Hyperspherical Universe without Singularities.

[Reality Check]

In Answer to your points Reality Check, ...

Wrong, Peter J Carroll. Yes, black dwarfs are hard to detect. No, black dwarfs are not black holes! As in the Wikipedia article you did not read: Black dwarfs should not be confused with black holes or black stars. The difficulty would be measuring their temperature.
Irrelevant derail about gas halos. You still have a fantasy that gas haloes around galaxies are "recycling yards" when they are just clouds of gas [and dust]!
Another display of ignorance about astronomy. Most stars having planets is expected from textbook astrophysics.
A repeat of your "recycling" fantasy.

ETA:
IF08a: What process in a gas halo "recycles" heavy elements into whatever you think they end up as (cite the textbook physics), Peter J Carroll?
IF08b: Show that this decreases entropy, Peter J Carroll, as your Entropy! post implies.

There is probably mainstream recycling here. Much of the gas halo will be hydrogen, helium and lithium around since the Big Bang. There is gas and dust blown out from the host galaxy. That will contain stellar material. The gas halo does not have stars itself but some of it may fall into the galaxy to form stars there. Hubble Maps Giant Halo Around Andromeda Galaxy

Thus, I cannot venture a quantitative answer to your IFOs 6 & 7.

Nothing to do with what went before and I did not ask for quantitative answers.
IF06: Where are the stars that are enormously older than 13.8 billion years, Peter J Carroll? (e.g. a trillion years old)
IF07: Why are stars still being formed in your "unbounded in both space and time" universe, Peter J Carroll?
If you cannot explain the answers in words then the lack of enormously old stars and the fact that stars are still forming debunk your idea. The universe cannot be unbounded in time because there is a observed boundary in time and there is still hydrogen being formed into stars. It only takes 10^14 years for star formation to stop when the availability of H falls too low.

A "you and I both found conflicting quotes about the Schwarzschild metric in the same article" lie when you have never mentioned anything in that article and I did not find any conflict. This is textbook physics which everyone who want to learns. The Schwarzschild metric is for the outside of a massive spherical body.
A repeat of the idiocy of HC using the Schwarzschild metric when you know that it is only valid outside of a massive spherical body, Peter J Carroll.

The "The" in

The Friedmann–Lemaître–Robertson–Walker metric is the "exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected.[1][2][3]" used in the Big Bang.

is that the metric is the one and only solution for a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected. I did not want to mess around with the quote to make this explicit. In any case, you should know this already because this is textbook cosmology !

[Peter J Carroll]

Wrong, Peter J Carroll. Yes, black dwarfs are hard to detect. No, black dwarfs are not black holes! As in the Wikipedia article you did not read: Black dwarfs should not be confused with black holes or black stars. The difficulty would be measuring their temperature.
Irrelevant derail about gas halos. You still have a fantasy that gas haloes around galaxies are "recycling yards" when they are just clouds of gas [and dust]!
Another display of ignorance about astronomy. Most stars having planets is expected from textbook astrophysics.
A repeat of your "recycling" fantasy.

ETA:
IF08a: What process in a gas halo "recycles" heavy elements into whatever you think they end up as (cite the textbook physics), Peter J Carroll?
IF08b: Show that this decreases entropy, Peter J Carroll, as your Entropy! post implies.

There is probably mainstream recycling here. Much of the gas halo will be hydrogen, helium and lithium around since the Big Bang. There is gas and dust blown out from the host galaxy. That will contain stellar material. The gas halo does not have stars itself but some of it may fall into the galaxy to form stars there. Hubble Maps Giant Halo Around Andromeda Galaxy


Nothing to do with what went before and I did not ask for quantitative answers.
IF06: Where are the stars that are enormously older than 13.8 billion years, Peter J Carroll? (e.g. a trillion years old)
IF07: Why are stars still being formed in your "unbounded in both space and time" universe, Peter J Carroll?
If you cannot explain the answers in words then the lack of enormously old stars and the fact that stars are still forming debunk your idea. The universe cannot be unbounded in time because there is a observed boundary in time and there is still hydrogen being formed into stars. It only takes 10^14 years for star formation to stop when the availability of H falls too low.

A "you and I both found conflicting quotes about the Schwarzschild metric in the same article" lie when you have never mentioned anything in that article and I did not find any conflict. This is textbook physics which everyone who want to learns. The Schwarzschild metric is for the outside of a massive spherical body.
A repeat of the idiocy of HC using the Schwarzschild metric when you know that it is only valid outside of a massive spherical body, Peter J Carroll.

