# Solution to the Galaxy Rotation Problem, without Dark Matter

Double the mass, double the gravity is not true. It is not directly proportional, it is exponentially proportinal. Double the mass quadruple the gravity is closer to reality. Though that is simplistic, if we increase the mass, we exponentially increase the force, so it is not double the mass double the effect. It is more like double the mass quadruple the gravity, or Gravitational Time Dilation. This stuff (the cosmos) only works because if I double the mass I quadruple the force of gravity.
I can't even imagine what has made you come to this conclusion!
Unless you are thinking about a black hole. If the mass of the Earth was compressed down to a black hole the gravity at its surface would be a lot higher than 9.8 m/sec^2. This is due to the r factor being reduced rather than the mass going up.

If we had an object that has a certain amount of kinetic energy and somehow it was able to go from one time zone to another, and in the time zone the time was 100% in Zone 1 and 50% in Zone 2 (Time Ticks were twice as fast or the duration of the second was only 50% of the original in Zone 2).

The object can't create or destroy energy and has to conserve momentum, what happens to the velocity as it goes through the transition of the time zones, either way?
I find it hard to imagine how this could happen in isolation. To get a time dilation of 200% (Zone 2 to zone 1) an object would have to accelerate to 0.866 the speed of light. Obviously it would have a lot more kinetic energy. so it can't be done that way.
In the case of a galaxies as the stars fall in toward the black hole they are maintaining the same speed, their kinetic energy is staying the same, their mass is staying the same, and yet they are moving from one time zone to another, so how do they do it?

There is normally a rise in orbital speed as the orbiting object get closer to the central body, but this isn't the case with the galaxy.
I tried to sleep again after writing this but struggled to get the complication of the solar system out of my mind.

They propose Dark Matter (DM) to speed up the stars in the outer parts and to hold the galaxy together. So how can they have one gravitational model for the stars and another for the planets of those stars? I'm going to have to look into how they account for the planets to have Newtonian physics in the face of all that Dark Matter.

I tried to sleep again after writing this but struggled to get the complication of the solar system out of my mind.

They propose Dark Matter (DM) to speed up the stars in the outer parts and to hold the galaxy together. So how can they have one gravitational model for the stars and another for the planets of those stars? I'm going to have to look into how they account for the planets to have Newtonian physics in the face of all that Dark Matter.

There are not 2 models. Dark matter does not have much effect on the solar system for the same reason it does not have much affect on you.

Lets look at it, about 99.85% of the mass of the solar system is the sun (assumed to by typical). This is about 2 x 10^30 kg. The solar system is about 10^-3 ly in diamter. Dark matter is more or less evenly dispersed throughout a descrete region in space. It is actually denser the closer you get to the center of the galaxy. So the relative effect of dark matter on the solar ssytem would be less than the effect on the stars around us.

The ratio of the solar mass to solar system diameter is :

2 x 10^30 kg / 2.8 x10^-6 cubic ly = 7.14 x 10^35 kg/cubic ly

For the diameter of 25 ly (33 stars most are re dwarfs) around us the ratio of mass (being very generous and using a multiple of 20x the solar mass) to diameter is:

4 x 10^31 kg / 490 cubic ly = 8.16 x10^28 kg/cubic ly

The density of dark matter is constant in the solar system and in the 25 light year sphere around Sol.

The solar system is almost 9 million times denser than the 25 light year sphere around us so dark matter has a much less significant effect (I would say insignificant) on the solar system than it does on the 25 ly sphere around us.

Hopefully I did not make an arithmetic error.

Well I am skeptical still, for didn't you correct Scott and tell him gravity is proportional to mass. The planets are denser than the Sun aren't they (must check this)? Therefore the DM must have a greater effect on the planets rather the Sun. What stops the DM coming around us?
I don't know enough yet to argue the case, but DM is going to be studied when I get time.

Average density of Sun = 1,408 kg/m^3 way less than average density of the Earth which is roughly 5,515 kg/m^3

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You are denser than jupiter - that has zero bearing on DM effect on you personally.

DM has a constant density in this area of the galaxy. That means that it has a constant gravitational effect per unit volume so there is little effect on high density areas where the gravity of normal matter overwhelms DM, like earth, the sun or the solar system. As you look at larger areas then the density of normal matter falls while the density of the DM remains constant so the realtive effect of the DM becomes stronger.

You are denser than jupiter - that has zero bearing on DM effect on you personally.

