Naive Question regarding Galaxy Rotation Curves

[Loudzoo]

Many apologies in advance if this question is ridiculous or if it has already been answered on another thread. I've searched and searched through the forums and haven't found the answer - please do direct me accordingly if that's possible. If not - please help!

Preamble:
We know from calculating Galaxy rotation curves that the visible mass in spiral galaxies is too low to be consistent with the observed orbital rotation velocity of galaxies.
Introducing the notion of dark matter to provide the "missing mass" solves the problem. Calculations demonstrate that dark matter would need to exist in a mass ratio of 5:1 to visible matter to explain galactic orbital rotation velocities.

In Special Relativity the mass of an object increases with velocity. According to the relativity calculators suggested by Marcus a relative velocity of 0.98c would increase the mass of an object by approx 5 times.

Question:
1) Does this velocity-mass relationship apply in general relativity? If so . . .
2) Would we expect to observe differences between (a) a model of a galaxy "at rest" with a dark to visible matter mass ratio of 5:1, and (b) a model of a visibly identical galaxy with velocity 0.98c (relative to our observational point of reference) and no dark matter?

Thank so much in advance for your help.

 

[Bandersnatch]

Would we expect to observe differences between (a) a model of a galaxy "at rest" with a dark to visible matter mass ratio of 5:1, and (b) a model of a visibly identical galaxy with velocity 0.98c (relative to our observational point of reference) and no dark matter?

Yes. For one, the relative motion can't change the dynamics of the system. For example, take an object in your hand, like a coffe mug. At this very moment, you and the mug are traveling at 0.999999c relative to some frame of reference. Do you feel the cup suddenly grow in mass and attract you to itself with its great gravitational potential, while at the same time you are crushed by the increadibly-inflated mass of the Earth?

Furthermore, the galactic rotation curves need dark matter to explain not simply due to missing mass, but also due to the way the missing mass needs to be distributed. Otherwise you could just postulate that the central black hole is more massive than we thought and voila! Dark matter needs to be in a halo-like structure around galaxies to make the curves work.

By the way, best drop the whole idea of relativistic mass altogether. The forum is full of posts detailing why it is an outdated concept.

 

[Loudzoo]

Thank you very much Bandersnatch. I had no idea relativistic mass was such an outmoded concept. It explains why few ask questions such as mine. I found this thread (www.physicsforums.com/threads/relativistic-mass.642188/) but if you know of one with a clearer critique one that would be much appreciated!

On that thread - is the following statement correct?
"Physicists are not trying to change the definition of mass as implicit given by Newton's p=m·v. With this definition mass was invariant in classical mechanics. In modern physics the definition of mass has been changed to make it invariant in relativity too."

With your coffee cup example I understand you wouldn't witness any change in the mass of the mug (or yourself) - you'd still be able to lift it to your mouth to drink from it. Furthermore you and the cup would not merge together under immense gravitational forces.

However you're ability to accelerate closer to the speed of light relative to the other frame of reference would be impeded by your already large relative velocity would it not?

 

[Bandersnatch]

but if you know of one with a clearer critique one that would be much appreciated!

Check this thread from the relativity FAQ:
https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-is-it-not-used-much.783220/

However you're ability to accelerate closer to the speed of light relative to the other frame of reference would be impeded by your already large relative velocity would it not?

Only from the point of view of that other frame of reference.

 

[Loudzoo]

Perfect - thank you very much.