I recently claimed that not only can Gravitational Time Dilation solve the Galaxy Rotation Problem, but can also do away with Dark Matter altogether by locating enough mass to agree with the Gravitational Lensing, such as observed around the Bullet Cluster.
There would be several starting points for solving both related galaxy questions, but all have flaws.
The most proper place mathematically, for clocking the stars in orbit around Andromeda would be to use a star that is under equal Time Dilation with our region. Locally, we experience minor fluctuations from one clock to another because these affect are quite small. The farther we propose to look into space the more we have to add to our overall, regional Time Dilation Clock, to view time properly in another potential region, and therefore our velocity calculations that will follow. We could guess at a region in Andromeda, maybe the same distance from the core as us, or even use a radius and velocity to mirror our region within our galaxy, but this will be only a guess as well. There are way too many stars near our target velocity between 250 km/s & 300 km/s. This has too many flaws.
We could start at the outer most visible star, and begin there by resolving the mass contained within that orbital sphere. We could say that that would be the entire mass of the Galaxy, and then we could chunk off ten percent sections of the overall radius and begin applying Time Dilation Calculations as they would then begin to apply to each successive region appropriately as we continue working inward toward the central mass. We would again solve the Galaxy Rotation Curve Problem, and its relationship to our overall picture of rotation, but this will actually show us far too much mass. Not because of our calculations as we divided the masses up properly with our corrections of Time Dilation as we went along, but because of our initial calculation. Our starting mass will be much larger than is the current overall known mass, and will be too large for our Gravitational Lensing Math. The reason is that we are Time Dilated from being located half way through the core of our galaxy, and so Velocity will be measured wrong to begin with. We could adjust for it in our initial mass, but again, we have no way of knowing yet, our own Clock’s benchmark to adjust for this. Our slower clock, will give us the idea that the outer most stars are going faster than they actually are, so the entire mass will exceed the Gravitational Lensing curves we observe of similar galaxies. The Dark Matter would go away very easily without adjusting for, and reducing the velocity properly with the corrected ‘over there’ clock. That would be wrong, only fun. This also has too many flaws.
The only place we can start is with the current estimated mass of the Black Hole at the center of Andromeda. We apply the Gravitational Time Dilation equation to correct the velocities successively in ten percent chunks or so, and correct the Galaxy Rotation Quiz without the Dark Matter, as Emmanuel Moulay has done here,
http://arxiv.org/pdf/1005.2826.pdf. As I may have explained briefly before, we apply the ‘lessening’ affect of the Time Dilation, by using the equation for each region. The problem with this is that we were now able to resolve the Galaxy Question by rearranging the mass, and correcting the curve, but the weakness is evident. We will have added very little mass compared to what is needed for our current overall mass predictions of Dark Matter, so we still need it in this solution to compensate for the Lensing.
Here is the final math then to answer both questions. We started in the right place, but we have to resolve the central mass once we have applied our first Gravitational Time Dilation orbital correction. So, we take the initial published mass, apply the clock correction to the central blue stars orbiting Andromeda. Then, we resolve the new, more proper mass of the Black Hole. As we proceed now we will see that we have found a considerable amount of mass as each Time Dilation region will have grown by quite a lot, within each orbital sphere. Each time we add mass through our corrections, is adds more to each equation as we proceed, so there is a little compounded interest.
Though this is getting pretty close to correcting the rotation and finding a lot of mass along the way, it will still fall short I believe. Once we have solved the new time corrected mass, we forgot an important step, which will carry, again, throughout our galaxy adding more mass along the way, and probably enough for both questions.
Starting over: we used the published mass of the Black Hole, used the Time Dilation equation to fix our slow clock, corrected the speeds of the blue stars, then we fixed the mass by applying our new more proper velocity. Now we have to use the Gravity Time Dilation equation AGAIN, because we used the old mass in our first clock adjustment. We go back again to the middle and add the next adjustment to the mass and so on, until we see the adjustment wane beyond observable meaning. Maybe three times will get it done, because the adjustments will drop off very quickly, but five would not be out of the question. This is not an infinite loop to magically add mass over and over, but I realized this problem and figured out that it will solve quickly enough. It’s merely fine tuning. I believe it is the correct approach.
Now if you thought I was crazy before, that’s the nail in the coffin, no? I don’t see an alternative as a starting point, but will be happy to see this worked out properly. If there is anyone capable of solving the Gravitational Time Dilation Equation a few times, and the orbital math needed please help. Send a PM, or we can work on it here.
