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# Superluminal Neutrinos and Empirical Evidence of a Static Cosmos with Beyond Time Interactions

**What if Neutrinos Fly Concurrently both in a Curved Static Cosmos and a Flat Expanding Universe?**

*Spirit of Truth, Enlighten and Guide our Research*

*O Mary Conceived without Sin, Pray for us who have Recourse to Thee*

The reader may have noticed in the news that on September 22, 2011 the OPERA Collaboration announced results showing that the neutrino travels at faster than the speed of light. A cosmological paradigm alternative to the Big Bang could reconcile such results with Einstein’s relativity, characterized by insurmountable speed of light. Such paradigm adds a physical domain to the Big Bang expansion. A hypothesis presented at the 2011 Dark Universe International Conference in Heidelberg is that Neutrinos may well travel faster than the speed of light in one of the two domains and adhere to the insurmontability of the speed of light c in the other. The former case would apply to all electromagnetic radiation and such relationship would change with the increasing distance from the observer.

**THE OPERA COLLABORATION EXPERIMENT**

The OPERA Collaboration brings together the efforts of about 160 researchers from 30 institutions and 11 countries. It partners with the CERN laboratories in Switzerland, which emit the neutrinos beam and with the LNGS/INFN for the detection of the beams at Gran Sasso in Italy. The beam is called the CNGS beam. The experiment (Opera Collaboration, 2011) consists of a high intensity and high energy beam of muon neutrinos produced at the CERN Super Proton Synchrotron in Geneva and directed towards the OPERA Collaboration detector located in Hall C of LNGS, 731 kilometres away (731 278.00 ± 0.20 m). The muon neutrinos arrived about 25 parts over one million sooner than assuming speed of light in vacuum ‘c’ (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×10^{-5}. The article was published after the usual scientific control for possible errors. Systematic errors consist of the systematic repetition of an experimental or theoretical phase or step that distorts the results. Such alteration may be spotted if different measurements differ significantly, or it may remain hidden if all measurements are shifted or transformed in the same way such that they remain reciprocally consistent. If the cause of the error is removed, the error disappears. Statistical errors are caused by unpredictable fluctuations in the readings of a measurement apparatus. These are unavoidable; while at the same time if the accuracy of the apparatus is increased then the accuracy of the measurement may also increase. The authors of the paper have performed error control for all the errors they could think of using all scientific instruments available today. The experiment was repeated 16,111 times, over a period of three years. The margin of error in nanoseconds is ± 6.9 (statistical) ± 7.4 (systematic), while the anticipation of arrival by neutrinos is of 60.7 nanoseconds. Sigma significance is 6-sigma, which indicates (in terms of standard deviations related to a normal statistical distribution) the confidence level allowed by the signal and the experiment. The higher than 5-sigma threshold the value is, the more negligible are the possibilities that the results would stem from chance. Values above 5 are considered scientifically meaningful in physics. Superluminality of particles had been postulated already, such as by Luis Gonzalez-Mestres (1995). The results are being discussed and some articles claim the superluminal interpretation of neutrinos can be refuted, for example one by Cohen and Glashow (2011) and one by the ICARUS Collaboration (2011).

**REMARKS**

Within current physics, with such data and such a scientifically competent team, it is difficult to believe that a systematic error has been missed and remains hidden in the data. The team proposed the results to the scientific community as an additional check and invited other teams to conduct an independent experiment as a normal practice. The team declared: “Despite the large significance of the measurement reported here and the stability of the analysis, the potentially great impact of the result motivates the continuation of our studies in order to investigate possible still unknown systematic effects that could explain the observed anomaly. We deliberately do not attempt any theoretical or phenomenological interpretation of the results. (OPERA Collaboration, 2011)”

Where is the novelty when velocities greater than the speed of light c have already been documented? Examples include phase velocity of X-rays through most glasses that can routinely exceed c; or spots of light from a fast moving laser beam, even if the moving physical entities remain under the constraint of the speed of light c; or quantum effects involving entanglement, even if it is impossible to determine the quantum state of the entangled particles, such that transfer of information is impossible; or the Hartman effect, in which some virtual particles tunnel through a barrier within a time that is independent of the thickness of the barrier, such that some exceed ‘c’. The characteristic of these situations is that transmitting and receiving the same information is impossible (Wikipedia).

In the case of neutrinos, at first these were gauged to be mass-less. They were later found to have mass, even if the mass is considered very light and had yet to be precisely determined. Einstein’s theory of relativity, with the famous E=mc^{2} equation, indicates that mass can reach the speed of light c at most, and only by applying an infinite amount of energy in order to push the mass. However small the mass, as long as there is some, then this applies. Therefore neutrinos would breach Einstein’s famous equation. Furthermore, neutrinos would be considered to bring information with them. In such a case, i.e. in the presence of greater than the speed of light c, causality would be muddled up as the future could cause the past in some frames of reference, with respect to others in which the past causes the future. With the current Big Bang cosmological paradigm, the final confirmation of this finding would put into very serious question Einstein’s relativity that has held up so well until now, unless there are other additional explanations. One of the members of the OPERA Collaboration team, i.e. one of the authors of the article on superluminal neutrinos time anticipation, Max Sioli (2011), in a light-hearted interview to “L’Undici” appreciates the interpretation according to which neutrinos would respect the speed of light and would take space-time shortcuts. Dario Autiero, another author of the team, mentioned in an interview reported by BBC that the implied changes to the laws of physics “can be summed up as a more complex space-time structure than the one used today.”

**AN ALTERNATIVE PARADIGM**

The hypothesis proposed here is that a cosmological paradigm as an alternative to the Big Bang paradigm is better suited to provide a less complicated explanation for the occurrence of neutrinos travelling faster than the speed of light c. Such a paradigm is presented in two articles published in Tidningen Kulturen (Benazzo, 2010, 2011a).

