2 2 k 2 A n C k ¡ v where is now a 4-component spinor. The above choice of the matrices B and A i linearises the operator in (25). We emphasise that this derivation has been independent of the SR formalism, as it must be as SR contains no actual relativistic effects that are not in Galilean Relativity. So the original derivation of this equation by Dirac from SR was fortuitous: it actually follows from neo-Lorentz Relativity. Eqn.(29) automatically gives the phenomenon of gravity within the context of the Dirac spinor.
The derivation of the rest mass energy mc 2 has always been problematic within SR; now we understand why -it is not deriveable from SR. Again in the limit of low k (29) reduces to the Pauli version of the generalised Schrödingier equation, involving the three P ¢ P Pauli matrices for spin 1/2.
Note: because of the fractally textured dynamical space, the v terms cannot be removed by a change of Frame of Reference, even locally, and which would be expected to have dynamical consequences for quantum systems, such as providing a mechanism for space-stimulated transitions, and for extreme space fluctuations, say near a black hole, the generation of new matter, and also in the earlier moments of the Universe.

Conclusions
It is now possible to give a definitive account of the Relativity Principle that has emerged from experiment, viz nLR, together with the dynamical space which underpins that RP. In contrast SR is not based upon experiment, but emerges logically from GaR, but historically emerged from the mistaken belief that the speed of light in vacuum was isotropic for all observers. Then in SR the relativistic effects, such as length contractions, and time dilations, are purely mathematical coordinate-dependent artefacts, whereas in nLR these dynamical effects emerge from dynamics, viz, the motion of actual objects and clocks wrt the dynamical space. As discussed herein experiments have tested these SR and nLR relativistic effects, and only nLR is in agreement with experiment.
Because clock rates, and object lengths, are affected by absolute motion, it is important to clearly specify, at least in principle, how space and time coordinates are defined. To that end, in nLR, in principle, one could measure distances and time intervals using rods and clocks, but then these measurements must be corrected for absolute motion effects, using an absolute velocity detector, with a number of practical designs being available. These corrected coordinates are then used in the neo-Lorentz RP, which are given in (1) and (2). So these definitions of coordinates depend upon the existence of the dynamical space. Of course these are only macroscopic coordinates; at a sufficiently small scales the concepts of space and time break down. So the nLR RP is the same as that for GaR, but requires refinements for the absolute motion effects. We have shown that SR is exactly GaR but using special mixed GaR space and time coordinates, constructed so that the speed of light in vacuum is isotropic, but only wrt these special coordinates. But then there are no true relativistic effects, as no actual dynamical space is a part of SR.
Experiments, astronomical observations and theoretical discoveries have resulted in a new account of reality, with the main development being the recent discovery of space as a dynamical and fractally textured system. This has changed our understanding of the appropriate "Relativity Principle", which gives us the reality-determined mapping between observations by different observers, and how a Frame of Reference is, in principle, to be defined, and the "Dynamics of Space", which now explains gravity as an emergent phenomenon and leading to an understanding of numerous gravitational and space phenomena. The experiments have now revealed that it is a neo-Lorentz Relativity that describes reality, together with the recently discovered dynamical theory of space. When setting up a FoR an observer must take account of the physics of reality, namely that the lengths of rods are affected by their absolute motion, or alternatively the distances defined by round-trip travel times depends on the observers absolute motion through space, given that we have now established that the speed of light is c, in vacuum, only wrt the dynamical space.. As well clocks are affected by their absolute motion. While demonstrating that GaR and SR are the same RP, it is also possible to show that the operation of the GPS is also derivable from the dynamical -3-space theory, contrary to the claim that it is a uniquely GR dependent technology.
Finally it is important to recognise the fundamental importance of the NASA spacecraft earth-flyby Doppler shift data [12,10], for it has confirmed numerous laboratory light speed anisotropy experiments, in a way that is independent of the modelling of those experiments. In particular that without the Fitzgerald-Lorentz contraction the 2nd order in v=c experiments would be inconsistent with the Doppler shifts, and with 1st order in v=c experiments [11]. An important new result is the reemergence of simultaneity as a meaningful actual phenomenon, for cosmic time exist, i.e. is now measurable. The existence of cosmic time, and simultaneity, implies that the universe is significantly more interconnected than previously considered. This will have major consequences for many phenomena including cosmology. Table 1 gives a comparative summary of the issues discussed.

