Problems with Radial Expansion and Spatial Curvature

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Problems with Radial Expansion and Spatial Curvature

Postby BurtJordaan on June 8th, 2020, 1:01 pm 

Because of analogies used in popular writings on cosmology, especially the balloon analogy, a wrong perception has been cultivated for the evolution of spatial curvature of the universe.

The balloon analogy suggests that the universe is closed and finite, with a positive spatial curvature, represented by the outside surface of the balloon. It is then easy to think that the balloon had so start small, with a high surface curvature and will gradually become bigger, with a smaller and smaller surface curvature.

The problem is that cosmological models based on GR don't work that way. For a matter+Lambda dominated universe the spatial curvature, if not exactly zero, initially evolves away from zero spatial curvature, not towards it, like shown below.

Curvature evolution with Lambda.png


The curve has been calculated for a presently 10% over-dense (closed) universe, i.e. one with energy density 10% above the critical density today. If it was not for the non-zero cosmological constant (Lambda), such a universe would eventually have collapsed onto itself, with curvature growing without limit. However, this sort of curvature behavior is completely incompatible with a radially expanding universe, which supposedly starts with high curvature and then evolves towards lesser curvature.

This is similar to a ballistic spacecraft not being able to escape from Earth's gravity if its kinetic energy is insufficient (i.e. below escape speed). The slightest kinetic energy deficit will make it deviate further and further from the required escape energy, i.e. the speed deficit will grow in an unlimited fashion until it starts to fall back to Earth.

The curve is equivalent to a case where a rocket motor kicks in before the speed becomes zero and accelerates the spacecraft towards escape speed again. In the case shown the curvature started imperceptibly positively, increased until the cosmological constant kicked in (about 5 billion years ago), driving the curvature back to zero as time increases without limit...
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Re: Problems with Radial Expansion and Spatial Curvature

Postby BurtJordaan on June 9th, 2020, 4:18 am 

Perhaps a more intuitive parameter for viewing the evolution of curvature is the radius of curvature, which is simply the inverse of the square root of the curvature parameter |k|.[a]

Curvature evolution with Lambda2.png

This curve gives the radius of curvature of a 10% over-dense universe for any time, as a multiple of the present Hubble radius (14.4 Glyr).

This dramatically illustrates the problem with a simple closed radial expansion model - the radius must shrink for the first 9 billion years or so and only then increases exponentially.

Remember that all the above is based on a fictitious over-dense universe that does not represent our own, but that follows the Friedman equations accurately.

Note [a]: The curvature parameter is the total energy density parameter Omega minus 1. The energy density parameter changes as the universe expands, giving the characteristic curves.
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Re: In the Bud?

Postby Faradave on June 9th, 2020, 12:19 pm 

I'll make every effort to extol real science here. However, some extension beyond conventional limits should be allowed, so long as it is firmly based upon accepted science. Still, it's a judgment call open to moderation.

Let's start with speed limit c. I treat c as finite, constant, universal, isotropic, invariant, and unidirectional with respect to its temporal component.

I treat "the cosmos"* as all space (and its contents) "now", a simultaneity in the rest frame of the cosmos at any given time.** The cosmos is at rest with respect to itself, making it a convenient, universal, inertial frame of reference. A consequence of this is that, as far as we can know, nothing in the cosmos is older than the cosmos because aging only slows with motion relative to the cosmos. It's true that time dilation is special relativity (SR) is relative (each inertial frame sees the other aging slowly). But for any object to have motion relative to the cosmos, it must have experienced prior acceleration (such as at the big bang), which locks in asymmetrically slower aging for such objects.

If this is unclear, I'll explain (or be corrected). If it is objectionable, I shouldn't continue.

*By contrast, I treat "the universe" as all space and all time, the entire 4D continuum and its contents.
**The rest frame of the cosmos is the one in which cosmic background radiation is isotropic.
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Re: Problems with Radial Expansion

Postby BurtJordaan on June 10th, 2020, 3:20 am 

Hi Fd, not a bad effort, but with some problematic statements. It is also somewhat of a pity that your first response was not a reply or question on the scientific material offered here, but rather a fairly obvious buildup for up-selling your own theory. I guess this is the normal pattern in the scientific sections on this forum...

Faradave » 09 Jun 2020, 18:19 wrote:I treat "the cosmos"* as all space (and its contents) "now", a simultaneity in the rest frame of the cosmos at any given time.** The cosmos is at rest with respect to itself, making it a convenient, universal, inertial frame of reference.

In cosmology, 'cosmos' and 'universe' is usually used interchangeably, by de-facto convention. But your "rest frame of the cosmos" is highly controversial, especially in the sense of the second sentence. The kind of frame where all observers see the CMB at the same temperature cannot be an inertial frame. It is called the co-moving frame, where every observer is stationary in its local spacetime, but is moving relative to every other such observer in the frame, in the sense that spatial separations increase over time. Take Minkowski spacetime and apply metric expansion, i.e. stretch the spatial axes and you have a comoving reference frame.

