Hyperspherical Universe without Singularities.

[Peter J Carroll]

Hello again, six years after my first 30 day session here, I believe that I have sorted out the problems with Hypersphere Cosmology, assisted by the feedback I received here, and by astronomers and mathematicians who noticed my website and gave me advice and links to more data.

The Hypersphere Cosmology model has now received over 350,000 reads but I have yet to receive any falsification, despite bringing it to the attention of Saul Perlmutter whose data I have reprocessed in an alternative scheme to yield an alternative idea to an accelerating cosmic expansion and dark energy.

In brief: - Abstract. Hypersphere Cosmology presents an alternative to the expanding universe of the standard LCDM-Big Bang model. In Hypersphere Cosmology, a universe finite and unbounded in both space and time has a small positive spacetime curvature and a form of rotation. This positive spacetime curvature appears as an acceleration A that accounts for the cosmological redshift of distant galaxies and a stereographic projection of radiant flux from distant sources that makes them appear dimmer and hence more distant. The acceleration A also accounts for the flat galactic rotation curves without dark matter.

The main paper lies here
https://www.specularium.org/hypersphere-cosmology
with links to pages of supporting mathematics

I welcome falsification, or advice on how to present it for publication in a suitable journal. I have been out of the academic environment for almost half a century. Regards, Pete.

[Noclevername]

Hello, Peter. Welcome back.

Could you summarize in your own words what Hypersphere Cosmology consists of and how it could be testable?

[cjameshuff]

The acceleration A also accounts for the flat galactic rotation curves without dark matter.

Then it is likely to have all the same problems that MOND theories have. Dark matter provides an explanation for galaxy rotation curves. It also explains some much more complicated observations, which MOND theories can't account for.

If your theory produces an effect without dark matter, and then dark matter sufficient to cause that same effect must be added to account for other observations, what do you think will happen?

[Swift]

Closed pending moderator discussion

[Swift]

The thread is reopened

[Peter J Carroll]

Question 1 from Noclevername
<Could you summarize in your own words what Hypersphere Cosmology consists of and how it could be testable?>
Einstein originally thought the universe remained a constant size and mentioned that it might consist of a Hypersphere, although he appears not to have explored the properties of the hypersphere in depth. Following the Friedman prediction that a static universe would implode and the discovery of galactic redshifts, the static universe model became discarded in favour of an expanding one. In the meantime, Gödel had developed a rotating universe model but that became discarded because no axis of rotation seemed observable. However, Gödel’s model used a basically spherical model, not a hyperspherical one.
A hypersphere (of the 3-sphere or Glome type) has no centre and no surface apparent to any observer within it. Great Circles within a hypersphere appear as Hopf Fibrations, circles randomly orientated but with every circle passing inside of every other circle. Rotation of matter about such circles does not give the hypersphere any overall angular momentum, but it does stop the hypersphere collapsing.
Within the hypersphere, linear motion in any of the spatial dimensions is opposed by an acceleration, nothing can escape, the hypersphere has an escape velocity of lightspeed, it works to turn linear velocity into orbital velocity, any long journey returns observers to their point of origin.
The omnidirectional deceleration within a hypersphere removes energy from electromagnetic radiation over long distances creating a redshift, and thus an illusion of expansion.
As the hypersphere exists as a gravitationally closed space it will naturally act as a vast lens, distorting sight lines over vast distances making observers who ‘see in straight lines’ perceive the universe in stereographic projection. This will make luminous objects towards the antipode of any observer look exceptionally faint as the antipode will appear spread over the observer’s entire spherical horizon. Thus, a mismatch will appear between redshift and distance which has conventionally become interpreted as an accelerating expansion driven by a hypothetical dark energy.
As I designed the HC model to explain most of the main common observations that led to the LCDM model it does not provide predictions against those observations, instead it provides reinterpretations of them. However, it does suggest that the Pioneer Anomaly really does represent new physics. I would like to see another deep space mission with high precision telemetry that can settle the argument about the amount of thermal recoil involved in the phenomenon. Secondly the HC model predicts that the angles between very distant galaxies will change slowly over time depending on the orientation of the planes of the orbital paths in which they rotate around the hypersphere. Unfortunately, such changes in angle of even near-antipode galaxies seem unlikely to exceed 0.01 arcseconds per century, nevertheless long-term observations could perhaps reveal it.
I have to say that our complete inability to find anything remotely resembling dark matter or dark energy ‘in the lab’ or the particle accelerator, or in vast fluid filled tanks, speaks for itself.




Question 2 from cjameshuff
<Then it is likely to have all the same problems that MOND theories have. Dark matter provides an explanation for galaxy rotation curves. It also explains some much more complicated observations, which MOND theories can't account for.

If your theory produces an effect without dark matter, and then dark matter sufficient to cause that same effect must be added to account for other observations, what do you think will happen?>
Good Question. Dark Matter has also been considered necessary for galaxies to form fairly rapidly after a big bang. However, in the Hypersphere Cosmology model galaxies have unlimited time in which to form. The presence of very large galaxies at very high redshifts and the existence of various mega-structures in the universe has led a number of cosmologists to ask if the LCDM model has a long enough timescale to account for these formations.
Dark matter has also been implicated in the motions of galaxies within galactic clusters. The additional Gödel angular velocity w = 2sqrt piGp should apply at all scales.
Dark matter supposedly also keeps the geometry of the universe ‘flat’ despite the apparent accelerating expansion. In the HC model, the positive curvature exactly balances the Gödelian rotation.
Various gravitational lensing effects also supposedly arise from the presence of dark matter within galaxies. However, the lensing remains commensurate with the mass of the galaxies derived from their rotation behaviour thus the Gödelian component of their rotation seems to effectively add to their mass/spacetime curvature.
The bullet cluster may not represent a fatal shot for MOND theories, see https://web.archive.org/web/20160721...ti_bullet.html
The recently discovered enormous diffuse gas halos around the nearby Triangulum and Andromeda galaxies appear to have masses at least equal to the galaxies themselves, indeed the gas halo around Andromeda seems to extend to graze the halo around our own galaxy. The two stellar portions of the bullet cluster should have a Gödelian rotation about each other and if a vast gas halo surrounds the cluster, augmenting the rotation, then it perhaps comes as no surprise that the centre of mass appears to lie somewhere in between the stellar portions.
See a brief calculation of mine here using the Gödelian rotation derived from a consideration of the entirety of the Triangulum galaxy, gas halo and all, applied to the MOND formula derived by Gomel and Zimmerman: -
https://www.specularium.org/hypersph...lum-m33-galaxy

[Shaula]

Great Circles within a hypersphere appear as Hopf Fibrations, circles randomly orientated but with every circle passing inside of every other circle. Rotation of matter about such circles does not give the hypersphere any overall angular momentum, but it does stop the hypersphere collapsing.

Can you please show this? What observational evidence would you expect to see if matter were following these paths?

As the hypersphere exists as a gravitationally closed space it will naturally act as a vast lens, distorting sight lines over vast distances making observers who ‘see in straight lines’ perceive the universe in stereographic projection. This will make luminous objects towards the antipode of any observer look exceptionally faint as the antipode will appear spread over the observer’s entire spherical horizon. Thus, a mismatch will appear between redshift and distance which has conventionally become interpreted as an accelerating expansion driven by a hypothetical dark energy.

Can you please derive your luminosity distance relationship? Can you please quantify the distortions you expect to see and what spatial variation you would expect to see in redshift patterns?

Dark matter has also been implicated in the motions of galaxies within galactic clusters. The additional Gödel angular velocity w = 2sqrt piGp should apply at all scales.
Dark matter supposedly also keeps the geometry of the universe ‘flat’ despite the apparent accelerating expansion. In the HC model, the positive curvature exactly balances the Gödelian rotation.

Can you please show how this fixes the MOND tension between galactic rotation curves and cluster velocity distributions?

So far it looks mostly like what has changed between this iteration of your idea and the last one is that you have added more assertions. Could you please pick one or more of your assetions and present detailed evidence here for it?

