Tuesday, December 1, 2020

Imaginative economists needed

  Within the past two decades we have experienced two great economic crises, the 2007 recession and the Covid-19 dislocation.  We were prepared for neither, so the remedies were inefficient, insufficient and harmful.  Too many people were economically crushed by each recession and the national debt increased too much; that is, had we responded rationally, then fewer people would have lost so much and the national treasury would not be so emptied (indebted).

Here are some emergency government actions that should be prearranged and ready for future economic crises – these in addition to standard safety-net responses.

1) Pay a modest need-based wage supplement to all adults, rather than the flat emergency payment.  Not enough to de-incentiveize work.

2) Levy a temporary personal-wealth tax, enough to cover much of the extra treasury draw.  This recovers some of the dollars transferred from treasury to the rich by Republican tax cuts.

3) Temporarily slow all debt payments and rent payments, so the above modest wage can prevent defaults and bankruptcies.  Payments should suffice to preserve essential banking service.

4) Temporarily and reversibly adjust mortgage bases to partially blunt effects of neighborhood-wide property-value snowballs/dominoes.  This shares such owner risks between borrower and lender.  Far fewer owners would then go under water.  I discussed this earlier:     https://ethicsblackhole.blogspot.com/2018/10/flexible-mortgage-contracts.html

5) Prohibit excessive mortgage-loan riskiness now, eg excessive interest jumps, excessive 2nd mortgages.

6) Frustrate property predators, vultures, speculators, corporations, foreign investors.

How should this emergency-action list be modified and elaborated by astute ethical economists, ones concerned with survival and justice as well as domestic tranquility?  There is still the homelessness problem and the trade-balance problem needing such economists, also the overpopulation and environmental problems, also the problem technologists and automation displacing workers.

I despair seeing that reason withers as tribalism thrives.

Monday, August 24, 2020

How does gravity happen?

How does gravity happen?  How do separated particles or masses accelerate each other selfward?  How does momentum get to and/or from particles in this acceleration?  I believe that answers to these questions can be found in properties and actions of a medium that fills all space, which was and still should be named aether.
After all of my musings about gravity and after writing this little essay, I've come believe that the truth is to be found in this YouTube talk

Gravity mechanisms
1)  One view holds that space is filled with (ie aether contains) momentum-bearing corpuscles or wavelets that push matter particles in the direction of their translation or propagation as they are absorbed (possibly diverted) by those matter particles.  Owing to this action, each matter particle is surrounded by a spherically divergent field of diminished corpuscle or wavelet traffic in the direction away from itself, hence a field of excess momentum toward itself.  All particles in the universe would be accelerated toward that matter particle and analogously toward each other.  Gravity is mutual.  I spent some time considering the implications of this view.
2)  Another view holds that particles consume, destroy or otherwise diminish adjacent escape potential (fugacity), resulting in a spherically divergent fugacity field, a fugacity gradient toward itself.  Particles in such a gradient are accelerated toward lower fugacity, ie toward other particles, in a manner analogous to a proton experiencing an emf.  Presumably a particle accelerated this way sends momentum-bearing wavelets (rocket-like) in the opposite (rearward, uphill) direction, momentum being a conserved quantity.  This picture comes to mind when I attempt to understand General Relativity.
3)  Another view holds that particles consume or destroy adjacent aether, thereby creating spherically divergent fields of selfward aether flow that wash particles toward each other.  Here I'm attempting to convey the mechanism proposed by Distinti and others.
The reader is invited to critique, correct, refine and add to these generalizations (address: xmsdavidr@gmail.com).