A consequence of this is that, as far as we can know, nothing in the cosmos is older than the cosmos because aging only slows with motion relative to the cosmos. It's true that time dilation is special relativity (SR) is relative (each inertial frame sees the other aging slowly). But for any object to have motion relative to the cosmos, it must have experienced prior acceleration (such as at the big bang), which locks in asymmetrically slower aging for such objects.

This is quite incorrect and apparently stems from clinging to a "radial time" model with a singularity in space and time at the big bang. The scientific theory being discussed in this thread says that immediately after inflation (or equivalent), the universe was extremely large, extremely hot, spatially extremely flat, extremely isotropic and uniform (to within 1 part in 10 thousand), with space expanding uniformly into all three dimensions at an extremely high rate. This is confirmed by observations of the CMB radiation.

There was no time dilation due to inflation and/or the resulting rapid spatial expansion and only a negligible gravitational time dilation in the over-dense "hot spots". Now the cosmological time we work with is the average for the universe at large, so theoretically, in the present day voids, time was always ticking faster than the average and in the present clusters and galaxies, time was always ticking slower than the average.

So, you have to somehow find the "voidest void" (voids still contain matter), before you can say that what the oldest thingie in the cosmos might be.

Can you see the difference between this and your approach?
Last edited by BurtJordaan on June 10th, 2020, 3:28 am, edited 1 time in total.
Reason: typos
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Re: Coming to Terms

Postby Faradave on June 10th, 2020, 11:43 am 

BurtJordaan wrote:It is also somewhat of a pity that your first response was not a reply or question on the scientific material offered here
I'm aiming at a specific reply but don't feel it would make any sense without some common ground as an introduction. Specifically, I wish to make the case that cosmology has badly mistaken the influence of gravity on expansion. But this requires a model of gravitation which cosmology lacks, i.e. a model which clearly and fundamentally equates mass-energy with gravitation (and information for that matter).

BurtJordaan wrote:a fairly obvious buildup for up-selling your own theory. I guess this is the normal pattern in the scientific sections on this forum … spatial separations increase over time.
Guilty! What can I say? I think this is too interesting a topic to go unreplied and I waited a bit to see if anyone wanted to go first. I'm prepared to step aside temporarily if/when a more desirable conversation develops.

BurtJordaan wrote:The kind of frame where all observers see the CMB at the same temperature cannot be an inertial frame.
Agreed! I had not allowed for apparent speed relating to expansion. Weird. I'm willing to consider a cosmic simultaneity as a set of rest frames. I need a term for all cosmic space at a given moment, i.e. that which is purported to be expanding radially in the OP. Is "comoving reference frame"" that term?

BurtJordaan wrote:The scientific theory being discussed in this thread says that immediately after inflation (or equivalent), the universe was extremely large, extremely hot, spatially extremely flat,
But the OP refers to "radial expansion", if only to discredit it. As I support radial expansion, I took this as an invitation. Debate demands at least consideration of radial expansion.

BurtJordaan wrote:extremely hot
So, these particles are moving (typically randomly) relative to each other and the comoving frame of the cosmos. It is their accelerations which lock in lower age than that attributable to the comoving frame (on average). But this is a fairly minor consideration. I can live without it.

I'm glad we seem to have no issues on my treatment of speed c. That is by far, the more important aspect of my intro. I'll continue from there if no objections.
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Re: Outward Bound

Postby Faradave on June 10th, 2020, 11:35 pm 

Cosmology considers gravity as working against cosmic expansion. I believe that notion is backward.

Newton believed that gravity acted instantaneously:
"The success of the Faraday-Maxwell interpretation of electromagnetic action at a distance resulted in physicists becoming convinced that there is no such thing as instantaneous actions at a distance (not involving an intermediary medium) of the type of Newton’s law of gravitation." - Einstein p.48

We now understand that gravitational influence propagates at speed limit c.
"In October 2017, the LIGO and Virgo detectors received gravitational wave signals within 2 seconds of gamma ray satellites and optical telescopes seeing signals from the same direction. This confirmed that the speed of gravitational waves was the same as the speed of light." - Wikipedia

Gravity is lightlike! I find it positively fascinating that Maxwell accidentally derived the speed of gravity from the electric (ε0) and magnetic (μ0) constants! One is tempted to model a single, unified field underlying both G and EM ...but I digress.

Gravitation occurs as a "field" about mass-energy, which provides the potential to attract objects in that field. Imagine a "particle" (mg) as a mass-energy event at a convenient point source in spacetime. As it persists, mg describes a worldline, which is a timeline in its rest frame. We may now model an instance of mg's gravitational field, occupying its forward light cone.

cone future.png
An instance of a particle's gravitational field describes its forward light cone arising from the spatial simultaneity (3-plane) of its rest frame.
By contrast, most were taught gravity as a field in space so I pause for any discussion…
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Re: Coming to Terms

Postby BurtJordaan on June 11th, 2020, 12:48 am 

Fd, I'm still a bit perturbed by the fact that you try to steamroller your private theory(ies) here, apparently without any proper knowledge of what General Relativity and/or the cosmological solution to GR says. If you did have that knowledge, I would have expected at least a few questions on how we get to the curvature curves of posts 1 and 2 above.