The first, ‘Curved Cosmos Seen as Virtually Flat in the Universe’ finds agreement between data from such alternative topology and the empirical evidence that is the same used for the Big Bang paradigm. The second, ‘An Evidence Based Solution to the Russell Paradox, Grounded in Cosmology’, investigates the metaphysics of such a paradigm from a philosophical point of view. The Big Bang paradigm considers the universe while the alternative one considers both the universe and the cosmos, i.e. two different physical domains. Neutrinos may well respect the insurmontability of the speed of light c through vacuum in one of the two domains, and travel at higher than the speed of light c in the other domain. The additional physical domain, with respect to that normally studied by cosmologists stems from the addition of the observer to the universe. The observer lacks the possibility to observe with her/his eyes or telescopes such cosmos, as the observer would need to pose herself/himself outside the cosmos and this is impossible. Null occurrence is considered outside the cosmos. To infer that the cosmos should have the same characteristic as the Universe that has been studied for the Big Bang is an understandable logical choice, in the forced absence of empirical evidence, which may and has been made. If an additional component is added to a studied entity, i.e. the observer, then the dynamics can be very much different. It is therefore completely possible that a ‘Curved Static Cosmos’ results from the aggregate of the ‘Observer’ with the ‘Observed Flat Expanding Universe’ (Cosmos = Universe + Scientist Observing). The cosmos so defined is, in other words, transcendental to the universe, i.e. even if it is experienced by the observer physically, it escapes direct empirical investigation. Being transcendental, it may well provide for paradoxical situations (Benazzo 2011a), unlike the living experience of the observer in the universe local space-time, who lacks the ability to simultaneously climb and descend a ladder, or to simultaneously exit and enter the same bus.

**GRAPHICAL CALCULATIONS ON THE ALTERNATIVE TOPOLOGY**

The calculations presented in the previous article (Benazzo, 2010) are represented graphically in this section. Expert physics readers may wish to skip or glance quickly through the first two paragraphs of this section.

The yellow thread cones in Figure 1 (marked n) represent a light cone, as normally used to represent light arriving from faraway astronomical bodies. As the paper is two dimensional and allows an easy representation of up to three dimensions, the representation uses only two of the three space dimensions, releasing the third vertical dimension and using it to represent time (marked tob for observer’s time). Events moving vertically on the central violet line are stationary in space, and move from the past (bottom) to the future (top) with respect to the observer’s position. The light cone is derived starting from the full three space dimensions plus the time dimension (Davies, 1982) by picturing a person holding a big yellow semi-transparent and fluorescent inflated ball. The surface of this ball is the light, and it contains a full 360 degrees sphere picture similar to what is used in the internet, for example to show all six sides of a hotel room with the scanning of the mouse. The fluorescent ball is held by a person in a dark night. Now the ball deflates by losing air and it shrinks. While this occurs, the person slowly and steadily, with the flow of seconds in time, lifts the ball from the floor and upwards, and the ball moves upwards and shrinks. A cone will be seen in the photo, with a semi-sphere at the bottom. Next, the ball is taken from three to two dimensions by taking only the horizontal section, i.e. a circle. This circle then moves from the ground upwards in time, while it shrinks. Its fluorescence draws a cone with a flat bottom on the photo. Taken at cosmological dimensions, the sphere that shrinks represents a picture of stars that shrinks to a centre, in this case Earth, where the observer scientist looks out at the sky. The observer would see such ball of light only when this has shrunk all the way until it reaches the observer’s eyes. While the ball (horizontal circle in two dimensions) shrinks, the stars that are encountered on the trajectory impress the ball as if it were a photo negative, such that encountered stars leave their information on the shrinking ball (circle in two dimensions) of light. In Figure 1, the bottom horizontal circle represents the past. This past moves upwards in the future and shrinks towards the observer, placed at the top of the upward cone (p(0)). At the vertex of the cone, there is the present time of the observer that receives the superimposed picture of all the stars met on the trajectory. The vertex is also the vertex of the downward cone of the future, sketched above the observer’s position. This represents the light signal sent from the observer and the Earth, for example the light of volcanoes, cities, airplanes, the colours of nature, continents and seas, outwards in the future.

Considering the light cone from the past, an astronomer receives the information at the speed of light c from the ‘light ball’ shirking. A comet with a flight path that is going to pass near Earth would travel at less than the speed of light c, so it would be traversed by the light ball and leave its impression on it, conveying the picture to the astronomer. If such a comet were somehow required to fly over Earth at the same instant as the arrival of a shrinking ‘light ball’, then it would need to forerun the faster light of such ball. It would have to start much closer to Earth. So a night photo of its trajectory, with time pictured upwards, would be a steeply sloped line internal to the cone and pointing to the vertex. Only physical entities travelling at the speed of light c would travel on the light-cone surface, also called null-cone. Slower physical entities would travel inside the cone, both in the past and in the future. In the standard Big Bang cosmology, neutrinos travelling at faster than the speed of light c would show a trajectory external to the light cone, unless the space-time structure is more intricate than the standard one.

In such normal frame of reference represented by the vertical light cone (Figure 1), space is inferred as the flat space (blue horizontal line in Figure 1, marked sn(50)). Time is inferred as the central axis of the light cone (violet vertical line marked tob). Both are beyond the light cone surface, where the electromagnetic signals bring information from the outer space. They therefore remain invisible to optical or radio instruments studying electromagnetic radiation and used for empirical investigation of the faraway stars. If the faraway space and time are tilted differently and they still impress their image on the shrinking ‘light-sphere’, then it is understandable that the observer may still interpret the faraway space-time as tilted in the same way as locally, as space and time are just deduced from the local vertical light cone (marked n), the latter being the empirical entity received on which data is gathered. The standard Big Bang paradigm considers that the universal structure has light cones that are in general vertical, apart from cases where mass bends space locally, in particular near a black hole. In comparison to this, the alternative paradigm hypothesises that in addition to this universe domain, in the cosmos domain the light cone tilts gradually moving away from the observer. This is represented in Figure 1 by the tilting of the violet lines (tl), for example the one marked tl(50), tilted at 50 degrees from the observer’s time axis (tob). Each violet line is considered as the central time axis of a tilted far away light cone. From such axes, signals fly to the observer through the observer’s vertical light cone surface (n - upwards cone). The space for such curved topology is presented as the green curved line (spo) that has a constant radius (r) from the centre, i.e. the intersection of the violet lines (o). Such space arrives back to its starting point (p(0)). The picturing in the mind of such going back is quite counterintuitive. The observer would need to consider a space probe sent in space straight ahead, and such a probe would arrive back from the opposite direction, always in a straight line. On Earth, a straight airplane flight in three dimensions brings the aircraft back to the starting point. In a four dimensions cosmos, the tilting of time together with space would generate such circularity. This would be due to some of the space in the straight direction being gradually transformed into time, and some of the time into space. As the observer sees objects, like comets receding from Earth as well as approaching it, a reasonable assumption is that the tilting of space and time leaves the space probe unaltered. If the space probe remains locally physically unaltered, the tilting then would need to generate a virtual deformation for the observers receiving the image of a cosmological body faraway. The curvature would create virtual effects, and empirics forced to overlook the adjustment of such deformations would be inevitably subject to what may be called confounding, i.e. the lack of possibility of separating two or more variables transforming such aggregated variables in a complicatedly entangled variable. The entanglement would behave as an extraneous variable. Experiments on such aggregated variables would constitute empirical virtuality of the cosmos.