Orbit features
General Relativity is a mathematical model that accounts for all observable orbits and all other gravity effects.  My wavelet model by itself can’t account for the simplest of orbits, two equal masses alone in an otherwise massless universe.  Not yet.
Perhaps something can be learned from two unequal masses alone in an otherwise massless universe.
Here we see some interesting locations between the masses – 1) the barycenter, c (center of gravity about which objects orbit, where fugacity is lower than elsewhere in the neighborhood) and 2) the fugacity saddle, s (where the two fields balance unstably and a test object would experience no gravity but would experience centrifugal force).  There are several other interesting locations in the system called Lagrangian points, where lighter objects can settle stably and co-orbit around the barycenter with the main masses.
It seems that the masses are accelerated toward and orbit the barycenter as if that were the source of the centripetally accelerating field.  It seems not to matter that the field everywhere is the sum of two gravity fields of masses that are moving and changing velocities.  The system behaves as if an object’s fugacity field is instantly established and/or eternal, despite the constant centripetal acceleration of the masses toward each other and the barycenter.  Perhaps the fields themselves are gravitationally accelerated as are the masses.  This raises the question whether a mass’s field plays a role in its responses to other masses, contrary to Newton’s laws.  I'm suggesting here that an object's gravity field responds to a neighbor's gravity field like light (as predicted by Einstein and observed by Eddington).
If you had no problem believing that two masses in an otherwise massless universe could orbit each other, then you tacitly agree that aether is, that aether sits or sloshes in an inertial frame of space.  Without a reference frame there can be no orbit and no centrifugal force to balance the centripetal force of gravity.  Moreover, the orbiting bodies must emit LIGO waves, losing kinetic energy (speed) to the aether; and they must gradually approach each other and merge – these two masses alone in an otherwise matterless universe.
        Losing kinetic energy to the aether is tantamount to experiencing a headwind, as expected of the wavelet mechanism of gravity.

Saturday, August 22, 2020

First-Sunday Seminar at Bellevue Christian

 For about half a year, I conducted a monthly Seminar on the Human Condidtion at Bellevue Christian.

These were the Sunday-School classes that should have been but weren't .

For this, I bought a lap-top and a large monitor and speakers, so all attendees could see and hear the material.

Each seminar consisted of experiencing and discussing three internet items:

a)  An existential song usually from the folk-revival movement.

b)  A trenchant lecture or report on a societal issue.

c)  A parable from the Country Pathos collection.

Here are all six seminars:


1a  One Voice    https://www.youtube.com/watch?v=Q41ctPLDHvU

1b  Collapse of Venezuela    https://www.youtube.com/watch?v=S1gUR8wM5vA

1c  These Hills    https://www.youtube.com/watch?v=9MWcRKKTxT0


2a  Both Sides, Now    https://www.youtube.com/watch?v=Pbn6a0AFfnM

2b  Jane Goodall    https://www.youtube.com/watch?v=51z7WRDjOjM&t=112s

2c  Unavailable    https://www.youtube.com/watch?v=UGRa7cBDoCA


3a  Mercy Now    https://www.youtube.com/watch?v=IT7NiFpJmvI

3b  Tribalism    https://www.youtube.com/watch?v=TWgM2gBRQrA&t=10s

3c  Coat of many colors    https://www.youtube.com/watch?v=c1zJzr-kWsI


4a  The Circle Game    https://www.youtube.com/watch?v=V9VoLCO-d6U

4b  Progressives hate progress    https://www.youtube.com/watch?v=PnitLNObR7c

4c  Tear Drops Falling    https://www.youtube.com/watch?v=K7T8ZbXVVcU


5a  Where have all the flowers gone    https://www.youtube.com/watch?v=bI3QVsW30j0

5b  Why societies collapse    https://www.youtube.com/watch?v=IESYMFtLIis

5c  Be Careful Of Stones That You Throw    https://www.youtube.com/watch?v=ZD46aUHMAQE


6a  Hard Times    https://www.youtube.com/watch?v=wE8L843iUy4

6b1  5 Important Questions    https://www.youtube.com/watch?v=fguhlv23lSg&t=1s

6b2  Case for Optimism    https://www.youtube.com/watch?v=t6JFr7QIkLE

6c  He Stopped Loving Her Today    https://www.youtube.com/watch?v=VExw77xJsBQ



Friday, August 21, 2020

Country Church at Bellevue Christian

On Second Sundays, some Singalong Pickers stayed and led the church-service music.
The Gospel Supplement was used as the hymnal.
On those days, congregational singing was spirited.
A misguided minister then forbad it and tried to turn the church Anglican, then came Corid 19.