Faradave » 10 Jun 2020, 17:43 wrote:Specifically, I wish to make the case that cosmology has badly mistaken the influence of gravity on expansion. But this requires a model of gravitation which cosmology lacks, i.e. a model which clearly and fundamentally equates mass-energy with gravitation (and information for that matter)

Sorry Fd, but this is utter nonsense. The Friedmann equations of contemporary cosmology are exact solutions of Einstein's field equations of GR, expressing the cosmic expansion in terms of the gravitational effects of all the energy sources in the universe - radiation, matter, curvature and vacuum energy (cosmological constant). Your very next post tries to build on this nonsense and is hardly worth a reply.

I need a term for all cosmic space at a given moment, i.e. that which is purported to be expanding radially in the OP. Is "comoving reference frame"" that term?

Yes, used with caution, this is the correct term, except that the term has nothing to do with radial expansion as per your 'radial time model'. The Wiki: https://en.wikipedia.org/wiki/Comoving_and_proper_distances#Short_distances_vs._long_distances does a reasonable job of explaining the concepts of comoving frames and comoving inertial frames. It has very solid references as well.


.
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Re: Outward Bound

Postby BurtJordaan on June 11th, 2020, 3:00 am 

Faradave » 11 Jun 2020, 05:35 wrote:Cosmology considers gravity as working against cosmic expansion. I believe that notion is backward.

Post-BigBang cosmology considers gravity as working both ways, initially against expansion and lately with expansion (the cosmological constant). There is a sense in which the cosmological constant works both ways at the same time, but that sense is not important here.

We now understand that gravitational influence propagates at speed limit c[i].

Depends on what you mean by 'gravitational influence'. The universal gravitational field has been established everywhere "at once" by the energy released in the BB and it is not propagating anywhere. Whenever something disturbs this field in a certain way[*] at some location in space, ripples in spacetime may spread out from there at speed c, with the usual qualifier of speed as measured locally over small distances. To fully comprehend gravitational waves, a deep knowledge of general relativity is required.

This brings me to a point that I should have made long ago. I think I understand your issues, simply because I have been there some 20+ years ago. My concept of special and general relativity and cosmology were much like what you are trying now and I have discussed it with interested people. Then one day a scientific colleague, also working in my engineering world, dropped a photocopy of a book titled Differential Geometry and Relativity Theory: An Introduction by Prof. Richard L Faber on my desk.

To make a long story short, after working through Faber, I eventually borrowed the same colleague's formidable Gravitiation by Profs. Misner, Thorne and Wheeler (the book is simply refered to as MTW in the literature). About halfway through it and about 2 years later, the veil eventually lifted and I could see why my ideas could not work. And why the GR based theory that matured over the last century can. It was then not too difficult to apply that insight to a world view of Cosmology as well.

I say this not to discourage you, but rather to encourage you to seriously try to understand modern physics from the proper sources. For cosmology, I have studied Principles of Physical Cosmology by Prof. PJE Peebles.

[*] The disturbance must be asymmetrical and also periodic to some degree, for gravitational waves to be radiated as ripples in the existing gravitational field. The simple formation of a black hole in a symmetrical way does not radiate gravitational waves, even if it is rotating, because the energy was all there before it collapsed.

But I'm not MTW and even they could not teach gravitational waves to anyone in a few forum posts...
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Re: Conic Session

Postby Faradave on June 11th, 2020, 7:05 pm 

BurtJordaan wrote:Fd, I'm still a bit perturbed by the fact that you try to steamroller your private theory(ies) here
Clearly, you recall my curved-space, radial-time model. When you post a thread purporting problems with radial expansion, how can I know you aren't challenging my model specifically? If in future you add a statement such as "FD's personal theories notwithstanding." I'll take it as a signal to stand down.

BurtJordaan wrote:FD… apparently without any proper knowledge of … the cosmological solution to GR … I would have expected at least a few questions on how we get to the curvature curves of posts 1 and 2 above.
The feeling is mutual. The cosmological solution seems naïve. For example, does it contain terms for strong and electrical interaction?* Why not? They're much, much more powerful than gravity (enough to explain rapid inflation).
"Gravity is the weakest of the four fundamental interactions of physics, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force " - Wikipedia

*For now, I avoid Weak interaction, which is also much stronger than G. I'm not yet sure how I want to include it. In isolation the Big Bang might be considered a super duper "decay" event. On the other hand, it's not inconsistent with a collision event, which might still involve weak interaction.