[Peter J Carroll]

Thankyou for the questions Shaula. I will address your second question first and show how I derived the redshift-distance relationship as the other answers all depend from that. It contains a controversial manoeuvre, {c}^{ 2} -dA. This arises from the problems in the way we handle the energy of the photon, using
{E}^{2 } = {m}^{2 }{c}^{ 4} + {p}^{2 }{c}^{2 } leads to an inelegant squaring of everything, so I have simplified by letting E = m{c}^{2 } stand in for photon energy.

Strictly speaking the equation does not give the distance d directly from redshift Z, it gives the relationship between Z, d, and L the antipode length, the antipode length comes from a consideration of the hyperspherical lensing equation.

The redshift -distance equation basically posits a type of gravitational redshift caused by the effect of the positive spacetime curvature A acting as an acceleration over distance d.

[Shaula]

Thankyou for the questions Shaula. I will address your second question first and show how I derived the redshift-distance relationship as the other answers all depend from that. It contains a controversial manoeuvre, {c}^{ 2} -dA. This arises from the problems in the way we handle the energy of the photon, using
{E}^{2 } = {m}^{2 }{c}^{ 4} + {p}^{2 }{c}^{2 } leads to an inelegant squaring of everything, so I have simplified by letting E = m{c}^{2 } stand in for photon energy.

Photons are massless. So this is a solution only for the unphysical case of zero energy since you have dropped the relevant bit for photons which is the bit containing momentum. It also leads to the result 0/0.

Where did this dA factor come from? For that matter could you please define your variables - I want to be sure what each component of the equations you are presenting is.

Strictly speaking the equation does not give the distance d directly from redshift Z, it gives the relationship between Z, d, and L the antipode length, the antipode length comes from a consideration of the hyperspherical lensing equation.

The redshift -distance equation basically posits a type of gravitational redshift caused by the effect of the positive spacetime curvature A acting as an acceleration over distance d.

So essentially you have an equation where there is a variable (the antipode length) that you can't measure and can just fit to any result? How does this lead to anything predictive? Or can you exaplain how you independently measure the antipode length.

[Peter J Carroll]

If we define photons as massless then E = pc where p equals momentum, and if p = mv, what can the v equal except c? Thus I have treated the mass associated with momentum as 'notional', the two 'notional' masses cancel out anyway.

The factor dA means the actual astronomical distance d multiplied by A the acceleration due to the curvature of the universe which equals {c}^{2 }/L.

L represents the antipode length of the hypersphere of the universe, this has a constant value of 1.23 E26 metres, ~13 billion light years. I derived this as follows:

1) Take the apparent magnitudes of the type 1a supernovae in Perlmutter's study and convert these into radiant fluxes (in Janskys).

2) Using the inverse square law calculate the apparent distances to the supernovae using the standardised measure of the flux from a hypothetical supernova at 10 parsecs having a magnitude of -19.3. Note that the apparent distances to supernovae with redshifts in excess of 0.6 tend to become enormous.
https://www.specularium.org/hypersph...here-cosmology

3) Using an algebraic/geometric model (shown below) which converts between actual distances within a hypersphere and the apparent distances which will appear when we see the hypersphere stereographically projected, as we must because of the assumption that we see in straight lines. Use this to convert the apparent distances to actual distances

4) Apply the distance-redshift-antipode relationship to the supernovae whose redshifts we have already had measured and whose actual distance we have calculated above and it yields an antipode value close enough to 1.23 E26 metres for all of them. (The small imperfections in the fit arise from the difficulties of measuring apparent magnitudes accurately, these small imperfections of course also remain in the Perlmutter interpretation.)

The elegance of the result leads me to suspect that the redshift-distance equation does give a realistic answer, even if the derivation looks a bit odd. I would welcome suggestions on how to make it look more acceptable.

[Shaula]

If we define photons as massless then E = pc where p equals momentum, and if p = mv, what can the v equal except c? Thus I have treated the mass associated with momentum as 'notional', the two 'notional' masses cancel out anyway.

No no no no. I'm sorry you just can't do this. You are mixing relativistic and non-relativistic equations horrendously here. p is NOT mv. The 3-momentum can be generalised to mv but in relativity momentum is a 4-vector. This whole section of the derivation is deeply flawed - you are using Einstein when it suits you, Newton when it doesn't. It is like fingernails down a chalkboard to a physicist.

I'll look over the rest in more detail later and get back to you. As it stands even if the method for deriving the antipode length is valid it still seems somewhat arbitrary - do you have other lines of investigation that support this number? Otherwise it just looks like another fitted parameter. All you have then done is say "Redshift is a change in wavelength which can be expressed as a change in energy. I can put in a scale factor that results in a loss of energy that fits the data". Which is exactly where dark energy started. And since, to use your argument, we haven't seen evidence of a hyperspherical universe in our Earth based labs...

[Peter J Carroll]

Thanks for looking it all over Shaula, I look forward to your analysis. One other line of supporting evidence perhaps lies in something that cosmologists usually dismiss as a mere coincidence at this epoch of the universe; for the observed baryonic matter and the apparent size of the observable universe, M/r ~ c^2/G.
We may have evidence of hyperspherical geometry in the 'lab' of the solar system, I don't think Anderson feels entirely satisfied with the thermal recoil explanation of the Pioneer Anomaly, plus the Fly-By Anomaly may arise from the boost to orbital motion that HC predicts, although the data there looks all over the place.

[Reality Check]

Einstein originally thought the universe remained a constant size and mentioned that it might consist of a Hypersphere,...

Hi Peter J Carroll, this is incorrect and irrelevant. Like many of the scientists at the time, Einstein thought that the universe was static with an unknown size. You do not cite any mention of a hypersphere by Einstein. The prediction from using the cosmological constant to make a universe static was that random fluctuations of density in the universe would make the universe contract or expand.
The Pioneer anomaly does not exist! The cause has been known for 8 years now - thermal radiation from the radioisotope thermoelectric generator.
Finding dark energy " ‘in the lab’ or the particle accelerator, or in vast fluid filled tanks" cannot be done. Not finding some dark matter candidates does not make the large body of evidence that dark matter exists vanish.

The rest is mostly unsupported assertions about your idea and mainstream cosmology.
Dark matter is needed to explain the large-scale structure of the universe. You assert more evidence for dark matter in galaxy formation.
An unsupported and irrelevant assertion of "a number of cosmologists" doubting that there was time enough for "very large galaxies at very high redshifts" to form. Even if the models of galaxy formation and evolution are wrong, this does not make your idea correct.
Galaxies in galaxy clusters do not obey the virial theorem showing that dark matter is needed. Guessing what a Gödel angular velocity will do does not fix this.
Gravitational lensing effects come from dark matter but not as you think inside galaxies. We measure dark matter inside galaxy clusters by looking at gravitational lensing of galaxies.
A few paragraphs on a 14 year old web page (Milgrom's perspective on the Bullet Cluster) on the WayBack Machine is not scientific literature.
Diffuse gas halos around galaxies supports the Lambda-CDM model! The elusive stellar halo of the Triangulum galaxy may not exist. Recently Hubble maps giant halo around Andromeda Galaxy. The mainstream prediction is that 4% of the universe is normal matter. There was the missing baryon problem (we could only detect half this amount). These gas haloes contribute to the mainstream prediction.
Writing about the Bullet cluster as if it were a galaxy! Galaxy clusters to not have a stellar halo.
Misunderstanding about the Bullet cluster. The evidence for dark matter is not any center of mass. The evidence is we detect the shockwaves of interacting gas that is separate from the majority of the mass detected from gravitational lensing. Most of the gas in the colliding clusters has passed through the clusters without interacting electromagnetically. That gas is dark.
An irrelevant "Rotation of the Triangulum M33 Galaxy" calculation. A galaxy rotation curve is not a single angular velocity.

[Reality Check]

This arises from the problems in the way we handle the energy of the photon, using
{E}^{2 } = {m}^{2 }{c}^{ 4} + {p}^{2 }{c}^{2 } leads to an inelegant squaring of everything, so I have simplified by letting E = m{c}^{2 } stand in for photon energy.