DM has a constant density in this area of the galaxy. That means that it has a constant gravitational effect per unit volume so there is little effect on high density areas where the gravity of normal matter overwhelms DM, like earth, the sun or the solar system. As you look at larger areas then the density of normal matter falls while the density of the DM remains constant so the realtive effect of the DM becomes stronger.
No it didn't go over my head but it did hit some dense dark matter inside.
As I said I'm going to study DM soon, but I'll keep in mind what you've said so far.

Oops, double post

Yes, guys. Got it. I would have to double the mass of both objects to have quadrouple the affect. It is dinstance only that increases gravity by a square, if you half your distance. Onward.

Here is another demonstration of the galaxy rotation problem. http://m.youtube.com/watch?v=fUAzc1evIBo&feature=related

Hey guys, check out the hypothetical orbit calcs this guy does within the radius of the Sun. I think it's right about minute 7. Every time I have seen Dark Matter mapped, it is primarily outside the radius of the objects we are clocking. He says that to calc the speed of any orbit, it is only the mass within that orbital sphere that is used in the math for that object. If this is true, Dark Matter outside the sphere could not speed up the stars, could it? Doesn't look very good for the DM in his equations.

Hey guys, check out the hypothetical orbit calcs this guy does within the radius of the Sun. I think it's right about minute 7. Every time I have seen Dark Matter mapped, it is primarily outside the radius of the objects we are clocking. He says that to calc the speed of any orbit, it is only the mass within that orbital sphere that is used in the math for that object. If this is true, Dark Matter outside the sphere could not speed up the stars, could it? Doesn't look very good for the DM in his equations.

What are you talking about? What do you mean by, "Every time I have seen Dark Matter mapped, it is primarily outside the radius of the objects we are clocking"?

This Gravitational time dilation (GDT) is quite tricky but it can at least be measured.
this blogger "Straight Dope" describes it in an easy way "Is higher faster? Does time pass more quickly when gravity is reduced?"

Only thing I was wondering is does length contraction negate GTD? No. because length contraction can NOT be measured in the frame where it is occurring but GTD can. So they don't cancel.

How do you measure the GTD in the frame it is occurring? For that matter how do you measure length contraction in the dilated frame? When both the clocks and rulers are equally dilated and contracted.

Confirming time dilation requires a reference in two frames, that does not amount to a direct measurement in the dilated frame. It is a relative comparrison of clocks.

We have no equivalent cooralary for rulers and must assume based on the confirmation of time dilation and otherwise success of the underlying theory that length contraction is likewise confirmed.., by the the confirmation of time dilation.

There are not 2 models. Dark matter does not have much effect on the solar system for the same reason it does not have much affect on you.

Lets look at it, about 99.85% of the mass of the solar system is the sun (assumed to by typical). This is about 2 x 10^30 kg. The solar system is about 10^-3 ly in diamter. Dark matter is more or less evenly dispersed throughout a descrete region in space. It is actually denser the closer you get to the center of the galaxy. So the relative effect of dark matter on the solar ssytem would be less than the effect on the stars around us.

The ratio of the solar mass to solar system diameter is :

2 x 10^30 kg / 2.8 x10^-6 cubic ly = 7.14 x 10^35 kg/cubic ly

For the diameter of 25 ly (33 stars most are re dwarfs) around us the ratio of mass (being very generous and using a multiple of 20x the solar mass) to diameter is:

4 x 10^31 kg / 490 cubic ly = 8.16 x10^28 kg/cubic ly

The density of dark matter is constant in the solar system and in the 25 light year sphere around Sol.

The solar system is almost 9 million times denser than the 25 light year sphere around us so dark matter has a much less significant effect (I would say insignificant) on the solar system than it does on the 25 ly sphere around us.

Hopefully I did not make an arithmetic error.

Only one of your ideas here sounds kind of odd. If Dark Matter were denser near the central mass, it would never be able to solve the Galaxy Rotation Problem, so it would not very likely have been discovered, would it?

How do you measure the GTD in the frame it is occurring? For that matter how do you measure length contraction in the dilated frame? When both the clocks and rulers are equally dilated and contracted.

Confirming time dilation requires a reference in two frames, that does not amount to a direct measurement in the dilated frame. It is a relative comparrison of clocks.

