Saturday, 12 March 2022 20:23
###
Quasar Distribution

**Quasar Distribution.**

Quasars seem to consist of active galactic nuclei where the swirling in-fall of matter towards the central black hole of a galaxy causes the emission of massive amounts of radiation.

We have observed about a million quasar galaxies amongst the estimated 100 or more billion galaxies. As quasars seem to emit such unfeasibly vast amounts of energy, theorists have concluded that they must emit it mainly as beams which project out of the spin axis of the black hole and its accretion disc, rather than spherically in all directions. In this they behave very much like Pulsars which consist of rotating neutron stars with radiation beams coming out of their magnetic poles.

Thus, we can only detect Quasars that have one of their radiation beams pointing roughly towards us.

The closest detected Quasar to us lies about 0.6 billion light years away and the apparent density of Quasars in the universe seems to increase markedly with distance. This has become interpreted as supporting evidence for a big-bang expanding universe theory in which earlier galaxies had more material close to their black holes and behaved as Quasars until the black hole had consumed it. This assumes that galaxies have tended to undergo a one way evolution from having an active nucleus to having an inactive one.

Additionally, if quasar light originates from close vicinity to a black hole then it may start its journey with a substantial gravitational redshift anyway. Some quasars seem associated with galaxies that have far lower redshifts.

Hypersphere cosmology asserts that galaxies recycle and reform themselves endlessly and that galaxies at all stages of change will appear over all observable space and time, and that observers will find more quasars at long distances because of the positive curvature of spacetime.

If we assume that the spin axes of widely separated galaxies lie randomly orientated with respect to each other, then we should only expect to observe a small proportion of all quasars. However, positive spacetime curvature has a lensing effect on light and other forms of radiation that allows us to see more of the surface of an object than in flat spacetime, and the effect increases with distance.

For example, observers can see 70% of the surface of a neutron star rather than just 50% of it because of the curvature of spacetime around such a dense object.

In a hyperspherical universe we could in principle see 100% of the surface of an object at antipode distance. It would appear as spread around the observer’s entire spherical horizon. If such an object consisted of a Quasar, the observer could in principle see both polar beams from it coming apparently from opposite sides of the universe.

Thus, the further away a Quasar lies from an observer, the higher the probability that spacetime curvature will ‘tilt’ the rotation axis of that Quasar in the observer’s direction.

**Breaking News**

https://academic.oup.com/mnras/article/522/2/1736/7035603

The occurrence of greater numbers of quasars at long cosmic distances has become interpreted as evidence for the evolution of galaxies since a big bang, on the basis that younger (more distant) galaxies would have plenty of gas surrounding their central black holes, this gas would become sucked in to give rise to the quasar effect, and then when it had become exhausted the quasar activity would cease.

It now seems that quasar activity arises from the collision of galaxies driving gas towards their central black holes.

In which case, quasar distribution ceases to provide supporting evidence for the big bang hypothesis!!!

Published in
Hypersphere Cosmology

Sunday, 21 November 2021 16:44
###
The CMBR

**The CMBR**

The Cosmic Microwave Background Radiation has become interpreted as evidence for the Big-Bang expanding universe LCDM standard cosmological model.

The CMBR consists of electromagnetic microwave radiation that peaks at a frequency corresponding to blackbody radiation with a temperature of 2.7^{0} Kelvin above absolute zero. It comes to observers here from all directions in space.

Standard cosmology interprets the CMBR as relic radiation leftover from a primeval fireball about a third of a million years into the supposed expansion of the universe from a spacetime singularity or near singularity. At this time the universe had supposedly expanded to a radius of a third of a million light years and cooled to a temperature of about 3,000K, at which point it deionised from a proton-electron plasma and allowed photons to pass freely through it. Such photons which allegedly had very high energies and short wavelengths, subsequently became much lower energy longer wavelength photons due to the expansion of space and they now appear to us as the microwave background radiation.

We cannot see the CMBR with the naked eye, but if we could the night sky would not appear dark between the stars because about 400 CMBR photons per square centimetre per second impinge from all directions, they represent a significant cosmic phenomena that demands an explanation.

In Hypersphere Cosmology, all the electromagnetic radiation that does not become absorbed on its journey will eventually return towards its point of origin after about 13 billion years but in a much redshifted form due to gravitational redshifting and lensing by the small positive spacetime curvature of the entire universe.

Cosmologists estimate that our galaxy, the Milky Way, has an age alarmingly close to the supposed age of the universe itself, somewhere around the thirteen billion year mark. They remain adamant that it cannot possibly have an age greater than their estimate of the age of the universe. Yet the Milky Way contains the so-called Methuselah star (HD 140283), whose apparent longevity does seem to severely challenge the cosmic age limit.

