Method of determining if Dark Matter is offset to our local dimension of space

[Kharakov]

(Note that in this case, and some other cases in which physicists/mathematicians (or nerds such as myself) refer to an orthogonal dimension they are referring to an additional axis of movement to the standard x, y, and z axis of 3d-space)

 

It is probably already known, but we can determine whether or not dark matter is simply present in a compactified form in our dimension of 3dspace (as in KK theories) or it is present in a "large" dimension some distance orthogonal to our standard 3 dimensions of space.

 

If it is present at some distance orthogonal to our 3dspace dimension, we should be able to tell by the dark matters gravitational effects.

 

Dark matter with a center of mass offset orthogonal to 3dspace would have a slightly different gravitational geometry than 3dspace objects. The radius from the object's center of mass would have a set minimum in 3dspace (the distance from 3dspace to the dark matter's center of mass). At this minimum radius, the gravitational acceleration due to the object would approach a mathematical limit (equaling zero at this point as the object cannot accelerate orthogonally). This minimum radius would be the closest point in 3dspace to the object.

 

The radius from the object's center of mass is calculated with these formulas:

 

r_3dspace= Distance from point closest to dark matter in 3dspace to measurement location in 3dspace.

 

r_orthogonal= Distance from point closest to dark matter in 3dspace to location of dark matter's center of mass orthogonal to 3dspace.

 

[math]r_{total}=\sqrt{r_{orthogonal}^2 \ + \ r_{3dspace}^2}[/math]

 

 

With this radius, we can calculate the gravitational acceleration due to the object (assuming we know the object's mass). Even if we don't have the mass of the dark matter object, we should see a gravitational geometry that indicates a constant (orthogonal distance squared) added to a distance in 3dspace squared.

 

This is different from 3dspace gravitational geometry. If the dark matter resides wholly in 3dspace (but as a mini black hole, a KK particle, or simply matter that doesn't interact with matter) it would have a gravitational geometry that does not include a constant added to the radius squared (from the center of gravitation).

 

The 2 different geometries would basically obey these equations (the first the standard 3dspace, the second designed for an object offset from 3dspace in an orthogonal direction):

 

 

[math]g_{ 3dspace \ acceleration}= -\frac{mG}{r^2}[/math]

 

 

[math]g_{ higher- \ dspace \ acceleration}= -\frac{mG}{(r_{orthogonal})^2 \ + \ (r_{3dspace})^2}[/math]

 

 

You can see that the latter equation will generate a different geometry as it approaches the point in 3dspace that is closest to its orthogonal location due to the presence of the unchanging orthogonal distance that is part of its geometry.

 

Of course, these equations are basically toy models- we would have to take into account other things as well (you know that at the center of the Earth, the acceleration due to the gravitational field of the earth= 0), but this assumes an orthogonal offset from our 3dspace dimension greater than the actual radius of the object (such as the radius from the surface of the Earth to its center).

 

If dark matter is simply matter than doesn't interact with "normal" matter: as you approach the center of the gravitational field you should have a steady drop in acceleration (like you would observe if you could travel towards the center of the Earth). If it is offset orthogonally, gravitational acceleration would steadily increase as you approached the center of the field (however at the very center of the field it would be zero after reaching the limit acceleration at a point infinitely close to the center of the field).

 

 

In addition (not related to primary topic):: We should be able to determine the objects distance from 3dspace with trigonometry: finding the location of the gravitational limit, we can measure the gravitational limit (the limit acceleration) by moving close to the point of zero acceleration (the point at which the object is closest to 3dspace). The point at which the gravitational acceleration is 1/2 the limit acceleration is the same distance from the point of zero acceleration as the center of mass of the object is.

[Pluto]

G'day

 

Its funny that people talk about dark energy and matter and have no idea what it is.

 

As for compacted matter such as Quark stars and other exotic stars and the so called black holes. There size and distance from us become quite difficult to see, but for the gravitational effects. This become dark matter because we are unable to see it.

 

It is not the same dark matter that is used to explain expansion and acceleration of the universe. Not that we can see expansion of acceleration.

[Kharakov]

G'day

Hi Dark Plutoid,

As for compacted matter such as Quark stars and other exotic stars and the so called black holes. There size and distance from us become quite difficult to see, but for the gravitational effects. This become dark matter because we are unable to see it.

I said compactified as in KK theories which implies it exists in a compact dimension within our own (click on the link to go to the Kaluza Klein wiki). The reason I also said mini black holes was that they are not the same thing (as hypothetical KK particles). I wasn't being redundant in this case.