This is wrong, Peter J Carroll.. There are no problems with how we handle the energy of the photon, especially the relativistic energy equation being "inelegant ". That equation is how the universe acts in experiments.
The mass of the photon is zero. What is the mass of a photon? Theory says exactly zero, experiment puts an upper limit of 7 × 10−17 eV. You have just written that photons have no energy.
The energy of a photon varies with wavelength.
Setting that photons do not have momentum means solar sails cannot work using radiation pressure.

Your image is a tired light theory with what looks like changing the speed of light to make it redshift. You need to consider E = m{c}^{2} and its role in fusion! Change c enough and stars cannot exist. Change c, the fine-structure constant changes and spectra change (1 paper has a slight increase over the last 10–12 billion years).

[Peter J Carroll]

Thank you for your points Reality Check.

‘You do not cite any mention of a hypersphere by Einstein.’

If he did not use the word explicitly in print, he certainly used the concept and then added his cosmological constant to prevent it collapsing. In HC, a Gödel type rotation prevents collapse.

://arxiv.org/ftp/arxiv/papers/1309/1309.6590.pdf
Einstein desired to eliminate what he called the "epistemological weakness" ["erkenntnistheoretischen Schwächen"] of Newtonian mechanics, the absolute space, from physics; he invented a world, finite and spatially closed static universe, bounded in space, according to the idea of inertia having its origin in an interaction between the mass under consideration and all of the other masses in the universe, which he called "Mach's ideas" (obviously not Ernst Mach's ideas as has been generally recognized and as Mach himself pronounced them). This would be later called by Einstein "Mach's principle" (more precisely Mach-Einstein principle).

https://blogs.scientificamerican.com...atest-blunder/

In his seminal Cosmological Considerations paper of 1917, Einstein showed that general relativity could indeed give a consistent model of the static universe. However, two assumptions were necessary. First, the universe was of closed spatial geometry (like a three-dimensional sphere) and had no beginning or end in time.

Concerning dark matter: -

Thanks for that link https://www.sciencedaily.com/release...0827141345.htm

Surely the recently discovered existence of an unexpectedly vast gas halo around the nearest next galaxy must lead to the question of whether some or most other galaxies possess them, despite the current difficulties in observing them, and whether that suggests a downward revision of the amount of dark matter required to account for their rotation curves?
Perhaps a downward revision to zero? In my calculation of the Triangulum galaxy, I have not attempted to compute the entire rotation curve, merely the extra angular velocity component required at the extremity of the stellar disc as identified by the Gomel and Zimmerman analysis. In this I have used estimates of the density of the entire Triangulum galaxy, new halo and all, and treated the galaxy as a sphere for the estimation of volume.
I would dearly like to try out the formula on the motions of galaxies within clusters, can you point me towards a suitable dataset? I do not have academic levels of access and would prefer not to join in the pay-journal racket. Maybe something on arxiv?

In response to your second post, I freely admit that the formula for removing energy from light by applying a deceleration to it does look like an ugly shortcut which somehow leads to a result that seems reasonable, Z =1 for objects halfway to the limits of observation, Z tending to unlimited value at the limits of observation, and when combined with the lensing equation it yields the same antipode distance prediction in the case of every Type 1a Supernova in the Perlmutter dataset.
Of course I do not wish to challenge the constancy of c, I want to challenge the momentum of photons with a deceleration.

[Peter J Carroll]

I think I may have something approaching a resolution, using gravitational frequency shift.

See http://hyperphysics.phy-astr.gsu.edu...blahol.html#c2

An equation shown there gives the effects of gravity on frequency, starting from this, a gravitational effect on wavelength in a hypersphere seems directly derivable without doing anything too dreadful.

See attachment below

[Reality Check]

If he did not use the word explicitly in print, he certainly used the concept and then added his cosmological constant to prevent it collapsing.

A basic bit of advice for anyone with an against the mainstream idea is to learn the mainstream science first, Peter J Carroll.

GR does not use anything like a hypersphere which "is the set of points at a constant distance from a given point ". Einstein did not use and GR does not contain even the concept of hyperspheres. GR has mathematical objects (manifolds) with points throughout them and with no center.

We know that Einstein like other people over a century ago believed in a static universe and added the cosmological constant wrongly to try to achieve this.

The "unexpectedly vast gas halo around the nearest next galaxy" has nothing to do with dark matter.
Finding more baryonic matter just addresses the missing baryon problem. Dark matter is non-baryonic matter in mainstream cosmology. When we had detected half of the predicted baryonic matter, the prediction of the universe being 4% baryonic matter was in doubt. Now we have found all of the predicted baryonic matter. This supports the Lambda-CDM model.

There is no "formula on the motions of galaxies within clusters" used in the galaxy cluster evidence for dark matter. The virial theorem is classical mechanics "that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system". See On the Masses of Nebulae and of Clusters of Nebulae by Zwicky, F. (1937) and section III "THE VIRIAL THEOREM APPLIED TO CLUSTERS OE NEBULAE".

I did not write that you did an "ugly shortcut". You did a scientifically invalid act ignoring that the photon has no mass and that the energy of photons changes with wavelength. E = mc^2 for a photon is zero and unchanging. You did the opposite of what is in physics textbooks, Wikipedia and other sources of science. When the relativistic energy equation is applied to photons, m = 0, the mc^2 part of the equation vanishes. and the energy of a photon is related to its momentum and thus its wavelength.

The momentum of photons is not p = mv and cannot be changed by a deceleration. The momentum of photons is the reduced Planck constant times the wave vector and has a magnitude of h*frequency/c = h/wavelength. The only deceleration that can be applied is changing the value of c. Thus you are stating that c must change in your idea.

[Reality Check]

I think I may have something approaching a resolution, using gravitational frequency shift.

See http://hyperphysics.phy-astr.gsu.edu...blahol.html#c2

You do not have a resolution, Peter J Carroll. Gravity and the Photon is mainstream science that you have not got even started to match from your idea. A guess that hypersphere will produce gravitational redshift is very bad when you do not even have gravity in your idea !

Arbitrarily plugging in a mainstream equation into your equations is invalid. Gravitational redshift is the redshift caused by differences in gravitational field strength (light climbing out of a gravity well). This universe is just about homogeneous. Galaxies are not arranged around us to make a gravity well, e.g. ever increasing densities of galaxy numbers. A fundamental assumption in cosmology is that we are not a special place in the universe . We are not the center of the universe.

You missed that r is the radius of the gravitational mass causing the redshift. Gravity and the Photon is not about the gravitational redshift inside the mass. By equating r to L (a ~13 billion light years length) you are looking at the redshift of a gravitational mass with that radius. This is the gravitational redshift of light climbing out of that mass - essentially leaving your universe! Your r* has to be > L. It cannot be a distance d within L.

[Peter J Carroll]

Thank you for your points Reality Check, I append below an upgraded version of equation 6 which now incorporates G to give the same overall result. I will shortly add this to the specularium paper. Thank you for pointing me in a productive direction.

I have only spent about 25 years on this reading and studying the books and papers available to a non-academician, nevertheless it does seem to me that LCDM cosmology itself steps far outside the scientific rigour of other scientific disciplines, it posits spacetime singularities, inflation without a mechanism, an initial condition which remains inexplicable, and dark matter and dark energy merely to patch the misfits with General Relativity. It appears to have developed as a path-dependent theory from an initial misinterpretation and so it has filled with phlogiston like elements. This wouldn't be a first in cosmology, remember Ptolemaic Epicycles?

Shaula, I present here my calculation and prediction for the potentially observable relative motion of gravitationally bound structures in the universe that lie widely separated, for example galactic clusters.

Cosmic rotation of galactic clusters.
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.

[Reality Check]

Thank you for your points Reality Check, I append below an upgraded version of equation 6 which now incorporates G to give the same overall result. ...

Still not understanding the physics that you are using, Peter J Carroll. So some formal questions.
IF01: What is the r in Gravity and the Photon?
IF03: Cite your evidence that galaxies in this universe are arranged so that gravitational redshift will produce cosmological redshift.

Some irrelevant misconceptions about the mainstream which is odd given your 25 years od study.