2018 Nov 
Prelude Sing:  75  Shall we gather at the river  C
Gathering Hymn:  46  Keep on the sunny side  F
Communion Hymn:  38  In the garden  G
Distribution Instrumental:  54  Lower lights  G
Offertory Performance: Tim Hollimon Traveling the hway
Invitation Hymn:  50  Life’s railway to heaven  G
Closing Hymn:  104  Will the circle be unbroken  G

2018 Dec
Prelude Sing:  1  Quietly rustles the snow
Gathering Hymn:  2  What Child is this
Communion Hymn:  3  Beautiful Star of Bethehem
Distribution Instrumental:  4  Sweetly the bells
Offertory Performance: Ruslan&Amelie 5 Christmas Angels
Invitation Hymn:  6  One Christmas eve
Closing Hymn:  7  Silent Night (repeat first verse acapella)

2019 Jan
Prelude Sing: 43 Just a closer walk with Thee
Gathering Hymn:  60 Never grow old
Communion Hymn:  64 Old rugged cross
Distribution Instrumental: 89 Using my bible for a roadmap
Offertory Performance:  99 Where could I go
Invitation Hymn:  77 Softly and tendrly
Closing Hymn:  11 Down by the riverside

2019 Feb 
Prelude Instrmtl 2 verses: 32 I feel like traveling on
Gathering Hymn:  62 Old country church
Communion Hymn: 24 He took your place
Distribution Instrmtl 2v: 56 Gathering flowers for Master’s
Offertory Performance: 67 One step more
Invitation Hymn: 68 Pass me not
Closing Hymn:  10 The darkest hour is just befor dawn

2019 Mar 
Prelude Instrmtl 2 verses: 37 I’ll sing for my Lord
Gathering Hymn: 45 Just over in the glory land
Communion Hymn: 58 My Jesus I love Thee
Distribution Instrmtl 2v: 95 When Heaven comes down
Offertory Performance: Jack&Bill 55 Mansion for me
Invitation Hymn: 18 Give me the roses
Closing Hymn: 33 I saw the light

2019 Apr 
Prelude Instrmtl 2 verses: 36 I’ll meet you in the morning
Gathering Hymn: 49 Leaning on the everlasting arms
Communion Hymn: 80 Sweet by and by
Distribution Instrmtl 2 verses: 94 When He calls
Offertory Performance: Regen Back Silent empty chair
Invitation Hymn: 91 Washed in the blood
Closing Hymn: 97 When the roll is called up yonder

2019 May 
Prelude Pickers Sing all: 99 Where could I go
Gathering Hymn: 79 Standing on the promises
Communion Hymn: 25 Hide me Rock of Ages
Distribution Instrmtl 2 verses: 20 Gone home
Offertory Performance: Ashlie 2 Angel band
Invitation Hymn: 100 Where the roses never fade
Closing Hymn: 35 I’ll fly away

2019 June 
Prelude Pickers Sing all: 8 Church in the Wildwood
Gathering Hymn: 93 What a friend
Communion Hymn: 42 Jesus Savior pilot me
Distribution Instrmtl 2+ verses: 4 Beautiful isle of somewhere
Offertory Performance: Ashlie He reached down
Invitation Hymn: 29 Hold to God’s unchanging hand
Closing Hymn: 84 This world is not my home

2019 July 
Prelude Pickers Sing all: 13 Dust on the Bible
Gathering Hymn: 21 Great Speckled Bird
Communion Hymn: 71 Precious Memories
Distribution Instrmtl  verses as needed: 57 Mother’s Bible
Offertory Instrumtl  verses as needed: 57 Mother’s Bible cont'd
Special Music: 5 A beautiful life
Invitation Hymn: 39 It is well with my soul
Closing Hymn: 7 Bringing in the sheaves