*Topological representation of a flat universe in a curved cosmos*

Figure 1: Geometry of Topological Representation of a Flat Universe in a Curved Cosmos

The described curvature of the cosmos would, in other words, remain invisible to direct empirical evidence obtained from electromagnetic radiation because the observation would be forced through the surface of the observer’s vertical light cone (see yellow line n in Figure 1), which is flat. This would force the curved faraway coordinates to remain hidden behind a virtual deformation. Virtual because the deformation would gradually disappear when the faraway bodies are approached. Empirical experiments performed on the light cone would need to determine how to account for this deformation. The universe would coincide with the empirical flat vision of a curved cosmos, i.e. with the yellow light cone. In addition, the curved green line of Figure 1 (spo), representing curved cosmos space, would occur at an identical concurrent cosmological time for the observer (violet radius r from the origin o).

Due to such curvature, vectors of far away tilted coordinates, both space and time (tilted violet axes tl of Figure 1), which are parallel to the observer’s space axis (i.e. to sn(50)) would result as completely visible in terms of space from the observer’s view, even those which correspond to faraway time coordinates (tl). Vectors of coordinates parallel to the observer’s time axis (tob) would result as completely visible in terms of time, even those of faraway space (spo) coordinates. In the previous article (2010), the alternative paradigm is appraised as being at least as good as the Big Bang paradigm in explaining many coincidences, those described by Davies (2006), that if changed slightly would bring to different and extremely inhospitable cosmological conformations compared to ours.

The curvature would generate the following four perspectives pictured in Figure 2.

* Due to D, the observer looks at B gazing through A, thus receiving empirically virtual C*

Figure 2 pictures how curved space (perspective D) obliges the observer to look at perspective B, glazing through perspective A as optical lens, which distorts perspective B into a virtual perspective C detected empirically. For a given angle, A, B and C have different dimensions. For a given identical dimension of A, B and C, these are situated at different angles. For the triangle with the space vector of 13.7 billion light-years, A is at 90 degrees, B at 60 degrees, C at 52.403 degrees.

The perspective A is the perspective of a flat universe. This represents the Big Bang representation of expansion without acceleration. The Big Bang acceleration is read differently by the alternative paradigm as a feature of curvature of perspective D. Therefore the Big Bang perspective considered is A, without acceleration. Perspective B is the perspective of the curved cosmos, of how a remote observer would locally experience space and time at a faraway location. Perspective C represents how the curved cosmos is perceived through the flat universe by means of the redshift, representing the empirical reading of the faraway cosmological bodies. Perspective D consists of the curved cosmos representation, i.e. the green arches and their time axes.

The previous article demonstration (2010) of how the topology fits with empirical evidence is reviewed below with more accurate perspectives definitions (as pictured in figure 2), which provide updated calculated data, especially for redshift.

In general, the distance of the stars from Earth is calculated with what is known as redshift (z in table 1). A star emits electromagnetic radiations that have peaks at certain frequencies. This generates specific signatures, depending on the general conformation of the star. The signature moves to longer frequencies, i.e. towards the red part of the visible spectrum, for stars receding from Earth. Empirical observations have shown that the farther the star from Earth, the stronger is the redshift. The Big Bang paradigm reads this as increasing recession velocity from Earth, i.e. as a feature of a spatial expansion of the universe. In comparison, the proposed alternative paradigm denotes the increasing redshift as due to a curvature in space time, such that increasingly far away stationary stars release light with an increasing angle to the observer’s light cone surface. Such virtual deformation would move the signature of the light of the stars to longer frequencies, i.e. with an increasing redshift. Figure 3 shows how the redshift is calculated.

*redshift (rWo(50)/n(50)-1), shaped via sigma, rho and Svil(50), shows virtual Swo(50), hiding spo(50)*

Figure 3 pictures how the redshift (rWo(50)/n(50)-1) is shaped and determined via the angles (sigma and rho) and via the faraway intercepted local virtual space (Svil(50)), determining in such a way the observed empirical virtual distance (Swo(50)), while leaving the effective curved space (spo(50)) hidden.

CALCULATIONS (figure 3)

[1] Definition

From perspective B, Svl(60) = Hubble distance = 13.70 billion light-years = faraway local virtual space at 60 degrees from observer’s present in p(0)

[2] Formula

r = Svl(60)/sin(radians(sigma))*sin(radians(180-90-sigma))

with sigma = 60 in this case

r = 7.909698688 billion light-years

[3] Variables

r = radius of curved space spo in perspective D

sigma = angle between faraway tilted time axis relative to p(sigma) and local observer’s vertical time axis relative to p(0)

rho = angle of perspective B, equals 180-90-sigma, between vertical time axis of p(0) and Svl(sigma) or Svil(sigma)

Svil = faraway local intercepted virtual space, i.e. intercepted by the observer’s light cone

[4] Equivalence relative to measures, determining the unit conversion factor

From perspective B, r = time from the Big Bang of perspective A = 13.7 billion years

13.7 billion years = r = 7.909698688 billion light-years

1 billion year = 0,577350269 billion light-years

[5] Formula: radius of the internal circumference sw, when/where wavelength was intercepted

rw(sigma) = r/sin(radians(180-60-sigma))*sin(radians(60))