• LCDM cosmology is a scientific model like most other scientific models with the same scientific rigor. The difference is that we cannot run experiment on this universe or other universes.
• LCDM cosmology does not "posit" singularities.
  The Big Bang singularity is the fact that density increases without limit as time goes toward zero. This is a signature of the theory breaking down and so t = 0 is generally excluded from LCDM cosmology.
  Singularities are common in physics. Every inverse square law has a singularity as r tends to 0. We do not throw away electromagnetism or Newtonian gravity because of this. We recognize that putting r = 0 is invalid.
  Quantum field theory uses renormalization to remove singularities and ends up with the most precisely tested theory in physics (quantum electrodynamics).
• Dark matter and dark energy are not patches for misfits with GR.
  You know that the first evidence for dark matter was applying classical mechanics to a galaxy cluster! Galaxy rotation curves are Newtonian gravitation. Colliding galaxy clusters are the application of GR (gravitational lensing) to measure the distribution of gas and see that it separates into 2 components - normal matter and dark matter. The large-scale structure of the universe needs dark matter. The theory of the CMB power spectrum needs dark matter to fit the data.
• Dark energy is the physical evidence that the expansion of the universe is accelerating. This matches GR perfectly because a non-zero cosmological constant will cause what we measure!

An irrelevant calculation. Shaula did not ask about galaxy cluster rotation. The closest Shaula comes is a question about any other lines of evidence. You have not answered that with imagining that they rotate once every 26 billion years and not producing any evidence of that rotation. I could make up that they rotate every 26 trillion years and be just as correct.

[Peter J Carroll]

Thanks for these questions and criticisms Reality Check, I will respond below: -

Still not understanding the physics that you are using, Peter J Carroll. So some formal questions.
IF01: What is the r in Gravity and the Photon?
IF03: Cite your evidence that galaxies in this universe are arranged so that gravitational redshift will produce cosmological redshift.

IFO1&3 Answers. The radius indicates the distance from the centre of mass (IFO1), and I understand the standard concept that gravitational redshift arises from differences of gravitational potential, we can for example observe a small gravitational redshift in light climbing out of the sun because we sit at a lower potential. Hypothetical sun dwelling observers would see light from us slightly blue shifted. I have not found anything useful about gravity within gravitationally closed spaces (except the singularity theorems which I will come to later). I’m basically proposing that a closed space with matter arranged isotopically and homogenously on the very large scale (IFO3) will have an omnidirectional curvature. Now as to how that may affect photons in transit, I have taken my cue from the Gravity and the Photon hyperphysics entry which uses one minus 2GM/r to show the effects on frequency rather than the usual one minus sqrt 2GM/r used to model things like the effects of gravity on length and time distortion. The equation I have proposed predicts that light in transit will become redshifted in proportion to the distance it travels in such omnidirectionally curved space. It predicts what we already observe for small redshifts and for higher redshifts it still holds under the hyperspherical lensing model which corrects apparent to actual distances.

Some irrelevant misconceptions about the mainstream which is odd given your 25 years of study.

LCDM cosmology is a scientific model like most other scientific models with the same scientific rigor. The difference is that we cannot run experiment on this universe or other universes.
LCDM cosmology does not "posit" singularities.
The Big Bang singularity is the fact that density increases without limit as time goes toward zero. This is a signature of the theory breaking down and so t = 0 is generally excluded from LCDM cosmology.

Answer. A singularity at a Big Bang seems widely asserted as a fact, although many physicists try to find a way around this with bounce hypotheses or extra dimensions. The Hawking-Penrose singularity theorems appear to simply say singularities must form within gravitationally closed areas of space, like black holes, because we cannot think of anything that could stop it. I suspect that the formation of hyperspheres will stop it. A hypersphere has a radius excess (more space inside than an outside observer would estimate from its circumference).

A hypersphere has no centre or perimeter to an observer inside of it, and to that observer all objects at antipode distance will appear to rotate around the horizon at lightspeed (see the answer at the very end).

If more mass falls into a hypersphere it just gets bigger. One often comes across calculations about the sizes of black holes of various masses, things like a black hole with the mass of the moon having the size of a golf ball etc. Well, a black hole with the baryonic mass of the observed universe would seem to have a size remarkably close to the limits of observation. Within LCDM this is dismissed as a mere coincidence at this particular epoch, in HC it becomes a cornerstone of the hypothesis. The observed universe cannot contract, if it tried to, its component masses would have to rotate faster than lightspeed, thus it seems unlikely that it ever went through a smaller size to get to its current size.



Singularities are common in physics. Every inverse square law has a singularity as r tends to 0. We do not throw away electromagnetism or Newtonian gravity because of this. We recognize that putting r = 0 is invalid.
Quantum field theory uses renormalization to remove singularities and ends up with the most precisely tested theory in physics (quantum electrodynamics).

Answer. Many physicists and mathematicians feel uneasy about renormalisation, it looks like two wrongs making a right because it cancels one set of infinities against another, and obviously real physical infinities cannot exist. Plainly if you treat particles as dimensionless points something will go awry at some scale. Something deeper must underlie quantum field theory. (Incidentally, I have played with the idea of quanta as micro hyperspheres but nothing to report so far.)

Dark matter and dark energy are not patches for misfits with GR.
You know that the first evidence for dark matter was applying classical mechanics to a galaxy cluster! Galaxy rotation curves are Newtonian gravitation. Colliding galaxy clusters are the application of GR (gravitational lensing) to measure the distribution of gas and see that it separates into 2 components - normal matter and dark matter. The large-scale structure of the universe needs dark matter.

Answer. Well both the galaxy rotation curves and the colliding galaxy clusters do not fit either Newtonian or GR mechanics without the addition of something else, I suspect that something else could consist of the Gödel-Gomel-Zimmerman MOND effect I mention rather than dark matter.

The theory of the CMB power spectrum needs dark matter to fit the data.

Answer. Perhaps, but only if the CMB does consist of relic radiation from a Big Bang. Long before the BB theory, theorists such as Eddington predicted that the universe would have an overall temperature, and the value he estimated seems fairly close to what we observe, just a few degrees above absolute zero.

Dark energy is the physical evidence that the expansion of the universe is accelerating. This matches GR perfectly because a non-zero cosmological constant will cause what we measure!

Answer. Hang on, shouldn’t that read ‘the accelerating expansion of the universe is the physical evidence for dark energy’? I disagree either way, hyperspherical lensing makes distant objects look fainter than we would expect from the inverse square law. If we don’t take this into account those distant objects will appear to be accelerating away from us.
In HC the rotation of objects around the universe supplies a cosmological constant in the sense that it prevents collapse.

An irrelevant calculation. Shaula did not ask about galaxy cluster rotation. The closest Shaula comes is a question about any other lines of evidence. You have not answered that with imagining that they rotate once every 26 billion years and not producing any evidence of that rotation. I could make up that they rotate every 26 trillion years and be just as correct.

Answer. I presented that calculation for two reasons, partly to show that HC does make potentially testable predictions, and partly to show that the rotation of objects around the universe could easily pass unnoticed. Apparently the profoundly eccentric Gödel would customarily enquire of his colleagues every day ‘is the universe rotating yet’ only to be informed yet again, ‘no its not Kurt’.
Regards, Pete.

[Reality Check]

Thanks for these questions and criticisms Reality Check, I will respond below:

Your answer to IF01: What is the r in Gravity and the Photon? is not complete. r is the the distance from the center of mass outside of the mass. No one would test gravitational redshift in a mine here on Earth and expect it to match the GR prediction for gravitational redshift above the surface because the change in the gravitational field is different.
You imply you know this in your reply ("gravity within gravitationally closed spaces"). That is why your equation only applies to outside of your universe.

A "closed space with matter arranged isotopically and homogenously on the very large scale (IFO3) will have an omnidirectional curvature" guess is not an answer to the question.
IF03 IF02: Cite your evidence that galaxies in this universe are arranged so that gravitational redshift will produce cosmological redshift.
Your universe needs to have the specific arrangement of galaxies that will produce gravitational redshift that matches cosmological redshift. This means making us the center of the universe ! That probably means an ever increasing curvature of spacetime with distance from us so increasing numbers of galaxies.

Once again: Gravity and the Photon is about gravitational redshift outside of the mass.

