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 1.0.
Sensitivity 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.