The average surface temperatures of all the billions of stars in a galaxy or a galactic cluster adds up to something resembling a blackbody radiation source at about 3,000K when seen from a cosmic distance.

Thus, the CMBR we observe in this region of the hyperspherical cosmos may well have originated from this region and reconverged back here in highly redshifted form thirteen billion years later. Observers in a deep intergalactic void may not observe any CMBR at all.

The following two diagrams show the combined effects of Hyperspherical Lensing and Hyperspherical Vorticitation. Hyperspherical Lensing brings electromagnetic radiation to a focus at the antipode point to its emission. Hyperspherical Vorticitation moves the source of emission to its antipode point in the same period. The first diagram shows this effect in the reduced dimension surface of a sphere representation of a hypersphere, and the second shows it in the reduced dimension ‘two-ball’ representation of a hypersphere. Thick arrows represent the movement of the source due to vorticitation; thin arrows represent the paths of emitted radiation.

Hyperspherical vorticitation will send this galaxy to its antipode point in the universe in a period of 13 billion years. Light emitted from this galaxy will also travel to the same antipode point in the same period and appear as incoming light. The galaxy travels in just one direction, the light travels in every direction. The incoming light will appear highly redshifted from stellar surface temperatures to 2.7^{0} K.

Hyperspherical lensing will make the incoming light appear to have come from a surrounding sphere with a diameter very much larger than the antipode distance but compressed into a smaller field of view and thus multiply imaged. This will effectively smear out temperature variations and absorption and emission lines to yield a CMBR with blackbody radiation characteristics as shown below.

Redshift-Distance-Apparent Distance Graph. Vertical scale = distance, antipode distance at 1. Horizontal scale = Redshift.

Red line = Redshift - Distance relationship. Green line = Redshift - Apparent Distance relationship.

Note that the Apparent Distance of a Redshift = 0.625 source gives an almost exact figure for the Antipode Distance of the universe.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:08
###
Equation 1

Equation 1

Schwarzschild found the first exact solution to Einstein’s field equations of General Relativity in 1916. He found that 2Gm/r = c^2, the equation that describes a static black hole. This became known as the Exterior Schwarzschild Solution as it gives the metric of a black hole in the reference frame of an observer outside of it in ‘flat’ three-dimensional Euclidian space.

Soon afterwards, Schwarzschild derived an Interior solution for the metric inside a black hole. Unfortunately, he derived this metric in terms of the reference frame of an exterior observer, not of an interior observer.

This seems to have led Einstein to making his celebrated ‘greatest blunder’, the ad-hoc addition of a ‘cosmological constant’ to his equations to counteract the collapse predicted by the Interior Schwarzschild Solution when treating the universe as the inside of a black hole.

A gravitationally closed spacetime with three spatial dimensions must have the geometry of a Glome-type hypersphere with a metric of 2Gm/L = c^2 in the reference frame of any observer inside of it, where L shows the antipode distance.

(An observer inside the black hole of the universe can still use the exterior Schwarzschild solution when observing any of the smaller black holes within the universe from outside of them.)

The is confusion of observer reference frames has led to more than a century of confusion in cosmology and the development of the entirely erroneous model of LCDM Big Bang Cosmology.

Using the Interior Schwarzschild Metric in the reference frame of an Exterior observer has the effect of creating ‘Coordinate Singularities’ in the universe and inside of black holes.

Lines of longitude and latitude converge to form ‘Coordinate Singularities’ at the north and south poles of the Earth. However, no actual geographical singularity occurs at either place, the geography itself does not collapse to a tiny point or expand from a tiny point. Polar bears do not shrink to the size of mice if they stray close to the north pole.

The singularities that appear on globes of the Earth appear because we draw straight lines on their surfaces and the straight lines converge on the curved surface.

We now appreciate that the Earth has a curved surface, we do not live on a Flat Earth. It does however appear flat on a small local scale.

Nevertheless, lines of latitude and longitude still provide a grid of useful rectangles so long as we do not rely on this system too close to the poles.

Cosmologists mainly assume the universe has the flat geometry of ordinary Euclidian three-dimensional space that we see on the small local scale.

The universe does not have a flat Euclidian three-dimensional geometry on the cosmic scale. The mass inside the universe causes it to form a closed curved three-dimensional space under its own gravity. We live inside an awesomely vast black hole about thirteen billion light years across on the inside. A black hole of such a size does not have the sort of internal densities that characterise the smaller ones within it. A light dusting of galaxies spread over lots of nearly empty space can still provide gravitational closure at such a scale.

