[Q] Gravitation Limit?

[modest]

The side issue of equal attraction in all directions... resulting in no movement... is not the issue here. The issue is that overall, a lot of matter beyond our visible cosmos... if it exists... and why wouldn't it?... would be attracting all the matter in our visible cosmos outward toward the matter beyond. The force of all gravitational attraction diminishes with distance, of course... but never zero, according to the universal law. And the closer our visible cosmos gets to the matter beyond attracting it, the stronger the force will be among all masses involved, and that would account for the increasing rate of expansion we observe.

 

A few points of fact:

• Our cosmic horizon is spherical
  
• Mass beyond the horizon would need to be homogeneous and isotropic if it were to have any observable affect in the horizon because observations of the CMB are isotropic.
  
• The mass beyond our cosmic horizon therefore makes a spherically symmetric shell of mass.
  
• Nothing on the inside of a spherically symmetric shell of mass can be accelerated gravitationally by the gravitational force of the shell.
  
• Therefore the expansion of the visible universe cannot be affected gravitationally by high density space beyond the cosmic horizon.
  

 

This is explicitly stated in Cosmology Tutorial - Part 2:

 

We can compute the dynamics of the Universe by considering an object with distance D(t) = a(t) Do. This distance and the corresponding velocity dD/dt are measured with respect to us at the center of the coordinate system. The gravitational acceleration due to the spherical ball of matter with radius D(t) is g = -G*M/D(t)2 where the mass is M = 4*pi*D(t)3*rho(t)/3. Rho(t) is the density of matter which depends only on the time since the Universe is homogeneous. The mass contained within D(t) is independent of the time since the interior matter has slower expansion velocity while the exterior matter has higher expansion velocity and thus stays outside. The gravitational effect of the external matter vanishes: the gravitational acceleration inside a spherical shell is zero, and all the matter in the Universe with distance from us greater than D(t) can be represented as union of spherical shells. With a constant mass interior to D(t) producing the acceleration of the edge, the problem reduces to the problem of a body moving radially in the gravitational field of a point mass. If the velocity is less than the escape velocity, the expansion will stop and recollapse. If the velocity equals the escape velocity we have the critical case. This gives

 

v = H*D = v(esc) = sqrt(2*G*M/D)

H2*D2 = 2*G*(4*pi/3)*rho*D2 or

 

rho(crit) = 3*H2/(8*pi*G)

 

For rho less than or equal to the critical density rho(crit), the Universe expands forever, while for rho greater than rho(crit), the Universe will eventually stop expanding and recollapse.

 

If you still disagree then let me ask you this: If we were to create a shell of mass... I'll give an example: if we were to hollow out the core of the earth so that there were an empty spherical cavity at the center of the planet then what do you propose would happen to a person in that cavity? Would they be weightless and feel no force of gravity or would they be gravitationally attracted to the walls of the cavity?

 

Newtonian gravity says that they would feel no acceleration no matter where they were in the cavity. They would not be attracted to the walls. The example you give of the cosmic horizon is just a bigger example of the same thing. Mass inside the horizon cannot be attracted to the "walls" of the horizon because of mass beyond. Newton's law of gravity says that will not happen.

 

The many links given in this thread tell you it won't happen. The one quoted above applies that exact rule to the expansion of the universe—your exact scenario. It says that mass beyond the sphere of consideration does not affect the expansion of mass in the sphere. It says it explicitly.

 

~modest

[Michael Mooney]

I am having an extremely hard time reconciling all of the above answers with the universal law of gravitation.

Will someone please address the question as to whether that law has been invalidated that says all matter in the universe attracts all other matter directly with massiveness and indirectly with the square of the distances between all masses?

 

If this law still holds true, then all matter everywhere pulls mutually on all other matter everywhere with the only limit being diminished force with distance.

I have received an infraction for my last post for making claims without supporting evidence. But I thought the universal law of gravitation itself was well established and would support the scenario I envisioned.