 

It is said that there is far too much Dark Matter to be explained simply by the existence of black holes, quark stars, and other exotic stars.

 

It is not the same dark matter that is used to explain expansion and acceleration of the universe. Not that we can see expansion of acceleration.

 

Dark energy is used in the standard model of cosmology to explain the expansion of space.

[Pluto]

G'day Kharakov

 

Yes I'm awear of compactification and KK theories.

 

So! What is the difference between compact matter and compactification of matter?

[Kharakov]

G'day Kharakov

 

Yes I'm awear of compactification and KK theories.

 

So! What is the difference between compact matter and compactification of matter?

 

Sheesh, I don't know. Sounds like the beginning of a physics joke:

 

A rabbi, a priest, and a neutron walk into a bar. The bartender glances at the rabbi and says "The cheapest brew for you my friend" as the rabbi pulls out a handful of change. He notices the priest next to the rabbi and hands him a list of wine, knowing full well the tastes of most priests. The priest nods to the bartender and looks towards the neutron to draw the bartenders attention to his friend.

 

The bartender nods in the neutrons direction and says "What'll ya have?" The neutron orders the most expensive drink in the place, glances at his friends and says "It's all on me boys". The bartender looks at the neutron carefully and says "For you, my good friend, no charge".

[Pluto]

G'day

 

Smile

[LogicTech]

Why wouldn't Dark Matter be present in our current universe/dimension? All available evidence suggests that Dark Matter is certainly very real and effects matter at galactic and intergalactic scales.

 

I'm not quite sure how your equations relate to this topic, you can't just take a bunch of random math equations and hope to get any physical meaning from them...

[Essay]

I'm not quite sure how your equations relate to this topic...

I think it's just designed to show how to calculate the deviation due to the offset of dark matter.

I just skimmed the equation, but isn't it just the average of the two (light & dark) gravity contributions?

===

 

Compact matter is dense, or condensed, matter.

 

Compactified matter is elsewhere, in another dimension, orthoganal to here ...right?

===

 

Thanks for the joke Kharakov, and the neat topic.

 

~ :)

[Kharakov]

Why wouldn't Dark Matter be present in our current universe/dimension? All available evidence suggests that Dark Matter is certainly very real and effects matter at galactic and intergalactic scales.

I agree with that assessment (not that I'm personally manning the observatories). I was suggesting that it is offset by another space dimension.

 

For 3dspace, we have 3 cartesian space dimensions: x ( left/right), y (up/down), and z (depth, or forward/backwards). Say that space has more dimensions than the standard 3 that we experience, such that objects can be offset in an additional direction (that we cannot easily traverse).

 

I'm not quite sure how your equations relate to this topic, you can't just take a bunch of random math equations and hope to get any physical meaning from them...

Here is a 2 dimensional example (with just x and y coordinates):

 

To calculate the distance from the origin, or point (0,0), to point (3,4) we use the Pythagorean theorum.

 

So, the distance to that point (we'll call the distance r for short):

 

[math]r=\sqrt {x^2 + y^2}[/math]

 

[math]r=\sqrt {3^2 + 4^2}[/math]

 

[math]r=\sqrt {9 + 16}[/math]

 

[math]r=\sqrt {25}[/math]

 

So, in this specific case r=5.

 

The radius equations I posted use the same principle as the distance formula example above (as this is how an orthogonal dimension distance would be added to the 3dspace distance to calculate the total distance from the center of mass of an object some distance from 3dspace).

 

have a good one,

k

[Kharakov]

I think it's just designed to show how to calculate the deviation due to the offset of dark matter.

I just skimmed the equation, but isn't it just the average of the two (light & dark) gravity contributions?

The equation you are talking about calculates the total distance from the center of mass of the object by adding the 3dspace distance to the orthogonal distance using the Pythagorean theorum. I think to average it we would simply add the 2 distances to one another and divide them by 2.

 

Compact matter is dense, or condensed, matter.

 

Compactified matter is elsewhere, in another dimension, orthoganal to here ...right?

I'd like to be a little more specific than that though: I was referring to matter that existed in a compactified dimension along the lines of Kaluza Klein theory.

 

The test (to determine dark matters offset distance from 3dspace) is designed to determine whether dark matter exists entirely within 3dspace, or some distance orthogonal to 3dspace. If it is in a compactified dimension (along the lines of KK theory), it probably won't have a large distance offset (or any offset whatsoever).

 

I was interested in either verifying the existence of or eliminating the possibility of a large orthogonal dimension of space.

 

Thanks for the joke Kharakov, and the neat topic.

 

~ :)

Thanks thanks. :)