Monday, May 11, 2020

Gravity Paradox

    Occasionally I enjoy contemplating a universe with only two bodies -- originally to address the questions of universal coordinates and space-filling aether, later to consider implications of LIGO waves, recently to see whether I would predict perihelion precession -- this time to see whether I can account for stable orbits.  As will be seen, I can't.
    Owing to their gravity fields, the two bodies would either crash together or orbit each other.
   Consider the simple case where the two bodies are of equal mass and they orbit each other on opposite sides of a circle as depicted below.
Fig 1.  Model of two equal bodies orbiting each other.  The sunbursts at top and bottom of the orbit circle show where the bodies are now.  The small circles at upper-left and lower-right of the orbit circle show where the bodies were earlier when forming the bits of gravity field reaching the bodies now.  Arrows toward the small circles and away from starbursts show the direction of the same bits of gravitational field then and now, respectively.  Dash lines show the paths of those bits between formation and action.  Vertical and horizontal arrows from starbursts show centripetal and tangential components of acceleration, respectively.
    As I began to construct this picture, I realized that the gravitational field experienced by each body now is that diverging from the other body earlier when it was behind where it is now.  As depicted, the gravitational acceleration is not purely centripetal as needed for orbit stability.  It is mostly centripetal, but there is (according to this picture) a small tangential component in the direction of the body's orbital motion -- exaggerated here for illustration.
    Naively viewed, the picture implies the energetically impossible continual acceleration of each body in its orbital direction --  at no cost to the source of the acceleration.  This paradox leads me to suspect that a gravitational field might coast along with the body from which it diverged, thereby accelerating the other body centripetally purely.  But would that field coast as if following the circle or the tangent?  By what mechanism?  Could it be that gravity's acceleratory force propagates in a medium (aether) that is pushed and/or pulled along by massive bodies?  Or could it be that the graviton doesn't leave the source until it impacts the target, since time cannot progress in a light-speed agent.
    Something amazing about the mechanism of gravitational-field propagation might derive from these considerations.
    My theory of gravity doesn't involve gravitons, , , yet:
 https://ethicsblackhole.blogspot.com/2020/03/mechanistic-theory-of-gravity.html


Tuesday, April 21, 2020

Glucose-Transport Rate Law

This is the back of our 60th-wedding-anniversary T-Shirt about 2018.

It's the model I produced as a graduate student about 1960 and studied for several subsequent years.

Here's a much later work product:
https://ethicsblackhole.blogspot.com/2017/09/ellipsoid-wall-thickness.html

Sunday, March 22, 2020

Letter to the editor Tennessean

   D. Bielawski’s Mar-20 letter, Put politics away, confuses me.  We both experienced the deprivations of the Great Depression and WWII, probably also unsupervised socialization, improvised recreations, unquestioned patriotism, hard work and awakening to racial injustice.
   All neighborhoods gave their sons to the war, sons who volunteered or responded proudly.  ‘War rich’ was a pejorative.  Word was bond.  The courage of our elders can hardly be imagined today – flying high-casualty sorties over Germany every day, launching beach assaults against well protected automatic weapons.
   With that life experience, I don’t know why Mr Bielawski doesn’t find draft-dodging Trump revolting.  How can he forgive Trump’s daily lies, his ignorance, lack of curiosity and his pretense, his long history of using lawyers to cheat contractors and investors?  How can he admire someone whose businesses have failed so unfailingly, someone utterly lacking modesty, generosity and empathy, someone who disrespects his spouses and brags about abusing defenseless girls?
   Those things “this president has done for this country” could have been done better by a president capable of respecting others, one surrounded by experts rather than toadies, one who considers unintended consequences before acting, one who loves truth and justice, one who doesn’t embarrass me every day.
   Disgust with Trump isn’t hate.  By contrast, Obama was subjected to unprovoked hate and lies from Fox and Breitbart pundits and from Trump throughout his tenure -- sadly also from many of my fellow bluegrass fans.

Monday, March 2, 2020

Wavelet Theory of Gravity

Prologue:  The wavelet theory described below predicts numerous observations and anticipates experimental results worth exploring, but I'm prepared to abandon it if it's found incompatible with general relativity.