[6] Formula: time intercept by observer’s light cone at start time signal

tiw(sigma) = rw/sin(radians(180-60-sigma))*sin(radians(60))

[7] Formula: virtual time felt by the observer due to redshifted wavelength

Two = distance between Tswo(sigma) and Tawo(sigma)

#### Stöd Tidningen Kulturen

Two(sigma) = (rw(sigma)/sin(radians(180-90-sigma))*sin(radians(90)))-(tiw(sigma)/sin(radians(90))*sin(radians(180-90-sigma)))

[8] Variables

Tswo = empirical virtual start time of redshifted wavelength

Tawo = empirical virtual arrival time of redshifted wavelength

Two = empirical virtual time from signal emission, experimented through redshift

[9] Formula: relative wavelength observed, due to curvature generating redshift

rWo(sigma) = Two(sigma)/sin(radians(30))*sin(radians(90))

[10] Formula: relative observer’s position local wavelength

n(sigma) = r/sin(radians(180-60-sigma))*sin(radians(sigma))

[11] Formula : redshift

z(sigma) = rWo(sigma)/n(sigma)-1

RATIONALE (figure 3)

The lower yellow cone represents the observer’s light cone at signal start time; the upper one represents it at signal arrival time. The same applies to the curved effective cosmos line: curve sw applies at start time, curve spo applies at arrival time. The larger ones of figure 3 represent the observer’s present, both in the curved cosmos and flat universe. The interception of the faraway star occurs at time Tswo(50) relative to tiw(50) on the starting light cone. The receipt of the signal occurs at Tawo(50) relative to the arrival light cone, when it has enlarged upwards moving the starting interception to tib(50)=rw(50).

The blue Svil(50) tangent to the green curved space sw(50) represents the angle of the local space at the faraway position rw(50). The slope of Svil(50) intersects the vertical observer’s time axis (at Tawo(50)). This intersection is read as bearing with its slope the measurement of the tilting of the space-time vectors of electromagnetic radiation, i.e. light of the faraway star. Such an intersecting point would define the perceived deformation of the wavelength emitted by the faraway electromagnetic radiation. The point would also represent the upper boundary of the time Two(50)) passed before the signal is received by the observer. Time is measured using units of space (see equivalence [4]), to allow for tilting the geometry (Benazzo, 2010). The angles of the unit conversion factors are calculated from an application of Einstein’s interchangeability between time and space to the light cone, which considers time as moving at the speed of light c. This requires an equilateral triangle for full substitution and reversibility (Benazzo, 2003). This provides a curved cosmos with a specific curvature that determines the degrees of the slope of the light vector: 30 degrees between the time and light vectors; 60 degrees between the light and space vector, and of course 90 degrees between the time and space vectors. This allows for performing measurements with the curvature and links among perspectives (see Carlo Rovelli (2008) on the removal of time).

The yellow slope at top left of Figure 3 (rWo(50)) represents the relative wavelength of the faraway star radiation. Its slope is inclined at the same degree of the left line of the observer’s light cone (n(50)). Graphically, this represents the impossibility for the observer to receive light at different angles than those defined by the speed of light c. The comparison of the two yellow sloped lines gives the ratio between the two wavelengths, a relative measurement. The classic measurement of the redshift is z = ((longer wavelength rWo) / (shorter normal local wavelength n) – 1). As the distance from the faraway stars is calculated with the redshift, the virtual flat space relative to the redshift is the whole blue horizontal segment Swo(50) (Swo stands for space-wavelength-observed). This is the measurement that would be taken empirically by the observer [perspective C].

There is an additional virtual space, that is the space tangent to the faraway curved space, measured by the tangent to the curved space (Svl(50), standing for space-virtual-local) in Figure 3, referred to virtual local space [perspective B]. This has a different slope than horizontal so it is bound to remain hidden to the observer. It is perceived through a transformation that makes it horizontal and is represented by the above defined horizontal virtual space Swo(50) [persp.C]. This perspective B, with Svl(50) represents an actually occurring local dynamic, as it represents the tilted local time, with relative tilted space (Svl) on the curved space (spo) and tilted light cone. It represents as such physical laws perceived locally by each observer at that each location (e.g. p(50)). As the observer scientist is part of cosmos and would be forced to stay only in one of the two locations, the empirical observation of the faraway location would show something different [persp.C]. This other perspective is represented by the perceived space Swo(50). The construction (called frame D) allows linking geometrically the other three frames of reference pictured in figure 2. Frame A could be called the one felt locally, i.e. the observer’s light cone. The frame of perspective B could be called the one representing the faraway local tilted physics, invisible to the observer, i.e. Svl(50). The frame of perspective C could be called the one by which the observer perceives the faraway cosmological body, i.e. Swo(50); an empirical perspective showing a virtual perspective B, i.e. a deformed perspective B.

In addition to the redshift, an additional measurement of the distance of stars from Earth has been calculated with a specific kind of stars, the supernovae, in specific those of type Ia. These constitute bursting stars releasing specific quantities of light. The intensity of this bursting has very specific characteristics that allow measuring their distance from Earth. Astronomers have been puzzled by the discovery of a specific kind of discrepancy when comparing the two measurements for supernovae. Saul Permutter, Brian P. Shmidt and Adam G. Riess have first discovered such discrepancy in 1998. The distance calculated by measuring brightness is larger than that calculated by measuring redshift. This discrepancy increases until a certain point and then decreases until reaches zero, after which it inverts (i.e. becomes less than zero). The Big Bang paradigm implies interpreting this as an acceleration of the expansion (Kowalski, M. et al., 2008, Lineweaver, Charles H. and Tamara M. Davis, 2005). The proposed alternative paradigm reads this differently (see Figure 4).