Cosmologists who persist in mapping the universe as flat will end up creating a Coordinate Singularity which looks like a Big Bang event in spacetime. This has no physical reality. The universe has the same curved geometry everywhere and at all points in time, rather like the surface of an ordinary sphere but in three dimensions.

Cosmologists mainly map or model the inside of black holes within the universe in terms of a Schwarzschild metric, but they speculatively map the internal metric in the reference frame of an external observer rather than in the reference frame of an internal observer of the metric. Thus, they wrongly conclude that a black hole must contain a spacetime singularity.

The Big Bang exists only as a Coordinate Singularity in the minds of theorists.

Beware of mistaking the map for the territory.

Because both the universe as a whole and the black holes within it consist of gravitationally closed spacetimes they have the curved geometry of Glome type Hyperspheres. These do not have real spacetime singularities but coordinate singularities will appear in predictions and calculations that mistakenly assume a flat geometry.

We do not inhabit a flat Earth. We do not inhabit a flat Universe either.

We inhabit a Hyperspherical Universe without Singularities.

How much spacetime does the universe contain? Conventional LCDM Big Bang Cosmology asserts that the observable universe has a radius of about 13.8 bnlyr, but that due to its apparent expansion since a hypothetical big bang it may now extend to perhaps 95 bnlyr and it may have the potential to expand into spacetime indefinitely.

Hypersphere Cosmology asserts that the entire universe consists of a finite but unbounded Hypersphere, closed in both space and time with an Antipode length of only13 bnlyr. This still makes it awesomely huge, but considerably smaller than the observable LCDM universe and certainly not even potentially spatially infinite. Such a Hypersphere will exist within a Black Hole with a radius equal to the Hypersphere’s Antipode length, as shown below.

Physicists commonly assume that if matter collapses under its own gravity to form a black hole with a Schwarzschild radius of 2GM/c^{2} then it will continue to collapse until the matter forms a zero size singularity inside that Schwarzschild radius. The Penrose – Hawking Singularity Theorems assert this, but only on the basis that they cannot conceive of anything that would stop it.

Hypersphere Cosmology asserts that matter will cease to collapse within a black hole when all the matter has collapsed to half the Schwarzschild diameter because at this point a Hypersphere will form within the Black Hole. Such hyperspheres will have a rotational velocity of lightspeed and will resist further compression which would push their rotational velocity past lightspeed.

If the Schwarzschild radius r and the Hypersphere antipode length L both equal 2GM/c^{2}, then L = r, or L = d/2. See A).

If we inhabit a universe that consists of the inside of a Black Hole and a Hypersphere has formed within it, then the optical horizon conventional cosmologists estimate to lie at ~13.4 bnlyr, and which Hypersphere Cosmology estimates to lie at almost exactly 13 bnlyr, represents the universe’s antipode distance not its radius.

If so, then the Hypersphere Cosmology universe has considerably less volume and a considerably higher density than conventional cosmology currently asserts. No surprise perhaps that the Hubble Deep Field contains so many galaxies.

Furthermore, a Black Hole of any mass within the universe should contain a Hypersphere.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:07
###
Equation 2

Equation 2

The physicist John Wheeler neatly summarised Einstein’s General Relativity with the quip that: -

“Space-time tells matter how to move; matter tells space-time how to curve”.

Einstein showed that what we call gravity consists of spacetime curvature. This rather neatly resolved the question of how gravity could act as a ‘force at a distance’ with nothing apparently carrying the force across the distance. This had bothered Newton.

Now the curvature of spacetime always manifests as an acceleration (as does gravity). Relativity shows the equivalence of gravity and acceleration, blindfolded you cannot tell the difference.

Equation 2 shows the acceleration within the hypersphere of the universe, or indeed within any hypersphere. The acceleration has a negative value, it acts as a deceleration in most situations. Formally, G has a negative sign, but we can ignore that for most purposes.

Glome type hyperspheres have no centres or circumferences but they do have a deceleration which acts against linear motion in any direction inside of them. This deceleration A corresponds to the positive spacetime curvature of a closed volume of spacetime.

We can conceptualise the curvature or deceleration as a fourth spatial dimension that lies orthogonal to all three spatial dimensions.

Mathematically speaking, ‘spheres’ come in many dimensions, a one-sphere consists of a one-dimensional line curved and closed into a simple circle, a two-sphere consists of a two-dimensional surface curved and closed to form the surface of a simple ball or globe, a three-sphere consists of a three dimensional space curved and closed to form something we cannot easily visualise and has the technical name of a Glome. The Glome and all higher dimensional spheres can bear the name ‘hypersphere’ but in this exegesis hypersphere will refer exclusively to the Glome or three-sphere.