We have no equivalent cooralary for rulers and must assume based on the confirmation of time dilation and otherwise success of the underlying theory that length contraction is likewise confirmed.., by the the confirmation of time dilation.
The Pound Rebka experiment measure Gravitational time dilation (like it was measured here on Earth in the Lab frame. Whereas I don't know of any length contraction experiments.
http://en.wikipedia.org/wiki/Pound–Rebka_experiment

"Gravitational time dilation has also been confirmed by the Pound–Rebka experiment, observations of the spectra of the white dwarf Sirius B and experiments with time signals sent to and from Viking 1 Mars lander."
http://en.wikipedia.org/wiki/Gravitational_time_dilation#Experimental_confirmation

I take their word for it. As I understand it Time dilation and Gravitational Time Dilation are totally different phenomena.

The Pound Rebka experiment measure Gravitational time dilation (like it was measured here on Earth in the Lab frame. Whereas I don't know of any length contraction experiments.
http://en.wikipedia.org/wiki/Pound–Rebka_experiment

"Gravitational time dilation has also been confirmed by the Pound–Rebka experiment, observations of the spectra of the white dwarf Sirius B and experiments with time signals sent to and from Viking 1 Mars lander."
http://en.wikipedia.org/wiki/Gravitational_time_dilation#Experimental_confirmation

I take their word for it. As I understand it Time dilation and Gravitational Time Dilation are totally different phenomena.

I think you misunderstood my intent. I was pointing out that time dilation (of any sort) cannot be measured directly in a single frame. It requires a comparrison of clocks or events as observed in two or more frames. It does not matter whether you compare atomic clocks in orbit relative to clocks on the surface of the earth or compare the redshit of a distant light source with theoretical predictions, both cases involve more than one frame.

You raise a separate issue with the statement, "As I understand it Time dilation and Gravitational Time Dilation are totally different phenomena."... Generally time dilation, as discussed on forums like this, is restricted to the framework of SR and can only be explored in hypotheticals or the lab where space-time can be treated as flat. Still, what is almost always being discussed is the phenomena, not the underlying mechanism.., the how and why of it... Which is also the case involving gravity and GTD.

Until we can name the how and why of things like gravity, inertia and time dilation related to inertial frames in motion relative to one another, we really cannot say that time dilation as described within SR and GTD are not in some way expressions of a common underlying mechanism. All we can do is describe the effect(s).

I think you misunderstood my intent. I was pointing out that time dilation (of any sort) cannot be measured directly in a single frame. It requires a comparrison of clocks or events as observed in two or more frames. It does not matter whether you compare atomic clocks in orbit relative to clocks on the surface of the earth or compare the redshit of a distant light source with theoretical predictions, both cases involve more than one frame.

You raise a separate issue with the statement, "As I understand it Time dilation and Gravitational Time Dilation are totally different phenomena."... Generally time dilation, as discussed on forums like this, is restricted to the framework of SR and can only be explored in hypotheticals or the lab where space-time can be treated as flat. Still, what is almost always being discussed is the phenomena, not the underlying mechanism.., the how and why of it... Which is also the case involving gravity and GTD.

Until we can name the how and why of things like gravity, inertia and time dilation related to inertial frames in motion relative to one another, we really cannot say that time dilation as described within SR and GTD are not in some way expressions of a common underlying mechanism. All we can do is describe the effect(s).
If they set 2 very precise clocks side by side and then raise 1 clock 1 meter up in the gravitational potential. It is then stationary, both clocks are in the same frame, but only 1 meter apart and they are observed to read the passage of time differently. That must be a different mechanism to time dilation caused by "inertial frames in motion relative to one another". There is no motion involved in the case of GTD.
from Wikipedia.
"In 2010 gravitational time dilation was measured at the earth's surface with a height difference of only one meter, using optical atomic clocks.[14]
[14] ^ a b Chou, C.W.; Hume, D.B.; Rosenband, T.; Wineland, D.J. (2010). "Optical Clocks and Relativity". Science 329 (5999): 1630–1633. Bibcode 2010Sci...329.1630C. doi:10.1126/science.1192720. PMID 20929843.

Note: I have not read the paper but just copied the summary from the Wikipedia page and the reference to it. I would like to access the paper at some stage.

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Only one of your ideas here sounds kind of odd. If Dark Matter were denser near the central mass, it would never be able to solve the Galaxy Rotation Problem, so it would not very likely have been discovered, would it?

The distribution of dark matter as I understand it decreases by a factor of \$\$r^{-2}\$\$ at large distances from the center of the milky way. You are correct that there is very little density change in the dark matter in the vicinity of the visible part of the milky way. Thanks for the correction / clarification.

