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Hey Tom, what do you think?: I propose that there is a minimum unit of matter which as part of its nature throws out a minimum unit or quantum of gravity, let's call that latter a graviton, distributed spherically and superficially around itself and pulling toward itself all of space and incidentally all mass in the universe but only out to a fixed radius, call it Rg, and outside the sphere of that radius, not at all. This radius Rg is say a third of a galactic radius for an average galaxy, or so. By "superficially", I mean that the pull on a bit of space at some radius is in proportion to the relative amount of the sphere's surface at the given radius occluded by that bit of space. Like a shadow effect, although another bit of space behind the first is no less pulled or squeezed because of the effect on the first.
Then the force of gravity on a particle will be in the direction of the average inverse-distance-squared-weighted center of gravity of the mass within the radius Rg of the particle. A triple integral over all space summing up these quanta of gravitational effects, zero outside Rg, will calculate the local effect of gravity.
Then matter far from the center of a galaxy will not be gravitationally influenced by the black hole at the center of the galaxy nor the other half of the galaxy across the other side nor even some part of the near side of the galaxy nor anywhere outside a sphere around it.
Then arms will form with matter orbiting, or rather slowly spiraling inward around, the center-lines of the arms.
7/23/2020: Although clear enough let me elaborate: Instead of orbitally rotating around the galactic center, each particle or star will rotate around its local center of gravity, which will only be the galactic center if that lies within Rg of the particle, but will instead be the centerline of its arm, if outside that radius. Also, because the mass in an arm is more at the root than at the tip, the local CoG will be closer to the center of the galaxy than the particle itself. This accounts for the whip-segment-like cohesion of an arm that pulls the next bit of the arm along behind the leading, adjacent, inner bit, and it further predicts, if you didn't figure this out already, that spiral arms should be (1) rotating around their centerlines and also (2) pulling toward their root, so there should be evidence of both in the pictures. Well, I made this prediction before I saw the photographs, because I'm just an armchair philosopher contemplating stuff in my head, but here is one in today's news of a lovely spiral arm galaxy (or two), and do you not generally speaking see light tending toward the red on one side of each spiral arm and light tending toward the blue on the other side of each spiral arm, consistent with the red-shift and blue-shift of light from objects moving away from and toward the viewer? Do you not further see several strands diagonally oriented in toward the center of the arm and toward the root thereof, as if drawn by some unseen force not just around the arm centerline but toward the arm root? Yes you do. There is a lot going on in such a photo, but yes those are generally generally true.Further, bars will form, swallowing up galactic arms as they spiral toward the greater mass in the bar end relative to the dispersed arm.
Furthermore, the de-linking of spiral arm style rotation from normal orbital rotation should occur at about Rg from the galactic center, and although rather discrete and discontinuous looking, that's because there is such a huge proporition of total galactic mass at its center, and when your chosen stars' distances start to go just about, and then slightly more than, Rg away from that center, the pull from that concentrated mass drops proportionately hugely. Next prediction is that spiral arms should be pulled to rotate around the galactic center more by way of following the next inner segment of the whip-line of the arm's center of gravity than by orbital mechanics a la Newton, and it's not exactly a problem if that rather peters out because it's really only getting pulled around at the root of the arm by a rather weak, transitive pull from whatever is also rotating interior to the transition point at Rg from the galactic center. So you might expect for that non-orbital rotational pull to weaken and dissipate, and indeed for a spiral to spiral itself inward to what is ultimately going to form a rather static bar, that doesn't rotate the galactic center at all, but only rotates around itself.
There you go. I just wanted to pop this into the argument here, after a nice night into and out of sleep, thinking about it. It's been quite a lovely puzzle. Oh, one more thing. Do you notice that the blue bits seem brighter than the corresponding red bits in the photo above? I'm thinking that instead of being a miraculous and coincidental distribution of interstellar dust at just the right places, it's because the Doppler effect not only shifts frequency, but also shifts total energy. So that from the same light source moving toward or away, appearing more blue = higher frequency (and because each sinusoidal wave component is a single pulse there are more of them and more total energy) while redder = lower frequency AND lower total energy, thus not as bright. So far, consistency.