Note that all spheres involve an ‘extra’ dimension. The one-dimensional line making up a circle bends through a second dimension, the two-dimensional surface making up a globe bends through a third dimension, the three-dimensional space of a hypersphere bends through a fourth dimension. In this sense the hypersphere represents a ‘four-dimensional object’ although the ‘fourth dimension’ here will appear as a spacetime curvature rather than as an extra ‘direction’ to observers within it.

The surface of a ball or globe thus provides a readily visualisable lower dimensional analogy of a hypersphere. Any point on the surface of a sphere has a corresponding antipode point on the other side of the sphere. The north pole has an antipode point at the south pole on the surface of the earth, the antipode of London lies in the sea off New Zealand. The distance to the antipode shows the maximum possible separation of any two points on the surface of a sphere. If the earth had a much greater mass that prevented light from escaping and confined it to traveling round the surface, then in principle, an observer standing on the north pole could see the south pole by looking in any direction, the south pole would appear faintly smeared all around the horizon of the observer.

Any attempt to represent a shape in a lower dimension involves some sort of distortion. The Mercator style projection of the surface of the earth onto a flat map distorts the polar and near polar regions making Canada, Greenland, and Antarctica look exceptionally vast.

Cartographers occasionally use polar projection maps which preserve the size of the polar regions but distort the equatorial regions. This kind of map consists two circular discs, one a ‘photograph’ of the earth taken from above the north pole and the other taken from above the south pole. The rims of both discs show the same equator so we can place the two discs flat on a surface touching at some point where the geography matches. Now we can roll one disc round the other and find that the geography matches all the way, so the map remains useful when planning journeys across the equator. This rather unusual two-disc type of map translates into a powerful method of visualising a hypersphere in three-dimensions.

Imagine two balls placed in contact. Here we concern ourselves with the three-dimensional space inside the balls rather than with their two-dimensional surfaces. Imagine that the two balls can roll around each other’s surfaces in any direction. Imagine that an observer resides in the centre of one of the balls. The centre of the other ball represents the observer’s antipode because the observer could travel or see in any direction out through the surface of the surrounding ball and back in through the surface of the other ball to its centre as the two balls ‘really’ lie with their entire surfaces touching, despite that we can only readily imagine them touching at one point. In this visualisation it becomes apparent that the observer could in principle see the antipode point by looking in any direction in three-dimensional space, so it would appear as a faint sphere surrounding the observer. This does not mean the observer occupies a special position. We could make a two-disc representation of the earth’s surface by taking ‘photographs’ from above any two antipode points. I could make one centred on my house and another point in the south pacific, in a hypersphere any observer can centre the universe on herself.

Note that all types of sphere have, in some sense, ‘more room inside’. Flatlanders living on a spherical surface would find that circles on that surface have more surface area than expected and that the radius of a circle seems longer than expected because it has to go over the curve of the surface. A gigantic circle of land on the surface of the earth will have a greater surface area than that within a similarly gigantic circle on a properly flat plane. The maximum amount of ‘radius excess’ occurs when the circle goes right round a great circle on the spherical surface, for example its equator. To Flatlanders the apparent radius would then equal half the circumference. An analogous effect occurs with a hypersphere, it contains more three-dimensional space than expected by any observer who looked at it from the outside and thought it consisted of a sphere. Within a hypersphere all ‘straight’ paths from a point to it antipode have the same length, so from the outside the antipode length equals half the circumference.

In Hypersphere Cosmology the observable universe constitutes the entire universe. Observable here means everything as far as the antipode, of course we cannot see everything in detail out to the antipode distance, but we can see some of the bigger galaxies at near antipode distance.

In Hypersphere Cosmology the universe has exactly enough mass/energy to provide the spacetime curvature to close it gravitationally into a hypersphere at its vast size, thus it consists of a black hole. If it had less mass it would have a smaller size, if it had more mass it would have a greater size. It has exactly enough mass for it size not by coincidence but because of the basic hyperspherical geometry of cosmic scale spacetime.

We usually think of black holes as regions of space containing a great deal of highly compressed matter at enormous densities, however vast black holes can have low densities inside because black holes arise not when the mass to volume ratio reaches a certain level, but when the mass to radius ratio reaches a certain level. As the volume and mass go up by the radius cubed it only takes a few atoms per cubic metre to close a universe the size of the observable universe. A hypersphere the size of the observable universe can consist mostly of space. Astronomers have noticed that the observable universe does seem to contain roughly enough ordinary matter to close it at its observable size, but Big Bang cosmologists dismiss this as ‘a mere coincidence’ and opine that we inhabit a universe which has by now accelerated far past the size we can observe.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:06
###
Equation 3 and 4

Equations 3 and 4

Some commentators have described Centrifugal Forces as ‘fictitious’ or even non-existent forces. Stationary observers do not observe centrifugal forces, but in the reference frame of moving observers, centrifugal forces become very real.