   1)  The wavelet theory is a version of the gravity theory advanced by Newton's contemporaries,  LaSage's Theory of gravitation In essence, I postulate "wavelets" (randomly propagated momentum-bearing light-speed disturbances of space) in place of their "ultra-mundane corpuscles" (momentum-bearing particles darting randomly throughout space faster than light).  I will postulate sources, properties and actions of wavelets that can account for gravity.  The analysis leads to the view that the G of Newton's law is not a constant but a location-dependent coefficient, highest in matterless outer space, very high at the edge of a galaxy, lower in mid-galaxy space where we live, lowest in the middle of mid-galaxy stars and black holes -- this because gravitational energy is absorbed as it accelerates matter.
   My speculation was encouraged when Saul Perlmutter ,  Adam Riess  and  Brian Schmidt  received the nobel prize and confidently postulated dark energy, a repulsive force emerging in space and accelerating expansion of the universe.  It occurred to me that dark energy could cause other mass-dependent actions at distance -- including: 1) classical gravity; and 2) the additional centripetal force holding too-fast-orbiting peripheral stars in galaxies, attributed to dark matter.
    The appendix presents several testable predictions with which the wavelet theory can be validated or not.
   2)  In this theory, the agent of gravity is the “wavelet”, a quantum deformation of space propagated through space at light speed.  Wavelets begin spontaneously and randomly in all volumes of space, probably in pairs departing with their momenta in random opposite directions.  Thus every volume of space is replete with wavelets from elsewhere propagated through it in all directions, together with a few locally produced wavelets.  Quantum fluctuations might be the source of wavelets or might be said wavelets.  Wavelets pass through each other without affecting each other.
   3)  A wavelet carries a quantum of momentum.  The relevant deformation in the wavelet is longitudinal compression.  Space elements step forward between receiving the pulse from behind and passing the pulse forward, analogous to air molecules during vocal-sound or trumpet-sound propagation (not diaphragm sound).  Hence, the medium (aether) drifts bitwise in the dominant direction of wavelet propagation, ie toward masses.  This might be germane to gravitational lensing or frame dragging.
   4)  Matter bodies (stars, planets, moons, people) are penetrated by wavelets at great frequency on all surfaces from all directions, a fraction of them hitting mass elements in the bodies, most of them leaving the other side unscathed like neutrinos (Fig 1).  If a wavelet hits a mass element, it gives its momentum to the mass element, accelerating it in the direction of that wavelet's propagation.  The wavelet is therewith absorbed by the mass element.  The mass element then coasts in that direction and shares its momentum with associated matter.  Matter is thereby accelerated in the direction of most wavelets hitting it and/or passing through it.  Galaxies differ from unitary bodies mainly in absorbing a much larger fraction of wavelets on a diameter path from near rim to far rim, owing to the billions of stars etc on the path (Fig 1).
   5)  Wavelets are produced spontaneously in all space.  In outer space, far from galaxies and galaxy clusters, they are rarely absorbed, so wavelets in any direction are balanced by wavelets (more correctly wavelet resultants) in the opposite direction.  A lone particle of matter (p1) in that environment would be accelerated by wavelets at random times in random directions, like Brownian motion.  Owing to wavelet absorption by p1, there is a deficit of wavelets in all directions away from p1, hence an excess of wavelets toward p1 from all directions.  That spherically diverging wavelet imbalance surrounding p1 would accelerate all other particles in the universe (eg p2) toward p1, and similar wavelet imbalance diverging around p2 would accelerate all other particles in the universe, including p1, towards p2.  That wavelet imbalance and resulting acceleratory potential would decline with distance from a particle according to the inverse square rule, it being a spherically divergent field.
Fig 0 illustrates spherically divergent wavelet paths through a small or distant object.  The shortfall of outgoing wavelets and consequent imbalance are exaggerated to make them obvious; but large imbalances might be typical of a black hole or neutron star or galaxy.