BurtJordaan wrote:The Friedmann equations of contemporary cosmology are exact solutions of Einstein's field equations of GR, expressing the cosmic expansion in terms of the gravitational effects of all the energy sources in the universe
Interesting! At the gravitational singularity of the Big Bang, we're supposed to believe that there was somehow enough energy (the "bang") to overcome infinite gravitation. Trouble is, energy is itself a source of gravitation, so…
"The quantities used to measure gravitational field strength are the scalar invariant curvatures of spacetime, which includes a measure of the density of matter. Since such quantities become infinite at the singularity, the laws of normal spacetime break down. …Neither general relativity nor quantum mechanics can currently describe the earliest moments of the Big Bang" - Wikipedia

I can help with that. As with all force, gravity is expansional.

BurtJordaan wrote:Yes, used with caution, this ["comoving reference frame"] is the correct term [for all cosmic space at a given moment]
Good! For brevity, I'll use the word "cosmos" to mean comoving reference frame(s) where all comoving observers see an isotropic background (and age according to cosmic time).

BurtJordaan wrote:Your very next post tries to build on this nonsense …Post-BigBang cosmology considers gravity as working both ways
Again, the feeling is mutual, but I don't see it as reason to quit.

BurtJordaan wrote:Depends on what you mean by 'gravitational influence'.
It's quite simple. When scientists imagine the sun vanishing without a trace, we're correctly told that earth would remain illuminated and orbitally constrained for ≈8.5 min. That's an expression of the sun's EM & G fields on its light cone (allowing it is not a point source, elliptical orbit, etc.)
sun field.png
Light and gravity experienced by earth now originated in the past.

What we refer to as a "particle" is an event on a particle's worldline. Any such event can only exert G or EM influence (i.e. apparent force) on an object on its future light cone. This is not personal theory. That cone is what I consider an "instance" of the particle's field. It's the simplest and most fundamental expression of field.* Science would benefit greatly by adopting it, but I won't hold my breath. The G field you mention can easily be constructed from the light cone so, the light cone field is more fundamental.

Thanks for the references (which I note) and advice. If none of those respected authors has recognized the light cone as the basis of a unified field, I expect the reading to be painful for me. They offer sophisticated but abstract descriptions of fields. I model physical explanations. My first principles are deeper than those of convention, which puts me pretty much on my own.

*Any deeper and "field" resolves to a lightlike radial field element (my "pinhole") with instantaneous chronaxial spin.
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Re: Conic Session

Postby BurtJordaan on June 12th, 2020, 4:35 am 

Faradave » 12 Jun 2020, 01:05 wrote:
BurtJordaan wrote:FD… apparently without any proper knowledge of … the cosmological solution to GR … I would have expected at least a few questions on how we get to the curvature curves of posts 1 and 2 above.

The feeling is mutual. The cosmological solution seems naïve. For example, does it contain terms for strong and electrical interaction?* Why not? They're much, much more powerful than gravity (enough to explain rapid inflation).

Being a science section, the intention of the thread is to give interested readers some insight as to why things like the balloon analogy for spatial expansion create false impressions on spatial curvature. A debate on that would surely have enlightened interested readers.

You are apparently trying to discredit the fundamental theory underlying such analysis by making unsubstantiated claims that might suit your private theory. You may see it as a service to this community, but many will not. Especially if a very superficial knowledge of the standard theory is evident.

You are not the only one implicated on this count, but it usually ends up leaving the community in the dark, because the few scientists around here soon tire of painstakingly pointing out every false perception of the standard theories stated by the personal theorist. The scientists then leave the thread and things are left somewhat open-ended.

I'm just going to point out one false perception created, already in the above quote, paraphrased: "gravity is the weakest force." In the physics used to describe the universe at large, gravity is not a force, but rather spacetime curvature, caused by the total energy content and its distribution in space. For a popular account, see
https://www.universetoday.com/108740/how-we-know-gravity-is-not-just-a-force/.
I quote just the closing remark:
universetody wrote:Each of these experiments show that gravity is not simply a force between masses. Gravity is instead an effect of space and time. Gravity is built into the very shape of the universe.

Every false perception challenged by a scientist normally spurs a flurry of quotes, mainly from sayings, writings or posts from the past, mostly without proper context. It then usually becomes a long debate in which tempers may flare up.

Hence, unless someone is interested in, or want to challenge the analysis given in the opening two posts, this thread should go dormant (not closed though).
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Re: Time to Move Forward

Postby Faradave on June 12th, 2020, 4:08 pm 

BurtJordaan wrote:…the intention of the thread is to give interested readers some insight as to why things like the balloon analogy for spatial expansion create false impressions on spatial curvature.
That's why I'm here. I believe curved space (balloon analogy) works with radial time, allowing that all forces modify the expansion rate (thus, creating a scale factor). In view of current debate, it's too soon for specifics.

BurtJordaan wrote: …the few scientists around here soon tire of painstakingly pointing out every false perception of the standard theories stated by the personal theorist.
My assertions are well founded. I provide multiple references from respected sources. If we still disagree, so be it. If I'm warned by a moderator to leave a topic, I do. That's not the same as intellectual defeat.