 

In reference to your question/scenario, Modest, as follows:

 

If you still disagree then let me ask you this: If we were to create a shell of mass... I'll give an example: if we were to hollow out the core of the earth so that there were an empty spherical cavity at the center of the planet then what do you propose would happen to a person in that cavity? Would they be weightless and feel no force of gravity or would they be gravitationally attracted to the walls of the cavity?

...

 

According to the law of gravity just reiterated above, it would seem that only in the very center of such a hollowed out sphere of matter would all forces in all directions be equal, yielding no net force in any direction resulting in no movement toward the surrounding shell.

 

However, if the person were not in the center of the hollow it would seem that the force of gravity would be greater in the direction of the closest point to the shell of matter (assuming equal matter density and thickness in the whole shell.). This appears to be true by virtue of the shorter "square of the distance" between the person and the shell and resulting greater gravitational force if he is off center.

If this is false, then the universal law of gravity is false and different distances between masses is not relevant anymore... according to all that math which I do not understand.

So, please tell me specifically, conceptually, not via more math, how the concept behind the math negates the law of gravity I have repeated so many times, believing that the "inversely with the square of the distance between masses" part of the law is still valid.

Thanks.

Michael

[modest]

I am having an extremely hard time reconciling all of the above answers with the universal law of gravitation.

Will someone please address the question as to whether that law has been invalidated that says all matter in the universe attracts all other matter directly with massiveness and indirectly with the square of the distances between all masses?

 

No, that law is indeed very valid. It is Newton's law of gravity.

 

According to the law of gravity just reiterated above, it would seem that only in the very center of such a hollowed out sphere of matter would all forces in all directions be equal, yielding no net force in any direction resulting in no movement toward the surrounding shell.

 

However, if the person were not in the center of the hollow it would seem that the force of gravity would be greater in the direction of the closest point to the shell of matter (assuming equal matter density and thickness in the whole shell.). This appears to be true by virtue of the shorter "square of the distance" between the person and the shell and resulting greater gravitational force if he is off center.

 

The 1/r² force law is the very law which tells us that the person in the hollow cavity is not gravitationally attracted to the walls no matter where they are in the cavity. When you are closer to one wall you are close to a small amount of mass near you and a greater amount of mass which is more distant behind you. Because of the geometry of a sphere no matter where you are in the sphere you are arranged in such a way that a 1/r² distance law will cancel exactly.

 

That is why nothing in a hollow cavity like we are discussing can feel any acceleration due to the shell. The force in every direction is canceled by the force in the opposite direction. The many links in this post <EDIT: "thread"!> show proofs of this.

 

If this is false, then the universal law of gravity is false and different distances between masses is not relevant anymore... according to all that math which I do not understand.

 

While it's true that this proof can be done with calculus you actually don't need math to prove the rule about the shell true of Newtonian gravity. You can use geometry to prove it just as easily.

 

Please, if you're going to argue that a person or galaxy in such a cavity is gravitationally attracted to the walls then cite some kind of source saying that is the case. There are many sources online which discuss the gravitational force in a spherically symmetric shell.

 

~modest

[Erasmus00]

According to the law of gravity just reiterated above, it would seem that only in the very center of such a hollowed out sphere of matter would all forces in all directions be equal, yielding no net force in any direction resulting in no movement toward the surrounding shell.

 

This is incorrect- if you work it out you'll find its true anywhere inside the sphere. The links modest gave might help you understand the calculation. It comes out from the interplay between the inverse square law of gravity and the r^2 area of a sphere. It does NOT contradict the Newton's gravity.

[TheBigDog]

Draw a circle. Make reference points around the circle at equal intervals. Put a dot in the circle. Calculate the force of attraction between the dot and each of the reverence points. Use some vectoring to calculate how much of the force is pulling up vs down, and how much of the force is pulling left vs right. Repeat for the top and the bottom. As the dot moves closer to an reference point the attraction between the dot and the reference point grows. But the number of reference points pulling in the opposite direction grows at the same time. If you have one reference point for every degree of arc, and you are up against one of those points, then that is the only point pulling you in that direction. 359 other points are pulling in the opposite direction at various angles from various distances. Inside the circle those forces are in balance no matter where you place the dot.