If one observer spins a second (smaller!) observer around in a basket on the end of a rope, the stationary observer must exert a centripetal pull on the rope. The spun observer will feel a centrifugal push into the basket. The two equal and opposite forces balance but only one of them exists in each of the observer’s reference frames.

Equations 3 and 4 show the centripetal aspect of the balanced forces that maintain the orbits of structures around the inside of hyperspheres. Equation 4 provides a simple method of calculating antipode length L from acceleration A, or vice versa, and it also plays a part in the derivation of the Redshift - Distance Equation 6.

For the equal and opposite complimentary centrifugal force see equation 5.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:05
###
Equation 5

Equation 5

Many items of rigorous mathematics with no obvious use can lie like buried swords awaiting discovery and application.

Kurt Gödel published another exact solution of the field equations of Einstein’s General Relativity in 1949.

https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.21.447

‘Matter everywhere rotates relative to the compass of inertia with an angular velocity of twice the square root of pi times the gravitational constant times the density’.

This came too late to prevent Einstein’s capitulation to the idea of an expanding universe which became generally accepted from around 1930, but not necessarily by Gödel.

Gödel’s model of a non-expanding rotating universe with a metric of w = 2sqrt (pi G p) rapidly became ignored because no axis of rotation in the universe seemed observable, and, because it also predicted closed time-like curves.

However, as equation 5 shows, the Gödel metric has complete compatibility with the internal hypersphere metric of 2Gm/L = c^2. It supplies the centrifugal force apparent to rotating observers within a hypersphere.

The absence of an obvious axis of rotation in the universe arises because the gravitationally bound mega-structures such as galaxies and galactic clusters all rotate around the randomly orientated great circles of the Hopf Fibration that delineate the hypersphere giving it no overall angular momentum in any direction and hence no axis of rotation.

Closed time-like curves in a hyperspherical universe simply imply finite and unbounded time. The universe does not have to do the same things on every revolution, it does not imply eternal recurrence of exactly the same events, or travel back to the past.

Note that in substituting mass/volume for density p the equation uses hypersphere volume 2L^3/ pi, and that the frequency f of rotation comes out at c/2L, showing that for a hypersphere ‘rotation circumference’ equals twice the antipode length.

2Gm/L = c^2 represents the Interior Hypersphere Metric in the reference frame of a stationary interior observer.

w = 2sqrt (pi G p) represents the Interior Hypersphere Metric in the reference frame of a rotating interior observer.

Neither metric implies real physical singularities or even mere coordinate singularities..

Hypersphere Cosmology predicts that gravitationally bound independently moving megastructures within the universe, such as galactic clusters or isolated galaxies will have a rotation around the universe.

Each revolution of 360 degrees equals 360 x 3600 = 1.296 e6 arcseconds.

Each revolution takes 26 billion years 8.2 e17 seconds, at 3.154 e9 seconds per century this yields 2.6 e8 centuries.

Thus, galactic clusters move at 1.296 e6 / 2.6 e8 = 0.005 arcseconds per century

HC predicts the clusters will rotate around randomly orientated planes thus the maximum observable differences in angle between any pair equals ± 0.01 arcsecond per century.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:05
###
Equation 6

Equation 6

The Redshift-Distance Equation.

We can readily observe Gravitational Redshift, for example light climbing out of the sun has all its wavelengths slightly shifted towards the lower energy ‘red’ end of the spectrum by the time it reaches us. For heavier stars, the effect becomes more pronounced. The gravity of the sun exists as a spacetime curvature which appears as an acceleration (a deceleration for anything trying to get away from it), this deceleration removes energy from light and causes a redshift.

Light traveling long distances across the universe becomes subject to its overall small positive spacetime curvature that also acts as a deceleration. This gives rise to a cosmological gravitational redshift in proportion to the distance travelled.

We calibrate redshift Z in terms of observed frequency over expected frequency and then subtracting one, so that the scale begins at zero rather than one.

Local galaxies have negligible cosmological redshifts. A redshift of Z = 1 corresponds to exactly half antipode distance. Light from near antipode distances has redshifts in excess of 10. Light from a luminous object at the antipode itself would have a redshift so high as to prevent its observation.

**Counterfactual Indefiniteness.**

Einstein famously asked if the Moon continues to exist when nobody looks at it.