The "The" in

is that the metric is the one and only solution for a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected. I did not want to mess around with the quote to make this explicit. In any case, you should know this already because this is textbook cosmology !

IFO8a. Many ‘facts’ in cosmology have a remarkably short half-life and many ‘facts’ in textbook physics have even shorter ones because they take a while to write and publish. The massive gas/dust halo material has only just appeared in papers.

IFO8b. If there is exchange of material between stars and their surrounding space, I’d need to know first which direction of movement raises the entropy in your book, before answering.

IFOs 6&7. Okay in words then, Firstly I dispute that there is an ‘observed boundary in time’ to me it appears as an ‘observed horizon’ in time, (and space). We cannot tell how old black holes are, cosmologists try extremely hard to interpret the ages of all stars and other structures to within the supposed temporal boundary. The concept of n-th generational stars muddies the waters. I see no problem in some processes showing evidence of having taken more than horizon length time. I see no problem in stars forming at any time, there now seems plenty of starting material in circulation. The discovery of a Black Dwarf star could provide supporting evidence for HC.

Well, we both have quotes supporting our case from the same article. We will have to agree to differ. Using the metric within the event horizon does seem to give results consistent with the rest of the HC model.

Yes, and the Gödel metric is one solution for a homogeneous, isotropic, rotating, non- expanding, non-contracting universe that is path-connected, but not necessarily simply connected.

Like many items of rigorous mathematics with no obvious use, it has lain like a buried sword awaiting its rediscovery and application.

Here on ‘Against the Mainstream’ we debate ideas that question the textbooks, thus the assertion that something ‘is textbook cosmology’ does not in itself constitute an argument.

(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.)

I look forward to comment and criticism of the last five equations I posted. These appear at the very end of the previous page (2) of this thread.

Regards, Pete.

[Copernicus]

The matter in the universe is not too old. The entropy is low. How is that explained in your theory?

[Peter J Carroll]

The matter in the universe is not too old. The entropy is low. How is that explained in your theory?

The Bekenstein-Hawking black hole conjecture states that the information/entropy of a black hole corresponds to its surface area measured in Planck units.

Equation 12 shows the entropy/information content for the universe considered as a similarly closed space. The entropy of both should remain constant.

The sky is cold, the stars are hot, plainly the entropy remains fairly low as you observe.

Now if 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 I simply assert that it must have some ongoing processes which increase entropy and some which do the opposite, and which between them maintain an overall constant entropy. In the last few posts I have tried to identify a few of them, but I suspect gravitation itself supplies the main entropy reversing mechanism.

The principle of ever increasing 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 if you have a really vast amount of gas it 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.

Regards, Pete.

[Reality Check]

IFO8a. ...irrelevancy snipped...
IFO8b. ...irrelevance and ignorance (see below) snipped...
IFOs 6&7. ...irrelevance and ignorance (see below) snipped...

Leaving
IF06: Where are the stars that are enormously older than 13.8 billion years, Peter J Carroll? (e.g. a trillion years old)
IF07: Why are stars still being formed in your "unbounded in both space and time" universe, Peter J Carroll?
IF08a: What process in a gas halo "recycles" heavy elements into whatever you think they end up as (cite the textbook physics), Peter J Carroll?
IF08b: Show that this decreases entropy, Peter J Carroll, as your Entropy! post implies.

What seems to be a "we both have quotes" lie when you have given no quote!
IF09: Link to your quote in this thread or the Wikipedia article stating that the Schwarzschild metric is valid inside a massive object, i.e. this universe, Peter J Carroll.
Read again what I wrote: The the Schwarzschild metric is only valid outside of a massive spherical body.
Read again what the Schwarzschild metric article states.

In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild vacuum or Schwarzschild solution) is the solution to the Einstein field equations that describes the gravitational field outside a spherical mass....
The Schwarzschild metric is a solution of Einstein's field equations in empty space, meaning that it is valid only outside the gravitating body. That is, for a spherical body of radius R the solution is valid for r>R}.

This clear English means that the metric cannot be applied where there is matter. You can only use it in your cosmology if your universe has no matter or an irrelevant use outside what is then is a "universe" !

FYI: The Schwarzschild metric is valid for black holes excluding the coordinate singularity at the Schwarzschild radius and the central singularity. This is still a solution of Einstein's field equations in empty space. There is a different interior Schwarzschild solution for the "interior of a non-rotating spherical body which consists of an incompressible fluid (implying that density is constant throughout the body) and has zero pressure at the surface". I emphasized that this is not a solution for your rotating universe.