The distribution of dark matter as I understand it decreases by a factor of \$\$r^{-2}\$\$ at large distances from the center of the milky way. You are correct that there is very little density change in the dark matter in the vicinity of the visible part of the milky way. Thanks for the correction / clarification.
Scott is arguing that there is no need for DM to come into it. I took it to mean he was saying if it was denser there how come it hasn't been found. Well that is how I took it.

Gravitational time dilation is evidenced by clocks ticking faster the higher up you go, so the higher the gravitational potential the faster the clock ticks. If it is measured by a traditional light clock the light must be bouncing faster than it does in a lower gravitational potential. Which in some ways makes it sound as if light travels at different speeds in different gravitational potentials (but this is something I have to clear up) for there is no motion (relative velocity) to speak of just an increase in height. But what I was looking at was the connection to gravitational potential (GP) and GP Energy. Lower gravitational potential is like lower to the gravity source, so in a higher gravitational potential some of the negative gravitational potential energy (GPE) has been paid back by the action of raising it up, so paying back the GPE is like speeding up time, in other words, the object lifted physically slows down for it can't travel so far in any given time interval. For example for the same mechanical energy, if initially the velocity is 10m/sec, then if the duration of a second (time interval) is shortened (time faster) it would be only able to achieve <10m/sec. That is in its own frame but looking from afar I don't know if you could see this reduction in velocity.

I might have this a little mixed up but any input would be welcome.

You would see this as a reduction in velocity by using our clock, and it appears to have slowed down, no matter how we have observed this velocity, even from a radio call back home. The radio call back home is just another way to measure the same results. In reality it has not slowed. It’s that we have measured from an inaccurate clock. Our clock just cannot be used to measure time if the amount of Gravitational influence is much greater, or much lesser than our own. Since it is not Special Relativity or Kinematic Time Dilation from proper motion, there is no change in any physical forces, or geometry, or energy. It is very simply a wrong clock to use to apply to a different Gravitational region of space. The velocity does not change over there, only the clock used. The only course then, is to correct our known skewed view of the reality of, over there.

As well, there is no need to measure it here, and no way to do that independent of another frame to comparing our clocks to. Everything works exactly as it should here, so there is no possible way to measure an effect on us in our frame. Everything, including time works exactly as it should as experienced over there. We need to know our Dilation Factor, but only to apply it properly to our observations of other frames’ clocks. If you were to travel from one area to a more dilated area, there are no experiential effects. It was predicted, and applied by the The Pound Rebka experiment, and GPS of course, by using two frames. This measured our level of Time Dilation compared to an area of no gravity, but only indirectly, by comparing one area to another. It fit the predictions, so indirectly measured our level of clock change.

However, no matter what frame we are viewing from, the relationship in this Galaxy from one area of heavy Gravitational influence to the other, we will witness the slower Clock near the more massive region, and the faster one near the outer edges. I will expand on this a bit later, our initial question of the Galaxy Rotation.

If they set 2 very precise clocks side by side and then raise 1 clock 1 meter up in the gravitational potential. It is then stationary, both clocks are in the same frame, but only 1 meter apart and they are observed to read the passage of time differently. That must be a different mechanism to time dilation caused by "inertial frames in motion relative to one another". There is no motion involved in the case of GTD.
from Wikipedia.
"In 2010 gravitational time dilation was measured at the earth's surface with a height difference of only one meter, using optical atomic clocks.[14]
[14] ^ a b Chou, C.W.; Hume, D.B.; Rosenband, T.; Wineland, D.J. (2010). "Optical Clocks and Relativity". Science 329 (5999): 1630–1633. Bibcode 2010Sci...329.1630C. doi:10.1126/science.1192720. PMID 20929843.

Note: I have not read the paper but just copied the summary from the Wikipedia page and the reference to it. I would like to access the paper at some stage.

Yes, Yes. Same frame for Special Relativity. Though Gravity is a kind of acceleration, it is actually distinguishable is some ways.

The distribution of dark matter as I understand it decreases by a factor of \$\$r^{-2}\$\$ at large distances from the center of the milky way. You are correct that there is very little density change in the dark matter in the vicinity of the visible part of the milky way. Thanks for the correction / clarification.

It's ok then that I thought Gravity Squared, if I picked up two bricks late last night?
lol. Mine was much worse.