I can now answer this with a (heavily qualified*) Not Necessarily.

An interesting example of this strangeness cropped up during some collaboration with a terrestrial correspondent upon Hypersphere Cosmology.

If cosmological redshift depends only on distance, then it has to remain indeterminate until measured.

See the graph below in which observed frequency (blue) decreases with distance travelled across the universe. This leads to an asymptotically increasing redshift of wavelength (red).

Note that as frequency decreases directly with distance travelled f_{o} = f_{e }(1-(d/L))

We cannot define what frequency a photon ‘would have’ at any point on a journey between two points, we can only calculate and confirm by measurement what frequency the photon has when we actually observe it. This means that the ‘counter-factual’ - the frequency that we do not observe, cannot have a definite but unknown value.

To take a simple example with rough figures: -

In Hypersphere Cosmology the antipode to any observer in the universe lies almost exactly 4 Gigaparsecs away, (1.23 E26 metres, 13 billion light years).

Imagine two distant galaxies ‘A’ at 2 Gigaparsecs, and ‘B’ at 1 Gigaparsec distant from an observer, with both laying roughly in the same direction. Light from A will have lost half of its frequency when it arrives at the observer. Light from B will have lost a quarter of its frequency when it arrives at the observer. This all accords with calculation and observation.

If we stopped the light from A at B, then we would find that it had lost a quarter of its frequency.

But what about the light from A as it flies unobserved past B? We cannot assign any value to its frequency that remains commensurate with the loss of a quarter of its frequency per Gigaparsec and a half of its frequency over 2 Gigaparsecs!

Plainly we have a quantum effect at play here. The frequency does not become defined until we stop the light and measure it, or equivalently it hits something and acquires a definite value.

Of all the interpretations of quantum mechanics, only Cramer’s Transactional Interpretation seems to offer a ‘reasonable’ or visualisable account of how this can happen. In this interpretation, retro causal advanced waves have to complete a quantum handshake across spacetime in any emission-absorption event before it acquires a definite value.

If, as in standard cosmology, the cosmological redshift arises from recession velocity in an expanding universe, then it can have a classical explanation that preserves the idea of a definite state of the unmeasured light at any point along its path.

**Trans-Antipodal light and the CMBR**

The sixth equation of Hypersphere Cosmology

https://www.specularium.org/component/k2/item/322-equation-6

shows how light become redshifted or frequency reduced as it travels across the universe by the universe’s small positive curvature which acts as an omnidirectional deceleration A.

It shows that light coming directly from the antipode point of any observer will lose all of its frequency and become unobservable: -

**f _{o } = f_{e} (1-(d/L))** where f

However, due to the counter-factual indefiniteness of the frequency of a photon in flight, an observer can still receive photons from trans-antipodal sources so long as such photons undergo some form of interaction enroute, perhaps reflection or absorption and re-emission, in which case the mechanism works re-iteratively: -

**f _{o } = f_{e} (1-(d_{1}/L))**

Clearly, if **d _{1} + d_{2} + d_{3}, etc > L **then light can still reach an observer without its frequency reducing completely to zero.

The CMBR represents the light from incandescent hydrogen at around 3,000 Kelvin downshifted by a factor of about 1100 to just 2.7 Kelvin, and it comprises a dominant proportion of the photon count of the entire extra-galactic background light (EBL) spectrum.

Now assuming that starlight does ‘bounce around’ occasionally in the course of epic journeys including perhaps multiple trans-antipodal journeys, then we can perhaps expect ordinary starlight to reach thermodynamic equilibrium with the background temperature of the universe and supply the relatively intense Cosmic Microwave Background Radiation that we observe.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:04
###
Equation 7

Equation 7

Mach’s Principle has intrigued physicists for more than a century. It exists in a variety of formulations, most of them philosophical rather than mathematical.

Broadly stated Mach’s Principle, or the Einstein-Mach Principle, says that the inertia of any single body should depend on the mass and distribution of the whole of the rest of the universe.

Thus, the inertial mass of any body may not arise as an intrinsic property of that body but may depend on the entire universe.

In the Newtonian paradigm the inertial mass and the gravitational mass of a body always have the same ratio. Newtonian theory accepts this without explanation. In Einstein’s relativity the equivalence of inertial mass and gravitational mass becomes a central principle. The gravitational constant G represents the constant ratio between inertial and gravitational mass, but where does that come from?

In a universe whose size and density varies with time, any expression of Mach’s Principle becomes problematic, either the ratio of inertial mass to gravitational mass and hence G will vary with time, or lightspeed will vary with time, or both. We have no evidence of that having happened.

Only in a universe of constant size and constant overall density can Mach’s Principle apply and take mathematical form.

