Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Murchie85 on 09/06/2010 13:25:24
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I know this has been touched upon before in some other posts but I would just like to get some final concrete clarification on this matter.
Ok so lets assume a perfectly spherical body the size of say planet earth or bigger, with a hollow centre.
Now a spherical object, say a lump of steel, is placed exactly in the centre of the planet in which its centre is in the same position as the centre of the planet.
Assume a perfect circumstance in which there is no irregularities in either the metal or the giant body.
What would be the gravitational effect on the steel sphere? Would the sum of the gravitational forces at each point equal to zero? Also would the spin of either the planet or the sphere internally effect the outcome?
Thanks in advance
Adam
Mod edit - formatted the subject as a question - please do this to help keep the forum tidy and easy to navigate, thanks.
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Hi Adam,
As you suggest, the sphere would experience zero gravitational effect from the hollow planet. That's probably not such a surprise, as all the forces would tend to cancel because of symmetry.
What was much more surprising to me when I learned it recently on TNS, is that any object inside the hollow planet will experience zero gravitational effect at any location in the hollow space. You'll find more information under "Shell Theorem".
Here's a link to a Wiki page on the subject http://en.wikipedia.org/wiki/Shell_theorem
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Within the framework of Newtonian mechanics, spin is not an issue. Taking general relativity into account, spin does become an issue but I do not know just what the effect is.
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If the planet is spinning, I think the object in the planet's centre should expierence "Lense-Thirring effect" and so rotate slightly in the same sense of the planet (Spacetime drag).
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I think Lightarrow is correct. I get the impression that the exact details of the effect is still unsettled http://philsci-archive.pitt.edu/archive/00002681/01/lense.pdf (http://philsci-archive.pitt.edu/archive/00002681/01/lense.pdf)
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I've been thinking about this for a while. The shell theorem doesn't say anything about the size of the sphere. One could imagine creating a huge space ship, or "moulding" an asteroid to play with this effect. When outside of the asteroid ball, you could walk its surface. If you have a cup of coffee you could pour it on the asteroid and imagine the coffee covering the entire asteroid in a thin layer perfectly symmetricaly. Let's say that we could remove the stuff that the asteroid was made of and just leave the coffee in place.
Anything inside this liquid sphere would be unaffected by gravity, except the liquid itself. The asteroid will collapse by its own gravity.
Now I'm pretty sure that while the asteroid collapse, everything inside the asteroid will be affected by gravity. Newtons shell theorem only holds for a solid sphere, able to maintain its form.
The reasoning behind this is the propagation delay of gravity. Only in the exact center there will be no gravity.
If the asteroid by some unknown means were to grow in diameter, the gravity would be pulling everything towards the center, while if collapsing everything would be pulled away from the center.
Only if gravity was instantaneous no gravity would be detected inside the sphere.
Now, imagine the entire universe surrounded by a collapsing sphere. All objects within that sphere would be pulled away from each other, right? Massive galaxies would spin slower than Newtonian gravity suggests, since the stars orbiting the center of the galaxy have help in keeping their distance from the black hole in the center of the galaxy. Distant objects would appear to move away from all other objects, and their acceleration should increase.
The shell theorem should apply for a shell consisting of immense numbers of galaxies, even if they were not entirely uniformly distributed as a sphere.
I've been thinking about this theory for many years now, and I've not been able to find anybody else with the same theory. Is it original?
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Frodeborli, I always have problems with gedanken experiments where mass either magically appears or disappears. This sort of thing has been discussed before with "what happens if the sun suddenly disappears?" type of question. The reality is that this can't happen and you have to be careful about whether the effects of the "magic" have any impact on your thought experiment.
Your suggestion, if I understand it, may not depend on "magic" as I think what you are proposing (initially) is a collapsing shell of liquid or, I assume, any material unable to support itself mechanically via other forces. And you expect correctly, that if perfectly symmetric, the collapse would behave as a shrinking sphere. Now I think you are suggesting that the accelerating motion of this collapse would mean that the concept of zero gravity experienced inside a shell fails when the particles of the shell are in mutual free fall and you are saying that a test object inside will be drawn outwards towards the nearest point on the shell inner surface, and I guess, experience tidal forces. You then go on to expand the concept into the reverse situation and then on to a cosmological model of the expanding universe.