Now, back to the original text from last summer.
Then we have an explanation for galactic spiral arms and bars, which otherwise should spin out and de-cohere like cream in coffee after a few rotations, if the effect of gravity were not quantized and local.
Tom said: Keep up the good work veatch.
Why should I not think so? Well, I have thought about standing waves quite a bit because I am a phonetician and wrote about them in my Ivy League dissertation, which at least some of my advisers actually read (thanks Mark!), and I have also been a whitewater kayaker (even taught kayaking at Stanford, if you want to glean some prestige value for this tidbit of knowledge), and yes standing waves are right there in the middle of both of them.
A standing wave is where there's a wave but it doesn't move downstream. There's a standing wave at the bar of the Columbia River, I've heard: a towering wave, and water rushing through it, but the wave doesn't itself move downstream like the water. It's pretty cool. You can also make a standing wave by tying one end of a rope to a door handle, then flip your held end up and down, so a wave travels down the rope to the door handle, then the reverse wave travels back toward you, and if you do another at the right time, instead of having what's obviously two waves going past each other in the middle of a medium (the rope), there gets to be something like a swing or a vibrating string on a guitar, or maybe a double-vibrating string where there's a lying-down S that reverses itself with every cycle.
Now I know of standing waves in two contexts: the human vocal tract in vowel resonances and the run-out section of a whitewater rapid leaving a drop and entering a flatwater section, while the rapid itself peters out in what are also called whoop-de-doo's (or as I later remembered, compression waves).
In both cases just like the rope and the guitar string, there is a stress-embodying medium, the rope or the air or the water, within a longitudinal channel, which is subjected to longitudinally-travelling waves of pressure (in the air) or lateral displacement (of the guitar string) or longitudinal displacement (of the water in the rapid).
In the case of the vocal tract a popping sound, which is like a sum of low, medium, and high frequency pops all together to make a pretty sharp pop, is created in the larynx once for each glottal cycle, which is called the fundamental frequency. This pop sends a high-pressure wave travelling toward the open end at the lips at the speed of sound. When the wave hits the open end the impedance caused by the constricting channel goes to zero, and the wave sort of falls out the open end, dissipating suddenly so that it pulls a bit of a vacuum behind itself at the lips, which then becomes a low-pressure wave travelling the opposite direction back down toward the glottis. And by the time it reaches the glottis, that might be closed again. When a wave hits a closed wall at the end of its channel, it bounces back up the channel once again. In this way positive and negative reflecting pressure waves travel up and down the vocal tract, added to by more waves with each glottal pulse.
The way to understand it is by considering what happens when two identical (same frequency) waves travel in opposite directions in the same channel. What happens is what you saw in the rope example, a standing wave: at a specific point, think about the two waves travelling past each other. When the high points of both waves pass each other, at that location, the pressures add together and there is double-high pressure there for an instant. At the same location, the low points of both waves (if they are the same length or frequency) will pass each other, half a cycle later in time, and when they subtract together, there is a double-low pressure at that point for an instant. So at that point, the pressure goes up and down, up and down. (If the two waves are of different frequencies, then you get chaos, but if they are the same, you get consistent, repeating, big action.) Whereas there is another point, called a "node", where the waves happen to cancel each other out: while the air particles move in and out at a maximum fluctuating velocity, the pressure level does not fluctuate. "Node" has a mnemonic: NO DElta, no change.
This is super cool stuff from Veatch 1991. The pressure node, just described, is also a velocity anti-node, where maximum fluctuation occurs, and the pressure anti-node where maximum pressure fluctuation occurs, described above, is also a velocity node. Because at a closed end, there can be no velocity fluctuation for the air particles there are right up against the wall at the end: push on them all you want, the wall is closed and you can only squish them, they aren't going anywhere. Does it make sense? If you'd like more details please have a look at my 1991 Dissertation chapter on vowel acoustics.