 

What is true for a circle in two dimensions is true for a sphere in three dimensions.

 

At the dead center of the circle/sphere you have 50% of the mass on either side of you no matter how you cut it. As you move closer to one edge you have less and less mass attracting you in that direction, and more mass attracting in the other direction. The closer you get to one edge, the greater the ratio of mass located on the other side. Closer = less mass; further = more mass. The geometry of a circle/sphere is such that the gravitational force inside the sphere is neutral.

 

I am in a circle that is 1 km in diameter. I am 500 meters from each edge, so there is the same amount of gravity pulling in every direction. You see that because all of the lines are obviously equal. Now move me to a point 100 meters from an edge. I now have an arc of (oh **** I hate this type of math) 73.74 degrees of the circle on the close side, and 286.26 degrees of the circle on the far side. I am close to one wall, but the greater mass of the opposite wall, even though farther away, has an equal pull on me. Put me 1 meter from the wall. I now have 3.62 degrees on the close side attracting me and 356.38 degrees pulling me to the far wall. Now if you do the math with the distances above, IE 100 meters and 900 meters in the first example and 1 meter and 999 meters in the second example, you won't get the same force. This is because that is not the distance to the center of mass of each of the arcs; it is the distance to the closest edge of the arc. In both cases the center of mass is closer than the edge. In the small arc the center of mass is very close to the edge. For the large arc the center of mass is further away from the edge.

 

Think of the center of mass like this... If you were to remove one of the arcs, you would be attracted to the one that remains along a line that bisects it. As you travel along that line you will reach a point where there is equal gravity pulling you to the ends of the arcs that you have passed as there is pulling you deeper into the arc. That is the center of gravity, not the distance to the edge. Without inertia you would never reach the edge unless your center of mass was further from your outside edge than the gap to the center of mass of the edge of the arc.

 

This is where my math ends. But I hope that the geometry of this demonstration gets through to you.

 

Bill

[modest]

When you are closer to one wall you are close to a small amount of mass near you and a greater amount of mass which is more distant behind you.

 

I thought it best to draw this:

 

 

~modest

[Michael Mooney]

Modest:

The 1/r2 force law is the very law which tells us that the person in the hollow cavity is not gravitationally attracted to the walls no matter where they are in the cavity. When you are closer to one wall you are close to a small amount of mass near you and a greater amount of mass which is more distant behind you. Because of the geometry of a sphere no matter where you are in the sphere you are arranged in such a way that a 1/r2 distance law will cancel exactly.

 

WOW! I finally got it. Thank you for explaining it in conceptual language rather than math. Believe it or not, it finally makes sense. The closer mass is perfectly balanced by the greater mass of all the rest of the shell.

I will contemplate the implications of this for "my cosmology" and get back to this forum with the results. I really am radically honest, and if this means my visions are wrong, it behooves me to admit it.

 

Does this really apply to our visible cosmos in relation to what mass might lie beyond? Maybe so! But if the "shell" of matter beyond what we can see is a concentric sphere around our little cosmos... or many layers of previously "launched" mass... would the same 'gravity inside a spherical shell of matter" still hold?

 

Seems like the possibility is still open that a shell of matter beyond our sphere of visibility could still be "pulling" directly on our visible cosmos... like layers of an onion, each having a gravitational effect, however small scale, on the inner layers. Am I missing something here?

Anyone?

Michael

[modest]

WOW! I finally got it. Thank you for explaining it in conceptual language rather than math.

No problem.

Does this really apply to our visible cosmos in relation to what mass might lie beyond? Maybe so! But if the "shell" of matter beyond what we can see is a concentric sphere around our little cosmos... or many layers of previously "launched" mass... would the same 'gravity inside a spherical shell of matter" still hold?