As the geometry is fractal due to the time axes diverging from a centre, the two green similar arches of figure 4, i.e. representing effective curved space, appear to have a different length on the figure, while discounting fractal geometry makes them exactly equal, but look different because of the time axes diverging. In perspective D, the length where/when the yellow position is intercepted by the light cone can then be measured in two ways depending on whether the fractality is discounted or not. The measurement of brightness would discount the fractality such that the arch sw(50) at the time where/when it is intercepted by the light cone (at n(50)) is the same length as the arch spo(50) at the present time (at p(50)), i.e. on the circle intercepting the observer’s position in time (at p(0)). To simplify matters, therefore, the measurement considered is the curved space spo(50) on the circumference intersecting the observer’s position (between p(50) and p(0)). The redshift measurement would use a flat geometry without the possibility of discounting the fractality and therefore its measurement is reflected by the arch sw(50) intersecting the yellow position (between n(50) and the observer’s vertical time axis). The discrepancy concerning the supernovae is then measured in perspective D as the relative difference between these two measures.

Figure 4 pictures supernovae relative difference between actual curved space detected at n(50) as equivalent to spo(50) relative to receipt time (r), i.e. (p(50) to p(0)), and sw(50) detected as shorter at start time (n(50) to p(0)). Values greater than zero.

*Supernovae discrepancy: relative fractal arches difference (spo(50) – sw(50)) > 0*

CALCULATIONS (figure 4 and 5)

[12] Formula: space arch measurement relative to brightness

spo(sigma) = r*radians(sigma)

[13] Formula: space arch measurement relative to redshift

sw(sigma) = rw(sigma)*radians(sigma)

[14] Formula for supernovae discrepancy between brightness and redshift measurements

Delta Distance in perspective D

DeltaD(sigma) = (spo(sigma)-sw(sigma))/spo(sigma)

Such a measurement from perspective D was obtained differently in the previous article (2010) giving exactly the same values. The discrepancies were projected on perspective B.

Both perspective B and D remain invisible to be observer, at least from afar. These measures have therefore a different value than those that would be calculated empirically by the scientists, i.e. in perspective C. The dynamic in perspective D and characteristics of a relation with perspective C are discussed in the next section.

After sixty degrees, as shown in Figure 5 of perspective D, the measurement inverts. For example, at 70 degrees tilting (figure 5), the observer’s light cone intersects the faraway star in the cosmological (curved) future (n(70)) with a greater cosmological time lapsed (rw(70)), compared to the observer’s cosmological time lapsed (r) on the curved cosmos: the external curved space circumference (sw(70)) is farther away from the time axes origin (o), compared to the actual blue position (p(70)) hidden behind the curvature.

*Supernovae discrepancy: relative fractal arches difference (spo(70) – sw(70)) < 0*

Figure 5 pictures supernovae relative difference between actual curved space detected at n(70) as equivalent to spo(70) to receipt time (r), i.e. (p(70) to p(0)), and sw(70) detected as longer at start time (n(70) to p(0)). Negative values below zero.

The yellow colour star in figure 4 (n(50)) and figure 5 (n(70)) represents the star image ‘photographed’ in the observer’s light cone, which arrives empirically through the observer’s light cone. At greater than sixty degrees from the observer, the blue star (p(70)) occurs in the universe past and is intercepted in the cosmological future by the light cone. The time lapsed in the universe domain in perspective A, between the emission of the signal from the star (n(70)) and the reception by the observer (p(0)), is the vertical time axis length reaching the observer (p(0)) and starting from the intersection of light cone base at ts(70) (at the height of n(70)), with the observer’s time axis; see Figure 5. This marks the yellow colour star position (n(70)) in a flat universe. Together and in harmony keeping with this, in the curved cosmos domain, the time lapsed (r-rw(70)) is the radial distance between the two curved space circles (spo and sw(70)), flowing towards the centre of the image, from the one relative to the yellow image (n(70)) impressed in the observer’s light cone to the one occurring concurrently with the observer’s cosmological present (p(70)). It can be measured on the observer’s time axis, i.e. curved space radius, as well as on the star tilted time axis. This cosmological time is directed backwards, i.e. it is negative. At above 60 degrees, the star is ‘photographed’ in the observer’s light cone from the cosmological future with respect to the observer’s signal receipt time. While time flows positively in the cosmos from the centre expanding outwards and time flows positively in the universe vertically from the bottom upwards of the figure, at degrees greater than 60 they interact inversely, such that the universe sees inversed cosmological time at greater than 60 degrees. Causality would therefore be inverted between the two domains at large angles from the observer. The inversion of causality is allowed by the different nature of the two domains, the flat universe resulting as an empirical measurement of the virtual image of the curved cosmos. Further investigation in this aspect is outside the scope of the analysis in these pages.

How do the data (see table 1) obtained with the calculations above compare with empirical evidence?

**AGREEMENT OF THE ALTERNATIVE TOPOLOGY WITH EMPIRICAL EVIDENCE**

In particular, the redshift z(sigma) was related to the space Svl(sigma). The perspectives clarification highlights that the first is from perspective C and the second from perspective B. The scientist derives the space from the redshift without measuring space directly. Nevertheless, perspective C, rather than perspective B results as the empirically measured perspective. The virtual deduted space empirically derived from the redshift would therefore be Swo(sigma) rather than Svl(sigma).

Swo is calculated as follows:

[15] Formula: empirical virtual space from intercepted signal

Swo(sigma) = rWo(sigma)/sin(radians(90))*sin(radians(60))

alternatively

Swo(sigma) = Two(sigma)/sin(radians(30))*sin(radians(60))

Empirical evidence interpreted in the Big Bang paradigm includes the following features:

FEATURE 1) The distance where stars recede at the speed of light c is the Hubble length, which corresponds in numerical value (overlooking measures units) to the Hubble time, which is an estimate of the age of the Universe. This is considered here at 13.7 billion light years. The cosmological constant lambda, the one proposed by Einstein, is currently calculated in the Big Bang paradigm as about 0.72 and is represented as dark energy, with repulsive force (WMAP, 2011). Dark matter is calculated at 23.3% of the universe. With these parameters, the Hubble length is at redshift z=about 1.39(Siobahn Morgan, 2011). Previously, it was calculated at z=about1.5 (Lineweaver, Charles H. and Tamara M. Davis, 2005).