The whitewater whoop-de-doo's are the same thing. When a rapid whooshes out from its free-falling channel into the constrained high-impedance zone of flatwater at the bottom, there is a reflecting wave going back upstream, which combines with the downstream-flowing wave to produce two waves crossing against each other, which looks just like, and is, a standing wave. That's why these occur only in the actual flatwater section, the surrounding flatwater is needed to support the reverse wave, and only so far as the free-falling water can really push a flow channel out of the resisting flatwater before it. So the whoop-de-doo's are typically short sections, and kayakers consider them as energy-dissipating structures which is also true. Also super fun because you can ride them right down the middle over the highest peaks and lowest valleys, which accounts for the name.
Now, galaxies have none of the qualities that make standing waves possible. First, there is no medium between the stars that presses the stars within a galactic arm alternatingly forward-faster and then slower as they move through node and anti-node, which pressure could create the acceleration of stars through the gap between arms and create the deceleration of stars entering the next arm to hang out there before the next swing on the standing wave swing. No. No medium, no stress-embodying rope or water or air that can transmit a pressure wave, so no standing wave.
Second, no longitudinal channel. I've never seen a standing wave without a channel, some zone of stuff which bounds the sides of the longitudinal transmission of energy that is the waves going both ways. Maybe you say the center and exterior are the "walls" of a planar rotational standing wave, where the super dense galactic core is one wall, and a super empty galactic exterior is the other wall, if you can figure out how to build a standing wave between wall and cliff without everything just falling, poof, off the cliff, maybe you can work it out but I don't quite see it just yet. Third, where's the counter-rotating wave of the same length in space or frequency in time? A standing wave is a sum of same-frequency directionally counter-traveling waves. So despite the fact that the whole galaxy is rotating left (some are upside down), we need to invent a hidden galactic arm set rotating right, incidentally at the same spatial frequency as the visible galatic arm and further both need to be effectively sinusoidal in density along the cylinders around the galactic center.
If you can mystically or mysteriously propose all that, then I see why you're saying the dark matter might be a disk of similarly structured spiral arms rotating the opposite direction from the non-dark matter spiral arms. Then they would pull toward the opposite-moving opposite-darkness matter, slow them down some to push them into a more dense spiral arm shape, but then accelerate them again after they're past the main part of one of these dark matter blobs, to chase backwards toward the next arm coming along? Really? Wrong. Shouldn't two sets of gravitationally interacting stuff basically form a single gravitational system rotating around its shared center of gravity? Shouldn't the slowing-down non-dark matter then fall toward the galactic center instead of continuing at a fixed radius from the center of the galaxy, and then after it has fallen shouldn't the acceleration toward an oncoming dark arm be along the orbital tangent from which the dark arm is coming? Or is it entirely convenient that the dark arm is spiralled so as to approach from a higher angle than the tangent, and if so wouldn't that also pull the dark arm itself inward toward the galactic center? It seems like a spiral would spin inward if it were two counter-rotating disks of dark and non-dark matter. Is there a stable orbital structure for a galaxy in these thoughts? Maybe this doesn't finish the argument here after all, but here's the coup de grace: Fourth.
