Local Nonuniform Expansion Pressure as a Model for Dark Energy and Dark Matter

[PatRKelley]

Hello, I'm a former BA forum alumnus, I've been away for a while (five or six years...) and in the meantime I've been slowly putting together something of an idea.

I'll get straight to the meat.

To quickly summarize, I've put together a paper about a possible explanation for dark matter and dark energy as aspects (both) of local nonuniform expansion. It doesn't postulate a mechanism, just a potential description of the behavior of the effect and its consequences.

Here it is:
https://docs.google.com/document/edi...3Yw9tafY&hl=en

[PetersCreek]

Welcome back, PatRKelley. I tried opening your link but Google Docs prompted me to log in. I have a login but not all members do. Besides, we frown on argument-by-link here. Please present your ATM theory, here in this thread and discussion can proceed from that basis. You may provide references via link, of course but I recommend they be readily accessible to all members.

Since it's been quite some time since your last visit, you might want to (re-)familiarize yourself with our rules, linked in my signature line below. I also recommend the Alternate Theory Advice link.

[PatRKelley]

Locally Nonuniform Expansion Pressure
as a Model for Dark Energy and Dark Matter

1. Introduction
This is a paper outlining a thought experiment.

Following and fleshing out the thought experiment led to several emergent properties. They appear to be supported by empirical data and provide a potentially unifying explanation for multiple phenomena.

This paper is broken into an abstract, a discussion, a section on possible predictions, a section on problems introduced by changing the expectations of current cosmology, a summary, and a section of issues with what the model assumes. It outlines additional problems with the assumptions of this model and contains a collection of errata, references and notes.

The concept is nonstandard. Every effort has been made to analyze it in light of the most current cosmological observations. It has been noted when either the model is no more predictive than other models, or where the initial predictions of the model diverge from existing papers and data.

The ideas presented here most closely resemble in action a postulated and described “dipolar” gravitational fluid [1], but go in a different direction to produce some predictions that could be potentially verified.

Essentially, the beginning concept is that negative pressure arises from the vacuum. This negative pressure is nonuniform (over local scales, typically less than 100 Mpc), and coupled with the distribution of matter. It interacts with the normal curvature of space time out of which arises the behaviors of dark matter, dark energy and potentially inflation. At the extreme, these properties are imagined as emergent and related rather than explicitly defined externally and fine tuned. Over greater than 100Mpc scales, however, it would still appear homogeneous.

There is another postulate that very nearly approaches the concept of this paper, postulating negative curvature.

...This means that the curvature between gravitationally bound systems (solar systems, galaxies, galaxy clusters, etc) must be negative. This conclusion applies to all globally flat universes with (semi-)localized gravitationally bound systems.[12]

However the conclusion that accelerating expansion is possibly illusory detailed in that paper is not part of the model presented here.


This idea and this paper do not posit an exact mechanism. This is, fundamentally, a thought experiment and description of the characteristics of this idea with a list of consequences for the observable universe.

It could be described as a nonparticulate localized (non-universal) negative pressure that increases with the mean radius of an adjacent void space, mimicking dark matter influence. This means a large region dominated by a dark matter halo can have, as a rule, smaller regions of dark matter influence (sub halos), none of which can be greater in magnitude than the “outermost” halo (usually at the cluster level).

The description of this negative pressure varying with the adjacent scale of local voids is an essential feature. It points to a reason for accelerating expansion, offers potential explanation for variations in dark matter halos of clusters, and produces simple coarse predictions for clusters of varying densities.

The final consequence is the potential modeling of dark matter, dark energy, and inflation as a single self-limiting effect, which could address the fine-tuning problem. There is no fine tuning if this is a single effect. It is behaving in a self-consistent manner rather than it being three or more separate forces acting serendipitously in concert.

[PatRKelley]

2. Abstract
The paper outlines an early thought experiment, takes it to further conclusions, and to possible predictions and problems. The model eventually involves the supposition of inhomogeneous negative pressure arising from the vacuum dependant upon void scale, and the effects that might be observed on larger scales as well as implications. It attempts to address the nature of dark matter and the cuspy halo problem, dark energy and accelerating expansion, and inflation. The possibility arises that all three (in addition to other observed effects of galactic evolution) could arise from the same modeled effect assumed to be the negative pressure from the vacuum arising from nonuniform expansion.

3. Discussion
The idea has a few presuppositions.

One is that, for now, we do not include universal, uniform expansion by way of a cosmological constant (additionally any scalars (simple calculations) designed to model expansion as a uniform featureless energy).

The other is that we suppress current concepts and definitions of dark matter and dark energy (without ignoring their associated data), with implications for the energy density of the universe and cosmological evolution scenarios. The observed effect of dark matter is concrete; this thought experiment interprets the potential source of it in a unique way, as a nonparticulate effect rather than a type of matter.

The model will eventually readdress the data associated with each of these concepts.

This idea started by wondering what anti-gravity would look like - negative pressure, effectively. Not the science fiction anti-gravity or the anti-gravity or photon universe of crank science, but what the real effect would look like. It is like asking what negative acceleration looks like. It is acceleration, the only thing really negative about it is the vector.

If we suppose that dark matter was not actual mass but instead a localized nonparticulate negative pressure, it still works to an extent. But this is simply reversing the sign and vector of gravitational acceleration, an exercise in simple math and not proof of anything.

What would distinguish a negative pressure from normal gravitational acceleration?

The negative pressure has to, in this model, have a source. Given that both dark energy and the cosmological constant were postulated to arise from negative pressure, we assume conservatively that this could be modeled in a similar way (negative pressure is not forbidden), basically a “pressure of expansion.” Why is it not uniform and universal? If we describe it as operating in an opposite fashion in curving space-time, the effect is opposed or suppressed by normal space-time curvature (standard baryonic matter gravitational influence).

The second supposition made is that if it (negative pressure due to expansion) varies, it has to have some rule for how and when it does. MoND (Modified Newtonian Dynamics) relies on the size and radius of galactic-level masses, and it has already been effectively ruled out by the pattern failing in some large elliptical galaxies. So we exclude the scale and diameter of visible matter as the sole varying factor in the scale of the negative pressure effect.

The other component in large scale structure that varies is the scale of intercluster voids. If we postulate that the scale of the effect relies on the scale of the adjacent voids (relatively low-density regions of space), increasing in effect with the scale of a void, there would be an in-between region where both would have an effect - essentially, the dark matter profile (shell) of spiral galaxies, and that it would vary more in attendance with void space than (just) galactic radius.

Still, this is not enough to distinguish it from dark matter. Up until this point, we have been reversing the signs. So we start to model the observable effects of this idea, absent dark matter and dark energy.

If it is opposed by gravitation (positive curvature), it should exert more effect on small, isolated masses (ones with less mass/imposing less curvature) within larger voids and less on the cores of large masses or masses in a region of smaller void space.

That is, a galaxy having a Keplerian/standard Newtonian dynamic stellar orbit distribution at its core would correlate with its overall mass. Generally, this is what we see: larger galaxies are more in line with predicted orbital velocities absent dark matter in their distribution at their cores (indicating a more “hollow” or “cuspy” dark matter profile). In short, larger galaxies generally have more pronounced central bulges.

But what about galaxies with comparatively less dark matter, as defined by stellar orbital velocities (inferred from red-shift measured edge-on)? That is, galaxies with nearly-completely Keplerian distributions (large ellipticals)? These typically are the galaxies cited in critiques of Modified Newtonian Dynamics as not obeying the distance/radius formula predicted for modified gravity and applied to spiral galaxies.

These should still have some dark matter effect at the edge, even at very high masses, unless they were at the center of a still larger mass, concentrated enough to mask out the dark matter effect, or in a region of relatively few voids all of a relatively small scale. The concept of smaller, more compact and less massive dark matter profiles interior to a cluster has been documented and analyzed[11], but again there are alternative explanations.

So, we have one of our first predictions: massive ellipticals (high surface brightness galaxies or early type galaxies ) should be interior to a larger mass, generally on the inside of massive clusters. Spiral galaxies (galaxies with their own dark matter profile) should exist at the edges of clusters, or in isolation or open clusters. This generally appears to hold up, as analyzed in Galaxy Occupation Statistics of Dark Matter Haloes: Observational Results [3]:

...the observed correlation lengths of early and late type galaxies in the 2dFGRS indicate that the former are preferentially hosted by massive haloes...
...
Among the total population, the fraction of early-type galaxies increases from about 25% in haloes with M ∼ 10^12h−1M⊙ to about 80% in haloes with M ∼ 10^15h−1M⊙. Among the central galaxy population, the increase of the fraction of early types with mass is stronger: in haloes with M >∼ 10^14h−1M⊙ virtually all central galaxies are early types.
...
In addition to a split in central and satellite galaxies, we have also divided the population in early- and late-type galaxies. The central galaxies in low-mass haloes are found to be predominantly late type galaxies, while those in massive haloes are almost entirely early types. This is in good agreement with the occupation statistics obtained from an analysis of the clustering properties of early- and late-type galaxies (van den Bosch et al. 2003a).

The statistics of galactic distribution show up as an emergent property in this idea, and do not take into account theories of galactic evolution. Saying that this validates nonuniform expansion pressure as a mechanism, however, is a potentially hollow assertion (no pun intended). Some of this distribution apparently is already predicted in CDM (Cold Dark Matter) models and simulations. [4]

In the speculative mental model presented so far, in a crowded enough region, not only is any major effect masked, but the nearby voids are too small to generate much of any effect locally. Additionally, the implications include the possibility that in larger groups, the dark matter halo effect would be asymmetrical - masked more to one side than another. A general observation of lopsidedness in galaxies with increase in group size possibly supports this idea as well.[9]

The implication of this is that a galaxy’s type (in non-dwarf galaxies) is determined by its position relative to other masses and voids, not only by its overall age.