FEATURE 2) The discrepancy between the measurement by brightness and by redshift becomes zero at redshift of z=about 1.33. See the binning performed by Wright (2011) on the combined data file provided by Conley et al. (2011) on the Supernova Legacy Survey, which provides a discrepancy near zero, i.e. 0.0961 at a redshift of z=1.32375.

FEATURE 3) The discrepancy concerning supernovae, between measurements by brightness and measurements by redshift, has a coasting point, between its increase and decrease that is at 1/3 of the distance from the observer in relation to the total distance from the Big Bang, i.e. 13.7 billion light-years. 1/3 is then at about 4.57 billion light-years from the observer, i.e. 9.133 billion light-years from Big Bang (Riess, A. G. and M. S. Turner, 2004).

FEATURE 4) This coasting point occurs at redshift between z=0.35 and z=0.58 (Wright (2011) on the combined data file provided by Conley et al. (2011) on the Supernova Legacy Survey), also depending on the model chosen (see Wright 2011).

Alternatively, such main data features are derived from the topology of the alternative paradigm. The 4 pieces of empirical evidence above are related to the three flat perspectives mentioned above (figure 2) in the following way.

The classical vertical perspective A gives signpost measurements. It gives the starting point of time at the Big Bang, at n(90) (figure 2). It gives the measurement of time lapsed from the Big Bang (r), 13.7 billion years on the vertical axis, and the expansion from the big bang, 13.7 billion light-years on the horizontal axis. Equivalence [4] above determines time in terms of space, allowing linking the four perspectives of figure 2 in a curved geometry.

The three perspectives are superposed, i.e. compared for the equivalent measurements. Specifically, two triangles are considered. There is the full-length triangle with a base of 13.7 billion light-years, and vertical side of 13.7 billion years (i.e. 7.91 billion light-yeas in terms of space). There is also the similar triangle representing two thirds of the distance from the Big Bang, i.e. one third from the observer. These two triangles are compared for the three perspectives.

Perspective A is considered the representation of the flat expanding universe without acceleration. It is suitable in the alternative paradigm, which transfers the supernova discrepancies representing acceleration to perspective D, in a curvature of space-time. This perspective is incompatible with current empirical evidence in the Big Bang paradigm, as it lacks acceleration.

As described in the previous article (2010), perspective B considers the local physical space-time dynamics, which turn out of sight when looked from afar. In other words, it represents the cosmos as it would be looked at from the outside. This representation is possible only logically in the mind, i.e. in theoretical physics, as the observer is part of the whole cosmos and direct empirical evidence would be impossible. So perspective B, at least from afar, remains transcendental. In this perspective, the measurements for the features mentioned above are the following:

B_FEATURE 1) Appearance of recession at the speed of light c occurs at a redshift of z=2 (60 degrees angle from the observer) with discrepancy from empirics (z=around 1.39).

B_FEATURE 2) The supernova discrepancy is zero at redshift of z=2 (60 degrees angle from the observer) with discrepancy from empirics (z=about 1.33).

B_FEATURE 3) The supernovae discrepancies coasting point agrees tightly as it occurs at 1/3 of the distance from the observer in relation to the total distance of 13.7 billion light-years.

B_FEATURE 4) This coasting point occurs at z=about 0.4 (30 degrees angle from the observer), in agreement with the empirical measurement (from around z=0.35 to around z=0.58).

Evidence (3) and (4) agree with empirical evidence, even if this perspective remains hidden. Interestingly, the redshift is exactly 2 for both feature (1) and feature (2). It indicates that where the supernova discrepancy is zero, it is also where the stars in the Big Bang paradigm would be perceived as receding at the speed of light c, i.e. at 13.7 billion light-years from the observer. In addition, the turning points occur at exact degrees, the supernova discrepancy coasting point at exactly 30 degrees from the observer and the zero supernova discrepancy at exactly 60 degrees.

Rather than this perspective B, empirical evidence would see and experiment perspective C which is rotated and sloped as the observer’s local space-time. Perspective B is necessary to consider logically the conformation of the cosmos. It links the represented observer’s local space-time flat perspective A with perspective C.

The virtual light vector with prolonged wavelength (rWo) that is used to calculate the wavelength (see calculations above) is also considered as the light vector of perceived far away space by the observer. Such space is horizontal, as the observer perceives it horizontally, and is calculated with formula 15 above.

The measurements of the occurrences in perspective C are as follows:

C_FEATURE 1) Appearance of recession at the speed of light c occurs at a redshift of z=1.334 (52.403 degrees angle from the observer), in quite close agreement with empirical evidence (see above; z=about 1.39).

C_FEATURE 2) Zero supernovae discrepancy has resulted as a feature that needs to occur where the distance from the observer is the Hubble length, taken here at 13.7 billion light-years. It then occurs at a redshift of z=1.334 (52.403 degrees angle from the observer) in close agreement with empirical evidence (see the binning performed by Wright (2011) on the combined data file provided by Conley et al. (2011): a discrepancy near zero, i.e. 0.0961 at a redshift of z=1.32375).

C_FEATURE 3) Comparing the empirical virtual space Swo(sigma) of perspective C with the far local virtual space Svl(sigma) of perspective B, Swo(sigma) is smaller than Svl(sigma) until sigma is about 22 degrees. A bit further on, it is 4.4 percent longer than Svl(sigma) where Swo(sigma) in perspective C is from the observer at 1/3 of 13.7 billion light-years. This occurs where sigma is 28.948 degrees. It is then 3.6 percent longer than Svl(sigma) in perspective B where this latter is at 1/3 of 13.7 billion light-years, where sigma is 30 degrees. The differences are small therefore a reasonable estimate of the supernova discrepancy coasting point in perspective C is as in perspective B, at a distance from the observer of about 1/3 of the 13.7 billion light-years.

C_FEATURE 4) Such coasting point occurs at redshift z=0.377, quite in agreement with empirical evidence (from around z=0.35 to around z=0.58).

The values of perspective C are calculated indirectly through perspective B, via geometrical representation of the physical variables. Only one empirically determined value, a 13.7 billion light-years Hubble distance, is inputted in the topology calculations. This is positioned at 60 degrees angle from the observer in perspective B (see definition [1]). The metaphysics (Benazzo, 2011a) represented geometrically is quite challenging as it involves counterintuitive aspects. On the other hand, this has been performed without any particular data fitting as the variables involved for each perspective are kept at a minimum and the three perspectives in the curved topology are interconnected by neat relations.