Fourth: if you want to believe the longitudinal standing wave theory you certainly must agree there is some number of ups and downs, equal numbers of ups as downs since they alternate with each other, but not necessarily EVEN numbers of both ups and downs. A standing wave in the vocal tract, for example, can have one, two, three or four Node-plus-AntiNode pairs, just like a guitar string or rope (I'm not sure about whoop-de-doo's, never counted them but I'm guessing there are odd counts as well as even. So there are not just even but also odd numbers of peaks in a standing wave. Yet we find, do we not, that spiral galaxies come with spiral arm PAIRS, which make for EVEN NUMBERED numbers of arms. Well, just go look at a hundred galaxies and you tell me, do half of them have odd numbers of arms? Or are they all, or are they mostly, even-numbered? Look, I'm happy to be wrong. But I think galactic bar shapes and spiral arms are like each other, a bar has two ends, and a spiral arm also has another end, at the end of its opposite on the other side of the galaxy. Simply put, each pair is a single thing; it was a bar, it was a blob cohering as it moved and rotated as one, it was a thing that held together and spread through or part of it swooshed as it rotated through the center to the far side, both ends still rotating together at the end like they were rotating together at the beginning. Hello, obviously. Even numbers equals Not Standing Waves. So, I'm sorry, maybe it was a fun dumb idea but it's a bad idea, it's wrong. Well, just my opinion, maybe I'm wrong.
Okay so the dark matter and the non-dark matter gravitate towards, and therefore by their own mass help to create, the same center of gravity of the galaxy we have always been talking about.
And therefore whether gravitational attraction is of matter dark or non-dark matter and toward dark or non-dark matter, any orbiting or rotating about or gravitational cohering into the structure of a galaxy that the dark matter contributes to is primarily effectuated by gravity itself and primarily toward the center of the galaxy, which the dark matter in a galaxy must itself also be centered upon.
And therefore the supposition of some amount of dark matter in a galaxy merely suggests the total mass of the galaxy is greater than without dark matter.
So if dark and non-dark matter both rotate about the galactic center, then how is it that the dark stuff will form strings out of the non-dark matter, unless it is formed in its own string like, galactic arm shapes to pull the non-dark matter as they rotate into the dark matter strings and then releases them as they rotate out of these strings, unless these inferred dark arms themselves exist. And if dark arms exist, rotating spirally and bar-like around galactic centers so as to explain non-dark arms rotating spirally and bar-like around galactic centers, have we not simply explained one mystery by deriving it from another? Obviously Ockham would be displeased with such galactic antics, such lunatic. For now we have the same problem, how to explain galactic bar and arm shapes made out of dark matter, rotating at one twentieth the rotations per billion years as their own Newtonian gravitational trajectories would require given the gravitational effects from and to dark matter we have just asserted.
Okay? So let's not pretend we have got an explanation, when we assert that mysteriously slow-moving visible galactic assymmetries are explained by invisible mysteriously slow-moving galactic assymmetries. Let's try something else.
Spinning coagulating masses, like forming galaxies or planetary systems or funnel spirals like tornadoes or hurricanes or spiral-flow toilets, seem to first acquire angular momentum equally distributed through the mass, or at least not more distributed on the edges than in the middle.
Then, (considering galaxies and planetary systems) under gravity, they flatten into a disc in the plane of the average rotation of the whole mass, because as you may notice the orbits are not typically polar to the disc, so things gradually tend to fall into the disc and get captured there, thus we have disc shaped distributions of planets and galaxies.
That's why they are called planets, because they are little thingies in a disc, like a plane of thingies, little plane-ettes. Makes sense to me. Has nobody else noticed this?
Well, okay, then under local fluctuations the distributed masses coagulate into bodies like planets or galactic arms. If you're near a small peak of local density, you'll tend to fall toward that direction as you all proceed through the sky, so scattered dust becomes bigger and bigger more or less coagulated chunks.
Then if the distribution of angular momentum is constant or, with the same effect, if it is random around some non-zero mean, then angular velocity is greater closer to the center, and even more so if the angular momentum per unit mass is greater in the interior. Therefore inner masses spin much faster than the outer ones, as the inner parts spin past the outer parts.
Thus the planetary year of Mercury or actually of each inner planet is shorter than each outer planet. Inner planets make a full round long before outer planets do. Isn't this a universal fact about planets? Please tell me I'm wrong.