Some "direction of movement raises the entropy" ignorance showing your ignorance of the definition of entropy when you are supposed to be writing a cosmology that includes entropy !
Entropy has to do with heat in classical thermodynamics, system states in statistical mechanics and information in information theory. Increasing entropy ihappens through the flow of heat or changes in state or changes in information. For example, the Sun is an enormous source of increasing entropy because heat is flowing away from it and because it is constantly changing microscopic states (not a computer so Shannon entropy does not apply!). Many mediums in space also very hot an increase entropy because heat flows away from them, e.g. The Milky Way's Hot Gas Halo ("between 1 million and 2.5 million Kelvins").

Black holes give an observed boundary in time. This is easy to understand. They eat matter and their mass grows with time. We can model that growth. Supermassive black holes are still surrounded by galaxies and still eating in many cases. That means the universe is bounded in time. Which leads to:
IF010: Where are the supermassive black holes that have basically eaten their galaxies as required by your unbounded in time cosmology, Peter J Carroll?
Astronomers try extremely hard and succeed in measuring the ages of stars and other objects. These all give an observed boundary in time.

[Reality Check]

Some of the errors in HC that makes it obviously false contradicting your claim in the OP, Peter J Carroll.

1. A universe "unbounded in both space and time" is not this universe where we have an observed boundary in time.
   No object in this universe has been measured to have an age greater than ~14 billion years.
2. The other side of the above is the ignorance of stating "unbounded in both space and time" when that is obviously not this universe.
   In this universe black holes, stars and galaxies evolve. Black holes gain mass. Stars consume their fuel and cannot be formed after ~10¹⁴ years. Galaxies interact and merge. This universe does not have enormously massive supermassive black holes that have essentially eaten their galaxies! This universe is still forming stars. This universe is not full of supermassive galaxies.
3. Ignorance of the mainstream science you are arguing against.
   That started here with abuse of relativistic energy because you thought squaring was "inelegant"! Photon energy is not E=mc^2.
   The ignorance that GR started with a hypersphere.
4. Cherry picking gravitational redshift from GR when you have no idea if GR exists in your universe.
5. Cherry picking the Gödel metric from GR when you have no idea if GR exists in your universe.
6. Asserting you are using the Schwarzschild metric when this is a solution for empty space (also cherry picking).
7. A "Gödel-Gomel-Zimmerman MOND effect" fantasy
   The Gomel-Zimmerman unpublished preprint is classical physics that does not use or reference Gödel's solution.
   A still unsupported assertion that you can get galaxy rotation curves from Gödel's solution alone confirms that this is a fantasy. The preprint gets the curves without Gödel. Adding Gödel should ruin their solution.

[Peter J Carroll]

Reality Check - I do not wish to be drawn by the 'broken record technique' into providing the same or different answer to a question after you have merely responded 'that's nonsense or ignorance'. If we go down that route, proper and courteous debate will collapse. Six years on I will not fall for that trick again.

Nevertheless I will repeat the quote that you seem to have mislaid.

IFO9.
https://en.wikipedia.org/wiki/Schwarzschild_metric

"The Schwarzschild metric has a singularity for r = 0 which is an intrinsic curvature singularity. It also seems to have a singularity on the event horizon r = rs. Depending on the point of view, the metric is therefore defined only on the exterior region r > rs ,only on the interior region r < rs or their disjoint union."

A boundary in time may be easy to understand, although difficult to believe. A horizon in time is a more subtle concept to grasp, but ultimately more believable.

IFO10. See equation 10 attached.

[Peter J Carroll]

Einstein’s ‘Greatest Blunder’ seems to me to have developed out of the following: -

https://en.wikipedia.org/wiki/Friedm...3Walker_metric

‘Einstein's field equations are only needed to derive the scale factor of the universe as a function of time.’

‘The relative expansion of the universe is parametrized by a dimensionless scale factor. Also known as the cosmic scale factor or sometimes the Robertson Walker scale factor, this is a key parameter of the Friedmann equations.’

Yes, so it appears they just put in the only bit that suited them.

Now look at this:

https://en.wikipedia.org/wiki/Interi...zschild_metric

That all looks extremely complicated, partly because of the use of radial coordinates but mainly because it mixes frames of reference.

There are three things to consider: -

1) The exterior Schwarzschild metric in the reference frame of an exterior observer.
2) The interior Schwarzchild metric in the reference frame of an interior observer.
3) The interior Schwarzchild metric in the reference frame of an exterior observer.

1) and 2) have the same equation.

