Superluminal Neutrinos and Some 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 c. 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).
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=mc2 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 deducted 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.
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.
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. This was considered before introducing acceleration as a reading of the mentioned discrepancy for supernovae. 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.
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)
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)
r = Svl(60)/sin(radians(sigma))*sin(radians(180-90-sigma))
r = 7.909698688 billion light-years
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
 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
 Formula: radius of the internal circumference sw, when/where wavelength was intercepted
rw(sigma) = r/sin(radians(180-60-sigma))*sin(radians(60))
 Formula: time intercept by observer’s light cone at start time signal
tiw(sigma) = rw/sin(radians(180-60-sigma))*sin(radians(60))
 Formula: virtual time felt by the observer due to redshifted wavelength
Two = distance between Tswo(sigma) and Tawo(sigma)
Two(sigma) = (rw(sigma)/sin(radians(180-90-sigma))*sin(radians(90)))-(tiw(sigma)/sin(radians(90))*sin(radians(180-90-sigma)))
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
 Formula: relative wavelength observed, due to curvature generating redshift
rWo(sigma) = Two(sigma)/sin(radians(30))*sin(radians(90))
 Formula: relative observer’s position local wavelength
n(sigma) = r/sin(radians(180-60-sigma))*sin(radians(sigma))
 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 ), 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.
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.
CALCULATIONS (figure 4 and 5)
 Formula: space arch measurement relative to brightness
spo(sigma) = r*radians(sigma)
 Formula: space arch measurement relative to redshift
sw(sigma) = rw(sigma)*radians(sigma)
 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.
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