I don't see why the zero-force-in-a-sphere rule would not be applicable to the visible cosmos. The concentric sphere thing: yes, it still holds if there are concentric layers. So long as the mass is spherically symmetric it holds. It's also impossible to say it would not be spherically symmetric and say it has any interaction with our visible universe because our observations of the visible universe are isotropic. This means any mass affecting our universe from beyond the horizon would need to be spherically symmetric to affect it isotropically. So, it's really quite impossible to say that mass beyond the horizon affects the rate of expansion in the horizon.

 

Seems like the possibility is still open that a shell of matter beyond our sphere of visibility could still be "pulling" directly on our visible cosmos... like layers of an onion, each having a gravitational effect, however small scale, on the inner layers. Am I missing something here?

Anyone

 

I don't see how this would be possible, but if you can somehow show that it is possible then I'm willing to listen.

 

~modest

[Boerseun]

Besides the calculus disproving it, it's impossible, purely from a causality point of view. Let me repeat myself:

Let A be us.

Let B be some distant object, ten billion light years away.

which is affected by an even further gravity source, C, another ten billion light years away from B..

 

In a linear path, "line-of-sight", if you will, the configuration would be like this:

 

A.....(10bly).....B.....(10bly)....C

 

You with me so far?

 

Okay. Let B be at the furthest end of our visible universe. Let's say our horizon stops at 10 billion light years. Keep in mind that gravity is propagated at light speed. B reacts to C's gravitational pull when C gets to be within B's horizon. The wavefront of information of C's presence is presented by |. Thus, as time flows, before B can react to C, it will progress like this:

 

1. - A.....B....|C

2. - A.....B..|..C

3. - A.....B|....C

4. - And only here will B be able to react to the gravitational pull of C.

5. - A....|.B....C

6. - A..|....B...C

7. - A|........B.C

8. - And only here will we be aware of B's reaction to C, when the wavefront of both C's mass and B's reaction thereto reaches us, simultaneously. There is no way for B to react to anything that is outside of our "visible universe" with the only evidence being us looking at it through a telescope. Because we're seeing it in the distant past, when the wavefront of information of everything around it has crossed our "path", too. This is the preservation of causality. Reams have been written about this, amongst others, the theory of relativity.

I hope it made sense to you.

 

There is no conceivable way in which matter beyond our visible horizon can be responsible for the Hubble Flow. If we see something's reaction to something else, then both must exist within our visible universe.

[modest]

Besides the calculus disproving it, it's impossible, purely from a causality point of view...

 

There is no conceivable way in which matter beyond our visible horizon can be responsible for the Hubble Flow. If we see something's reaction to something else, then both must exist within our visible universe.

 

I essentially agree, but there might be some caveats worth mentioning. The visible universe is not precisely the same as the observable universe (the particle horizon). We cannot see past the last scattering surface, but we can presumably see gravitational effects of matter there because the last scattering surface is a limit to visibility and not observability. In current models I believe there's a 2% difference between the size of the two. Reported by wiki, that is:

 

The radius of the observable universe is about 2% larger than the radius of the visible universe by this definition.

 

Observable universe - Wikipedia, the free encyclopedia

 

I would agree that nothing beyond our past light cone can gravitationally affect an event which we can currently observe. But, we would have to stipulate that our past light cone is always growing (or, at least, it can in some models where expansion doesn't overtake it) and if the universe has greater than the critical density it is possible for matter once outside our cosmic horizon of observability to reenter it. Since the rate of expansion is increasing it doesn't seem that will ever be the case.

 

On a separate issue, the particle horizon is not the same as the Hubble horizon. As this image shows, we can see things outside the Hubble distance which I find really confusing :hihi:

 

~modest

[Michael Mooney]

Boerseun:

I hope it made sense to you.

 

Would your reasoning in the above (repeated) post still hold if gravity were a steady pull... all matter on all matter... from the beginning of the bang or bangs... or whatever "launched" all matter, both seen an beyond?