BurtJordaan wrote:A debate on that [expansion curves] would surely have enlightened interested readers.
Thread views are climbing faster since I arrived.

BurtJordaan wrote:I'm just going to point out one false perception created, already in the above quote, paraphrased: 'gravity is the weakest force'. …gravity is not a force
This is nit picking. Actually, I avoided calling gravity a "force" but now that you mention it:
"…imagine …a plane circular disc, which rotates uniformly in its own plane about its center. An observer who is sitting eccentrically…is sensible of a force which acts outwards in a radial direction …he regards as the effect of a gravitational field…" - Einstein pp.79-80

Einstein does the same with the elevator gedanken. An observer finds upward acceleration (by F=ma) indistinguishable from a uniform gravitational field below. Thus, we're free to consider gravity as either. Physics competently treats weight as a force.

As for spatial curvature, it's a nice first attempt but the model is too complex. My characterization is better because it's simpler, yet accommodates GR exactly as well. Here's the difference.

Since gravity has the same effect in every spatial direction, we can consider all three dimensions together as a 3-line. To curve any line requires an extra dimension. For example, a straight line can exist in one dimension but a curved line requires at least a 2D plane in which to curve. To curve a 3-line requires at least 4D. That models a geometric increase in complexity (especially if you deny radial time).

By contrast, I model gravity as a loss of separational capacity. Instead of curving, space simply loses its capacity to hold objects apart. This occurs in a radial gradient about a point source of mass-energy. It is the gradient of separational insufficiency which curves. No extra dimension! Like opening a vacuum, the dimensions of the atmosphere don't change, but a density (and pressure) gradient occurs, falling toward that opening.

Both models have the same effect on trajectories, etc.

BurtJordaan wrote:Being a science section … unless someone is interested in, or want to challenge the analysis given in the opening two posts, this thread should go dormant
If anyone else shows up, I'll suspend posting until the "grown ups" have had their discussion. In the meantime, you referred to my light cone field instance as "utter nonsense … hardly worth a reply … unsubstantiated claims". Using accepted science, I showed exactly why it does make sense and you ignore it. You're welcome.

Here's why the light cone field fundamental to your discussion.

1. That instances of both G and EM coincide exactly on the light cone is grounds for their unification. They might both be considered fields of potential force or both considered fields of structural effect on the continuum. We've already discussed G.

"…the existence of the positive charge, in some sense, distorts, or creates a “condition in space, so that when we put a negative charge in, it feels a force." – Feynman p.30

"…Maxwell's equations-which determines the fields produced by charges…the character of 'space' is changed by the presence of charged matter" – Feynman p.142

"It is very possible that there is a hidden relation between gravity on the one hand and electromagnetic field and material particles on the other, but nobody is prepared today to say what kind of relation it is." – Gamow p.13

"Einstein was persuaded that the electromagnetic field must also have some purely geometrical interpretation." – Gamow p.137

My model does both by defining force as structural (a hole in the continuum), acting as a conduit for energy transfer. After all, that's what force accomplishes by acceleration.

2. Most important to this thread, force is lightlike. We can draw a potential G or EM force on a future light cone from an event on a particle's timeline. If the force is attractive the spatial component will be inward toward the timeline. If it's repulsive it points away from it. Either way however, the temporal component is always futureward.

That means whether particles are drawn toward or away from each other in space, they are always drawn equally to the future. If the cosmos is expanded in the future (balloon analogy or expanding block) then all force is expansive. No big crunch, regardless of mass-energy density. Quite the opposite.
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Re: Time to Move Forward

Postby BurtJordaan on June 13th, 2020, 2:37 am 

Faradave » 12 Jun 2020, 22:08 wrote:
BurtJordaan wrote:…the intention of the thread is to give interested readers some insight as to why things like the balloon analogy for spatial expansion create false impressions on spatial curvature.
That's why I'm here.

Really? You have not even once addressed the problem of spatial curvature for radial time models that the OP exposed.

Faradave » 12 Jun 2020, 22:08 wrote:
BurtJordaan wrote:A debate on that [expansion curves] would surely have enlightened interested readers.

Thread views are climbing faster since I arrived.

For general information, the text in square brackets was FD's insert. The OP is not about expansion curves, but about spatial curvature evolution. Any form of radial expansion analogy has problems with that. Do you understand the difference?

And what has thread views got to do with it? Thread views are mostly driven by add bot visits anyway, says TheVat.

Faradave » 12 Jun 2020, 22:08 wrote:
BurtJordaan wrote:…the few scientists around here soon tire of painstakingly pointing out every false perception of the standard theories stated by the personal theorist

My assertions are well founded. I provide multiple references from respected sources. If we still disagree, so be it. If I'm warned by a moderator to leave a topic, I do. That's not the same as intellectual defeat.

I can dissect virtually all of your quotes from authority and show non-applicability or wrong context/interpretation of the quote, but this will probably take this thread even farther off its rails.

