# Ehrenfest Special Relativistic Galactic Distortion

Discussion in 'Physics & Math' started by danshawen, Jun 16, 2017.

1. ### danshawenValued Senior Member

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Here's my attempt at making up a 'fun' problem for all our math folks.

If you look diametrically opposite where you are standing on the outside rim of a relativistic merry-go round, you will see the greatest degree of Lorentz length contraction (distance contraction between the ponies or the stars), compared with the ones on the same side of the rim as you are.

First, satisfy yourselves that this is the case, and then tell us, what would be the effect of said contraction on your perception of the gravitational pull of those billions of stars being smooshed together in an area far beyond the black holes in the center of the galaxy? Does it make any difference that you can't actually see the contraction?

How does this square with the late Vera Rubin's observation of the anomalous rotation profiles of spiral galaxies? Could this effect explain the additional gravitational pull she attributed to "dark matter"?

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3. ### danshawenValued Senior Member

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For the purposes of this problem, you may ignore the increase in relativistic mass of the stars. We are only interested here in the relativistic effect of billions of stars that seem to us to be packed more densely on the diametrically opposite rim of the galaxy.

No GR effects need be considered here either, unless you really wish to do so.

You may assume the diameter of the Milky Way galaxy to be 180,000 light years.

You may assume the relative instantaneous velocity of stars at the opposing rim at the same distance we are from the center of the galaxy to be approximately 2 x 850,000 km/hr.

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5. ### danshawenValued Senior Member

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No takers?

Okay, I can see that the mechanism doesn't work. Only the total mass is important, not density.

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7. ### danshawenValued Senior Member

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It still seems like I'm missing something that should be obvious here.

Forget about the anomalous rotation for a moment. If all 100 billion stars of the Milky Way galaxy except for our own were suddenly concentrated in the black hole Saggitarius A at its center, would our solar system achieve escape velocity or not?

The solar system is traveling at 230 km/sec around the center of the Milky Way.

Local escape velocity is estimated to be around 537 km/sec (more than twice as fast)

Looks like a total non-problem, locally, or at least until we collide with Andromeda.

8. ### danshawenValued Senior Member

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Who is really to say with conviction that a spiral galaxy with an anomalous rotation profile will NOT eventually fly apart? It's not like we have time to wait it out and see what happens to it in a million years, is it? From that perspective, hypothesizing dark matter to explain any number of spiral galaxy anomalous rotation profiles appears to be as premature as it is without merit.

Shapes for spiral galaxies have to evolve over time. As they expand, angular velocity must decrease, and this means as they age, the rotation rate slows down to conserve angular momentum. Earlier stages may not yet have achieved this equilibrium.

Does anyone here have a good argument to counter this?

As I said in another thread, cosmology is not really my favorite subject. This is why.

Last edited: Jun 17, 2017
9. ### Q-reeusValued Senior Member

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I would do a rough order of magnitude check before fielding such a conjecture. From #2:
"You may assume the relative instantaneous velocity of stars at the opposing rim at the same distance we are from the center of the galaxy to be approximately 2 x 850,000 km/hr."
Assuming no orders of magnitude error there, half that value gives the rim velocity wrt centre. Half again to get a rough average for the galactic matter overall. Comes to ~ 59,000m/s. Convert that to a
γ = 1/√(1-v²/c²) ~ 1/√(1-(59,000/300,000,000)²) = 1/√(1- 0.000,000,000,039). You can complete that. Significant NOT.

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10. ### Q-reeusValued Senior Member

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https://en.wikipedia.org/wiki/Futur...ants_escape_galaxies_or_fall_into_black_holes

11. ### danshawenValued Senior Member

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Exactly my point.

So, our own spiral galaxy, way out here on the Orion spiral arm, is NOT subject to Vera's anomalous galactic rotation, and we are not exceeding galactic escape velocity.

Even if other young or old spiral galaxies Vera observed did exhibit the anomalous rotation characteristic, what exactly does that prove? We already know, there is a lot of stellar debris and mass that is not associated with or is floating between galaxies. For that matter, our own galaxy is in the process of colliding with another larger galaxy, and when they are further along in the collision, or pass through, we may find ourselves within a mass not associated with either of the galaxies that are colliding. One look at our current relative galactic velocity compared with our increasing velocity toward Andromeda demonstrates this. It only appears static on our scale of time. Andromeda could eventually remove the rest of this small galaxy from our proximity. Dark matter won't make much difference. Gravitational lensing may continue to appear to us for some time after whatever mass was lensing it has already moved or otherwise dispersed. It can be many more light years for a photon to go around something than to directly travel through it, just like differences in optical path lengths through glass lenses.

I see no good reason right now to float the idea of dark matter as an explanation for anomalous spiral galaxy rotation. Something seems to be happening with the unseen masses doing gravitational lensing in the Coma and Bullet clusters, but that may turn out to be a different issue entirely. General Relativity never predicted that all galactic spiral structures must hold together at every stage of their evolutions, because there never was, or is, such a requirement.

Thanks for the cosmology link. It is easy to see from the Wikipedia analysis and timeline that dark matter occupies a much smaller niche in the cosmological grand scheme of things than dark energy does, at least in this era.

Last edited: Jun 17, 2017
12. ### LaurieAGRegistered Senior Member

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Doesn't anyone think about why the total matter%/visible matter% = 2 Pi +/-1% from the Planck 2015 observation data?

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