Equation 7 shows a mathematical expression of Mach’s Principle. It has no conceivable use, but it does look holistically and philosophically satisfying.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:03
###
Equation 8

Equation 8 deals with the Pioneer Anomaly.

https://en.wikipedia.org/wiki/Pioneer_anomaly

As you can see this remains a controversial topic. The degree of thermal recoil involved in the anomalous deceleration seems the most disputed point.

HC predicts a deceleration (A) of 7.317 e-10 metres/second squared. And this seems close to the residual deceleration after the effects of thermal recoil appear to have declined due to cooling.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:02
###
Equation 9

Equation 9

Galaxies rotate but they do not rotate in accordance with our standard ideas about gravity.

A large discrepancy exists between the rotation curves for disc galaxies expected from a classical or relativistic consideration of their baryonic mass distributions, and the rotation curves observed. This discrepancy has led to the hypothesis that a mysterious ‘Dark Matter’ must make up the difference.

Gomel and Zimmerman show that an apparently ‘Non -Inertial System Component’ in the form of an angular velocity ‘w’, can account for this discrepancy.

v(r) = vi(r) + w(r)

https://www.preprints.org/manuscript/201908.0046/v1

This paper asserts that the angular velocity w arises from a Gödelian rotation component of the galaxies where w = 2sqrt (pi G p)

https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.21.447

‘Matter everywhere rotates with an angular velocity of twice the square root of pi times the gravitational constant times the density.’

Thus, v(r) = vi(r) + 2sqrt(pi G p) r

Now because the wr component of galactic rotation dominates at the extremities of galactic discs, thus creating ‘flat’ rotation curves, and because the outer edges of all disc galaxies rotate with the same time period of almost exactly one billion years, irrespective of their varied sizes.

https://astronomy.com/news/2018/03/all-galaxies-rotate-once-every-billion-years

It follows that we can calculate w with high accuracy to w = 2 e-16 radians/second.

Calculation: distance/velocity = time

2 pi r / wr = t

2 pi / 2 e-16 = t

pi e16 = t = 3.142 e16 seconds. (A billion years equals 3.155 e16 seconds)

Thus, it seems far more likely that all disc galaxies have a Gödelian rotational component of precisely 2 e-16 radians/second rather than dark matter halos with sizes and masses precisely and mysteriously tailored for each galaxy’s distribution of ordinary baryonic matter to create the observed rotation curves.

(Aside - just a little aside I came across whilst reading science news daily site - a flurry of papers have come out about 'Self-Scattering Dark Matter', apparently it will have to have this amongst its other miraculous properties to account for some of its predicted distribution. Phlogiston ended up with a negative weight variety.)

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:02
###
Equation 10

Equation 10

Here we show the modification to Newtonian Dynamics expected in a positively curved spacetime that has a negative acceleration A. Force does not exactly equal mass times acceleration on the very large scale, we have to subtract the very small deceleration.

Substituting this effect into the equation for the acceleration due to gravity we find that it increases that acceleration and also the orbital velocity.

As hyperspheres, black holes have an orbital velocity of lightspeed.

A black hole hypersphere within the hypersphere of the universe will tend to acquire extra orbital velocity from the spacetime curvature of the universe. The effect will increase with the size of the black hole.

Exactly what will happen when the material inside a black hole begins to push up against the lightspeed limit remains an open question, but it seems likely that the hole will begin to shed mass/energy in some form or other.

This predicted effect seems similar to the Hawking Radiation predicted to emerge from smaller black holes.

The effect may prove difficult to observe because large black holes usually remain obscured by dense clusters of stars and large fluxes of radiation from their accretion discs and infalling matter.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:01
###
Equation 11

Equation 11

The Dirac Large Numbers Hypothesis suggests that a huge dimensionless number, or perhaps just a few huge dimensionless numbers, seem to characterise many ratios in the observed universe that relate the quantum scale to the cosmic scale.

https://en.wikipedia.org/wiki/Dirac_...ers_hypothesis

https://arxiv.org/ftp/physics/papers/0502/0502049.pdf

If the universe exists in a state of expansion, then the equality of all these ratios appears as an extraordinary coincidence at only this particular epoch of the universe and we just have the good luck to observe it now.

On the other hand, if the universe exists as a non-expanding Hypersphere, finite and unbounded in space and time, then the Large Numbers simply represent the permanent ratio between the smallest components of the universe as shown by the quantum scale and the whole universe.

The universe and the quantum realm have characteristic units of mass, length, time, energy and acceleration, the same equations govern both: -

m/l = c^2/G t = c/l e = mc^2 a = c^2/l

A single number underlies the ratios of the quantum scale to the cosmic scale, this number which we can call The Ubiquity Constant U has a value of the order of 10^60, or e60.