I'm asking you to read the two opening posts carefully and reply to them properly, and in context. Show where they are wrong, or if unclear, ask. If you can show that your model satisfies such a spatial curvature evolution, we we can surely discuss your model further here. Else, off it goes to Personals.
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Re: Freed Man

Postby Faradave on June 14th, 2020, 1:55 pm 

BurtJordaan wrote:I'm asking you to read the two opening posts carefully and reply to them properly, and in context.
BurtJordaan wrote:[OP:] Remember that all the above is based on a fictitious over-dense universe that does not represent our own, but that follows the Friedman equations accurately.
I've carefully reread the two OPs. It appears that you wish to discuss interesting aspects of the Freidman equations. If you entitle a new thread as such I'll abstain. (I mistook "Problems with Radial Expansion"” as a personal invitation.)

Your second OP is correct about the intuitiveness of the Hubble radius. I suggest you stick with that and drop the first graph. Also, any hint that gravity "works both ways" seems preposterous and needs elaboration.

BurtJordaan wrote:[OP:] This dramatically illustrates the problem with a simple closed radial expansion model - the radius must shrink for the first 9 billion years or so and only then increases exponentially.
Why must the radius shrink? My impression is that Freidman sees gravity (or mass-energy density) as the reason.
"...both ordinary and dark matter contribute in favour of contraction" – Wikipedia

That's why it's important to consider if gravity is actually expansional.

Your statement (and the curves) seem to ignore much of the "early universe" (where Cosmology needs the most help). I think that should be explicitly acknowledged.

BurtJordaan wrote:You have not even once addressed the problem of spatial curvature for radial time models that the OP exposed.
The earlier title: "Problems with Radial Expansion" naturally provokes the question "Expansion of what?". That's why I offered a definition of "cosmos" in my first post – all space at a given time in the rest frame of the cosmos. Fine to understand that as "comoving frames".

If force (including gravitation) is expansional, I'm afraid the Freidman equations must be completely restated, in all likelihood abandoning dark energy. That should have been apparent from what I wrote, but perhaps not.

BurtJordaan wrote:And what has thread views got to do with it? Thread views are mostly driven by add bot visits anyway, says TheVat.
You tell me. I presume SPCF provides these counts for some reason. The bots have a sense of humor, as the huge views of Laughter is the Best Medicine seem to indicate.

BurtJordaan wrote:…your quotes from authority
SPCF must make up its mind if it requires support in the science sections or not. I provide these at some effort and in good faith. Their refutation is welcome and may be instructive to the bots.

It is not at all surprising for Einstein and Gamow to imply that, seeing G field as geometrically structural, the remarkably similar EM field morphology may also be. I extend that to see a single unified force as fundamentally structural object (a radial field element). Then a "field" may be seen as both one of "potential force" and a "structural gradient" (specifically, of separational insufficiency).

Non-linearity in scale factor a(t) should then be supplied by consolidations (or "condensations") of matter: quarks, nuclei, atoms and gravitational accretions.

BurtJordaan wrote:If you can show that your model satisfies such a spatial curvature evolution, we can surely discuss your model further here.
You'll be relieved that I do not believe I meet your criterion. I find "curvature" an unfortunate characterization of what is much more accurately described as a gradient of separational insufficiency (a loss in spatial capacity to maintain separation).
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Re: Problems with Radial Expansion and Spatial Curvature

Postby BurtJordaan on June 15th, 2020, 6:03 am 

Fd, this is a very much more reasonable and measured response from you. Thanks for that.

Faradave » 14 Jun 2020, 19:55 wrote:It appears that you wish to discuss interesting aspects of the Freidman equations. If you entitle a new thread as such I'll abstain. (I mistook "Problems with Radial Expansion"” as a personal invitation.)

No, I think the title as stated is correct for the problem addressed, i.e. that no (physical) radial expansion analogy, like the balloon analogy, whether radial time or not, is compatible with the way spatial curvature evolves - first away from zero and only in the later exponential phase, towards zero.

FD wrote:Your second OP is correct about the intuitiveness of the Hubble radius. I suggest you stick with that and drop the first graph.

It is not about the Hubble radius, but about the evolution of radius of spatial curvature over time. The only connection with the Hubble radius is that the result is expressed as so many present Hubble radii.

FD wrote:Also, any hint that gravity "works both ways" seems preposterous and needs elaboration.

Agreed, but I only referred to the gravity of the cosmological constant (dark energy, if you wish), not the gravity of matter and radiation. The 'both ways' comes from the difference in GR's pressure term. Normal energy sports positive energy and positive pressure. Dark energy has positive energy, but negative pressure, causing exponential expansion.

FD wrote:
BurtJordaan wrote:[OP:] This dramatically illustrates the problem with a simple closed radial expansion model - the radius must shrink for the first 9 billion years or so and only then increases exponentially.

