The causal set universe collapse represents cosmic time, which is different from the velocity dependent atom time. As a result of universe collapse, there is both a scalar Newtonian gravity as well as a vector gravity. The velocity of an orbiting body as both Newtonian scalar and vector terms as
Vector gravity is the well known relativistic equation for the perihelion shift of orbiting bodies, notably the perihelion shift of the planet Mercury. Einstein first derived this term from the principles of general relativity to first order, but causal set vector gravity has the same term. However, mass loss by radiance does not result in any extra velocity in relativity, but is key source of gravity on the cosmic scale with discrete aether.
In causal set gravity, matter and action represent velocity in space and time with changes of matter. This means that radiant energy also contributes to orbital velocity as change in mass just like relativity shows a change in mass with velocity.
The constant rotation velocity of galaxy stars is inconsistent with Newtonian gravity for two reasons. Not only is Newtonian orbit velocity not constant with radius, it also slows with increasing radius. The K.E. of galaxy rotation then exceeds Newtonian gravity potential energy by a large amount. According to the virial theorem, a bound system like a galaxy must have its K.E. equal its P.E.
For example, the Sun rotation velocity of 251 km/s exceeds the Newtonian velocity of 194 km/s by 30% and so the Sun should have escaped the galaxy long ago. This plot below shows the velocity profile of the Milky Way along with the observed Sun velocity as opposed to the Keplerian Sun velocity. The observed Sun velocity is about 29% greater than the Keplerian Sun velocity reported by Sofue et al, 251 vs. 194 km/s. The Keplerian gravity force at the Sun at 8.0 kpc is 8.4e14 kg m/s^2, which is consistent with a Sun velocity of 194 km/s as opposed to the actual Earth velocity of 251 km/s.
However, there is a matter-action radiant vector gravity force that couples star motions and transfers momentum from inner to outer stars. The Sun radiance is 4.2e9 kg/s and results in a radiant vector force of 4.2e9 kg/s x 2.51e5 m/s / 2 = 5.5e14 kg m/s^2. Thus, the scalar gravity plus this vector gravity of the Sun give a total gravity force of 1.4e15 kg m/s^2, which is now consistent with the 29% increase in Sun velocity as sqrt(1.4e15/8.4e14) = 1.29. Radiant vector gravity completes the virial energy theorem for galaxies without any need for dark matter.
The figure below shows the biphoton shadows of scalar gravity along with the radiant vector gravity momentum transfers from inner to outer stars. The Sun is quite a bit more luminous than the average MW star, which is why the Sun rotates faster than the galaxy. The MW average rotation velocity is 204 km/s where the sun is at r = 8 kpc while the Sun rotation is 251 km/s, which suggests that the Sun is 251 / 204 = 23% greater than the average stellar MW luminosity. Since the average stellar luminosity is 2.1e10 Lsun / Nstars, this result further suggests that the number of MW stars is 91 billion MW stars as Nstars = 2.1e10 / 0.23, which assumes that MW stars at r = 8.0 kpc are representative of the whole MW. This MW 91 billion star estimate is at the lower end of the typical 100-400 billion star number estimate often cited.
The luminosity of a galaxy is largely due to the luminosities of all of its stars and the luminosity of the universe is then also largely due to the luminosities of all of its stars. Just like static gravity is actually due to stellar bond shadows with the universe, radiant vector gravity is likewise due to the average dynamics of star shadows with the universe and not really with just other stars.
Stars begin life in clusters with very strong static and radiant vector gravity coupling among stars. Generally stars begin life as binaries with a CofM along with their cluster CofM and then their static and radiant vector gravities couple stellar motions within the birth cluster to galaxy spiral modes. When a binary star entangles a galaxy spiral mode, one star of a binary accelerates and the other decelerates. This dynamic stellar choreography is the basis of radiant vector gravity and provides the extra binding force that holds galaxies and galaxy clusters together at the cosmic scale that dark matter now represents.
Galaxies with greater luminosity rotate faster and the Tully-Fisher relation shows that galaxy luminosity is proportional to the fourth power of galaxy rotation velocity. The galaxy luminosity is proportional to the galaxy kinetic energy, Mgvg2, by the matter-action principle, and therefore also proportional to vg4, since the mass of a galaxy, Mg, is proportional to vg2.
There are many stars that have up to 1e6 times the sun luminosity, and yet stars and star clusters all rotate at a single mean rotation velocity about some relative standard deviation, 230 km/s +/-11%. This result is only for stars within the parallax limit from earth, for which there are velocities. All star motions couple with luminosity and very luminous stars tend to be very young and so couple within their birth clusters. It is then the cluster luminosity that couples with the galaxy spiral waves, not really the individual star luminosities.
For instance, Deneb is a hot supergiant 2,615 ly from earth and rotates SagA* at 236 km/s despite having a luminosity of 2.0e5 Ls and a mass of 23 Ms. Since Deneb is only about 10 million years old, it has not even completed 5% of our sun’s galaxy orbit of 225 million years.
Procyon is a double star where ProcyonA has transitioned into a red supergiant and so has a luminosity of 11.5 Ls. However, ProcyonA would have spent most of its 1.9 Byr life on the HR main sequence just like the Sun.