The early– and late–type galaxy populations exhibit a significant segregation in mass: late-type galaxies dominate at low masses while early–type and intermediate objects dominate the high mass tail.[6]

We take this further - what happens to a spiral galaxy that moves towards the center of a large cluster (into a region of smaller voids and more mass)? In the environment of this idea, it would become more shielded from the dark matter effect, and would lose its spiral profile. The mass that was kept in check by its dark matter shell would spin out into the intracluster medium.

At z=0 we find evidence for strong evolution induced by the environment (Nurture). Transformations take place mostly at low luminosity when star forming dwarf galaxies inhabiting low density environments migrate into amorphous passive dwarf ellipticals in their infall into denser regions. The mechanism involves suppression of the star formation due to gas stripping, without significant mass growth, as proposed by Boselli et al. (2008a). This process is more efficient and fast in ambients of increasing density. In the highest density environments (around clusters) the truncation of the star formation happens fast enough (few 100 Myr) to produce the signature of post-star-burst in galaxy spectra. PSB galaxies, that are in fact found significantly clustered around the largest dynamical units, represent the remnants of star forming isolated galaxies that had their star formation violently suppressed during their infall in clusters in the last 0.5-1.5 Gyrs, and the progenitors of future dEs.[7]

This also means that we should see spiral galaxies undergoing distortion in the absence of other masses as they move towards the interior of a dense cluster. Any former elliptical galaxies would slowly regain a spiral profile if they moved out of the interior of a dense cluster (a potential explanation for “ring” galaxies, now able to retain the high velocity gas and dust from aging stars going supernova).

The outcome of this is that the intracluster medium should resemble the gas and dust that ellipticals lack. To an extent, this is true; however, the ratio of gas and dust in the intracluster medium differs from predicted rates of element production from type Ia and type II supernova of later generations of stars alone, possibly representing ratios produced by type II sn of early population III metal-poor stars[8].

The generally accepted theory for explaining the loss of star-forming gasses is ram-pressure stripping of galaxies passing through the intra-cluster medium. While this is a factor, there are some anomalous results that show a continuum of the ram-pressure stripping force with distance from a cluster center irrespective of the density variations in the ICM (intracluster medium)[10].

There should be no galaxies in isolation outside of a cluster or other large mass that lack dark matter.

There should also be no higher density knots of dark matter interior to another shell of dark matter (that is, densities higher than the outer profile).

Since the dark matter effect is reliant upon void “scale” (the larger an adjacent void, the higher the vacuum pressure), the effect of dark matter on galaxies should appear to be less backward in time (generally as voids would have been smaller). Spiral galaxies should become better defined over time.

The vacuum pressure should accelerate (increase over time) as regions of vacuum expand and merge. This does match somewhat the discovery of accelerating expansion, but isn’t truly a test. If this were also the effect of expanding space time, it would explain one of the conundrums of dark energy: the manifestation of local expansion, which would depend on adjacent voids and hence be relatively minor especially as measured in a region of relatively small adjacent voids (such as in a laboratory).

[PatRKelley]

4. Possible Tests and Predictions
This paper has outlined a few observational consistencies which can be put to empirical analysis. Mathematical models with the outlined self-limiting parameters might also bear this out, possibly by providing a model with little to no required fine-tuning, and capable of modelling conditions starting with just after recombination and ending with the current nearby universe.

A recent conversation has pointed out that evidence might be testable or recoverable based on the lensing effects of the proposed idea potentially differentiating it from CDM models. Given that a number of observations regarding predicted and observed gravitational lensing do not match[14], it might be possible to present ideas to more closely model observation with prediction in lensing data, and provide some support or refutation.

The author of this paper initially did not know about ram-pressure-stripping, lopsided spirals, the general trend of elliptical and spiral populations, the constituent gases of the intracluster medium, reheating, or many other aspects of cosmology. Many of these effects emerged as potential tests of the initial idea, however given that all were already established observations and many have alternative explanations, it remains to establish a testable, falsifiable scenario or prediction of this idea.

It might be possible to test this effect at a local level, if measurements could be taken that were accurate enough. One early effort made at estimating scales of effect resulted in a force on a small 1 gram mass at roughly ten meters of massless vacuum on the order of 10E-12 compared to its weight (gravitational acceleration) - in other words, roughly the scale of the gravitational constant, which itself isn’t easy to measure.

With smaller masses on smaller scales, the effect would be difficult to separate from the Casimir effect.

However, creating a hard enough vacuum in a large enough region, one might be able to measure an effect versus gravitational acceleration on a small mass suspended near another surface, and differentiate it from other tests not performed in a large hard vacuum but otherwise similar.

In other words, the antigravitational magnitude of the vacuum is not something that is amenable to harnessing for a flying car.

5. Problems
Removing dark matter and the cosmological constant present problems that have to be accounted for if this model is to be thought of as remotely plausible.

First, absent dark matter, the early structure problem resurfaces.

If we suppose that we have two forces driving matter to higher concentration (gravitation and negative pressure) we can then look at both high and low concentrations of matter as driving structure, each reinforcing the other when it comes to creating concentrations of matter and spaces of void. One idea of the outcome of this would be concentration of early matter into sheets of density around nearby voids.

Next, absent a cosmological constant or uniform dark energy, shouldn't there be disparities in measures of acceleration and expansion (if it is piecemeal and not uniform)?

Over long distances (megaparsec scales (100 Mpc +) beyond our local group) it would not affect the measure of expansion to an appreciable degree, since concentrations of mass and vacuum expansion would average out (the universe appears homogenous at scales above approximately 120 Mpc). However, it would result in more local disparities (less accurate or unexpected values of expansion measured in the local group and within 20 or so Mpc). Locally, the peculiar motion of galaxies and clusters appears to override the estimated values for hubble flow.

The next problem we encounter is that inflationary cosmology currently relies on amounts of dark matter being created to slow expansion after inflation, otherwise resulting in continued high rates of expansion and a resulting lack of structure due to the amount of dark energy. Add to this the estimates of matter versus dark energy required to make the universe appear “flat.”

If dark energy equalled vacuum pressure, then the expansion is self-limiting. The amount of vacuum pressure is limited to the scale of a region of void in large scale structure, which in the early universe is rather small. As time passes, its influence would increase as its expansion would cause voids to expand and merge, increasing its effect.

Inflationary cosmology also might be addressed as instead an initially massless vacuum. In the model presented in this paper, such a vacuum would expand extremely rapidly. At high enough expansion rates, it might be possible that the random fluctuations of the expanding vacuum would produce energy from an effect similar to Hawking radiation near a black hole: the expansion rate, exceeding the velocity of light, might be enough to separate virtual particle pairs. The energy produced would serve to halt the exponential vacuum expansion that caused it (the energy/particles) to precipitate in the first place, as the formerly free vacuum would be full of energy and thus mass. Inflation in this model is analogous to this nonuniform dark energy and is self-limiting as it approaches this rate of expansion: there is a flashover point, and expansion stops abruptly, slowly ramping up again until the void scale is large enough for the cycle to repeat.

The problem of course is calculating the magnitude and density of energy released, as the prediction of element abundances is one of the great successes of inflationary cosmology.

[PatRKelley]

6. Summary
We start with a supposition that the vacuum expands in the absence of matter. The more vacuum (the larger the void), the more the expansion, so it accelerates over time. This expansion produces a local negative pressure, but over megaparsec scales averages to nearly uniform expansion. This negative pressure manifests as the dark matter effect (a surrounding of negative pressure indistinguishable, currently, from a shell of matter). Because it is negative pressure, the effect diminishes in the presence of matter that exerts normal (positive) curvature of space time.

Larger clusters of galaxies can shield central galaxies from this effect, just as individual galaxies in open clusters can shield their own central bulge (diminishing dark matter profile towards the center of galaxies and clusters). In the absence of matter, conceptually the expansion could become so rapid that, much like Hawking radiation around a black hole, it would separate virtual particle pairs, releasing massive amounts of energy and producing enough energy and mass to halt its own acceleration. This requires a massive region of expanding relatively empty space (much larger than any current voids by orders of magnitude) and it should be stressed that this is not akin to a steady-state universe model of continuous matter generation. Rather, we are far away from any such state, specifically 13.7 billion years away, and essentially the future state of expansion (which most likely would occur over the horizon from existing masses) would resemble the initial inflationary conditions of the early universe.

This idea so far appears to have support in its predictions from observation, and the author’s ignorance of the current state of research and data meant surprise on finding out some of the predictions appeared to have empirical correlation; however, there is not currently a “fine” or differentiating test outlined here that would move this from a simple idea to a viable idea, so for now it remains an interesting thought experiment, nothing more.