I did not ask you questions about LCDM cosmology.

• The Big Bang singularity was mathematically real 40 years ago. Thus we excluded t = 0 from the theory because it was obvious that it broke down there. Today: There Was No Big Bang Singularity- "One thing that we can mathematically demonstrate, in fact, is that it's impossible for an inflating state to arise from a singularity.". Inflation says we cannot know whether the universe starts with a singularity or not.
• The Penrose–Hawking singularity theorems "answer the question of when gravitation produces singularities" and do not apply to LCDM cosmology.
• A fantasy that just writing hypersphere solves stuff when your idea does not even have gravity in it !
  This is a fantasy because you are (ab)using GR theory when GR has no hyperspheres. Gravitational redshift, etc. exists in this universe. What you need to show is that they exist in your universe.
• An irrelevant "rotate around the horizon at lightspeed" speculation.
• Some "more mass falls into a hypersphere" ignorance.
  By definition a universe is everything there is. Your hypersphere will contain all of the mass in the universe.
• Universe as a black hole ignorance.
  Black hole cosmology does not use the size of the observable universe (46.5 billion light-years) which is much larger than the Hubble radius (14.4 billion light years).
  The mass in the observable universe being close to that of a black hole with the Hubble radius is thought to be a coincidence. The universe is also known to be larger than the observable universe so the mass does not give a black hole with the Hubble radius.
• A "Many physicists and mathematicians feel uneasy about renormalisation" rumor.
• You still do not understand galaxy rotation curves or the colliding galaxy clusters.
  Galaxy rotation curves do not fit calculations from Newtonian gravitation. There must be more matter than what is visible.
  The evidence for dark matter from colliding galaxy clusters does not add anything. Gravitational lensing is used to map all of the matter in the clusters.
• A "Gödel-Gomel-Zimmerman MOND effect" fantasy.
  There is no such effect.
  An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation (Kurt Gödel, 1 July 1949) is a solution with particles[ that have rotation. This leads to "Matter everywhere rotates relative to the compass of inertia with the angular velocity:". So a galaxy would have angular velocity. This is irrelevant to galaxy rotation curves (stars with different velocities in their orbits).
  The Discrepancy in Galaxy Rotation Curves by Gomel and Zimmerman (5 August 2019) is an unpublished preprint. More importantly, this is not MOND. It is a speculation that astronomers have been ignorant about physics for the past 50 years!
• More ignorance about the CMB!
  The physical properties of the CMB means that it is cosmic, i.e. "relic radiation from a Big Bang": nearly perfect black body spectrum that cannot come from any current objects, a temperature that varies as predicted with time, imprint of galaxy clusters, etc.
  Eddington calculated an effective temperature of starlight in the Milky Way in a book about stars. Read CMB: Thermal (non-microwave background) temperature predictions. Eddington's Temperature of Space explains why this is nothing to do with the CMB.
• A "hyperspherical lensing" making distant objects look fainter fantasy
  We measure that the expansion of the universe is accelerating. We call this effect dark energy. The cosmological constant is GR is the best cause. It is not a "misfit" wit GR. It is a fit with GR!
  The first evidence for dark energy came from supernovae.
  

  In 1998, the High-Z Supernova Search Team[20] published observations of Type Ia ("one-A") supernovae. In 1999, the Supernova Cosmology Project[21] followed by suggesting that the expansion of the universe is accelerating.[28] The 2011 Nobel Prize in Physics was awarded to Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess for their leadership in the discovery.[29][30]

  Distances to Type 1a supernovae are found by measuring how their light varies. This gives their intrinsic brightness. Their measured brightness gives their distance. This is a robust method confirmed by other techniques.

[Peter J Carroll]

There seems little point in clouding this debate with invective and I will thus ignore your six accusations of ignorance and fantasy, but thank you anyway for these questions and criticisms Reality Check, I will respond below: -

Your answer to IF01: What is the r in Gravity and the Photon? is not complete. r is the the distance from the center of mass outside of the mass. No one would test gravitational redshift in a mine here on Earth and expect it to match the GR prediction for gravitational redshift above the surface because the change in the gravitational field is different.
You imply you know this in your reply ("gravity within gravitationally closed spaces"). That is why your equation only applies to outside of your universe.
A "closed space with matter arranged isotopically and homogenously on the very large scale (IFO3) will have an omnidirectional curvature" guess is not an answer to the question.

Answer: If you measure gravity inside anything you will get a contribution from absolutely everything that surrounds you. The HC equation, now with the gravity clearly shown, reflects this and makes the specific prediction of an omnidirectional curvature that acts as an omnidirectional deceleration which is a testable prediction.

IF03 IF02: Cite your evidence that galaxies in this universe are arranged so that gravitational redshift will produce cosmological redshift.
Your universe needs to have the specific arrangement of galaxies that will produce gravitational redshift that matches cosmological redshift. This means making us the center of the universe ! That probably means an ever increasing curvature of spacetime with distance from us so increasing numbers of galaxies.

Answer. Indeed, it does make us the centre of the universe, but we have no privileged position. All observers within a hypersphere can consider themselves at the centre of their observable universe in the same way that any observer on the surface of an ordinary sphere can consider herself at the centre of that surface. The observable universe consists of the three dimensional ‘surface’ of the hypersphere, its ‘fourth dimension’ only appears to us as its curvature.

Once again: Gravity and the Photon is about gravitational redshift outside of the mass.

Answer. Indeed so, but it shows a relationship between frequency and one minus GM/c^2 from which I have derived a formula for a relationship between wavelength and surrounding matter. This acts as another specific and testable prediction of HC.


I did not ask you questions about LCDM cosmology.

Answer. If you assert that the assertions of LCDM falsify HC, then I have to interpret those assertions as questions to answer.

The Big Bang singularity was mathematically real 40 years ago. Thus we excluded t = 0 from the theory because it was obvious that it broke down there. Today: There Was No Big Bang Singularity- "One thing that we can mathematically demonstrate, in fact, is that it's impossible for an inflating state to arise from a singularity.". Inflation says we cannot know whether the universe starts with a singularity or not.

Answer. To quote from the final paragraph of that article:

There may have been a singularity at the very beginning of space and time, with inflation arising after that, but there's no guarantee. In science, there are the things we can test, measure, predict, and confirm or refute, like an inflationary state giving rise to a hot Big Bang. Everything else? It's nothing more than speculation.

Okay, so if a hypothetical singularity is incompatible with a hypothetical inflation then one or both hypotheses must go. Inflation was devised to explain the horizon problem inherent in the big bang hypothesis and has since become extended to avoid the embarrassment of a singularity. However, inflation makes even more extreme and complicated claims about initial conditions in the universe than singularity and an application of Occam’s razor does not favour it.


The Penrose–Hawking singularity theorems "answer the question of when gravitation produces singularities" and do not apply to LCDM cosmology.

A fantasy that just writing hypersphere solves stuff when your idea does not even have gravity in it !
This is a fantasy because you are (ab)using GR theory when GR has no hyperspheres. Gravitational redshift, etc. exists in this universe. What you need to show is that they exist in your universe.
An irrelevant "rotate around the horizon at lightspeed" speculation.

Answer. If LCDM purports to describe the evolution and structure of the universe then surely it must either encompass or refute singularity theorems, or do you propose that inflation refutes cosmic singularity but that singularities can still form within blackholes?

Gravity does now appear explicitly in the HC redshift derivation, at your request.

Rotation around the horizon at lightspeed is a specific testable prediction of HC, 0.005 arcseconds per century.

Some "more mass falls into a hypersphere" ignorance.
By definition a universe is everything there is. Your hypersphere will contain all of the mass in the universe.

Answer. Well of course the universe consists of everything, by definition. I thought it abundantly clear that ‘more mass falling into a hypersphere’ meant more mass falling into a black hole within the universe as all black holes will consist of hyperspheres if they are spatially closed. More mass falling into a black hole/hypersphere will obviously make its event horizon expand, it can never have a size below what its mass dictates.

