How Does Infinite Matter Distribution Affect Gravity in a Mineshaft?

[PaulDent]

If you go down a mineshaft, gravity reduces because the pull of gravity is due only to matter between r=0 and the radius R you are at, and force due to all matter outside that radius R where you are integrates to zero. Assume, perfectly spherical, uniform matter density distribution.

But now extend the matter distribution to infinity while you remain at R. Classical theory says you experience no change. But when in the limit you are in an infinite, spherical, homogegous distribution of matter, why should you feel a pull in any particular direction?

This is relevant to understanding whether "Dark Matter" really solves anything as regards the anomalous galactic rotation.

 

[granpa]

dark matter doesn't extend infinitely far. it clusters around each galaxy

 

[MikeLizzi]

Some astronomers are suggesting that the presence of Dark Matter is the cause for some stars rotating faster around the galactic center than predicted by their calculations (which only take into account visible matter and black holes). I

PaulDent’s predicament:

If the distribution of Dark Matter around a galaxy was a spherically symmetrical shell, and all the visible matter moved within the shell, then the presence of the Dark Matter should not influence the movement of the visible matter.

I agree. So, I assume the astronomers believe that the distribution of Dark Matter must not be symmetrical or that some of the Dark Matter resides within the orbit of the aforementioned stars.

But I could be wrong. I’m not an astronomer.

 

[kaksmet]

Some astronomers are suggesting that the presence of Dark Matter is the cause for some stars rotating faster around the galactic center than predicted by their calculations (which only take into account visible matter and black holes). I

PaulDent’s predicament:

If the distribution of Dark Matter around a galaxy was a spherically symmetrical shell, and all the visible matter moved within the shell, then the presence of the Dark Matter should not influence the movement of the visible matter.

If I am not completely out of my mind that is because there is black matter within the galaxy as well..

 

[Antenna Guy]

If I am not completely out of my mind that is because there is black matter within the galaxy as well..

Let's say you pick the darkest point in the night sky, and send a detector to record how much energy exists at that point.

Would the detector record an energy of zero, or the energy associated with the light from all observable sources?

Regards,

Bill

 

[kaksmet]

Let's say you pick the darkest point in the night sky, and send a detector to record how much energy exists at that point.

Would the detector record an energy of zero, or the energy associated with the light from all observable sources?

This might take me a bit far away from the subject originally in this thread.. but..here I go

That would of course depend on what kind of detector you use.. but if detects all kinds of energy then it should detect the energy from all light sources, and other electromagnetic waves as well. It should detect the background energy in the universe (temperature of 3.7K or so if I remember correctly) from when the electrons/protons decoupled first decoupled from photons. It should also detect any dark mass and perhaps even the dark energy.

 

[Antenna Guy]

It should also detect any dark mass and perhaps even the dark energy.

I don't know what dark energy might be, but I think it would be prudent to verify that it is not simply a correction to get from expected to actual energy density.

Regards,

Bill

 

[PaulDent]

If I am not completely out of my mind that is because there is black matter within the galaxy as well..

I continue to do a few math computations to understand this, and I just looked at gravity within a disc of matter.
Now while gravity at radius R within a sphere of matter experiences zero pull from the spherical shells at radius greater than R, unless I have a bug in my prgram, this is not true for a disc. The Gravity at radius R within a disc of matter is affected by annuli of matter at radius greater than R. There is an outward pull due to them, which reduces gravity in the interior of the disc significantly. Conversely, the gravity further out increases faster than you would thin it should due to this effect.

The problem with the dark matter explanation is that it would take a VERY SPECIFIC distribution of dark matter, different than the distribution of luminous matter, to explain the flat rotation curves. Note that these curves are not flat ANGULAR velocity, which is what you would get with a spherical distribution, but flat VELOCITY.

So the dark matter explanation has two probelms: 1. What is dark matter, and 2) Why does it have a distribution different than the luminous matter, and exactly the right distribution to give flat velocity versus radius curves?

I am on the verge of a novel explanation, but I need to solve Einstein's equations in he 4D, non-static case to see if it works, and I don't have sheet of paper big enough to expand all the products of Christoffel symbols and WHY. I plan to get MAPLE to do the algebra and formulate the partial differential equations.

My explanation is that we are already in a Black Hole, and our inexorable chute to the central singularity is the passage of time, while what was time outside this Black Hole is one of our spatial dimensions. It turns out that the mass of this black hole, most of which has already reached the central singularity, is an order of magnitude higher than the mass of the matter in our universe, but exerts the same effect on galactic rotation as if it were distributed throughout our spatial dimensions. Dark matter is therefore matter which exists in our space with a time-shift relative to us so that we do not interact with it except insofar as it affects the metric of our spacetime. My original question relates to the fact that an infinite, uniform, spherical distribution of matter in our universe would seem, under the Newtonian approximation, to have no effect. But I believe under GR it will, and that when I compute the orbits of stars in galaxies under this metric, it will show the flat rotation curves.
That is what I am hoping, as if it does, since this model already explains the accelerating expansion of our universe and also gives answers to a bunch of hitherto unanswerable questions, then it is probably the truth.

 

[olgranpappy]

If you go down a mineshaft, gravity reduces because the pull of gravity is due only to matter between r=0 and the radius R you are at, and force due to all matter outside that radius R where you are integrates to zero. Assume, perfectly spherical, uniform matter density distribution.

But now extend the matter distribution to infinity while you remain at R. Classical theory says you experience no change. But when in the limit you are in an infinite, spherical, homogegous distribution of matter, why should you feel a pull in any particular direction?

It's because of the slow (1/r^2) fall-off of the gravitational force.
The surface of the sphere is never "far enough away" to ignore thus you are not in a "homogegous" space.