================================================== ====
7. Cited Articles

[1] Model of dark matter and dark energy based on gravitational polarization
Physical Review D, vol. 78, Issue 2, id. 024031
Luc Blanchet* and Alexandre Le Tiec†
GRεCO, Institut d’Astrophysique de Paris—UMR 7095 du CNRS, Université Pierre & Marie Curie, 98 bis boulevard Arago, 75014 Paris, France
http://arxiv.org/PS_cache/arxiv/pdf/...804.3518v2.pdf

[2] Void hierarchy in the northern local void
Cosmological Parameters and the Evolution of the Universe. Edited by Katsuhiko Sato. Publisher: Dordrecht, Boston: Kluwer Academic, 1999. ("Proceedings of the 183rd symposium of the International Astronomical Union held in Kyoto, Japan, August 18-22, 1997"., p. 185
Faint structures in low density regions of the nearby Universe
U. Lindner and K.J. Fricke and J. Einasto and M. Einasto
Universit¨ats–Sternwarte, G¨ottingen, Germany and Tartu Astrophysical Observatory, T˜oravere, Estonia
http://arxiv.org/PS_cache/astro-ph/p.../9711046v1.pdf

[3] Galaxy occupation statistics of dark matter haloes: observational results
Monthly Notices of the Royal Astronomical Society, Volume 358, Issue 1, pp. 217-232.
Xiaohu Yang1,*, H. J. Mo1, Y. P. Jing2, Frank C. Van Den Bosch3
1Department of Astronomy, University of Massachusetts, Amherst MA 01003-9305, USA
2Shanghai Astronomical Observatory; the Partner Group of MPA, Nandan Road 80, Shanghai 200030, China
3Department of Physics, Swiss Federal Institute of Technology, ETH H¨onggerberg, CH-8093, Zurich, Switzerland
http://arxiv.org/PS_cache/astro-ph/p.../0410114v2.pdf

[4] Theoretical Models of the Halo Occupation Distribution: Separating Central
and Satellite Galaxies
The Astrophysical Journal, Volume 633, Issue 2, pp. 791-809
Zheng Zheng,1,2,3 Andreas A. Berlind,4 David H. Weinberg,1 Andrew J. Benson,5 Carlton M.
Baugh,6 Shaun Cole,6 Romeel Dav´e,7 Carlos S. Frenk,6 Neal Katz,8 and Cedric G. Lacey6
http://arxiv.org/PS_cache/astro-ph/p.../0408564v2.pdf

[5]Hierarchical Disk Galaxy Assembly as the Origin of Scatter in the z 1 Stellar Mass Tully-Fisher Relation
e-Print archive
Nicola Atkinson1, Christopher J. Conselice1⋆, Nicole Fox1
1University of Nottingham, School of Physics & Astronomy, Nottingham, NG7 2RD UK
http://iopscience.iop.org/2041-8205/..._714_1_L79.pdf
http://arxiv.org/PS_cache/arxiv/pdf/...712.1316v1.pdf

[6]The evolution of early and late type galaxies in the COSMOS up to z~ 1.2
The Astrophysical Journal, Volume 701, Issue 1, pp. 787-803 (2009).
M Pannella, A Gabasch, Y Goranova, N Drory,U Hopp, S Noll, R P Saglia, V Strazzullo and R Bender
http://arxiv.org/PS_cache/arxiv/pdf/...906.2810v1.pdf

[7]A snapshot on galaxy evolution occurring in the Great Wall: the role of Nurture at z=0
Astronomy and Astrophysics, Volume 517, id.A73
Giuseppe Gavazzi1, Mattia Fumagalli1, Olga Cucciati2, Alessandro Boselli2
http://arxiv.org/PS_cache/arxiv/pdf/...003.3795v1.pdf

[8]Intermediate-element abundances in galaxy clusters
The Astrophysical Journal, Volume 620, Issue 2, pp. 680-696.
A. D. Romeo, J. Sommer-Larsen, L. Portinari,V. Antonuccio-Delogu
http://arxiv.org/PS_cache/astro-ph/p.../0309166v1.pdf

[9]Lopsided spiral galaxies
Physics Reports, Volume 471, Issue 2, p. 75-111.
Chanda J. Jog & Francoise Combes
http://arxiv.org/PS_cache/arxiv/pdf/...811.1101v1.pdf

[10]Galaxy evolution in Abell 85:
Astronomy and Astrophysics, Volume 495, Issue 2, 2009, pp.379-387
H. Bravo–Alfaro1 ⋆, C.A. Caretta1, C. Lobo2,3, F. Durret4, and T. Scott5
http://arxiv.org/PS_cache/arxiv/pdf/...811.2686v1.pdf

[11]Truncation of galaxy dark matter halos in high density environments
Astronomy and Astrophysics, Volume 461, Issue 3, January III 2007, pp.881-891
M. Limousin1, 2, J. P. Kneib3, S. Bardeau4, 2, P. Natarajan5, 6, O. Czoske7, I. Smail8, H. Ebeling9, and G. P. Smith10
http://www.astro.ku.dk/~marceau/PaperII.pdf

[12]Inhomogeneous structure formation may alleviate need for accelerating universe
The Open Astronomy Journal, vol. 3, issue 1, pp. 145-149
Johan Hansson & Jesper Lindkvist
http://arxiv.org/PS_cache/arxiv/pdf/...906.3403v1.pdf <== Suspect article ("open" == "not refereed?")

[13]Chaplygin gas and effective description of inhomogeneous universe models in general relativity
Classical and Quantum Gravity, Volume 27, Issue 17, pp. 175013 (2010).
Xavier Roy and Thomas Buchert
http://arxiv.org/abs/0909.4155

[14]Effects of Dark Matter Substructures on Gravitational Lensing: Results from the Aquarius Simulations
Monthly Notices of the Royal Astronomical Society, Volume 398, Issue 3, pp. 1235-1253.
D. D. Xu1⋆, Shude Mao1, Jie Wang2,3, V. Springel2, Liang Gao3,4, S.D.M. White2,
Carlos S. Frenk3, Adrian Jenkins3, Guoliang Li5, Julio F. Navarro6
http://arxiv.org/PS_cache/arxiv/pdf/...903.4559v2.pdf

8. Reference

EVOLUTION SINCE Z = 1 OF THE MORPHOLOGY-DENSITY RELATION FOR GALAXIES
Graham P. Smith 1, Tommaso Treu 1,2, Richard S. Ellis 1, Sean M. Moran 1 and Alan Dressler 3
http://iopscience.iop.org/0004-637X/...X_620_1_78.pdf

Bulge and Clump Evolution in Hubble Ultra Deep Field Clump Clusters, Chains and Spiral Galaxies
Bruce G. Elmegreen 1, Debra Meloy Elmegreen 2, Maria Ximena Fernandez 2 and Jenna Jo Lemonias 2
http://arxiv.org/PS_cache/arxiv/pdf/...810.5404v1.pdf

The Rise and Fall of Passive Disk Galaxies: Morphological Evolution Along the Red Sequence Revealed by COSMOS
Kevin Bundy1,13, Claudia Scarlata2, C. M. Carollo3, Richard S. Ellis4, Niv Drory5, Philip Hopkins1, Mara Salvato4,10, Alexie Leauthaud6,12, Anton M. Koekemoer7, Norman Murray9, Olivier Ilbert8, Pascal Oesch3, Chung-Pei Ma1, Peter Capak2, Lucia Pozzetti11, Nick Scoville4
http://arxiv.org/PS_cache/arxiv/pdf/...912.1077v2.pdf

CENTRAL DARK MATTER TRENDS IN EARLY-TYPE GALAXIES FROM STRONG LENSING, DYNAMICS AND STELLAR POPULATIONS
C. Tortora1, N.R. Napolitano2, A.J. Romanowsky3, P. Jetzer1
http://arxiv.org/PS_cache/arxiv/pdf/...007.3988v2.pdf

Dark Energy and the New Cosmology
Michael S. Turner1;2
http://www.supernova.lbl.gov/~evlinder/turner.pdf


On Anisotropic Dark Energy
R. Chan, M. F. A. da Silva, J. F. Villas da Rocha
http://arxiv.org/PS_cache/arxiv/pdf/...803.2508v2.pdf

9. Acknowledgements
Thanks is owed to:
Ethan Siegel, PhD, a theoretical astrophysicist at Lewis & Clark college in Portland, OR, for his time and astute analysis of some of the assertions in this paper, pushing the author to research properly.



10. Issues
Issues brought up recently include:

1. Accounting for disparities in reporting and analysis regarding the amount of dark matter in elliptical galaxies (“none” versus high radius/cuspiness analyzed by x-ray) the assumption of this paper thus far is that the dark matter shell in ellipticals is far enough out (‘cuspy’ enough) to preclude any observational change in rotational velocity (the ‘disk’ falloff is beyond their furthest edge, as in the center of dense clusters). Due to commentary and ongoing research, the terms have been revisited and changed to ensure that the extreme “no dark matter” was removed, as there exists no research supporting the contention of ellipticals completely without dark matter. This did, interestingly enough, lead to discovery of papers detailing lopsidedness in spirals[9], and the trend of dark matter profiles in crowded conditions[11].

2. The falloff rate of the dark matter shell in dwarf galaxies (some reports suppose this is either a data artifact or a result of a sample that is too small for proper analysis).

3. Further research into the positional features postulated here appear to hold in a general sense for non-dwarf galaxies in open versus high-mass high-density clusters, including features of lopsidedness and increasing populations of high mass ellipticals. The “positional” predictions given in this idea (for instance: open versus dense clusters: specify ‘critical’ density?) which appear to not bear out. Analysis on this will include attempting to ascertain the relative position of ellipticals (is “within a cluster” a hard and fast rule, or a general observation?) Information on the position of ellipticals (high surface brightness) was obtained second-hand, see “voids” report below (low surface brightness outside of large and superclusters, high surface brightness generally seen within (usually meaning low dust/older and nominally elliptical)). There appears to be an evolving relationship where the ratio of dark matter to visible matter does not change for some redshift intervals in spiral galaxies:

There is also no evolution in the stellar mass-total halo mass relation at the same redshifts (Conselice et al. 2005a), suggesting that the stellar and dark mass components of disk galaxies grow simultaneously throughout this period. This result was later also found to be the case by e.g., Flores et al. (2006) and Bohm & Ziegler (2006).[5]

4. The latest dark matter research and simulations versus observation, matching and non-matching (prediction not correlating with observation).