Let me give you a somewhat similar example. Suppose you spin a cup of coffee with your spoon, and drizzle cream quickly in a line diametrically across the center. Very soon the line becomes a spiral, like a spiral galaxy, but after a few rotations the spiral spins out and loses coherency, either looking more like a bunch of circles or circle-arcs, or a merged creamy coffee. In this case the edges slow down by friction against the cup walls rather than by an equal distribution of angular momentum, but the point is quite analogous. Cream soon loses its spirality; why not galaxies?
When a galaxy has arms curving a quarter, half, or rarely a full turn per arm, how old must that galaxy be, in full-galaxy rotations?
Let's say the arms start, as makes sense, as a straight elongation of a newly-formed rotating galactic disc, then the interior should gradually turn a lot more than the tips of the arms. Half a radius inward, given constant angular momentum, should yield half a turn slip per full turn of the disk. The amount of slip and the age of the formation are inversely related. If the spiral formation was created ten turns back, the spirals should have the half-radius part of the arms 5 turns ahead of the tips of the arms, by this reasoning. 5 full spirals for each arm.
If the universe began with random distributions of galaxy- and star-forming masses coagulating by gravity alone keeping everything together and on center, then a half-turn spiral arm galaxy should be half a rotation in its age, since the elongation began.
Therefore all these galaxies are brand new.
But astrophysicists claim these typical spiral galaxies have spun many times. A universe of 12B years, and a galaxy rotation time of 100M years, maybe? I forgot the exact numbers. But many times, lets say at least 10 times.
Well, that could only be true if they are something more like rigid plates than like gravity-controlled, center-orbiting masses.
Because, yes, a spiral painted on a frisbee maintains its spiral shape irrespective of spinning, but independent orbiting masses may only very temporarily form a coherent spiral shape. Therefore, some force imparting rigidity of mutual location, on the scale of galactic radii, other than gravity, must be responsible for spiral arm galaxies. QED.
SOLVE ME THAT ONE, my pretties!
Math friends have me thinking a different way. Newton's law of universal gravitation says:
F = g m1 m2 / r^2(g is a very small constant, m1 and m2 are the two masses pulling on each other, and r is the radius or distance between them. If you substitute out the famous equation F=m1*a you will see that we accelerate toward the remote mass, m2, at a rate, g m2 / r^2. That rate, times our own mass, is the Force of gravity on us.)
Note that this quantity is NEVER zero if m1 and m2 are >0 and no matter how large is r. Because the law of universal gravity is universal.
This is also called the inverse square law because the pull of gravity is proportional to the inverse square of the radius between the objects (planet and sun). If you go out to twice the radius, the pull of gravity drops off to one quarter.
So consider two equal-mass planets on circular stable orbits around a much larger star, one at radius R, the other at radius NR. Are their speeds related to the radii? Let's pick a start time, and observe that after a short time, dT, the first planet has travelled a short distance, dC, around the circumference and now travels in a direction that has been turned by some small number of degrees, dD=360*(dC/(2*pi*R)), and has adjusted its radius (or height) by some small radially-oriented height, dH, deflected toward its star from its original trajectory, due to the gravitational pull, F1, of the star at distance R. Its speed is distance / time = dT / dC.
Now the second planet, at radius NR, has an orbit N times the size of the first, which is identical geometrically except for being scaled by N in its radius, its diameter, its circumference, and any corresponding similar part thereof. Let's see how to get the same corresponding values for force and speed and time etc., when gravity is attenuated by the inverse square law.