All the other ‘cosmic coincidences’ such as e20, e40, e60, e80, e120 all arise as multiples of it and reflect something fundamental about the universe at any point in time.

Amusingly the ‘vacuum catastrophe’ which arises if you mistakenly try to explain the non-existent cosmological constant in terms of the non-existent quantum vacuum energy, comes out by a factor of e120 wrong, the largest mistake cosmologists have ever admitted to.

The origin of U, the ratio of the quantum scale to the cosmological scale remains a mystery but at least it reduces all the mysterious large number coincidences to a single mystery.

Equations 12, 13, 14, and 15 show how the Ubiquity constant defines the size of quanta, the pixilation of the universe, the effective uncertainty, and the mass of stable particles in the universe.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 17:00
###
Equation 12

Equation 12

The Bekenstein-Hawking conjecture arose to explain the behaviour of entropy in a black hole.

https://en.wikipedia.org/wiki/Black_hole_thermodynamics#Overview

It asserts that the entropy does not disappear but becomes preserved by an increase in the surface area of the hole in Planck units if matter falls in.

As the universe itself consists of a black hole in Hypersphere Cosmology then its surface area should represent the total amount of entropy that it contains.

Using the square of the antipode length L over the Planck area to approximate the entropy we obtain an entropy of the order of e120.

If the entropy of a system equates to its information content, then e120 bits of information must suffice for the e180 Planck volumes within the universe.

This implies only one bit of information per e60 Planck volumes or one for each e20 Planck length.

The universe thus has insufficient information to specify anything below this level of its effective pixilation.

See equations 13,14, and 15 for the consequences of this.

None of this supports the Holographic Universe hypothesis. The surface area defines the entropy/information content, but the information is not ‘encoded’ on the surface.

We can obtain a similar result by using the ratios of 3D surface hyper-areas.

**The Conservation of Entropy.**

Hypersphere Cosmology asserts that the overall entropy of the universe remains constant.

The second law of thermodynamics states that the entropy of a closed system must either increase or remain constant, it can never decrease.

The sky is cold, the stars are hot, plainly the observable entropy remains fairly low, but many of the processes going on around us appear to increase entropy

Now as the limits of observation represent a temporal horizon rather than a temporal boundary, the matter and energy within it has had unbounded time during which it has plainly not achieved thermodynamic equilibrium and maximum entropy.

Thus the universe must have some ongoing processes which increase entropy and some which do the opposite, and between them maintain an overall constant entropy. Gravitation itself may supply the main entropy reversing mechanism.

The principle of never decreasing entropy, the second law of thermodynamics, grew out of the age of steam and observations of the flow of heat in gasses. It takes no account of the attractions between particles. Observe some gas with an uneven distribution of heat or pressure and it will soon homogenise or dissipate. However, a really vast amount of gas will compress itself and ignite as a star. I submit that it be considered as an entropy reversing effect.

If gravity worked repulsively it would fit the simple view of entropy nicely, matter and energy would dissipate. Interestingly the sign of G is formally negative, although we can usually ignore that, but in a sense, gravity reverses the (entropic) arrow of time.

'Entropy increases with time because we measure time in the direction in which entropy increases' - Stephen Hawking.

Equation 10 shows that black holes within the universe will not persist indefinitely.

Neutrons build up as stars burn and create heavier elements but heavier elements breakdown into neutron plasma inside neutron stars which eventually explode. Free neutrons in space decay back into hydrogen.

The recently discovered Giant Gas Halos around nearby galaxies suggest that all galaxies probably have these difficult to observe halos. Such halos, which also contain heavy element dust from exploded stars, may well act as the recycling yards for the stellar parts of the galaxies.

We have no means of determining the ages of black holes and some structures within the universe seem to have an age very close to, or in excess of, the temporal horizon.

It does not seem unlikely that the closed spacetime of the Hyperspherical Universe can maintain a constant leel of entropy.

Published in
Hypersphere Cosmology

Monday, 22 February 2021 16:58
###
Equation 13

Equation 13

The universe has an information deficit in the sense that it has only one bit of information/entropy for every e20 Planck lengths and this represents the universe’s pixilation or ‘grain size’. Equations 14 and 15 show what this means for quantum particles.

The pixilation level also has the effect of raising the effective Heisenberg uncertainty/indeterminacy level of the universe by twenty orders of magnitude. This does not make the universe excessively Chaotic in principle, but it does make it about as Chaotic as it appears in practice.

Published in
Hypersphere Cosmology