To properly address these issues, more research will be undertaken to accumulate measures of hot X-ray emitting gas (primary current indicator for dark matter shells around elliptical galaxies and clusters given possible problems with using angular velocity (line of sight/highly eccentric orbits)), conventional rotational velocity curves (analyzing for cuspiness of dark matter versus size in spiral galaxies with an eye towards central bulge/mass correlation, not radius necessarily ). Proper analysis would be to analyze the data statistically from a “random” (usually edge-on galaxies, assumed to be representative of the population as a whole) assortment of spiral galaxies and see where the mean and outliers fall, attempting to see if there is a statistically significant correlation between dark matter falloff and mass in spiral galaxies. Further to this would be to analyze elliptical galaxies and see if the mass formula correlates as well (determine if some ellipticals are all bulge, no disk because of dark matter cusps).

[Nereid]

Locally Nonuniform Expansion Pressure
as a Model for Dark Energy and Dark Matter

1. Introduction
This is a paper outlining a thought experiment.

Following and fleshing out the thought experiment led to several emergent properties. They appear to be supported by empirical data and provide a potentially unifying explanation for multiple phenomena.

This paper is broken into an abstract, a discussion, a section on possible predictions, a section on problems introduced by changing the expectations of current cosmology, a summary, and a section of issues with what the model assumes. It outlines additional problems with the assumptions of this model and contains a collection of errata, references and notes.

The concept is nonstandard. Every effort has been made to analyze it in light of the most current cosmological observations. It has been noted when either the model is no more predictive than other models, or where the initial predictions of the model diverge from existing papers and data.

The ideas presented here most closely resemble in action a postulated and described “dipolar” gravitational fluid [1], but go in a different direction to produce some predictions that could be potentially verified.

Essentially, the beginning concept is that negative pressure arises from the vacuum. This negative pressure is nonuniform (over local scales, typically less than 100 Mpc), and coupled with the distribution of matter. It interacts with the normal curvature of space time out of which arises the behaviors of dark matter, dark energy and potentially inflation. At the extreme, these properties are imagined as emergent and related rather than explicitly defined externally and fine tuned. Over greater than 100Mpc scales, however, it would still appear homogeneous.

There is another postulate that very nearly approaches the concept of this paper, postulating negative curvature.

...This means that the curvature between gravitationally bound systems (solar systems, galaxies, galaxy clusters, etc) must be negative. This conclusion applies to all globally flat universes with (semi-)localized gravitationally bound systems.[12]

However the conclusion that accelerating expansion is possibly illusory detailed in that paper is not part of the model presented here.


This idea and this paper do not posit an exact mechanism. This is, fundamentally, a thought experiment and description of the characteristics of this idea with a list of consequences for the observable universe.

It could be described as a nonparticulate localized (non-universal) negative pressure that increases with the mean radius of an adjacent void space, mimicking dark matter influence. This means a large region dominated by a dark matter halo can have, as a rule, smaller regions of dark matter influence (sub halos), none of which can be greater in magnitude than the “outermost” halo (usually at the cluster level).

The description of this negative pressure varying with the adjacent scale of local voids is an essential feature. It points to a reason for accelerating expansion, offers potential explanation for variations in dark matter halos of clusters, and produces simple coarse predictions for clusters of varying densities.

The final consequence is the potential modeling of dark matter, dark energy, and inflation as a single self-limiting effect, which could address the fine-tuning problem. There is no fine tuning if this is a single effect. It is behaving in a self-consistent manner rather than it being three or more separate forces acting serendipitously in concert.

Welcome (back) to BAUT, PatRKelley!

Some 'setting the scene' questions, if I may.

The ideas presented here most closely resemble in action a postulated and described “dipolar” gravitational fluid [1]

What is [1]?

...This means that the curvature between gravitationally bound systems (solar systems, galaxies, galaxy clusters, etc) must be negative. This conclusion applies to all globally flat universes with (semi-)localized gravitationally bound systems.[12]

What is [12]? If [12] is not the source of the quote, what is?

This negative pressure is nonuniform

Are you using the standard definition of (negative) pressure? If not, what definition are you using?

In what sense is the negative pressure "nonuniform"?

... and coupled with the distribution of matter

How is it coupled? As in, what is the relationship between the non-uniformity (?) of the negative pressure and (what aspect of) the distribution of matter (I am not asking for the mechanism; your ATM idea does not deal with mechanisms, if I understand correctly)?

What is matter? Specifically, does "matter" include baryonic matter (both hot and cold)? CDM? neutrinos? photons?

[caveman1917]

Hi Nereid, just wanted to point you to post #6, where the references [1] etc are linked to.
He probably had to put things over multiple posts due to character limits.

[PetersCreek]

He probably had to put things over multiple posts due to character limits.

Yes, and I cleared some of those posts through the moderation queue just a while ago. Please bear this in mind until Mr. Kelley has a few more posts under his belt, at which time his posts will no longer be delayed by the queue.

[Nereid]

Hi Nereid, just wanted to point you to post #6, where the references [1] etc are linked to.
He probably had to put things over multiple posts due to character limits.

So I see, and thanks to PetersCreek for the reason why I did not see those posts when I responded with mine (the time stamps don't tell you when PatRKelley's posts became visible here, merely when they were first posted to BAUT).

I think I'll wait a day or so before posting further here ...

[PatRKelley]

My apologies, again. I wasn't aware that would happen.

I'm hoping it's reassuring for me to say this is the whole of the current paper, as of right now. So, no more late posts of walls of text.

I'm not sure if the rest of the paper helps to address your original question, Nereid: I'd meant Baryonic matter of practically any stripe, but of course not including CDM or indeed any particulate dark matter. The relationship of expansion pressure (negative pressure) to matter is that matter imparts positive curvature, which opposes negative pressure. Negative pressure, being the pressure of expansion, means that anything that effectively suppresses negative pressure suppresses expansion. The relationship comes from the pattern of void spaces defined by baryonic matter: the larger the empty void space, the more pressure of expansion at its periphery.

[Tensor]

I'm not sure if the rest of the paper helps to address your original question, Nereid: I'd meant Baryonic matter of practically any stripe, but of course not including CDM or indeed any particulate dark matter. The relationship of expansion pressure (negative pressure) to matter is that matter imparts positive curvature, which opposes negative pressure.

I would point out that the key paragraph in [12] is a just flat out wrong assumption. To clarify, here is the paragraph:

In general relativity, gravitationally bound systems have a positive space- time curvature. At the same time we know, from observations of the cosmological microwave background radiation (CMBR)[4],[5], that the global geometry of the universe most probably is flat. This means that the curva- ture between gravitationally bound systems (solar systems, galaxies, galaxy clusters, etc) must be negative. This conclusion applies to all globally flat universes with (semi-)localized gravitationally bound systems.

The paper makes the erroneous assumption that the overall topographical shape of the universe must be the average of the local topography. I notice that that paper has no topographical definitions within it. When considering whether global shape requires averaging of local shape:

1. When talking about positive curvature and negative curvature, are they talking about sectional or scalar curvature?
2. Is the manifold under consideration with positive and negative curvatures locally symmetric or just symmetric.
3. Is the manifold under consideration complete? Is it connected?

I didn't get started on this until late tonight, so I'll get back to you on the rest of this. But starting with a reference to a paper that uses a rather wrong statement about topographical conditions and then doesn't even bother to back up the statement with any kind of topographical explanation, is, reflects rather poorly on the idea presented.

They authors also seem rather unknowing about General Relativity. And how, exactly it uses energy and pressure terms from the Stress-Energy Tensor, times a constant, to determine the warpage of spacetime, using the curvature terms in the
Ricci Curvature Tensor. Gravitationally bound systems (remember gravity's reach is infinite so all systems are gravitationally bound) can have curvature terms that can be positive or negative (or zero) due to the tidal gravitational terms. If they would have bothered to actually run some numerical relativity through a computer (instead of just blowing it off) they may have realized that.

[PatRKelley]

I would point out that the key paragraph in [12] is a just flat out wrong assumption. To clarify, here is the paragraph:



The paper makes the erroneous assumption that the overall topographical shape of the universe must be the average of the local topography. I notice that that paper has no topographical definitions within it. When considering whether global shape requires averaging of local shape:

1. When talking about positive curvature and negative curvature, are they talking about sectional or scalar curvature?
2. Is the manifold under consideration with positive and negative curvatures locally symmetric or just symmetric.
3. Is the manifold under consideration complete? Is it connected?

I didn't get started on this until late tonight, so I'll get back to you on the rest of this. But starting with a reference to a paper that uses a rather wrong statement about topographical conditions and then doesn't even bother to back up the statement with any kind of topographical explanation, is, reflects rather poorly on the idea presented.

They authors also seem rather unknowing about General Relativity. And how, exactly it uses energy and pressure terms from the Stress-Energy Tensor, times a constant, to determine the warpage of spacetime, using the curvature terms in the
Ricci Curvature Tensor. Gravitationally bound systems (remember gravity's reach is infinite so all systems are gravitationally bound) can have curvature terms that can be positive or negative (or zero) due to the tidal gravitational terms. If they would have bothered to actually run some numerical relativity through a computer (instead of just blowing it off) they may have realized that.

I could remove the reference - the introduction (the beginning) - I attempted to comb the literature available (arxiv) for just about anything even remotely similar to this idea - I agree that the paper is not something I'm attempting to model ( I also disagree with their conclusions). I'm mostly in the opening paragraph attempting to address one of the initial comments I got on this paper five years ago: "If it worked like this, wouldn't somebody have already tried to model it this way?"

I wanted to be as thorough as I could in researching any other idea even remotely similar. I'm definitely not counting on their mathematics, and if it's not a good paper, I'd rather not refer to it.

[PatRKelley]

Addendum regarding sources:
I do not have access to an academic library, so where possible I took arxiv versions of what were peer reviewed and published articles found via Google Scholar, limited to publications after 2000 (roughly when accelerating expansion was discovered).