Universe as a black hole ignorance.
Black hole cosmology does not use the size of the observable universe (46.5 billion light-years) which is much larger than the Hubble radius (14.4 billion light years).
The mass in the observable universe being close to that of a black hole with the Hubble radius is thought to be a coincidence. The universe is also known to be larger than the observable universe so the mass does not give a black hole with the Hubble radius.

Answer. I dispute that the observable universe is KNOWN to have a size of 46.5 bnlyr. That figure arises from the questionable assumption of the expansion hypothesis which all depends on the redshift = recession velocity assumption.

A "Many physicists and mathematicians feel uneasy about renormalisation" rumor.

Answer. https://www.quantamagazine.org/how-r...sics-20200917/

Feel the unease.

You still do not understand galaxy rotation curves or the colliding galaxy clusters.
Galaxy rotation curves do not fit calculations from Newtonian gravitation. There must be more matter than what is visible.
The evidence for dark matter from colliding galaxy clusters does not add anything. Gravitational lensing is used to map all of the matter in the clusters.

A "Gödel-Gomel-Zimmerman MOND effect" fantasy.
There is no such effect.

Answer. Do you have a specific criticism of the Gomel-Zimmerman paper or the Gödel paper?

An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation (Kurt Gödel, 1 July 1949) is a solution with particles[ that have rotation. This leads to "Matter everywhere rotates relative to the compass of inertia with the angular velocity:". So a galaxy would have angular velocity. This is irrelevant to galaxy rotation curves (stars with different velocities in their orbits).

Answer. Gödel’s paper models a dust solution. It shows that all particles will have an angular velocity about each other. For the universe this means that all the distinct galaxies or galactic structures which are not strongly gravitationally bound to each other will slowly swirl around each other. Stars within a galaxy will have various angular momentums around the central core due to Newtonian/Relativistic mechanics, to which if we add a component of angular momentum specified by Gödel, we can obtain values which match observations.

The Discrepancy in Galaxy Rotation Curves by Gomel and Zimmerman (5 August 2019) is an unpublished preprint. More importantly, this is not MOND. It is a speculation that astronomers have been ignorant about physics for the past 50 years!

More ignorance about the CMB!
The physical properties of the CMB means that it is cosmic, i.e. "relic radiation from a Big Bang": nearly perfect black body spectrum that cannot come from any current objects, a temperature that varies as predicted with time, imprint of galaxy clusters, etc.

Eddington calculated an effective temperature of starlight in the Milky Way in a book about stars. Read CMB: Thermal (non-microwave background) temperature predictions. Eddington's Temperature of Space explains why this is nothing to do with the CMB.

Answer. I quote directly from that article:

“The near equality of the energy densities of starlight (Eddington's blue curve) and the CMB is just a coincidence.”

It only remains just another coincidence under the maintenance of the redshift = expansion assumption.

A "hyperspherical lensing" making distant objects look fainter fantasy
We measure that the expansion of the universe is accelerating. We call this effect dark energy. The cosmological constant is GR is the best cause. It is not a "misfit" wit GR. It is a fit with GR!

The first evidence for dark energy came from supernovae.
In 1998, the High-Z Supernova Search Team[20] published observations of Type Ia ("one-A") supernovae. In 1999, the Supernova Cosmology Project[21] followed by suggesting that the expansion of the universe is accelerating.[28] The 2011 Nobel Prize in Physics was awarded to Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess for their leadership in the discovery.[29][30]

Distances to Type 1a supernovae are found by measuring how their light varies. This gives their intrinsic brightness. Their measured brightness gives their distance. This is a robust method confirmed by other techniques.

Answer. Permit me to clarify. All type 1a supernovae are presumed to have the same intrinsic brightness, permitting their use as ‘standard candles’. Perlmutter’s team collected measurements of their apparent magnitudes and their redshifts.

When they turned the apparent magnitudes into distances, they found that as redshifts increased the distances seemed to increase in an exponential rather than a linear manner. This led to the idea of an accelerating expansion and the hypothesis of a dark energy to somehow account for it.

I have reprocessed the raw data here:

https://www.specularium.org/hypersph...here-cosmology

To show that if we take the curvature of the entire universe into account, we can correct the distances calculated by Perlmutter and recover a linear relationship between redshifts and actual distances, and from this we can calculate the actual size of the universe. Perlmutter had only calculated apparent distances from apparent magnitudes.
Regards, Pete.

Incidentally, I would also welcome observations and questions and falsifications of the HC hypothesis from other experts here on this forum. Don’t be shy.

I suspect that current observations can falsify neither LCDM nor HC conclusively, and whilst HC may appear radical and offensive to some people’s beliefs, it at least has Occam’s razor on its side, as it is far simpler.

[Reality Check]

There seems little point in clouding this debate with invective and I will thus ignore your six accusations of ignorance and fantasy, but thank you anyway for these questions and criticisms Reality Check, I will respond below: ....

You are ignoring what the answer to IF01: What is the r in Gravity and the Photon? means. You applied this equation for gravitational redshift outside of a mass to inside your universe. That makes your equation invalid.
ETA: You are also using a GR result when you have no evidence that GR exists io your HC. GR works with a geometry that is not hyperspheres. Solutions of GR state that the universe must expand, contract or be static (but not stable).

Still no answer to IF02: Cite your evidence that galaxies in this universe are arranged so that gravitational redshift will produce cosmological redshift. This is nothing to do with a universe that is a hypersphere. It is the physical arrangement of galaxies needed in this universe to produce cosmological redshift from GR's gravitational redshift. This is the equation you are using.

You repeat your error that an equation only valid outside of a mass can be applied inside a mass !

Inflation was not "extended" to exclude a singularity. As in There Was No Big Bang Singularity It is basic math - an exponential increase when reversed never gets to 0.
Inflation was not just "devised to explain the horizon problem". Guth was investigating why there were no magnetic monopoles seen today. Inflation also solves are the horizon and flatness problems. Inflation is a scientific theory that makes predictions that match our universe.
Ignorance about Occam’s razor (the scientific use is that if you have 2 competing theories that are give the same results, favor the one with the fewer entities).

Try reading Penrose–Hawking singularity theorems.

Hawking's singularity theorem is for the whole universe, and works backwards in time: it guarantees that the (classical) Big Bang has infinite density.[2] This theorem is more restricted and only holds when matter obeys a stronger energy condition, called the dominant energy condition, in which the energy is larger than the pressure. All ordinary matter, with the exception of a vacuum expectation value of a scalar field, obeys this condition. During inflation, the universe violates the dominant energy condition, and it was initially argued (e.g. by Starobinsky[3]) that inflationary cosmologies could avoid the initial big-bang singularity. However, it has since been shown that inflationary cosmologies are still past-incomplete,[4] and thus require physics other than inflation to describe the past boundary of the inflating region of spacetime.

My emphasis added.

"Gravity does now appear explicitly in the HC redshift derivation" ignorance. Invalidly applying gravitational redshift derived from GR which has no hyperspheres is not a derivation or gravity.
IF03: Show how you derive GR in HC so that you can then use gravitational redshift inside a mass, Peter J Carroll.

Big Bang "all depends on the redshift = recession velocity assumption" ignorance. If we ignore cosmological redshift, there still is an overwhelming body of other evidence for an expanding universe starting with Olbers' paradox.
Frequently Asked Questions in Cosmology: What is the evidence for the Big Bang?

An ignorant citation of How Mathematical ‘Hocus-Pocus’ Saved Particle Physics. There were doubts about renormalization 60 years ago when it was being developed. The article is about the removal of those doubts.

The "Gödel-Gomel-Zimmerman MOND effect" is a fantasy because the papers you cite are not about MOND, neither is about your HC, one is not even about galaxy rotation curves, and one is not even a paper !
An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation (Kurt Gödel, 1 July 1949).
The Discrepancy in Galaxy Rotation Curves by Gomel and Zimmerman (5 August 2019).
IF04a: Cite where in Gödel's paper he uses a hypersphere as in your HC (hint: what is the title?), Peter J Carroll.
IF04b: Cite where in Gödel's paper he derives a varying rotation with distance from a center as in galaxy rotation curves, Peter J Carroll.
IF04c: Cite where in Gomel and Zimmerman they uses a hypersphere as in your HC, Peter J Carroll.
IF04d: Why is a groundbreaking paper (Gomel and Zimmerman showing dark matter does not explain galaxy rotation curves) not published at all (), especially in a high impact journal, Peter J Carroll.