   6)  To emphasize:  A wavelet that accelerates a particle is stopped by the particle and doesn’t continue to the other side.  The particle casts a spherically divergent shadow of wavelet-traffic shortage away from itself, hence a spherically divergent field of excess wavelet traffic towards itself distributed like gravitational potential in Newton’s Law of Gravity.  The wavelet imbalance accelerates all other matter in the universe toward that particle.  The wavelet deficit is a tiny fraction of wavelet traffic at that location.
   7)  If the universe had only one matter body, eg a star, it would be surrounded by a spherically diverging shadow of departing-wavelet shortfall, ie arriving-wavelet excess, this imbalance being the body's gravity field.  The shortfall or imbalance is a modest fraction of wavelet traffic into the star (unlike Fig 0).  Add to this universe a second matter body, eg a planet.  Each body would be surrounded by a spherically divergent shadow of excess wavelets towards itself.  Each body is accelereted toward the other body by the other body's wavelet imbalance.  They will crash together unless they have momentum transverse to the line between, ie unless they orbit each other providing balancing centrifugal force. [It’s fun to contemplate two matter bodies alone in the universe, orbiting each other, providing centrifugal forces balancing gravity.  Wouldn’t they send LIGO waves to the rest of the universe at the cost of their orbital momentum -- then collide or absorb each other when orbital momentum is insufficient.  How could this happen without a space-filling aether or universal coordinates for them to move with respect to – contrary to the conclusion of Michelson and Morley upon which modern cosmology is founded?]
   8)  Owing to wavelet absorption by a body's mass elements, the concentration of wavelets in a given direction declines “exponentially” along the path through a matter body in that direction (Fig 1).  Since that applies to all directions, the concentration of wavelets per se declines between points outside the body and the center of a body (Fig 3).  Particles nearer the body's surface encounter more wavelets and so contribute more to the body's gravity field than do more central particles.  This corollary seems contrary to Newton’s thinking.  In stars and smaller bodies this inhomogeneaity may be inconsequential.
   9)  Accordingly, Newton’s gravitational constant, G, declines with depth into a star (Fig 3).  The same applies to a galaxy with its trillions of wavelet-absorbing stars, planets and moons, its black hole and its massive dust and gas clouds.  G should be significantly greater at the galaxy’s rim than near the galaxy’s middle where we experience it and measure it.  This would account for the ability of stars near the galaxy’s rim to stay with the galaxy despite reaching expected escape velocities according to our local G.  Thus, the behavior attributed to dark matter is due to the gradient of wavelet concentration (hence G) between outer space and inner galaxy.
   As an aside, this thinking suggests that a galaxy's gravitational field might be oblate-spheroidally divergent, the details and implicatioins of which I've yet to ponder.
   10)  The wavelet hypothesis described herein seemed supported by the discovery that expansion of the universe is accelerating and by the postulate that this is due to a repulsive force accelerating galaxies away from each other.  That force was named dark energy and was said to emerge spontaneously in space, maintaining constant concentration between galaxy clusters as they separate from each other.  I began to suspect that dark energy might be quantum fluctuations producing momentum-bearing wavelets that carry out the accelerations -- including those of gravity.  It seemed that being pushed away from emptier space was the same as being pushed toward other matter and being pushed toward other matter was the same as being attracted to that other matter.
   However, it is not so obvious that this thinking explains the accelerated expansion of the universe that set me on this quest.  To explain accelerating expansion of the universe with this theory, one needs to suppose that there is a void outside the observable universe or matter outside of the observable universe to which the universe’s wavelets can go but from which wavelets aren’t coming into the observable universe.  That would result in a wavelet imbalance accelerating matter away from the universe's center and toward whatever is outside the observable universe.
   11)  It is worth noticing that each wavelet leaves a trail of wavelet-size aether advancements in its wake, so a wavelet imbalance moves aether, bit by bit, toward massive bodies.  This might account for gravitational lensing, the bending of light towards mass.  If so, space isn’t bent around massive bodies, it (aether) drifts towards massive bodies carrying light with it.
   12)  The wavelet theory of gravity implies a mind-boggling, hard-to-swallow corollary: the intensity of gravitational force in a neutron star or black hole is within us and all around us, unnoticed because it is mostly randomly directed, hence mostly balanced.
   13)  I hope to reconcile the wavelet theory of gravity with the Higgs mechanism when I can understand the latter.  Likewise for relativity.