A Appendix: Gas-Mode Michelson Interferometer
We derive the calibration constant k 2 for the Michelson-Morley interferometers in the case of Lorentzian Relativity. For the case of Galilean Relativity the derivation is simply repeated -without any contraction effect. The two arms are constructed to have the same lengths when they are physically parallel to each other. For convenience assume that the value L0 of this length refers to the lengths when at rest wrt space The Fitzgerald-Lorentz effect is that the arm AB parallel to the direction of motion is shortened to where vR is the speed of the arm relative to space.
gas gas E Fig. 3: Schematic diagrams of the gas-mode Michelson Interferometer, with beam splitter/mirror at A and mirrors at B and C mounted on arms from A, with the arms of equal length L0 when at rest. D is the detector screen. In (a) the interferometer is at rest in space. In (b) the instrument and gas is moving through 3-space with speed vR parallel to the AB arm. Interference fringes are observed at D when mirrors B and C are not exactly perpendicular -the Hick's effect. As the interferometer is rotated in the plane shifts of these fringes are seen in the case of absolute motion, but only if the apparatus operates in a gas. By measuring fringe shifts the speed vR may be determined. Following Fig.3 let the time taken for light to travel from A 3 B be tAB and that from B 3 A be tBA, where V is the speed of light relative to the gas, which is moving with the detector. We shall also neglect the Fresnel drag effect, so V a c=n. Then V tAB a L k C vRtAB and V tBA a L k vRtBA: (31) tABA a tAB C tBA a L k V vR C L k V C vR However if the data is analysed not using the Fitzgerald-Lorentz contraction (30), then, as done in the old analyses, the estimated time difference is ¡t a PL0V which again for vR ( V gives ¡t a n 3 L0v 2 R c 3 : With Fresnel drag and n % I, the sign of ¡t in (37) is reversed [4]. Symmetry arguments easily show that when rotated we obtain a os@PA factor in (37). When analysing the data the temperature induced drift in L, and the Hick's effect, need to be taken into account, see [10]. Examples of fringe shift data from Michelson and Morley, and Miller, are shown in Fig.4, with speeds determined using (37). These speeds agree with speeds from 1st order experiments, and from the spacecraft earth-flyby Doppler shift data.

B Appendix: Clock Slowing in neo-Lorentz Relativity
The two arms of the Michelson interferometer act as two independent "photon" clocks, with one "click" defined to be the As shown in Sect.7 when v R is time dependent and/or inhomogeneous (14) results in refraction of quantum matter waves, and also EM waves. This is the explanation for gravity. However this clock slowing effect is not universal, for we can construct a "photon" clock with a gas present. Then from the above the round-trip travel time now depends on the angle between the clock arm and the direction of motion of the clock through space. It is important to understand that it is clocks that are affected by motion through space. Intrinsic or cosmic time may be determined by observing clock time, as defined say by (41), and then correcting for the absolute motion effect by independently measuring v R , using say a 1st order in v R =c detector.

C Appendix: Different Fresnel Drag in SR and LR
The Fresnel drag effect is another case where LR and SR differ, and where experiment agrees only with the LR prediction. The Fresnel drag is a phenomenological observation that gives the speed VD, measured wrt a dielectric (with refractive index n), when the dielectric has speed vR wrt space: VD a c n C vR I I n 2 (42) This is confirmed by the Optical-Fibre -RF Coaxial-Cable experiment [11], by Ring-Laser experiments that detect the sidereal effect, see [10], and by the operation of Optical-Fiber Gyroscopes. However there is a spurious "derivation" of this using SR. Using the SR choice of coordinates in (5) leads to the "composition law of velocities" in (8) (44) is wrong is that the Fresnel drag effect is not present in RF coaxial cables [11], whereas (44) makes no such distinction. So SR fails to give the observed properties of the Fresnel drag effect. This is to be expected, since in SR it is purely a coordinate effect, and not an actual dynamical effect.

D Appendix: Twin Effect
The twin effect is that a clock C2 making a round trip journey, r0@tA, will, when returning to the "stay-at-home clock" clock C1, be retarded wrt C1. However this is not generally true within nLR, as this description of C1 is not well defined within nLR, because both C1 and C2 could be in motion wrt space, and the space may not have a uniform velocity wrt either observer. The elapsed proper time for C2 is and it trivially follows that ¡2 < ¡1 a T , which is the twin effect.
This effect is a consequence of absolute motion wrt space.