Thank you for explaining that. I was under a completely different impression of what density waves were. I thought the theory said that all matter in any given galaxy is evenly distributed. However, there are undetectable "density waves" that intensify the visibility of the objects in the density wave. This, of course would reduce the credibility of the density wave theory down to the level of credibility of other theories such as aether, phlogiston, and God. That is to say if a person makes an observation that they cannot explain then they simply attribute the cause to something they cannot detect. That is not science as it is not observable or testable. However, I think you have given me a much clearer understanding of what the density wave theory actually says. Now it is observable and detectable (theoretically)
Well, if that was what density wave theory actually says, I'd reject it too!
Your street magicians example was a very good one for explaining the position to me. but in my opinion the pedestrians have an ability that the planets do not. That is, they are self propelled.
True, but the analogy still holds since pedestrians are attracted to each other just as stars are attracted to each other - it is merely the source of motive power / kinetic energy that differs.
The real point of difference between my analogy and the density wave theory is that the street magician is an external influence. If my analogy truly reflected the density wave theory, then we would have a spontaneous congregation of fifty people, who then attracted more new crowd members while current crowd members got bored ... but I think as a pedagogical device my example works well enough.
However, now I have a new batch of questions
1) Does the density wave theory predict that objects slow down as they cross the center of the wave? If so, what force prevents them from falling out of orbit?
2) Does the density wave theory predict that objects speed up as they exit the wave? If so what force accelerates them?
3) it appears to me that the density wave theory postulates that the gravity of orbiting bodies affect each other. If the gravity that orbiting bodies exert on each other is negligible (the gravity of the moon slowing down the spin of the earth by 1.7 milliseconds per century due to tidal friction, for example) then we would have a rather elegant answer for the cause of the spiral shape. That is, everything is traveling at the speed it is in order to maintain orbit relative 99.999% of the time to the thing it is orbiting. If the density wave theory postulates that the gravity of orbiting bodies affect each other more than .001% to create a density wave, what prevents them from pulling each other out of orbit? especially if they are capable of pulling the planets of neighboring solar systems out of orbit.
In regards to Q3, it is in fact Newton's Law of Gravitation / GR itself that predicts that orbiting objects attract each other gravitationally. What the density wave theory predicts is that these interactions work coherently to produce the arms of spiral galaxies.
I can't exactly answer your other questions, since I'm not an astrophysicist, but I can give you a rough idea of the orders of magnitude involved by considering our Sun.
Our Sun orbits the Galactic Center at a distance of about 8 kiloparsecs (kpc); the Galactic Center harbors a supermassive black hole, Sag A*, which is thought to have a mass of about 2 million solar masses (Ms). By comparison, the closest stars to the Sun are the Alpha Centauri system, which has a mass of about 2 Ms at a distance of 1.3 parsecs (pc).
Now Newton's gravitational law (which should suffice - no need for GR) says that the gravitational force is proportional to the mass of the attractor over the distance squared. (The mass of the sun is the same in each case, so it can be eliminated from the equations.) Now 2 million / (8000)^2 is about the same order of magnitude as 2 / 1.3^2 : the gravitational influence of Sag A* at the Galactic Center is comparable to that of Alpha Centauri, our neighbor in our current density wave.
Of course this is a very crude argument: there is more mass towards the Galactic Center than just Sag A*, and there is more mass in our local arm than just Alpha Centauri. But I hope it gives you an accurate picture of the masses involved, and helps you answer your questions.
(As a comparison, the moon's mass is 0.0123 Earths at about 0.0025 AU, while the Sun's mass is 333,000 Earths at 1 AU. Thus the Moon's influence is (in units of Earths/AU^2) 0.0123 / (.0025)^2, which is about 2,000, which is less than 0.1% of the Sun's gravitational influence of 333,000.)
**edit** wait a minute, if most orbits are elliptical and the spiral shape simply denotes the apogee for all given radii, that might explain it, I will have to think about that though since if that is the case then I can't picture why gravity would have anything to do with it.
Well, gravity keeps them in elliptical orbits, and gravity causes the individual elliptical orbits to correlate with each other.