In that case there would be no time delay for gravity to reach between all masses... if it has been constant (tho diminishing with distance) since "the beginning" (or beginning of this cycle.)

 

I too am convinced that the force of gravity travels at the speed of light, as demonstrated in *changes* in its force... such as the Sirius A and B alignment traveling at lightspeed. and effecting our rate of rotation simultaneously with the visible alignment. But of course, there is no gap between "waves of gravity" as Earth orbits Sun, i.e., it is steady tho it takes over 8 min to travel the distance.

 

What do you think?

Michael

[Michael Mooney]

Me:

Seems like the possibility is still open that a shell of matter beyond our sphere of visibility could still be "pulling" directly on our visible cosmos... like layers of an onion, each having a gravitational effect, however small scale, on the inner layers.

Modest:

I don't see how this would be possible, but if you can somehow show that it is possible then I'm willing to listen.

 

I'm still chewing on the difference between your example with a single body of mass (like a person) inside a hollow in the earth... which I now see... and concentric shells of matter.

I can only approach it conceptually (lame at math, as you know) but it seems a significantly different scenario with inner and outer shells of matter evenly distributed as concentric spheres.

 

I other words, the off center distance between the person and the shell in your example is no longer a factor as the distance between inner and outer shells is the same all around. So it seems that a given body of mass in the outer shell and a given body of mass in an inner shell, both along a radius from their mutual center would be mutually attracting each other in a way to pull them closer together... and likewise for all bodies of mass in both shells.

 

Anyway, I will be mulling it over and open to further feedback.

Michael

 

It is difficult for me to imagine that there would still be no gravitational effect between shells pulling them closer together.

[Boerseun]

Would your reasoning in the above (repeated) post still hold if gravity were a steady pull... all matter on all matter... from the beginning of the bang or bangs... or whatever "launched" all matter, both seen an beyond?

Now we're getting somewhere!

 

Yes, all matter is pulling on all matter, and all matter that originated in the Big Bang exist in each other's horizons. Why the universe's expansion seems to be accellerating, could be due to dark energy, or a host of proposed solutions of happenings within our horizon. (I have my own pet theory, but it needs much development before I can use it to argue from - so I won't). It simply cannot be from a source outside our horizon of fifteen billion years, otherwise causality would be violated. You don't see a buck drop dead before you see the gun shot. You don't get run over before the train crosses the intersection. Nor would any observer view a violation of causality in any of these cases, regardless of their position relative to these happenings. And exactly the same applies to gravitational pull of objects at the furthest reaches of our universe.

 

This is not to say that those very same objects aren't reacting to something outside our universe right now. But we simply won't be aware of it for billions of years to come, when both the information of what they're reacting to, and their reaction to it, reaches us. The fact that we're witnessing the Hubble Flow right now (well, in the past, really), means that the information of what they're reacting to, must also have reached us already. It must exit within our horizon.

In that case there would be no time delay for gravity to reach between all masses... if it has been constant (tho diminishing with distance) since "the beginning" (or beginning of this cycle.)

Yes. Everything in this universe is under the gravitational "spell" of everything else. The argument, plus the causality argument above, is more arguments in favour of everything having come from a common origin.

I too am convinced that the force of gravity travels at the speed of light, as demonstrated in *changes* in its force... such as the Sirius A and B alignment traveling at lightspeed. and effecting our rate of rotation simultaneously with the visible alignment. But of course, there is no gap between "waves of gravity" as Earth orbits Sun, i.e., it is steady tho it takes over 8 min to travel the distance.

 

What do you think?

I am not too sure what you're asking there. Do I think gravity is propagated at light speed? Yes - I do. If gravity was propagated instantaneously, then we could use gravity modulation (somehow - some advanced society might think how) to communicate instantaneously, once again violating causality.

Do I think there are "gaps" in the waves of gravity as it hits earth? It depends on what you mean. If you mean it to be gaps where suddenly there is no gravity for a second and then there is, then no - obviously not. If you're talking about resonance gaps in the waves or spots of constructive or destructive interference, then yes - Lagrange points could very well be seen as "gaps" in gravity, where everything balances and equals out.