Okay: Let's think about the correspondence of similar wedges of the orbital circle. After travelling a distance of N*dC around its N* scaled circle, the second planet has been similarly turned by dD degrees, because the arc has the same shape in two similar wedges. Further, its trajectory has been deflected from a straight path by a fall toward the star of N*dH, which was correspondingly been effected on planet 1 in dT time. How long did it take on planet 2? If it were travelling at the same speed as planet 1, it would take N*dT to go N*dC distance. E.g., twice as long to go twice as far. The force pulling it downward would then have N times longer to operate, but it is 1/N^2 times weaker, and indeed it has to do sqrt(N) more work to achieve the same deflection because the deflection work is also scaled by N. So a planet at a radius of NR should take N*dT to make its similar wedge, and N times its neighbor's year to make its own full circle around the star. Anyway a galaxy ought to be the same, and a half-radius spiral arm segment ought to make a full rotation around its galactic center in 1/2 the time the outer segment does. I have to check my arithmetic. Would you?
But I say, after two rotations of the spiral arm tips, the half-radius segments ought to be multiple full rotations ahead, which to me would be hard to identify as a spiral galaxy any more, it would be all spread out and unorganizedly disc-like.
What's your conclusion?
Dark matter? No, stuff would be rotating around the dark matter just the same as it does around matter we can see, you just wouldn't see the dark parts. It seems more like stiff space. Could space really get stiff, or you might say, might space itself be chasing around the matter that is in it, at some appropriate scale? I don't know, I'm just a plumber.
But gravity sure doesn't seem to be true in spiral galaxies that are older than a rotation or two. Which means it's not actually true, where I come from, because true means true everywhere. As in, true.
Am I wrong? Happy to be wrong. Email me! Tell me why!
If I had to guess I'd say gravity stops working quite the same when it's at the scale of galaxies. Stuff seems sticks to itself more than it falls inward to the average local center of gravity when that center is a fat part of a galactic radius away. Thus bars form and remain coherent rather than falling inward to their galactic centers, and thus spiral arms also form and remain coherent and hold together as they spin around the galactic center without being stretched and "wound" as much as they would if the gravity of the center were actually pulling on them as much as it is supposed to.
Perhaps the force of gravity has fallen off so far when the radius part of the gravity equation, 1/r^2, brings the force so close to zero that maybe only a zero or one quantum of gravity can occasionally get that far out, or maybe mostly zero quanta of gravity get that far out, they are so reduced in concentration at galactic radii. Or perhaps the gravity that gets out to such a distance has to be entrained and supported by more gravity (or mass or ...) in the area, providing it a sort of minimum paved surface or a road or a travelling trough or even an amplifying or a multiplier effect of other gravitons in the area or something whereby it can only barely reach out to such enormous distances as across a galaxy to the far bits of a spiral arm. That is, this might be a quantum round-off error in the effect of gravity from such large radii.
Just imagining possibilities here, but the density wave concept offered on Wikipedia also seems like BS to me; suspended particles don't accelerate and decelerate in a density wave unless there is a medium pushing them back and forth or stars somehow push each other away like masses of air in a resonating column, for which there appears to be no physical basis, since what they actually do is pull each other together using gravity. Is the interstellar medium of an ion every 100 cubic meters supposed to make space springy for stars? No. And anyway, that doesn't explain why it's in a spiral formation, or a bar, either. No, spiral arms, and bars, are just stickier than they seemingly ought to be. If there's another parameter for gravity that limits its distance of application, that would seem right to me. Then galactic bars and arms can hold together while the galactic center, or center of gravity doesn't hold their parts individually as tightly. Maybe.
On the other hand, isn't the issue here the rapidity of the tips rather than the slowness of spiral arm midpoints? That is, the tips are able to fall toward the center more rapidly than expected, and thus to maintain their circular orbits at a higher velocity than expected. Then the galaxy is almost a circumferentially-driven vortex, or like a railed track held together more tightly than gravity for the outer bits.
So perhaps gravity is accentuated rather then attenuated at longer distances.
These are mere idlings of a curious character, who is willing to be considered a fool while still figuring stuff out. But if your first thought was to disagree with and contemptuously dismiss the title, Gravity is BS, well, the fool was not me, as it merely restates and clarifies Wikipedia's comment: "higher than expected from Newtonian dynamics". Looks like something needs fixed, and we are all fools until it is.