I think your initial concept is worth testing mathematically first. To be honest, I don't know whether your assertion that an object inside a collapsing sphere would know anything of the collapse until the surface impacts it. You may be right that the zero field inside a shell does not hold if the shell is collapsing but it is not trivial to calculate in GR, though maybe someone here can do it with enough time on their hands :-)
I don't really follow your extrapolation to the universe though. The model is not the same.
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Graham, I don't pretend to know a lot on this but doesn't virtual particles "appear" and dissapear all the time? Can't the same be true for particles with mass?
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I think the idea of quantum fluctuations (zero-point or vacuum energy) and whatever net mass they possess is open to debate. The vacuum energy thought to exist as demonstrated by the Casimir effect are 10^120 too great to be responsible for Dark Energy needed to give the universe's accelerated expansion. This is an area that is yet to be resolved. There are some ideas about spectral frequency limits being imposed for the vacuum energy to fit the results but it seems a bit artificial.
In any case this is a hugely different level of issue from spontaneously creating or destroying a vast amount of mass. It can be an exercise in thought but can be misleading. In this case I think it actually does not need to be invoked anyway.
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Ok well for my initial idea then instead of the object in the centre appearing, it can be brought from infinity to that point (much like the same way when dealing with electric charges in calculations. I don't think that will change my initial idea so much in that I am looking for the end product. What would happen to a sphere surrounded by a giant shell of huge mass.
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"The reasoning behind this is the propagation delay of gravity. Only in the exact center there will be no gravity."
No, it's not.
It works fine for classical Newtonian gravity which is "instant".
Did you look at the wiki page?
A liquid would collapse by surface tension anyway so it's not a reasonable model.
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BC, if I understand Frodeborli correctly, he is saying that the shell producing no gravity field (in Newtonian theory) is because gravity propagation is instantaneous, which you agree with I think. And he is saying that if you allow for finite propagation speed, then a collapsing shell will not produce a zero field.
I have not done the maths for this (which is a bit hard) but he may be right here. If you assume a test mass inside a shell but close to the surface and that the shell is held in place (to prevent collapse) by an external (but light) rigid frame, the mass will not experience any gravitational force. If the frame is caused to release the shell by a signal sent from the sphere's centre (say), the shell will start to collapse. The test mass will "see" the surface closest to it approaching before any other part of the shell and the gravity increase from this segment will exceed any balancing gravity from the parts still not perceived to be accelerating because the field change has not yet propagated to it. I think, therefore, that the zero field inside the shell is not valid for a collapsing shell except at the centre.
I don't see how this relates to a cosmological model though.
Murchie, I appreciate this has diverged from your original question, but I think this was answered by lightarrow and others. None of my comments regarding magical movements of mass apply to your question I think. And I don't think they apply to Frodeborli's point either, providing the thought experiment is constructed so as to avoid the issues.
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Graham D,
Bravo, very good observation! Of course I don't mind that this has diverged in fact, the whole reason I do physics is to share ideas so this has been quite a good double thought experiment. Again thought I would ask that in the second point brought up by Frodeborli, again would spin of the shell affect this? Say for example create a drag effect or have a GR effect?
It got me thinking, that as we are looking for an explination for dark energy which is causing the expansion of space is it even possible that it could be an effect of our known visible universe being inside an even greater shell of matter say millions more universes. This may offer a realistic answer to why the universe is expanding without having to create new physics. This shell could be multi-dimensional even as to create an expanding effect in the required directions thus the only force that would be causing this would be again gravity?
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I still don't see how the shell concept applies to any cosmological model. There is no evidential reasons to assume that the universe, or any subsidiary part of it, comprises a "shell" of material.
Spin will also break the "zero field inside a shell" I think, but I have not studied anything much on the Lense-Thirring effect.
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Graham,
What I am saying is I know its chalk and cheese although I am thinking more "what if" although im reluctant to post it as a new theory as I am really just asking the question.
I know that there is no evidence to point to there being a shell of matter but then again how can there be? We only see 14 billion light years in each direction and the universe is bigger than that. But the universe IS expanding and something is causing that, now im applying a simple idea to a larger scale and asking would matter expand outwards if there was an even greater density of matter surrounding it in all directions?
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I think that the answer may be "yes" but I would not bet my life on it. I think such a scenario would need to be analysed mathematically. The shape of spacetime would be complex because of the non-uniform density and solving Einsteins field equations for such a metric may be impossible and require computer modelling. The simple "flat space" concept we discussed previously may not apply on a cosmic scale - this was just Newtonian but with added finite propagation delay for a gravitational field.