Why must the radius shrink? My impression is that Friedman sees gravity (or mass-energy density) as the reason.
"...both ordinary and dark matter contribute in favour of contraction" – Wikipedia

Precisely. Only the dark energy density part of the total budget is accelerative in nature, while radiation, ordinary and dark matter simply slow down the expansion rate (da/dt).

FD wrote:Your statement (and the curves) seem to ignore much of the "early universe" (where Cosmology needs the most help). I think that should be explicitly acknowledged.

Yes, the standard cosmological model excludes the inflationary epoch, which can be seen as 'the Bang', ending at something like 10-32 seconds after t = tPlanck. At that time the presently observable universe was in an extremely hot, dense state, expanding extremely rapidly, with spatial curvature extremely close to zero (i.e. spatially very flat). The LCDM model takes it from there. Inflation is something to be sorted out as part of quantum gravity.[*]

FD wrote:
BurtJordaan wrote:…your quotes from authority
SPCF must make up its mind if it requires support in the science sections or not. I provide these at some effort and in good faith. Their refutation is welcome and may be instructive to the bots.

The way SPCF requires sources to be referenced is generally through a link to the actual article, paper or book, preferably with at least a page, equation or paragraph number given. Snippets quoted from such sources cannot be verified for context by the reader. This is crucially important when authority is leveraged in support of a claim, which might or might not align with the paper.

FD wrote:
BurtJordaan wrote:If you can show that your model satisfies such a spatial curvature evolution, we can surely discuss your model further here.
You'll be relieved that I do not believe I meet your criterion. I find "curvature" an unfortunate characterization of what is much more accurately described as a gradient of separational insufficiency (a loss in spatial capacity to maintain separation).

OK, that settles it then, no discussion of "FaraCosmo" or "FaraGravity" allowed under the sciences sections. They are personal theories, not compatible with peer reviewed published scientific papers. IMO, the time of serious students of the sciences should not be wasted on them.

You are obviously welcome to interrogate the standard theory here. It is even OK to ask 'why can't it work like this?" But please give your solutions to the your perceived problems with the standard theory in the Personal Theories section. Keep in mind what TheVat has said to AndreX; this chat form is not for full-length treatises. Do that on you own website or on viXra and then link to there from the Personal Theories section, not from the Science sections.
===o0o===

Note [*] The Friedmann equations can give quite a good, plausible account of the inflationary epoch, with just one set of caveats: that the cosmological constant was very large at t = tPlanck and then underwent a sudden 'phase change' some 10-32 seconds later, when the large value dropped to a very low residual value. The excess energy was dumped into radiation and the fundamental particles of matter-energy. Many (not all) of the leading inflationary theories of today are variants and flesh-outs of this simple Friedmann scenario.

Note [**] It is reasonable to think that the radius of curvature might have been small before inflation and was driven to a very large radius, i.e. flatness, by inflation. But because things were in the quantum regime then, we have no way of knowing if that is true or not.

If anyone is interested in that, I can post something on inflation in a new thread.
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Re: Constant (Λ) Companion?

Postby Faradave on June 15th, 2020, 12:52 pm 

BurtJordaan wrote: I think the title as stated is correct for the problem addressed
BurtJordaan wrote:Remember that all the above is based on a fictitious over-dense universe that does not represent our own, but that follows the Friedman equations accurately.
I suggested renaming the thread to "Interesting Aspects of the Friedman Equations" because you represent a 10% over dense condition. As I don't find the common trumpet profile in your graphs, I think it would be helpful to post graphs for both normal and over dense conditions for comparison.

Image

BurtJordaan wrote:radiation, ordinary and dark matter simply slow down the expansion rate (da/dt)
Inasmuch as convention purports massless "force carriers" (photons, gluons, theoretical gravitons) as having lightlike worldlines, so must the forces they are purported to carry. So, any EM, S or G force should be considered to have a unidirectional (forward only) temporal component. Otherwise, it seems we revert to only the spatial component (attraction & repulsion) in an instantaneous manner, familiar to Newton. I'm astounded that Einstein and Friedman do this (and everyone follows).

A forward temporal component means that whatever shape the future cosmos may have, mass-energy compels the cosmos to it. Had science incorporated this, the need for a cosmological constant (Λ) would fall into question. The fact that we observe an expanding cosmos then suggests a spherical or expanding block geometry.

Note to readers and bots: With rare exception, underlining in my posts indicate active links. For example, an underlined author's name next to a quote (or snippet) links to the respective reference, as is true for all my above posts.
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Re: Constant (Λ) Companion?

Postby BurtJordaan on June 16th, 2020, 1:07 am 

Faradave » 15 Jun 2020, 18:52 wrote:I suggested renaming the thread to "Interesting Aspects of the Friedman Equations" because you represent a 10% over dense condition. As I don't find the common trumpet profile in your graphs, I think it would be helpful to post graphs for both normal and over dense conditions for comparison.