 

But I'm not entirely too sure about your question, I hope this helped.

[modest]

I'm still chewing on the difference between your example with a single body of mass (like a person) inside a hollow in the earth... which I now see... and concentric shells of matter.

I can only approach it conceptually (lame at math, as you know) but it seems a significantly different scenario with inner and outer shells of matter evenly distributed as concentric spheres.

 

I other words, the off center distance between the person and the shell in your example is no longer a factor as the distance between inner and outer shells is the same all around. So it seems that a given body of mass in the outer shell and a given body of mass in an inner shell, both along a radius from their mutual center would be mutually attracting each other in a way to pull them closer together... and likewise for all bodies of mass in both shells.

 

I think I understand your question now. Given a sphere with concentric rings like an onion, do any two given rings each pull toward the other? The answer is unequivocally, no. Since this example is spherically symmetric we can say that always will any given ring pull downward toward the center of the rings regardless of anything above it.

 

If you think of the crust of the earth as a ring—a concentric ring like you're saying—it is not pulled up in the slightest by the collective mass of the universe above it. It cares only about the mass below it toward the center of the earth in deciding how it's going to be accelerated. Again, if you think of the mantle of the earth—another concentric ring—it cares not at all about the crust in deciding how much it will be accelerated toward the center of the earth.

 

The mantle doesn't pull toward the crust while the crust pulls toward the mantle. The mass of the crust cancels for the mantle so that it has no effect on the gravitational acceleration of the mantle. Of course, the weight of the crust creates pressure in the mantel—that's an entirely separate issue. But, the answer to your question as best as I can figure is, no, never does the smaller of two concentric rings get pulled up toward the larger. Not when both are spherically symmetric.

 

~modest

[Michael Mooney]

Modest:

I think I understand your question now. Given a sphere with concentric rings like an onion, do any two given rings each pull toward the other? The answer is unequivocally, no. Since this example is spherically symmetric we can say that always will any given ring pull downward toward the center of the rings regardless of anything above it.

 

How does this reconcile with the law that *all masses pull on all other masses*?

I get that the pull on a body way off center close to (within) a spherical shell is perfectly balanced by all the pull of all the rest of the shell... though more distant also more mass than just the closest point.

 

So, say, just to exaggerate the principle, that an extremely dense and massive shell surrounds a sphere of hydrogen gas. The gas is still not pulled outward by the outer shell?

Still seems to me to "violate the law."

 

I'm ready to let it go, tho unless you can spell it out for me in the above case. It is just inconceivable to me.

Boerseun,

All I meant was that if gravity is steady among all masses everywhere throughout whatever cycle/cycles (decreasing of course with distance and vice-versa) then delay of any or all forces is not a factor but for changes in the force.

Michael

[Erasmus00]

So, say, just to exaggerate the principle, that an extremely dense and massive shell surrounds a sphere of hydrogen gas. The gas is still not pulled outward by the outer shell?

 

You can think of the hydrogen gas as just a bunch of individual, tiny masses. Since no individual mass is pulled outward by the shell, then the collection won't be pulled outward by the shell. However, the gas itself will attract other gas particles, which will cause the gas to clump up.

[freeztar]

I've been thinking about this and it seems that the spherical shell reference only goes so far. Just throwing this out there for thoughts.

 

Say you hollow out a sphere and place people inside. Well, as has been shown, those people will have no gravitational preference for one side or the other.

 

Now, we bring in the a massive body (a 'neutron star'). It doesn't affect the people inside the spherical shell, or does it? Well, not directly...they are still floating around inside the spherical shell with no preferential gravitation. Nonetheless, their spherical shell is moving towards the 'neutron star'.

 

"But freeztar, this is not the way the universe works".

I agree!

 

If we can't "see" the 'neutron star', then it is not possible that it is acting on us, or the spherical shell for that matter.

 

And that's all she wrote.