The above paper represents 3), but it does confirm the hyperspherical qualities of a gravitationally closed space with its mention of radius excess and extra space inside (from the viewpoint of an external observer’s reference frame)

There is a very good reason to use 2) instead of the FLWR metric for the entire universe, because for the observable universe 2M/L ~ c^2/G.

[Reality Check]

Some of the errors in HC that makes it obviously false possibly contradicting your claim in the OP, Peter J Carroll.
Some of my questions illustrate these errors.

Your last post was not an answer to IF09. I told you about the singularities in the Schwarzschild metric. The Schwarzschild metric is still a solution for empty space outside of mass.
An abysmally ignorant assertion is not an answer to IF10. You are using GR which states that nothing at all gets out of the event horizon of a black hole. This is a basic, well known aspect of the Schwarzschild metric. Travelling thru the event horizon is a one-way journal. Everything inside the horizon has the central singularity in its future light cone.

If you use the Schwarzschild metric then you have to accept its consequences. That includes a one-way event horizon .

IF02: Cite your evidence that galaxies in this universe are arranged so that gravitational redshift will produce cosmological redshift.
IF03: Show how you derive GR in HC so that you can then use gravitational redshift inside a mass [or any other result from GR], Peter J Carroll.
IF05: Show how adding Gödel's angular momentum produces galaxy rotation curves that match observations, Peter J Carroll.
IF06: Where are the stars that are enormously older than 13.8 billion years, Peter J Carroll? (e.g. a trillion years old)
IF07: Why are stars still being formed in your "unbounded in both space and time" universe, Peter J Carroll?
IF08a: What process in a gas halo "recycles" heavy elements into whatever you think they end up as (cite the textbook physics), Peter J Carroll?
IF08b: Show that this decreases entropy, Peter J Carroll, as your Entropy! post implies.
IF09: Link to your quote in this thread or the Wikipedia article stating that the Schwarzschild metric is valid inside a massive object, i.e. this universe, Peter J Carroll.
IF010: Where are the supermassive black holes that have basically eaten their galaxies as required by your unbounded in time cosmology, Peter J Carroll?

[Reality Check]

Einstein’s ‘Greatest Blunder’ seems to me to have developed out of the following: -...

Another ignorant and irrelevant post, Peter J Carroll.
Einstein wrote his GR paper with his blunder in 1915. Obviously the Friedmann–Lemaître–Robertson–Walker metric came after the blunder (work starting in 1922) !
Irrelevant nonsense about the interior Schwarzschild metric.
An ignorant "confirm the hyperspherical qualities..." fantasy. Nothing in GR uses a hypersphere.
You shoot yourself in the foot with "a gravitationally closed space" when you have a. ignorant fantasy that a black hole is not gravitationally closed (magically ejects matter out of a one-way event horizon to lose mass when spinning!). This fantasy is ignorant because you know that the Kerr metric has an event horizon.
Ignorance of wanting to use the interior Schwarzschild metric which requires that a body has a physical surface with nothing outside of it instead of FLWR metric.
Ignorance of treating the observable universe as a black hole and thinking that its event horizon is a physical surface with nothing outside of it ("for the observable universe 2M/L ~ c^2/G"). That word observable means is that we cannot see beyond a limit. It does not say the universe stops there.

You do not understand your own fantasies! You want the universe to be the most massive ever rotating black hole. These are the black holes you want to magically eject matter. But you are using a metric that requires a surface with no pressure (i.e. matter or energy) outside of it.

[Peter J Carroll]

For the reasons given in post #67 and to encourage others here to ask questions, I shall make no further responses to the author of the last two intemperate posts.

I present, attached below, the last of the 17 equations of HC.

Mach’s Principle, sometimes known as the Einstein-Mach Principle, has been debated for many years, largely philosophically rather than mathematically.

https://en.wikipedia.org/wiki/Mach%27s_principle

I submit that only in a universe of constant size can we formulate Mach’s Principle mathematically without suggesting that fundamental constants vary with time.

The formulation presented in equation 7 perhaps has descriptive power, but probably zero predictive power. Nevertheless, I present it for the sake of completeness and philosophical holism.

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.

I would be pleased to take questions on any of the 17 equations and associated ideas in the remaining few days of this debate.

Regards, Pete.

[PetersCreek]

For the reasons given in post #67 and to encourage others here to ask questions, I shall make no further responses to the author of the last two intemperate posts.

Then this thread is closed pending moderator discussion.

This thread may continue but...

• Participants must be polite
• Answers must be timely and direct
• Other members will not be ignored
• Problem behaviors are to be reported, not called out

[PetersCreek]

The OP has withdrawn from the discussion so this thread is closed.