While the characteristics of the discrepancies for supernovae give intersections and turning points in agreement with empirical evidence starting from perspective B, their empirical measurement in science is performed on perspective C. It differs in the quantities and should be reconciled considering that measurements are taken in a different way on a curved static cosmos (perspective D) in comparison to a flat expanding universe (perspective C) and on different perspectives. Here, the brightness versus redshift discrepancy is measured in terms of light-years calculating them on a transcendental curved cosmos domain. The empirical data are instead measured in terms of brightness magnitude and redshift, considering a flat space paradigm.

Gurzadyan and Penrose (2011), analysing Wilkinson Microwave Background Probe’s (WMAP) cosmic microwave background maps discovered important empirical evidence, with up to 6-sigma significance, of concentric circles in the cosmic microwave background. Such structure of glares means an uneven universe just after the Big Bang, while the standard current theory provides for an initial fast expansion, called inflation, which would smooth evenly the Universe. Gurzadyan and Penrose drop the inflation and interpret the findings as evidence of what they define conformal cyclic cosmology, i.e. of the expansion of a previous universe in time ending up in the start of a new expansion. This is understood as an elegant and sound interpretation of such data in a flat expanding universe paradigm. It implies a sempiternal universe both looking backwards in time and forwards in the future, indefinitely.

The alterative paradigm could compare such concentric circles to the horizon glare at sunset on Earth. On Earth there are three dimensions and the glare from beyond the horizon is a line. With time adding one dimension and the topology described above, the glare could be circular and with concentric circles. This remains outside the scope of the present pages, which are more paradigmatic, i.e. philosophical and metaphysical.

Given that superluminal velocities would occur in the curved cosmos domain of the alternative paradigm discussed in these pages, an analysis is performed on where the geometry of its topology would measure neutrinos flying faster than the speed of light c.

**SUPERLUMINAL VELOCITIES AND MEASUREMENTS OF NEUTRINO VELOCITIES AT DIFFERENT ANGLES**

There are a number of variables in the topology. The three flat perspectives pictured in figure 2 (A, B and C) all provide flat space-time calculations with a constant relation represented in angles among space, time and light vectors. The speed of light c, considering the measure of time in years and the measure of space in light-years, would give a unit of measure of light, i.e. velocity measured in terms of speed of light c. The ratio provided by such angles is 1 thus equating to the speed of light c, which is when time is normally considered in years (rather than in terms of units of space as it is done in the topology to make calculations concerning the relation among the different perspectives at different angles). These perspectives indicating velocity at the speed of light c (i.e. 1) cannot as such represent the superluminal velocity measured for neutrinos, that would give a ration of some 25 parts over one million greater than one (OPERA Collaboration, 2011).

Moving on now to perspective D of a curved cosmos, the dynamics of the curved cosmos are compared with the other flat perspectives where the velocity is at the speed of light c. Starting from below 60 degrees tilting, the time of the signal is visibly shorter in the curved cosmos space, where it equals to the radial distance between the two arches (r-rw(50) in figure 4), compared to the observer’s flat universe, where it equals the vertical vector of the displacement (r-ts(50) in figure 4). The difference between the two depends on the tilting. In addition, curved space is comparably longer than flat space in a given framed perspective. The light signal then travels faster in the curved cosmos frame of reference D (longer space and shorter time), depending on the curved space distance (spo). At 60 degrees (see figure 2), the two arches, the one relative to the starting time (sw(60)) and that relative to the arrival time (spo - pictured star on the same circumference of the observer’s one), have an equal time radius (r) from the time origin (o), i.e. the centre. This overlapping signifies that the time needed by the signal to travel the long space to reach the observer is zero (r-r) in the curved cosmos domain, while time is extremely long in the flat universe domain (r-ts(60)). Velocity in the cosmos domain would be absolute at 60 degrees, in the sense that transmission would happen faster than instantaneously, i.e. beyond time. At angles greater than 60 degrees, velocity would be faster than absolute such that time is reversed, as discussed above.

Such curved perspective, allows various velocities above the speed of light c, providing a frame where measurements of neutrinos flying faster than the speed of light c are possible.

In more detail, while on the longer distances separated by empty space perspective C only could be measured directly, on the short distance, where two points are connected by mass, a hypothesis is made that it could be possible to measure time and space on the actual curved cosmos space-time (perspective D), while the speed of light c (or just below and near the speed of light c) would be flown in the flat observer’s light cone (perspective A), the one that applies locally. For perspective D, calculations need to check at how many degrees the ratio between the curved space (spo) and the radial measurement of time (Delta t = r-tw, figure 4), gives a value of some 25 parts over one million greater than one (considering time in billion years (aeon in the table 2)). Given the distance of 730 kilometres, the result of such curvature would indicate a radius and circumference of curved space that could be a combination of the general curvature of the cosmos plus the local curvature given by masses of the Earth and solar system. Considering the distance and anticipation values of the experiment, assuming that the neutrinos travel at or near the speed of light in vacuum on the flat universe, a measured anticipation of 25 parts over 1 million would occur at 9.924x10^{-4} degrees from the observer. Doubling the curved space considered to 1460 kilometres by doubling the degrees, the value would be 50 parts over one million (relative measure). The anticipation of arrival (absolute measure) with double the distance would quadruple.

Another possibility is that two of the flat space-time perspectives are mixed such that, because of curvature, time is measured in a smaller similar space-time triangle while space is measured on another larger similar space-time triangle, for each angle sigma from the observer. In this case, longer virtual space is flown with reference to a shorter time, generating results of superluminal velocity. In the paradigm shown, perspective C is derived from the redshift. Such a case seems to be a bit unlikely because it would mean that the measurement of space and time would have been performed with instruments that measure different perspectives. If this were possible, time would be considered on perspective A and space on perspective C, for each angle. A velocity resulting 25 parts over one million faster than the speed of light c would occur at 49.607x10^{-4} degrees. By doubling the distance to 1460 kilometres, the superluminality would be 50 parts over one million faster than the speed of light. The anticipation of arrival with double the distance would quadruple.