Earlier versions:
https://ethicsblackhole.blogspot.com/2019/10/gravity-theory.html


GRAVITY THEORY ILLUSTRATED

According to the wavelet theory:

Momentum-bearing wavelets propagated in all random directions permeate all space, including that in all matter.  In passing through a matter body some wavelets are absorbed in giving their momentum to the mass elements encountered in the matter. This results in less wavelets leaving the matter body, hence an excess of wavelets toward the matter body --  a net acceleratory potential pushing all matter toward the body.  That pushing potential is gravity.  The distribution of that external centripetal force able to push  matter toward the body is the body's gravity field.  It extends to the edge of the universe, diminishing as 1/r^2.

Figs 1 - 3 illustrate the intensity of wavelets between opposite edges of a matter body (star, planet, moon) or of a collection of matter bodies and black holes (galaxy).  An intensity or density or concentration of 1.0 is that of distant space far from any galaxies, so the charts show intensity or density or concentration of wavelets relative to that in the universe's most matterless space.
Fig 1 shows the exponential decline of rightward wavelets along the path from left edge to right edge of a matter body and the exponential decline of leftward wavelets from right edge to left edge, with six different absorption fractions: 5%, 20%, 50%, 90%, 99% and 99.9%.  I suspect that a star absorbs less than 5%, a planet absorbs less than 1%, and a moon absorbs less than 0.1% – in each case probably much less.  A galaxy, by contrast, may contain 1 trillion stars, so it might absorb more than 90% of wavelets along a diameter between its rims.  The absorption of radially-directed wavelets between opposite rims of the galactic disc would be greater than the absorption of axially-directed wavelets between faces of the galactic disc -- implying interesting shape of a galaxy's gravity field.

Fig 2 shows the net wavelet traffic between edges of a lonely matter body or of a lonely galaxy.  Plotted is the difference between opposing wavelet traffic and actions, with absorption fractions of 5%, 20%, 50%, 90% and 99%.  The net wavelet traffic at an edge is 1.0 minus that which makes it from the other side.  If, for example, 20% is absorbed and 80% gets across, the difference at the edge is (1.0 - 0.8) = 0.2, that being a measure of the acceleration forcing the edge matter towards the middle.  The acceleration declines towards the middle, where the difference between opposing wavelet actions is zero.  That is, matter at a body’s center is pressed centripetally by more peripheral matter, but it is not accelerated by local wavelets, which are in balance at that spot.  I believe I'm saying that this theory has no singularities.  Likewise, a body in a galaxy’s center of gravity is not accelerated centripetally.  Interestingly, bodies at the galaxy’s rim are most strongly accelerated centripetally, that possibly being the extra force preventing stars near the rim from escaping despite angular velocities greater than presumed escape velocity – this being the effect historically attributed to dark matter.  The straight-line declines of acceleration vs position at absorptions less than 50%, are like those of Newton's law.  The bent-line declines at 90% and 99% predicting extra centripital force at galaxy's rim are peculiar to the wavelet theory.

Fig. 3 shows the wavelet density at positions between edges of a body or galaxy.  It’s just the average of rightward wavelet traffic and leftward wavelet traffic along a diameter.  At the edge, a 50% absorption results in a density of (1.0 + 0.5)/2 = 0.75.  The higher absorptions (>90%) are associated with a significant dip in the profile, there being significantly more wavelet traffic near the edge than near the middle.  This distribution should result in stronger gravity fields around stars near a galaxy’s edge than around similar stars near the galaxy’s middle.  Planets should orbit their stars faster near the galaxy’s edge than near the galaxy’s middle.  That might be a distinguishing feature of the wavelet theory of gravity.

Fig. 4 shows the dependence of gravity on mass.  The dependent variable is gravitational attraction relative to an hypothetical maximum, that maximum being that which would occur if a matter body absorbed all of the wavelets coming to it.  The independent variable is actual mass relative to the mass that would absorb all wavelets, were the beginning proportionality to continue like the dashed line.  I speculate that stars, planets and moons absorb less than 5%, and so would be on that part of the relation at the lower-left corner, which is essentially rectilinear and proportional as Newton supposed.  Galaxies, with their trillion stars, planets and moons, plus dust, gas and black holes, might absorb more than 90%, so more mass would not increase their rim-to-center acceleration proportionally.  Sensitivity is fractional change in a dependent variable per fractional change in an independent variable.  Sensitivity of attration to mass in stars, planets and moons is postulated here to be about 1.0Sensitivity of centripetal attraction to mass in a galaxy might be about 0.1.