Firstly, in order to demonstrate the closed universe, expanding from a point-like singularity (like your radial time model), the universe must be over-dense. I exaggerated the effect by choosing 10% over-density for the purpose of illustration. For a critical density case, the curvature would be zero and the radius of curvature infinite, not offering any insight. For even a small deviation from zero curvature, the curves that I offered will show the effect as I depicted, just lesser so.

Through the radius of spatial curvature route, I tried to show that there is no way in which radial-time models can represent the correct curvature, as predicted by GR.

Secondly, I wrote about the spatial curvature and radius of spatial curvature. This is not demonstrated by the common trumpet profile, which depicts the radius of the observable universe over time. They are not simply related to each other. In fact the 10% under-dense (open), flat and 10% over-dense (closed) cases will all give you the same trumpet-like shape, with minor differences.[*]

Image

FD wrote:Inasmuch as convention purports massless "force carriers" (photons, gluons, theoretical gravitons) as having lightlike worldlines, so must the forces they are purported to carry.

Granted, but gravity (which is the only long-range player in GR) is attractive, not expansive. In the light of this fact, the rest of what you wrote does not make sense, i.e.
FD wrote:So, any EM, S or G force should be considered to have a unidirectional (forward only) temporal component. Otherwise, it seems we revert to only the spatial component (attraction & repulsion) in an instantaneous manner, familiar to Newton. I'm astounded that Einstein and Friedman do this (and everyone follows).


Remember that hypothetical gravitons don't wield a force, but rather set up any changes in spacetime curvature in a lightlike action. Then matter simply follows the geodesics predicated by the preset local spacetime curvature. There is no gravitational force operating on distant objects. This is what Einstein, Friedmann and contemporaries first understood.

* That picture is an artistic rendering, not conforming to any scale used in cosmology. As an example, the inflationary slope following "quantum fluctuations" lasts for only 10-32 seconds. Compare that to the other indicated times and scales and one can see the problem.
A much more realistic picture is given by this Wiki: https://en.wikipedia.org/wiki/Inflation_(cosmology)#Theory

Image
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Re: Granted, It's a Stretch

Postby Faradave on June 16th, 2020, 12:58 pm 

I like the wiki graphic, thanks. Am I correct in assuming that the graph in your second post, having a vertical axis calibrated as a ratio of calculated radius to Hubble radius, would be a flat horizontal line (at y = 1) for normal density? If true, that would be worth stating explicitly.

BurtJordaan wrote:gravity (which is the only long-range player in GR) is attractive, not expansive. In the light of this fact, the rest of what you wrote does not make sense
Understood. We seem to agree that G acts indirectly on surrounding objects by its effect on the intervening continuum. At least some scientists (based on above quotes) have not ruled out the possibility that the other forces have a structural explanation.

Consider a couple of rubber rings concentrically fitted to radial metal rods such that only unidirectional outward stretching of the rings can occur (e.g. a zip tie connection mechanism). Now imagine a web of threads connecting the inner ring to the outer one by sliding attachments. The threads are initially wet and contract as they dry, applying an attraction between the rings. It should be clear that the inner ring will expand as the threads contract. This illustrates a mechanism whereby attraction can produce expansion.
Expansion by attraction.png
Fundamentally unidirectional radii (black) convert a web of attraction (orange) to expansion of inner ring (blue) toward outer.

I think Friedman was smart enough that allowing attraction to be cosmically expansive (via unidirectional, radial time), he might have modeled quarks condensing (by S) into pairs up to 10-32 sec., then to quark triplets at 1 μ sec., then to nuclei through 3 min. and (by EM) to atomic hydrogen at 380,000 years and by G thereafter.
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Re: Granted, It's a Stretch

Postby BurtJordaan on June 17th, 2020, 3:09 am 

Faradave » 16 Jun 2020, 18:58 wrote: Am I correct in assuming that the graph in your second post, having a vertical axis calibrated as a ratio of calculated radius to Hubble radius, would be a flat horizontal line (at y = 1) for normal density?

No, normal (critical) density means spatial flatness, i.e. with an infinite (or at least extremely large) radius of curvature. I do not understand your rubber ring idea and why it needs to be considered.

FD wrote:I think Friedman was smart enough that allowing attraction to be cosmically expansive (via unidirectional, radial time), he might have modeled quarks condensing (by S) into pairs up to 10-32 sec., then to quark triplets at 1 μ sec., then to nuclei through 3 min. and (by EM) to atomic hydrogen at 380,000 years and by G thereafter.

I would rather think that Friedmann was smart enough to have understood that if the cosmological constant (vacuum energy density) was good for holding Einstein's original static cosmic model from collapsing under its own mass-energy, it was also good for driving expansion. I'm not sure if it was Friedmann who discovered that Einstein's original static model was in unstable equilibrium, and that the slightest perturbation would have made it to either expand or collapse exponentially in either way.

Anyway, Einstein later acknowledge that and thought that if vacuum energy was present, it had to be of approximately zero density. The cosmological constant is an interesting beast and perhaps requires a thread on its own. Enough here to say that it could have given the cosmic expansion the original push...
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