I also did not want to simply cite articles that sounded appropriate based on abstracts and claim support or affirmation of some of my ideas. So I tried my best where I could to read and understand.

I cannot say they all were taken from reputable sources. I am going to go back and attempt to find out which were peer reviewed, and which were not, and pick more carefully in the future.


I'll admit my grasp on the equations of relativity are not what they could be, which is part of the reason so far I haven't put in a mathematical formula.

================================================== =========
After reviewing another recent thread (here), I realize I am in the dark (no pun intended, again) regarding current descriptions of the expansion of space. My approach appears to turn the normal view on its head: the expansion of space is a cause, not a consequence, in my model versus it conventionally being viewed as a consequence of recessional velocities between galaxies. The approach I outline, instead, appears to make the estimation of "local" expansion measures possible, but requires that dark matter be an effect of this expansion. Back to the paper to make sure my terminology is correct.

[Nereid]

So far, it seems you've limited your review of astronomical observations to galaxies, clusters, and voids.

Have you looked at the observations - and analyses - of the CMB (cosmic microwave background), and of BAO (baryon acoustic oscillations)? These sets of observations are, AFAIK, fully consistent with LCDM models; in particular, with a universe that includes CDM at approx the same fraction of total mass-energy as inferred from galaxy and cluster observations (i.e. excluding dark energy).

I'd meant Baryonic matter of practically any stripe, but of course not including CDM or indeed any particulate dark matter.

What is the status of neutrinos? They are, after all, both particulate and dark (and matter)!

Are there any quantitative predictions, from your idea? If so, what?

[PatRKelley]

So far, it seems you've limited your review of astronomical observations to galaxies, clusters, and voids.

Have you looked at the observations - and analyses - of the CMB (cosmic microwave background), and of BAO (baryon acoustic oscillations)? These sets of observations are, AFAIK, fully consistent with LCDM models; in particular, with a universe that includes CDM at approx the same fraction of total mass-energy as inferred from galaxy and cluster observations (i.e. excluding dark energy).

No, I haven't, for a few reasons. For one, I'm not certain right now if (or how) a signature would appear from the early universe in this model: part of the model is that expansion is self-limiting (that is, in this case the "reheating" is the actual particle generation via expansion, which serves as a feedback mechanism to drastically halt expansion) and I'm not familiar enough with particle physics to know what such a signature would look like.

In short: I don't know. It is one of the (current) limits of this mental model.

What is the status of neutrinos? They are, after all, both particulate and dark (and matter)!

From my limited understanding, neutrinos make up an (estimated) minor fraction of the total dark matter required both for LCDM models and cluster and galaxy motion dictated by estimated DM component to visible matter component ratio. My personal take is that neutrinos are demonstrable, real particles: as such, they are not dark matter in the sense of the undetected (so far) fraction of particles that are otherwise almost exclusively gravitationally interactive.

They would be "standard" matter in this model, as far as I can surmise.

As far as their overall distribution and source nearby, I'll leave that to the ice cube neutrino detector to sort out. I do not currently have a specific prediction for neutrinos alone.

Are there any quantitative predictions, from your idea? If so, what?

Unfortunately, I'm still attempting to draft this up. I was looking at possibly deriving some of this from observing dark matter influence and attempting to coordinate magnitudes with nearby voids - such as attempting to figure out if the "great attractor" was actually an example of some of this effect: what's in the opposite direction to our local peculiar motion of our cluster and nearby clusters. I cannot find anything in the literature so far.

I hope to eventually formulate this, but it's been a while since I've been in calculus, and I think that's what I'm going to need at a minimum given that (at least in the ram-pressure stripping example and in examples of dark matter fraction increasing with galactic radius) the effect appears to follow a continuum. I don't think linear algebra would be enough.

As an example, the "shape" of a dark matter halo is not a simple sphere, especially in the case of a semi-open cluster (a cluster with a defined dark matter halo effect of its own) in this idea. Formulating how those shapes would appear would go a long way towards one of the definitive tests: attempting to model gravitational distortion of background galaxies.

I'm hoping to eventually devise a formula for smaller regions of void, and calculate if some effect could be teased out of laboratory experiments involving very cold, hard vacuum and experimental masses.

I'm glad you're taking a look at this. I appreciate it : )

[Nereid]

2. Abstract
The paper outlines an early thought experiment, takes it to further conclusions, and to possible predictions and problems. The model eventually involves the supposition of inhomogeneous negative pressure arising from the vacuum dependant upon void scale, and the effects that might be observed on larger scales as well as implications. It attempts to address the nature of dark matter and the cuspy halo problem, dark energy and accelerating expansion, and inflation. The possibility arises that all three (in addition to other observed effects of galactic evolution) could arise from the same modeled effect assumed to be the negative pressure from the vacuum arising from nonuniform expansion.

3. Discussion
The idea has a few presuppositions.

One is that, for now, we do not include universal, uniform expansion by way of a cosmological constant (additionally any scalars (simple calculations) designed to model expansion as a uniform featureless energy).

The other is that we suppress current concepts and definitions of dark matter and dark energy (without ignoring their associated data), with implications for the energy density of the universe and cosmological evolution scenarios. The observed effect of dark matter is concrete; this thought experiment interprets the potential source of it in a unique way, as a nonparticulate effect rather than a type of matter.

The model will eventually readdress the data associated with each of these concepts.

This idea started by wondering what anti-gravity would look like - negative pressure, effectively. Not the science fiction anti-gravity or the anti-gravity or photon universe of crank science, but what the real effect would look like. It is like asking what negative acceleration looks like. It is acceleration, the only thing really negative about it is the vector.

If we suppose that dark matter was not actual mass but instead a localized nonparticulate negative pressure, it still works to an extent. But this is simply reversing the sign and vector of gravitational acceleration, an exercise in simple math and not proof of anything.

What would distinguish a negative pressure from normal gravitational acceleration?

The negative pressure has to, in this model, have a source. Given that both dark energy and the cosmological constant were postulated to arise from negative pressure, we assume conservatively that this could be modeled in a similar way (negative pressure is not forbidden), basically a “pressure of expansion.” Why is it not uniform and universal? If we describe it as operating in an opposite fashion in curving space-time, the effect is opposed or suppressed by normal space-time curvature (standard baryonic matter gravitational influence).

The second supposition made is that if it (negative pressure due to expansion) varies, it has to have some rule for how and when it does. MoND (Modified Newtonian Dynamics) relies on the size and radius of galactic-level masses, and it has already been effectively ruled out by the pattern failing in some large elliptical galaxies. So we exclude the scale and diameter of visible matter as the sole varying factor in the scale of the negative pressure effect.

The other component in large scale structure that varies is the scale of intercluster voids. If we postulate that the scale of the effect relies on the scale of the adjacent voids (relatively low-density regions of space), increasing in effect with the scale of a void, there would be an in-between region where both would have an effect - essentially, the dark matter profile (shell) of spiral galaxies, and that it would vary more in attendance with void space than (just) galactic radius.

Still, this is not enough to distinguish it from dark matter. Up until this point, we have been reversing the signs. So we start to model the observable effects of this idea, absent dark matter and dark energy.

If it is opposed by gravitation (positive curvature), it should exert more effect on small, isolated masses (ones with less mass/imposing less curvature) within larger voids and less on the cores of large masses or masses in a region of smaller void space.

That is, a galaxy having a Keplerian/standard Newtonian dynamic stellar orbit distribution at its core would correlate with its overall mass. Generally, this is what we see: larger galaxies are more in line with predicted orbital velocities absent dark matter in their distribution at their cores (indicating a more “hollow” or “cuspy” dark matter profile). In short, larger galaxies generally have more pronounced central bulges.

But what about galaxies with comparatively less dark matter, as defined by stellar orbital velocities (inferred from red-shift measured edge-on)? That is, galaxies with nearly-completely Keplerian distributions (large ellipticals)? These typically are the galaxies cited in critiques of Modified Newtonian Dynamics as not obeying the distance/radius formula predicted for modified gravity and applied to spiral galaxies.

These should still have some dark matter effect at the edge, even at very high masses, unless they were at the center of a still larger mass, concentrated enough to mask out the dark matter effect, or in a region of relatively few voids all of a relatively small scale. The concept of smaller, more compact and less massive dark matter profiles interior to a cluster has been documented and analyzed[11], but again there are alternative explanations.

So, we have one of our first predictions: massive ellipticals (high surface brightness galaxies or early type galaxies ) should be interior to a larger mass, generally on the inside of massive clusters. Spiral galaxies (galaxies with their own dark matter profile) should exist at the edges of clusters, or in isolation or open clusters. This generally appears to hold up, as analyzed in Galaxy Occupation Statistics of Dark Matter Haloes: Observational Results [3]:



The statistics of galactic distribution show up as an emergent property in this idea, and do not take into account theories of galactic evolution. Saying that this validates nonuniform expansion pressure as a mechanism, however, is a potentially hollow assertion (no pun intended). Some of this distribution apparently is already predicted in CDM (Cold Dark Matter) models and simulations. [4]

In the speculative mental model presented so far, in a crowded enough region, not only is any major effect masked, but the nearby voids are too small to generate much of any effect locally. Additionally, the implications include the possibility that in larger groups, the dark matter halo effect would be asymmetrical - masked more to one side than another. A general observation of lopsidedness in galaxies with increase in group size possibly supports this idea as well.[9]

The implication of this is that a galaxy’s type (in non-dwarf galaxies) is determined by its position relative to other masses and voids, not only by its overall age.



We take this further - what happens to a spiral galaxy that moves towards the center of a large cluster (into a region of smaller voids and more mass)? In the environment of this idea, it would become more shielded from the dark matter effect, and would lose its spiral profile. The mass that was kept in check by its dark matter shell would spin out into the intracluster medium.