A "if we add a component of angular momentum specified by Gödel, we can obtain values which match observations" assertion so
IF05: Show how adding Gödel's angular momentum produces galaxy rotation curves that match observations, Peter J Carroll.
Note that Gomel and Zimmerman do not cite or use Gödel.

An irrelevant quote Eddington's Temperature of Space which shows that Eddington's calculation is not about the CMB

Misconception about type 1a supernovae ("presumed to have the same intrinsic brightness"). Type 1a supernovae are known to have same peak magnitude! Textbook astrophysics shows the white dwarfs will explode at about the same mass. Closer supernovae can have their distances measured by other means and we see that the distances match.

Type 1A supernovae and Hypersphere Cosmology is nonsense because it uses HyperSphere Cosmology. That is a obviously invalid cosmology.
You have not shown that GR exists in a hypersphere universe and you use results from GR ("This derived from General Relativity") !
You have an obviously irrelevant hypersphere volume. This is a hypersphere. It has points at a constant distance from the center with no points inside it. Any hypersphere universe is on the "surface" where all the spacetime points are.

[Shaula]

Thanks for looking it all over Shaula, I look forward to your analysis. One other line of supporting evidence perhaps lies in something that cosmologists usually dismiss as a mere coincidence at this epoch of the universe; for the observed baryonic matter and the apparent size of the observable universe, M/r ~ c^2/G.
We may have evidence of hyperspherical geometry in the 'lab' of the solar system, I don't think Anderson feels entirely satisfied with the thermal recoil explanation of the Pioneer Anomaly, plus the Fly-By Anomaly may arise from the boost to orbital motion that HC predicts, although the data there looks all over the place.

So a few points I've not seen you address:

Using E=mc2 for the photon is never going to work. It is a zero term. Don't care how much you like the result. Ditto p=mv.
The Pioneer anomaly is a deceleration, you predict an acceleration. So your supporting evidence from the solar system ''lab' isn't supportive.
You have no independend proof for L so it remains a fitted parameter. Your ideas can probably replicate most observations with enough free parameters you cannot test via other means.
Stereographic projections are angle but not area or distance preserving. Given the isotropy we observe in the 'projected' universe this calls for a very strange distribution of matter in higher dimensions - if indeed there is one that works for all observers. Why do we see isotropy?
You still haven't addressed the issue that a fixed acceleration doesn't work. It is largely why MOND has had so many issues. So your ideas might work for a few of the more standard galaxies but won't work for most or for clusters.

Overall I don't see that much has changed since your last thread - your ideas have the same or similar issues. You have not presented any detailed tests (mostly it is just-so stories or assertions as far as I can see). You propose a difficult test that will require years of data collection and stop there - I can't believe that there are not more tests we can perform. So I don't find what you have done that compelling so far.

[Peter J Carroll]

I will divide my answers to the last two posts into three posts as they seem individually too big to post.

Thank you for your points and questions Reality check, replies below: -

IF03: Show how you derive GR in HC so that you can then use gravitational redshift inside a mass, Peter J Carroll.

Answer. To my knowledge nobody before has attempted to calculate gravitational redshift inside of a gravitationally closed space, my formula thus acts as a PREDICTION, and as this prediction appears coherent with the rest of the hypothesis and observational data interpreted via the HC hypothesis.

Big Bang "all depends on the redshift = recession velocity assumption" ignorance. If we ignore cosmological redshift, there still is an overwhelming body of other evidence for an expanding universe starting with Olbers' paradox.
Frequently Asked Questions in Cosmology: What is the evidence for the Big Bang?

Answer: Olber’s paradox does not create a problem in HC, the HC universe is not infinite, it is finite but unbounded, rather like the surface of a sphere but in 3 dimensions instead of two. (see the visualisation model at the end of this post). Besides, redshift in proportion to actual distance and hyperspherical lensing also prevent the amount of light reaching an observer from all over the universe rising to ridiculous levels.

An ignorant citation of How Mathematical ‘Hocus-Pocus’ Saved Particle Physics. There were doubts about renormalization 60 years ago when it was being developed. The article is about the removal of those doubts.

Answer. I’d rather not become diverted too far into quantum field theory here, but one might easily interpret that article as saying physicists eventually just got used to formulae that worked, no matter how strange they looked. This seems highly characteristic of the ‘shut up and calculate’ school of Copenhagen Interpretation – don’t ask about the fundamental reality because it seems impossibly weird, just use the formulae and the recipes we have cooked up by very odd mathematical means.

The "Gödel-Gomel-Zimmerman MOND effect" is a fantasy because the papers you cite are not about MOND, neither is about your HC, one is not even about galaxy rotation curves, and one is not even a paper !
An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation (Kurt Gödel, 1 July 1949).

Answer. No, but Gödel’s insight seems particularly adaptable to HC and MOND, fields he wasn’t aware of when he wrote it.

The Discrepancy in Galaxy Rotation Curves by Gomel and Zimmerman (5 August 2019).
IF04a: Cite where in Gödel's paper he uses a hypersphere as in your HC (hint: what is the title?), Peter J Carroll.

IFO4 Answer. Again, No, but Gödel’s insight seems particularly adaptable to HC and MOND, fields he wasn’t aware of when he wrote it. Plus, it makes predictions consistent with the rest of the HC hypothesis, and current observations interpreted through the hypothesis.

IF04b: Cite where in Gödel's paper he derives a varying rotation with distance from a center as in galaxy rotation curves, Peter J Carroll.

IFO4b Answer. He calculated w = 2sqrt pi G d where w = angular velocity, you can apply that w as acting on anything that rotates about anything chosen as a centre. This makes only an infinitesimal difference at planetary scales but a significant difference on the scale of galaxies, and a big difference on the scale of the entire universe.

IF04c: Cite where in Gomel and Zimmerman they uses a hypersphere as in your HC, Peter J Carroll.

IFO4c Answer. They didn’t, but I sent them my paper and the idea that the “galaxies local inertial frames” which they identify as the missing component in galactic rotation curves corresponds exactly to the Gödelian rotation if you consider the entire galaxy, newly discovered spherical gas halos and all, in calculating d, density. They expressed positive interest and said they were continuing their work; I do not know whether they will add the idea eventually or not.

IF04d: Why is a groundbreaking paper (Gomel and Zimmerman showing dark matter does not explain galaxy rotation curves) not published at all ( ), especially in a high impact journal, Peter J Carroll.

IFO4d Answer. I expect the ferocious guardians of orthodoxy would not let a paper like that through on its own because whilst it may make sense it also breaks a lot of the rest of the orthodox LCDM cannon by implication, and they have not addressed that.

The LCDM will only break if a lot of it goes at once.

A "if we add a component of angular momentum specified by Gödel, we can obtain values which match observations" assertion so
IF05: Show how adding Gödel's angular momentum produces galaxy rotation curves that match observations, Peter J Carroll.

IFO5 Answer. https://www.specularium.org/componen...lum-m33-galaxy Here I calculate the value at which the curve goes flat. When my consulting mathematician drops in sometime after covid I’ll get him to run a dataset through a suitable program. Good idea RC. I did do the same calculation for Andromeda which has also been shown to have a vast gas halo and got s similarly satisfying result, I’ll try and find the piece of paper.

Note that Gomel and Zimmerman do not cite or use Gödel.

Answer. Not yet, See IFO4c.

An irrelevant quote Eddington's Temperature of Space which shows that Eddington's calculation is not about the CMB

Answer. Indeed not, the idea didn’t exist then, but the energy equality between the temperature of space, the black hole non expanding universe equality, and a lot of the material in the Dirac Large Numbers hypothesis provide three interesting very ‘coincidences’.

Misconception about type 1a supernovae ("presumed to have the same intrinsic brightness"). Type 1a supernovae are known to have same peak magnitude! Textbook astrophysics shows the white dwarfs will explode at about the same mass. Closer supernovae can have their distances measured by other means and we see that the distances match.