As the alternative presented paradigm provides a different frame in which physics occurs, other possibilities are also open to examination.

If such superluminal velocities calculations were transposed from the experiment to the curvature of the cosmos calculated above, then the first scenario calculated on perspective D would give absolute velocity at 60 degrees from the observer, where the redshift is measured z=2. The second one, compared to the redshift, has an equivalent formula that relates in an equivalent way perspective C with perspective A. It gives the same rates as the redshift. The redshift would then reflect the measurements of virtual superluminality. At the Hubble distance, the excess velocity over the speed of light c, measured as 1, would be an additional 1.334 times; it would be 2 additional times the speed of light c at 60 degrees from the observer and absolute velocity at 90 degrees. Such superluminality would be virtual, as in the actual perspective D absolute velocity would occur at redshift z=2.

There is a difference in behaviour of neutrinos between the OPERA experiment and the neutrinos detected for the Supernova SN 1987A. In the first case, results give superluminal velocities, while neutrinos emitted from the supernova travelled without significant superluminal speed (Evslin, 2011). The small discrepancy of maximum 3x10^{-9} superluminality is expected to be due to unavailability of sufficiently accurate data or to other effects. Neutrinos detectors could have possibly detected neutrinos at an earlier stage rather those for light. Applying the alternative paradigm, light is expected to behave like neutrinos for an experiment with a light-beam flowing though a straight tunnel on Earth for some 730 kilometres. The experiment is expected to give the equivalent superluminal results with the OPERA Collaboration experiment; an early arrival with respect to local speed of light in vacuum. With Supernova SN 1987A, there being only space for measurements, perspective C should appear empirically, which implies flight at the speed of light c in current physics. In other words, superluminality would remain hidden at the large scale and would apply in general to the structure of the cosmos rather than only to neutrinos.

**FURTHER RESEARCH**

If the OPERA experiment showing superluminal neutrinos flying faster than the speed of light c is confirmed, this would confirm evidence for interactions with particles flying at faster than the speed of light c. In the alternative paradigm this is read to apply to the cosmos, rather than the universe where Einstein’s relativity should hold. If the empirical measurement of superluminality is taken from perspective D (first hypothesised scenario), this would imply that somehow empirical evidence can be gathered on the cosmos, i.e. on the sum of the universe plus the observer. This poses metaphysical challenges as the cosmos, considered metaphysically as the sum of the observer plus the observed universe would be assumed to be transcendental, i.e. beyond direct empirical evidence. If the empirical measurement derives from comparing perspective C with A, this would fit with the analysis of these pages and with the metaphysics implied (Benazzo, 2011a). This latter case seems therefore more likely. Further investigation could clarify the issue.

In the alternative paradigm, anticipation stems from the combination of the spatial and time differences. Such relation changes with the increasing distance of flight from the observer. Further experiments with longer distances and more accuracy are expected to show changing measured velocity. Experiments targeted at highlighting which perspective or combination of analysed perspectives would actually apply are more difficult as the divergences in measures among different perspectives would need higher experimental accuracy, at given distances.

The alternative paradigm provides for the universe inverting the forward time of the cosmos, at certain degrees from the observer, i.e. greater than 60, and further investigation of the dynamics involved between different perspectives could shed more light into the subject. The paradigm calculations presented in these pages have been performed from 0 to 90 degrees from the observer. Further research could examine dynamics at larger angles. Another case such as SN 1987A, though with more accurate measurements on neutrinos, could help clarify the comparison of photons with neutrinos.

The evidence found by Gurzadyan and Penrose (2011) could also be interpreted and situated with the alternative paradigm presented in these pages.

Further research could shed more light on the matter whether superluminal particles in general and neutrinos in particular could actually carry unaltered information. In the herewith alternative paradigm this would be possible, however it would need to consider how to take into account the redshift and implied virtual distortion.

**CONCLUDING REMARKS**

An alternative cosmological paradigm is related to empirical data, the same supporting the Big Bang paradigm. The values calculated with the alternative paradigm, found with perspective selection rather than with data fitting, match with the empirical data, providing an empirical foundation to the alternative paradigm. Such an alternative paradigm provides for a specific interpretation of the neutrinos travelling and higher than the speed of light c. The neutrinos would fly concurrently in a flat universe and a curved cosmos. The OPERA Collaboration experiment would measure space-time coordinates related to a curved static cosmos domain, and with them measure a flight of neutrinos in a flat expanding universe domain. The neutrinos would still respect the insurmontability of the speed of light in vacuum on their flat-universe trajectory, while they would combine harmonically this flight with a displacement in a curved cosmos domain, in which the space-time curvature would provide for variable superluminal velocity increasing with angles, up to absolute velocity beyond time, at 60 degrees angle from the observer, occurring at a redshift measuring 2. In addition to that, at even longer distances, the forward time flow in the universe would reflect an inversion of the forward time flow of the cosmos, providing for negative values in the discrepancy for supernovae between the measurement by brightness and that by redshift. There being three flat perspectives and one curved, with different possible combinations of effects due to curvature, there are some possible combinations that could give superluminal velocity of neutrinos. Some hypothesis and measurements are made.

The alternative paradigm excludes the possibility that the superluminal velocity would be constant. Further research at sufficiently high precision and sufficiently different distances to gauge dynamics is expected to give empirical evidence of the analysed curvature in space-time.

###### Piero Benazzo

**ACKNOWLEDGMENT**

I am grateful to Sim Smiley for her native English proofreading skills, which brought to light some linguistic issues. I am also grateful to Marelise van der Westhuizen, Shree Vasam and Sandro Cimino for some paragraphs proofreading and some comments, to my wife and family, to editor in chief Guido Zeccola for unbiased mindset and to all occasions of inspiration that were gifted for this research. Any remaining issues are the author’s alone.

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**ANNEX – TABLES 1 AND 2 – VALUES CALCULATED APPLYING THE PARADIGM**

*Large scale: data calculated applying the paradigm*

*Variables caption and two hypothesised neutrino superluminality measurements*