This also means that we should see spiral galaxies undergoing distortion in the absence of other masses as they move towards the interior of a dense cluster. Any former elliptical galaxies would slowly regain a spiral profile if they moved out of the interior of a dense cluster (a potential explanation for “ring” galaxies, now able to retain the high velocity gas and dust from aging stars going supernova).

The outcome of this is that the intracluster medium should resemble the gas and dust that ellipticals lack. To an extent, this is true; however, the ratio of gas and dust in the intracluster medium differs from predicted rates of element production from type Ia and type II supernova of later generations of stars alone, possibly representing ratios produced by type II sn of early population III metal-poor stars[8].

The generally accepted theory for explaining the loss of star-forming gasses is ram-pressure stripping of galaxies passing through the intra-cluster medium. While this is a factor, there are some anomalous results that show a continuum of the ram-pressure stripping force with distance from a cluster center irrespective of the density variations in the ICM (intracluster medium)[10].

There should be no galaxies in isolation outside of a cluster or other large mass that lack dark matter.

There should also be no higher density knots of dark matter interior to another shell of dark matter (that is, densities higher than the outer profile).

Since the dark matter effect is reliant upon void “scale” (the larger an adjacent void, the higher the vacuum pressure), the effect of dark matter on galaxies should appear to be less backward in time (generally as voids would have been smaller). Spiral galaxies should become better defined over time.

The vacuum pressure should accelerate (increase over time) as regions of vacuum expand and merge. This does match somewhat the discovery of accelerating expansion, but isn’t truly a test. If this were also the effect of expanding space time, it would explain one of the conundrums of dark energy: the manifestation of local expansion, which would depend on adjacent voids and hence be relatively minor especially as measured in a region of relatively small adjacent voids (such as in a laboratory).

If we suppose that dark matter was not actual mass but instead a localized nonparticulate negative pressure, it still works to an extent. But this is simply reversing the sign and vector of gravitational acceleration, an exercise in simple math and not proof of anything.

I'm trying to understand what 'dark matter' is, in this ATM idea, and I'm stuck right at the beginning, with this para.

Mass - cold, dark, matter - is well understood, in both Newtonian gravity and GR (General Relativity).

In each of these theories of gravity, mass does not have to be 'particulate' ('particles' are found in a very different, and incompatible, theory - quantum physics).

'Pressure' is also found in both theories of gravity, though there are some subtleties involved, unlike the concepts of mass.

The rotation curve of a spiral galaxy* can be modelled using a distribution of mass, without making any assumptions as to what the mass 'is'. Ditto, the velocity dispersion of stars in ellipticals and irregulars*. Ditto the velocity dispersion of galaxies* in a cluster. And so on.

What I don't understand is how models of the distribution of mass can be replaced by models of location-dependent pressure.

Can you explain please? Perhaps starting with a clear definition of 'pressure', as you use the term in this ATM idea (and, if possible, relating - compare and contrast - this to pressure in Newtonian mechanics and/or GR).

* these galaxies need not be limited to 'non-dwarfs'

[Nereid]

From post #4:
---------------------------------------------------------------------------------------------------------------------
The model eventually involves the supposition of inhomogeneous negative pressure arising from the vacuum dependant upon void scale

The other component in large scale structure that varies is the scale of intercluster voids. If we postulate that the scale of the effect relies on the scale of the adjacent voids (relatively low-density regions of space), increasing in effect with the scale of a void, there would be an in-between region where both would have an effect - essentially, the dark matter profile (shell) of spiral galaxies, and that it would vary more in attendance with void space than (just) galactic radius.

If it is opposed by gravitation (positive curvature), it should exert more effect on small, isolated masses (ones with less mass/imposing less curvature) within larger voids and less on the cores of large masses or masses in a region of smaller void space.

These should still have some dark matter effect at the edge, even at very high masses, unless they were at the center of a still larger mass, concentrated enough to mask out the dark matter effect, or in a region of relatively few voids all of a relatively small scale.

n the speculative mental model presented so far, in a crowded enough region, not only is any major effect masked, but the nearby voids are too small to generate much of any effect locally.

The implication of this is that a galaxy’s type (in non-dwarf galaxies) is determined by its position relative to other masses and voids, not only by its overall age.

We take this further - what happens to a spiral galaxy that moves towards the center of a large cluster (into a region of smaller voids and more mass)?

Since the dark matter effect is reliant upon void “scale” (the larger an adjacent void, the higher the vacuum pressure), the effect of dark matter on galaxies should appear to be less backward in time (generally as voids would have been smaller).

the manifestation of local expansion, which would depend on adjacent voids and hence be relatively minor especially as measured in a region of relatively small adjacent voids (such as in a laboratory).
---------------------------------------------------------------------------------------------------------------------
What is a 'void'?

From the above, it is a "relatively low-density region of space". But that's not very helpful; relative to what? And how low is 'low'? And 'density' of what?

How can the scale of a void be determined, quantitatively?

What is "void space"?

How can "a region of relatively few voids" be determined, quantitatively?

How nearby is 'nearby'? I.e. when does a distance stop being 'nearby'?

[PatRKelley]

If we suppose that dark matter was not actual mass but instead a localized nonparticulate negative pressure, it still works to an extent. But this is simply reversing the sign and vector of gravitational acceleration, an exercise in simple math and not proof of anything.

I'm trying to understand what 'dark matter' is, in this ATM idea, and I'm stuck right at the beginning, with this para.

Mass - cold, dark, matter - is well understood, in both Newtonian gravity and GR (General Relativity).

In each of these theories of gravity, mass does not have to be 'particulate' ('particles' are found in a very different, and incompatible, theory - quantum physics).

Again, I'm not that familiar sometimes with proper terminology.

In this idea, dark matter is not actually matter. It is an effect. It is not derived from calculating point masses, clouds of particles, or actually anything at all as a mass imparting curvature. The behavior (for the most part) in how it acts on galaxies and clusters is retained (the observations are valid, not discounted).

It is the source in this idea - the source being not a cloud surrounding galaxies and clusters - but instead the idea of the structure of low density regions that imparts the dark matter effect.

That's one of the reasons I'd mentioned that, in part of the thought experiment, we have to suppress current concepts of dark matter.

Despite the evidence for dark matter as a force in retaining high velocity gas that emits in the X-ray portion of the spectrum and as the cause of spiral galaxies retaining their fast-orbiting outer disk stars and gas and dust, there is no observational data of dark matter directly - only indirectly through its gravitational influence.

And in this idea, it is supposed there is no evidence for dark matter as either massive non-interacting particles or as "dark" conventional matter because it is not matter at all.

This model changes the source, but does not deny or refute the dark matter effect.

'Pressure' is also found in both theories of gravity, though there are some subtleties involved, unlike the concepts of mass.

The rotation curve of a spiral galaxy* can be modelled using a distribution of mass, without making any assumptions as to what the mass 'is'. Ditto, the velocity dispersion of stars in ellipticals and irregulars*. Ditto the velocity dispersion of galaxies* in a cluster. And so on.



* these galaxies need not be limited to 'non-dwarfs'

Well, as it's mentioned early on - the mass component of dark matter is not factored in as mass in these ideas. That's the part that might be difficult to get around - there is no real dark matter in this model: only an effect that mimics the influence.

While it is possible to represent a galaxy with visible and dark matter, it can get difficult to model the "cuspy" halo, as well as accounting for varying dark matter halos in clusters, the role of dark matter in galactic evolution, the profile of dark matter in dwarf galaxies, and the list goes on. In replacing dark matter with a dark matter effect, a lot of the properties of galaxies and galaxies in clusters and populations of galaxies ended up being predictions of the model.

That's part of what started this: the cuspy nature of halos made me start thinking about this, about modeling the influence of dark matter instead as an external force, or pressure, instead of as distributed mass.

In this case, also, I don't really know what it 'is.'

What I don't understand is how models of the distribution of mass can be replaced by models of location-dependent pressure.

Can you explain please? Perhaps starting with a clear definition of 'pressure', as you use the term in this ATM idea (and, if possible, relating - compare and contrast - this to pressure in Newtonian mechanics and/or GR).

This is again where it gets difficult, and my terminology might fail. I've deliberately used negative pressure as, basically, being a force that acts in an opposite fashion to standard space-time curvature. I don't want to use "antigravity" - as that's not really what it is: the way I think about it is vacuum as a gas that acts by increasing in pressure with volume, the opposite of a standard gas.

If a region gets larger, the pressure increases. This pressure acts in a "pushing" manner on matter, so it is effectively a "negative" pressure, or opposite to gravity. So, I'm probably abusing the term - but it appeared to be the closest I could get to the idea without inventing new terms or using such zingers as "anti-gravity." It really is, in this model, the pressure of expansion.

It would require a new model - a model that varies in the amount of dark matter effect based on the mass involved and the scale of the surrounding voids.


The next post asks about a definition of voids: if you don't mind I'll answer both in the same post.

What is a 'void'?

From the above, it is a "relatively low-density region of space". But that's not very helpful; relative to what? And how low is 'low'? And 'density' of what?

"Void" in this paper - yes, it looks like I'm going to have to go back and make a firm declaration of the definitions in this paper; I'm only generating a lot of confusion now, partly because the concept isn't modeled with mathematics yet.

A "void" is a region of space that is
a) relatively free of a high or moderate density of standard mass or matter (probably less than .1 atom/cm^3) and
b) relatively free of the influence (curvature of space) of concentrations of matter.

Most often, I'm talking about intercluster voids (on scales of 4-30 Mpc in size) - but this doesn't preclude the influence of smaller voids, just that (in this model) they have less and less effect as they decrease in size. Curvature of space (in this model) bounds voids, as do overdense regions.