Answer. Yes indeed an intrinsic peak brightness corresponding to -19.3 magnitude at 10 parsecs corresponding to a luminous flux of 1.9055 e11 Janskys.

Type 1A supernovae and Hypersphere Cosmology is nonsense because it uses HyperSphere Cosmology. That is a obviously invalid cosmology.
You have not shown that GR exists in a hypersphere universe and you use results from GR ("This derived from General Relativity") !
You have an obviously irrelevant hypersphere volume. This is a hypersphere. It has points at a constant distance from the center with no points inside it. Any hypersphere universe is on the "surface" where all the spacetime points are.

Answer. I will provide a short piece at the end that shows how we can visualise the geometry inside a glome style hypersphere to help clear up difficulties and misconceptions.

[Peter J Carroll]

Shaula, thank you for your questions and observations, answers below:

So a few points I've not seen you address:

Using E=mc2 for the photon is never going to work. It is a zero term. Don't care how much you like the result. Ditto p=mv.

Answer. I have now upgraded Equation 6 in the main paper

https://www.specularium.org/hypersphere-cosmology

to show he effect in terms of gravity. I left the dA/c^2 bit in as it provides an intuitive picture of what happens.

The Pioneer anomaly is a deceleration, you predict an acceleration. So your supporting evidence from the solar system ''lab' isn't supportive.

Answer, perhaps I have used the word acceleration loosely in places to also mean negative accelerations, it always acts as a deceleration.

You have no independent proof for L so it remains a fitted parameter. Your ideas can probably replicate most observations with enough free parameters you cannot test via other means.

Answer. L arises from calculations based on measured redshifts and apparent magnitudes. Put an arbitrary value of L in and run those calculations backwards and silly values of Z and distance will result. That L came out close to the Hubble distance came as a great relief, but not a surprise.

Stereographic projections are angle but not area or distance preserving.

Answer. The projection I have used to derive equation 16 here:

https://www.specularium.org/hypersphere-cosmology

Is based on a model in one fewer dimensions, the projection of a sphere on to a plane. Imagine a wire frame sphere with the wires representing lines of latitude and longitude. Place it on a sheet of paper, south pole down. Place a lightbulb just inside the tiny ring at the north pole, the shadows on the paper plane below show a projection of the sphere to a plane, the southern hemisphere will appear only slightly extended, the northern hemisphere progressively more so, the north pole (the antipode to the south) will go right off a sheet of paper of any size.

Given the isotropy we observe in the 'projected' universe this calls for a very strange distribution of matter in higher dimensions - if indeed there is one that works for all observers. Why do we see isotropy?

Answer. In HC all matter lies in 3D space, but that space has a curvature in all directions which renders it closed. See the bit at the end. I think it likely that galaxies will appear less frequent at very high redshifts but that’s only because we see space more spread out at cosmic distances because of the lensing from the curvature of the whole hypersphere.

You still haven't addressed the issue that a fixed acceleration doesn't work. It is largely why MOND has had so many issues. So your ideas might work for a few of the more standard galaxies but won't work for most or for clusters.

Answer. Equation 9 does not show a fixed acceleration. It shows the result of taking the classically expected angular velocity at any radius of a galaxy and then adding an angular velocity factor calculated for the entire galaxy. Gomel and Zimmerman attribute this factor to that galaxy’s ‘unique inertial frame’ and which I attribute to its Gödelian rotation.

Overall, I don't see that much has changed since your last thread - your ideas have the same or similar issues. You have not presented any detailed tests (mostly it is just-so stories or assertions as far as I can see). You propose a difficult test that will require years of data collection and stop there - I can't believe that there are not more tests we can perform. So I don't find what you have done that compelling so far.

Answer. Yes, so far, I can only think of a rigorous re-run of Pioneer with high quality telemetry, or a long wait to look for a mere 0.005 – 0.01 arcsecond/century rotation. Maybe someone will spot another possible test before we finish this thread.

[Peter J Carroll]

Please respect my copyright on this piece, I'm writing a book.


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. (1)
We usually think of black holes as regions of space containing a great deal of highly compressed matter at enormous densities, however really 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.

[Peter J Carroll]

I hope that you have all had a good weekend.

It seems to me that: -

1) LCDM and HC both remain unfalsified.

2) LCDM and HC both remain falsifiable.

5) LCDM has the weight of authority behind it but HC has Occam’s razor behind it because ‘entities should not be multiplied without necessity’ and it does without singularity, inflation, expansion, dark matter or dark energy, at the small price of a small positive spacetime curvature, a rotation, and a novel gravitational redshift.

4) We perhaps need to run some calculations and Reality Check has implied something we could do here to provide more hard evidence either way.

5) May I suggest that we create rotation curves for the nearby galaxies of Andromeda and Triangulum which have been recently shown to have vast gas halos, using Equation 9 from the main paper here https://www.specularium.org/hypersphere-cosmology
For this we would just need datasets on the expected rotation of the baryonic stellar matter at various radii, plus also the observed rotation figures.
As it seems a four figure IQ is required to use excel equation syntax and my mathematician friend is stuck in Australia, would someone care to run the calculation?

Regards, Pete.

[Shaula]

1) LCDM and HC both remain unfalsified.
2) LCDM and HC both remain falsifiable.

Actually when you said that each galaxy has its own "unique intertial frame" that you calculcate independently of any considerations of the Hypersherical universe your ideas became lagely unfalsifiable. What you have said that you can find fitting parameters for any case. Well, yes. I am sure you can. It doesn't lead to anything predictive or falsifiable. Meanwhile LCDM provides a way to test the predictions because you can look for the effects of the extended DM halo through tests like weak lensing and modelling the dynamics of the system.

I'd also say that the HC is unfalsified because you have not really given any predictions other than this almost unmeasurable rotation factor for clusters. You are acting as if the HC idea has passed anything like the number of tests that LCDM has - it really hasn't.

5) LCDM has the weight of authority behind it but HC has Occam’s razor behind it because ‘entities should not be multiplied without necessity’ and it does without singularity, inflation, expansion, dark matter or dark energy, at the small price of a small positive spacetime curvature, a rotation, and a novel gravitational redshift.

No, LCDM has a large corpus of work done to test it. Your idea has one prediction and a lot of arbitrary fitting. Any idea that is not worked out in detail looks simple - applying Occam here is a very poor argument. As many have pointed out the singularity you harp on about isn't part of the theory. And your energy sapping effects of spacetime have not been shown to avoid the pitfalls of tired light theories. Dispersion and the lack of evidence for an intrinsic radshift in the galaxy which, if the effect is so large that we see it impacting the Pioneer measurements it would be strange to then not see if for galactic objects. Again, consistent numbers throughout the thread would have helped.

It is definitely a false equivalence to put HC next to LCDM as you have - they are not at anything like the same stage of testing or development.

4) We perhaps need to run some calculations and Reality Check has implied something we could do here to provide more hard evidence either way.

It has been done extensively for the LCDM theory. And "You need to do some calculations" was essentially what you were told in the last thread. Getting to the end of this one and saying "Oh, goodness, maybe I should have actually treated my ideas like a scientific theory and tested them" implies that you didn't really listen last time.

5) May I suggest that we create rotation curves for the nearby galaxies of Andromeda and Triangulum which have been recently shown to have vast gas halos, using Equation 9 from the main paper here https://www.specularium.org/hypersphere-cosmology
For this we would just need datasets on the expected rotation of the baryonic stellar matter at various radii, plus also the observed rotation figures.
As it seems a four figure IQ is required to use excel equation syntax and my mathematician friend is stuck in Australia, would someone care to run the calculation?

It is your idea - you should probably have done this before reopening the discussion. Instead of coming back with evidence you have come back with more assertions, some dodgy equations (no, I'm not forgiving your use of E=mc2) and walls of text about what you think will happen. What we needed were predictions and tests. Numerical predictions that show a scientific theory or model working.

I'm not going to claim your ideas as obviously wrong - I don't feel like you have given us enough insight into the model here to evaluate it (and no, I am not going to your site to get the paper - rules are you present it here). You have made a lot of claims and not really backed them up. So I'd say your ideas remain unproven and I don't see enough detail here to allow any one to independently use them.