As seen, this project consumed the last of the Dietzgen Graph Paper that I kept since retiring 25 years ago.

Appendix, Experimental expectations:
The wavelet theory of gravity predicts several experimental results which, if observed, might validate the theory.  At least some of them might reveal limits to Newton's law and/or Relativity.

1. a) If one gradually lowers a G-measuring device (sealed in a vacuum bulb and protected from temperature, vibrations, electromagnetic fields and shock) into the 12 km hole dug by Russia in a competion with the USA , it will show G declining slightly with depth toward the earth's center according to Fig 3.
1. b) If one gradually lowers that G-measuring device into the deepest part of the ocean, it will show G declining slightly with depth toward the earth's center according to Fig 3, hopefully detectably.
1. c)  If one lofts the G-measuring device into space and probes areas nearer the sun and throughout a trip toward outer solar-system limits, it will show G increasing with distance from the sun and other massive bodies, implied in Fig 3.  This finding would strongly support the wavelet theory of gravity.
1. d)  If one could send that device further toward space outside the milkyway, it will show G increasing with progress into more empty space as in Fig 3.

2.  a)  If one estimates G from planet-orbiting velocities near our galaxy's middle and near its rim, the G will be much greater near the rim than near the middle, this owing to less wavelet traffic near the middle, as in Fig 3.
2.  b)  The same would be expected with axial distance from our galaxy's central plane, as in Fig 3.

3.  If one calculates G from velocities of stars orbiting a galaxy, that G will be maximal near the galaxy's rim and minimal near the galaxy's middle, as in Fig 3.  This is well established and evoked the postulate of dark matter.

4.  If it were possible to estimate relative galaxy masses by visual means and to estimate relative galaxy field strengths from effects on neighboring galaxys' trajectories, it might be found that gravitational field strength increases less than proportional to mass, as in Fig 4.

Discussion:  
  The Michelson/Morely experiments not withstanding, I believe that light and gravity are propagated in aether, and that aether provides a frame in which and relative to which matter and energy move.  Accordingly, the orbiting bodies producing the LIGO waves would have sent the waves, lost speed and merged even if they were the only masses in the universe.  Newton would agree, having contemplated centrifugal force in a lonely system.
  Most physicists would reject the wavelet theory because it predicts that moving bodies would be slowed by headwind, the frequency and momentum of wavelet interactions encountered from the front being greater than those catching up from behind -- apparently defying Newton's first law of motion.  But: 1) The headwind would be minuscule in bodies moving slowly relative to the wavelets (and light); 2) Gravity wavelets might be faster than photons, in which case the headwind would be minuscule even if bodies were moving near light speed; 3) Newton's first law is untested axiom (common-sense assumption); moving bodies must experience headwind.  Specifically, all moving bodies must produce LIGO waves as they are deflected by gravity from all other bodies in the universe, the energy of those waves being at the expense of the body's velocity.
  A matter body always has its gravity field, as it is an assembly of particles having gravity fields since inflation. What departs from a body with the speed of gravity is a wave of acceleration, and this is subdued since it involves momentum-conserving interactions.  Thus, two bodies passing in space or orbiting each other might interact as if gravity action is infinitely quick.
  I don't know why General Relativity predicts planetary motions better than do Newton's laws.  The geodesic talk sounds spooky and not explanatory.  Gravitational-potential gradients and accelertions are probably more germane.  In other words, I believe that matter bodies in space are steered by axial and transverse accelerations rather than geodesic grooves.
   I don't have a clear notion of the potential referred to above.  I suppose it acts on mass elements like heat acts on gas molecules.  Perhaps it should be called fugacity potential.  Perhaps my wavelets bear escaping energy rather than momentum.
  It is fun to contemplate how two lonely bodies passing each other in opposite directions would perceive each others locations and fields and find themselves in mutual orbit.  And that's what I'll continue doing.