So, voids within the space-time curvature of a large concentration of mass expand less (have less pressure of expansion) Since a void is bounded by regions of space-time curvature, bounding (and thus scale) could be said to be the mean diameter of the void related to nearby mass - if the nearest mass to the "center" of a void is 2 pc, the expansion pressure will be very low compared to that of a region with, say, 4 Mpc on average to nearby masses. The scale of the masses and their arrangement determine how much bounding effect they can impart.

How can the scale of a void be determined, quantitatively?

Part of the quantitative model, which I need to work on. Near as I can make it, it's based (currently, in my mind) on the mean distance to nearby masses that impart curvature and thus bound the void (they prevent expansion, effectively putting a limit on the rate of expansion for that region, and thereby putting a limit on the amount of negative pressure). A 4Mpc diameter void would have influence starting at, say, 1x at its periphery, while a 25Mpc diameter void would have an influence that starts at 3x. Just to put numbers out there.

What is "void space"?

Whoops. New term, huh? Let's just say "void" and "region of void" - kind of what I meant.

How can "a region of relatively few voids" be determined, quantitatively?

I should have said "region of relatively small-diameter voids" - it's not that there are fewer, it's that the rough diameter of a region of void is smaller, and is more influenced (expansion is more limited) by nearby masses.

How nearby is 'nearby'? I.e. when does a distance stop being 'nearby'?

"Nearby" in this means adjacent - for a spiral galaxy, the "nearby" voids are those which are immediately adjacent - when a galaxy is within a cluster, the "nearby" voids are those now smaller scale regions which, again, are immediately adjacent. A galaxy within a cluster might have an intercluster 25Mpc void close (at the edge of the cluster), but it is more strongly influenced by adjacent voids.

[Nereid]

How does your ATM idea differ, in its 'negative pressure', from an inhomogeneous, generalised Chaplygin gas?

Specifically, how does this idea differ from those of Bilic et al. (2002)? Or Caldwell et al. (1998)?

(FYI there are hundreds of papers published on this)

[PatRKelley]

How does your ATM idea differ, in its 'negative pressure', from an inhomogeneous, generalised Chaplygin gas?

Specifically, how does this idea differ from those of Bilic et al. (2002)? Or Caldwell et al. (1998)?

(FYI there are hundreds of papers published on this)

Well, based on my limited understanding of what's being stated in the paper, it appears that (and, again I might be wrong) a crucial difference would be the evolving scale factor in my idea. In the model given in Unification of Dark Matter and Dark Energy: the Inhomogeneous Chaplygin Gas:

Thus for the inhomogeneous Chaplygin gas we can take over the dust results bodily up to z ≃ 0. The picture which emerges is that on caustics, where galactic halos and clusters form, we have w ≃ 0, i.e., the fluid behaves as dark matter. Conversely, in the voids w ≃ − drives the acceleration as dark energy. Here the answer to the coincidence question mentioned earlier is that acceleration sets in only once the observed cellular structure develops.

...it appears (according to my reading) that the gas described here has the domains *(and thus the larger scale structure) forming well ahead of the migration of matter. That is, the domains where it acts like dark matter or dark energy are established without interaction with matter except after the fact, and not modified or affected by the distribution of matter. It also appears that they don't offer any smaller scale structure (or at least, that's my reading of it) beyond the initial 'caustics' defined as the large-scale variations in the CMB.

In Cosmological Imprint of an Energy Component with General Equation-of-State, dark matter is still assumed to be actual matter, and Quintessence is instead an inhomogeneous cosmological constant - with a set value that evolves over time. While it is "sensitive" to the initial mass-perturbations that drive large scale structure, and thereby appears to reinforce them, its magnitude is, again, set exclusive to the evolving scale of the structure around it.

The primary difference appears to lie in the assumption (in my thought experiment) that matter and the negative pressure component are directly co-evolving, rather than one force being a template for the rest of visible (or in the case of dark matter, invisible) matter. There is an immediate feedback in the growth and change of the negative pressure component that varies directly in proportion with the surrounding environment, specifically the distribution of matter. So, it drives some changes in the structure of matter, which consequently also defines its bounds and limits. This is a direct co-evolution in comparison to external brane or in-universe fields that do not vary in accordance with current changes in matter distribution.

At least, if my understanding of the two papers given is correct.

I initially did (by the way) see the explanations of Chaplygin gas models, and though that it might be the same as the model I was proposing - but (from what I could tell then, and my current reading) it's not the same. (I keep wanting to spell "Chaplygin" with an "m" for some reason...)

Another primary difference (from what I can tell) is that both of these models given above (QCDM and Chaplygin gas) the details of structure and predictions of galactic evolution and distribution are not affected or modified - the focus appears to be more on early very large scale structure and perturbations in the CMB.

[Nereid]

I think you're conflating cosmological models which incorporate an inhomogeneous, generalised Chaplygin gas with the concept itself.

From what you've written - to the extent I understand it! - I can't see any difference between your 'negative pressure' concept and an inhomogeneous, generalised Chaplygin gas.

Now it may be that your 'negative pressure' concept, as an inhomogeneous, generalised Chaplygin gas, includes some extra properties (e.g. the inverse of "the domains where it acts like dark matter or dark energy are established without interaction with matter except after the fact, and not modified or affected by the distribution of matter"), but otherwise seems to behave just as you describe 'negative pressure'.

The primary difference appears to lie in the assumption (in my thought experiment) that matter and the negative pressure component are directly co-evolving

This part I don't understand at all; can you clarify please?

Specifically, how does matter change, in your ATM idea, through interaction with 'the negative pressure component'? For example, do electrons gain mass? or do neutrinos change into protons? Or is it simply that the motion and distribution of matter is the net result of forces acting on the matter, which includes, in addition to those already factored into standard astrophysical models (gravity, electromagnetism), 'the negative pressure component'?

[PatRKelley]

I think you're conflating cosmological models which incorporate an inhomogeneous, generalised Chaplygin gas with the concept itself.

From what you've written - to the extent I understand it! - I can't see any difference between your 'negative pressure' concept and an inhomogeneous, generalised Chaplygin gas.

Now it may be that your 'negative pressure' concept, as an inhomogeneous, generalised Chaplygin gas, includes some extra properties (e.g. the inverse of "the domains where it acts like dark matter or dark energy are established without interaction with matter except after the fact, and not modified or affected by the distribution of matter"), but otherwise seems to behave just as you describe 'negative pressure'.

The primary difference appears to lie in the assumption (in my thought experiment) that matter and the negative pressure component are directly co-evolving

This part I don't understand at all; can you clarify please?

The Chaplygin gas, in its concept, apparently,

...it can behave as cold dark matter at small scales and as a negative-pressure dark energy component at large scales.

Cosmological consequences of a Chaplygin gas dark energy

Unfortunately, this doesn't explain much of how it is supposed to behave. The effect appears to be scale-dependent. That is, how the gas behaves (whether as dark matter or as dark energy) is determined by a scale factor.

It is not, from all that I can read and understand of these (sometimes very dense and complicated) papers, affected by matter. Rather, its effect is determined by scale and superimposed on matter.

The difference lies partly in this description of behavior: the pressure I'm attempting to model is the same effect at all scales - it always acts as a negative pressure, but is scale variant directly with the distribution of matter.

This partly means that, in the very early universe, regions of void would have been very small, but the effect would have been the same effect. Some models of Chaplygin gas appear to imply there is a state change based on "cells" forming due to matter mapping to the distribution of the Chaplygin gas, and that accelerating expansion occurs after the visible matter component aligns with the distribution of inhomogeneity in the Chaplygin gas.

None of the papers I can find explain much about fine scale structure regarding Chaplygin gas models, specifically how it models dark matter at the galactic scale. Most model it starting with perturbations in the CMB (Cosmic Microwave Background) and state simply that at a scale factor of n the behavior undergoes a transition, and could substitute for dark matter, so it could form the first large scale structure.

However, none of them appear to go into detail how that would apply, or what differences would be noted, in simulations should this be true beyond possibly earlier large scale structure.

The primary upshot of the difference between the two (imposition on matter and covariance with matter) is that the cuspy nature of halos does not appear to be addressed in a Chaplygin gas model - why would the effect of the Chaplygin gas (in its dark matter behavior-mode) diminish interior to the edge of a galaxy (in larger mass spirals with a pronounced central bulge), if it relies on a scale transition of a particular value?

The two behaviors it has - as dark energy and dark matter - allow for a transition phase, but this is (supposedly) at a larger scale than that of a cluster, much less a galaxy, and it comes up in my mind what the explanation is in this model for the cuspy halo problem?

I don't expect you to address this question; I'm curious about this, however, in that these models do not appear to attempt to simulate this gas below the level of large scale structure; this unfortunately impairs my ability to compare and contrast the two.

Specifically, how does matter change, in your ATM idea, through interaction with 'the negative pressure component'? For example, do electrons gain mass? or do neutrinos change into protons? Or is it simply that the motion and distribution of matter is the net result of forces acting on the matter, which includes, in addition to those already factored into standard astrophysical models (gravity, electromagnetism), 'the negative pressure component'?

Frankly, that's not something I've attempted to model or figure out: the exact nature of the effect.

I think of it (negative pressure) as a force - something like a Casimir effect writ large - so I suppose it would be "...the net result of forces acting on the matter, which includes, in addition to those already factored into standard astrophysical models (gravity, electromagnetism), 'the negative pressure component'"

It might also be something akin to what MoND attempts to model, although I hate to speculate in that direction.

[Nereid]

Repeating this (set of) question(s); they do not seem to have been answered in the last post, PatRKelley.

Your words:
The primary difference appears to lie in the assumption (in my thought experiment) that matter and the negative pressure component are directly co-evolving

This part I don't understand at all; can you clarify please?

Specifically, how does matter change, in your ATM idea, through interaction with 'the negative pressure component'?

For example, do electrons gain mass? or do neutrinos change into protons?

Or is it simply that the motion and distribution of matter is the net result of forces acting on the matter, which includes, in addition to those already factored into standard astrophysical models (gravity, electromagnetism), 'the negative pressure component'?

[PatRKelley]

Repeating this (set of) question(s); they do not seem to have been answered in the last post, PatRKelley.

Sorry, I'd noted that in editing the previous post - I'll post what I put in there in here, too...

Your words:
The primary difference appears to lie in the assumption (in my thought experiment) that matter and the negative pressure component are directly co-evolving

This part I don't understand at all; can you clarify please?

Specifically, how does matter change, in your ATM idea, through interaction with 'the negative pressure component'?

For example, do electrons gain mass? or do neutrinos change into protons?

Or is it simply that the motion and distribution of matter is the net result of forces acting on the matter, which includes, in addition to those already factored into standard astrophysical models (gravity, electromagnetism), 'the negative pressure component'?

Frankly, that's not something I've attempted to model or figure out: the exact nature of the effect.

To explain the "co-evolving" (sorry, have to keep a check on myself against introducing new terms that might not have a common definition; I have a problem with that occasionally, assuming an audience has the same concept of a term as I do...) - by that I mean:

Vacuum expanding "pushes" on matter, and the amount of this "push" is limited by the surrounding matter. The space expands, and the amount of "push" on surrounding matter increases. So, as the size of a void (I guess described as I did it in the last post or two) increases, it's "push" on the surrounding matter increases as well. The matter shows the effect of this "push" in the effect of dark matter.

Since the amount of "push" is dependent upon the size of the void, and matter defines the void periphery, they evolve in their behavior simultaneously (one affecting the other).


I think of it (negative pressure) as a force - something like a Casimir effect writ large - so I suppose it would be "...the net result of forces acting on the matter, which includes, in addition to those already factored into standard astrophysical models (gravity, electromagnetism), 'the negative pressure component'"

It might also be something akin to what MoND attempts to model, although I hate to speculate in that direction.


I apologize if my adding at the end of the last post after the fact meant it looked like I was being evasive.

[Nereid]

[...]

The next post asks about a definition of voids: if you don't mind I'll answer both in the same post.

What is a 'void'?

From the above, it is a "relatively low-density region of space". But that's not very helpful; relative to what? And how low is 'low'? And 'density' of what?

"Void" in this paper - yes, it looks like I'm going to have to go back and make a firm declaration of the definitions in this paper; I'm only generating a lot of confusion now, partly because the concept isn't modeled with mathematics yet.

A "void" is a region of space that is
a) relatively free of a high or moderate density of standard mass or matter (probably less than .1 atom/cm^3) and
b) relatively free of the influence (curvature of space) of concentrations of matter.

Most often, I'm talking about intercluster voids (on scales of 4-30 Mpc in size) - but this doesn't preclude the influence of smaller voids, just that (in this model) they have less and less effect as they decrease in size. Curvature of space (in this model) bounds voids, as do overdense regions.

So, voids within the space-time curvature of a large concentration of mass expand less (have less pressure of expansion) Since a void is bounded by regions of space-time curvature, bounding (and thus scale) could be said to be the mean diameter of the void related to nearby mass - if the nearest mass to the "center" of a void is 2 pc, the expansion pressure will be very low compared to that of a region with, say, 4 Mpc on average to nearby masses. The scale of the masses and their arrangement determine how much bounding effect they can impart.

How can the scale of a void be determined, quantitatively?

Part of the quantitative model, which I need to work on. Near as I can make it, it's based (currently, in my mind) on the mean distance to nearby masses that impart curvature and thus bound the void (they prevent expansion, effectively putting a limit on the rate of expansion for that region, and thereby putting a limit on the amount of negative pressure). A 4Mpc diameter void would have influence starting at, say, 1x at its periphery, while a 25Mpc diameter void would have an influence that starts at 3x. Just to put numbers out there.

What is "void space"?

Whoops. New term, huh? Let's just say "void" and "region of void" - kind of what I meant.

How can "a region of relatively few voids" be determined, quantitatively?

I should have said "region of relatively small-diameter voids" - it's not that there are fewer, it's that the rough diameter of a region of void is smaller, and is more influenced (expansion is more limited) by nearby masses.

How nearby is 'nearby'? I.e. when does a distance stop being 'nearby'?

"Nearby" in this means adjacent - for a spiral galaxy, the "nearby" voids are those which are immediately adjacent - when a galaxy is within a cluster, the "nearby" voids are those now smaller scale regions which, again, are immediately adjacent. A galaxy within a cluster might have an intercluster 25Mpc void close (at the edge of the cluster), but it is more strongly influenced by adjacent voids.

A "void" is a region of space that is
a) relatively free of a high or moderate density of standard mass or matter (probably less than .1 atom/cm^3) and
b) relatively free of the influence (curvature of space) of concentrations of matter.

Why does a void have this particular definition? For example, why isn't the Earth's atmosphere a 'void' (it has, after all, a relatively low density compared with the Earth's oceans and crust)?

All mass-energy curves space - that's built into GR - even a hydrogen atom, or a neutrino, or a radio frequency photon ... When does 'curvature of space' become an influence small enough ('relatively free') to qualify for a region of space being a void?

in this model they have less and less effect as they decrease in size

How does the effect scale with size? Is it linear, for example, or exponential?

Curvature of space (in this model) bounds voids, as do overdense regions

What does 'curvature of space' mean? Specifically, how does it differ from something with a similar name, in GR?

What is an 'overdense region'? How do the 'curvature of space' regions (which bound voids) differ from 'overdense regions'?

The scale of the masses and their arrangement determine how much bounding effect they can impart

What does 'the scale of the masses and their arrangement' mean? Specifically, how does this relate to the average density? Some kind of concentration parameter?
---------------------------------------------------------------------------------------------------------------------
Let's look at the Local Group, some hundred+ galaxies dominated by our own (the Milky Way) and M31 (the Andromeda galaxy). Where are the voids in the Local Group? How big are they?

Taking a slightly larger view, encompassing the galaxy groups 'nearby' our own; where are the voids? how big are they?

[PatRKelley]

A "void" is a region of space that is
a) relatively free of a high or moderate density of standard mass or matter (probably less than .1 atom/cm^3) and
b) relatively free of the influence (curvature of space) of concentrations of matter.

Why does a void have this particular definition? For example, why isn't the Earth's atmosphere a 'void' (it has, after all, a relatively low density compared with the Earth's oceans and crust)?

All mass-energy curves space - that's built into GR - even a hydrogen atom, or a neutrino, or a radio frequency photon ... When does 'curvature of space' become an influence small enough ('relatively free') to qualify for a region of space being a void?

in this model they have less and less effect as they decrease in size

How does the effect scale with size? Is it linear, for example, or exponential?

Curvature of space (in this model) bounds voids, as do overdense regions

What does 'curvature of space' mean? Specifically, how does it differ from something with a similar name, in GR?

What is an 'overdense region'? How do the 'curvature of space' regions (which bound voids) differ from 'overdense regions'?

The scale of the masses and their arrangement determine how much bounding effect they can impart

What does 'the scale of the masses and their arrangement' mean? Specifically, how does this relate to the average density? Some kind of concentration parameter?
---------------------------------------------------------------------------------------------------------------------
Let's look at the Local Group, some hundred+ galaxies dominated by our own (the Milky Way) and M31 (the Andromeda galaxy). Where are the voids in the Local Group? How big are they?

Taking a slightly larger view, encompassing the galaxy groups 'nearby' our own; where are the voids? how big are they?

I hope you don't mind if I slow this down a little, for my own sake. Taking it a piece at a time.

I've apparently gotten myself in quite a bit of trouble; a lot of confusion over terms, and a lot of (apparently) exasperation.

I'm going to take this particular post and review it, because it asks quite a few questions for which, right now, I don't have precise answers. The quantitative model, for instance, is a lot of what this asks about. Unfortunately, I don't think I have the mathematics to accurately evaluate and attempt to put into equation form what, for me, has been a more intuitive thought-experiment.

These may be what forces me to withdraw, if I can't come up with satisfactory answers in my own mind. This is part of what I wanted when I came here - specific challenges that might help to refine, define, or refute the idea entirely.

I won't ask for help, since that isn't what this forum is about, but there may be a substantial delay as I ask a teacher friend of mine to give me a crash-course in re-learning Calculus. I only ask for your patience, as I'm not attempting to be evasive, but rather to answer (for your sake and mine) the questions put to me in this post.

Thank you, and I hope to be back in a few days with either some meat to chew on, or a humble withdrawal of the entire proposal.

Pat Kelley

[Nereid]

No worries PatRKelley!

And no need to apologise; I've posted quite a bit, and, as you say, it takes time to write a decent response.

A suggestion, if I may: break your responses up into several posts, each addressing a compact part of the question/idea, and add 'to be continued' (or similar) at the end. That may make it easier to follow the various sub-threads, and also shows that you haven't overlooked a question (thus pre-empting any 'bump!' posts).

FWIW, the way you've addressed challenges, and answered questions, about the ATM idea you've proposed in this thread is exceptional (good!) ... few others who've proposed ATM ideas here have been as attentive, clear, focussed, and responsive as you have.

[Nereid]

PatRKelley, you might want to ask a mod to lock this thread until you're ready to resume. If you don't, it'll get locked 30 days after it was begun, and that's the only shot you'll have for your ATM idea. If the thread is locked now, the clock is stopped.

[Jim]

And with that in mind, I'm locking this thread. PatRKelley, when you're ready to resume, Report this post and ask to have the thread reopened.

(BTW, as Nereid said, you have done an exceptional job of following the intent and spirit of ATM.)