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I lose myself here "If the asteroid by some unknown means were to grow in diameter, the gravity would be pulling everything towards the center, while if collapsing everything would be pulled away from the center."
The center is the exact center inside that perfect sphere right?
And if that sphere by some magical means would grow, the center would still be located at the same exact spot right? So as the sphere grows the added distance to that spot will diminish the effect by gravity, but if we consider the invariant mass added then we still might see an added gravitational pull from it? But that center seems to me to be much the same any which way the sphere moves, inward or outward? That is, the 'spot' where gravity takes itself out, or am I thinking totally up the walls here?
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Hi Yor_on. I was unable to interpret your questions, although your English is infinitely better than my Swedish so I can't complain :-) I was expanding on the suggestion from Frodeborli though I don't know whether my interpretation of what he was saying was correct. In any case, it seems to be true that the "zero field inside a spherical shell" does not hold if the shell is expanding or contracting if you take into account the finite propagation speed of a changing gravitational field. I tried to explain this 5 or 6 posts ago. I have not thought much about it since that post though. The centre of the sphere will remain with zero field but not elsewhere inside the shell, unlike the static case.
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Ok Graham :)
Are you thinking of it in terms of 'gravitons' traveling at the speed of light? And then depending on which way the sphere moves, inward or outward, delayed effect(s) will make different changes at that spot depending on what way the sphere moves?
And I on the other hand naively look at it as a 'field' where 'gravity' will take itself out at that exact spot at all times. No matter if the sphere grows or shrinks, the 'field' won't collapse, well as i think. The only way that field or 'bent space' whatever you want to call it can collapse is if that sphere disappears, as I see it?
In a way it gives me very weird questions, as we do have have objects 'collapsing' into a perfect 'nothing', well as I see it. Namely a black hole, if the idea of an absolute 'weightlessness' holds true, would a black hole have such a 'center' too?
I know it is a 'singularity' and that the question rightly might be a very moot one, but there have to be a minimum circumference where our physics still works and where that singularity begins, the Chandrasekhar limit or?
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A lot of black holes are spinning so at the centre might actually be a ring and not a point.
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That is also a nice one Murchie. Made me think, but, if we assume a exact 'middle point' inside a spinning object would that points motion really form a ring? As seen from the outside, assuming we could see it, being stationary relative the spinning object, it would certainly spin, but why would it assume a ring? Tidal forces?? And even if I assumed it would do so, wouldn't it still create yet another center 'inside' it? As a 'ring' always will have a center of its own, just like a wheel. Or maybe you meant it some other way that I miss?
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Yor_on, a zero field in the centre of a spherical shell is only zero because, even classically, because the integrated sum of all the vector components from all parts of the shell exactly cancel. When the shell starts moving, and the distances to each of these parts change, the finite time it takes for a test body to feel the influence of these movements will not generally be perfectly balanced. The changes in field are propagated as a gravitational wave at lightspeed, but as far as a thought experiment goes, you can just think of the test body only seeing the movement and feeling the field change after the time it takes (on his local clock) for the information to reach him.
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According to Micheo kaku, at the centre of spinning black holes is an eye, like the eye of a storm with the matter swirling around it, its a relatively new proposal.
Yes according to newtonian equations if you equate the field by integrating the parts then the vectors will cancel, although part of the question would be "is this really an accurate description of reality? (gravity)"
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Nice Murchie, it then becomes our idea of geometry against?
And this eye wouldn't then have a center?
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Yeah, but with a perfect sphere Graham?
Would they still be unbalanced?
Either we have one, or we don't :)
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Yeah, but with a perfect sphere Graham?
Would they still be unbalanced?
It might be balanced at first, but I'm guessing it would be unstable, so it would not take long to go out of balance.
Wonder if I guessed right? [:D]
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Well, then it won't be a perfect sphere will it?
:)
But sh*, I don't know either :)
It's like Murchie said.
Is it an accurate description of 'reality'? :)
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Well, then it won't be a perfect sphere will it?
True. But like they say, "No body is perfect".
Sorry for that! But, in fact, it's probably true. It's more about the stability of the system. A system that is "perfectly" balanced but intrinsically unstable will disintegrate in no time. Noise will guarantee it, and there is no escape from noise.
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If all mass and energy was at one point in time concentrated at one spot, isn't it symmetrical then? If it suddenly explodes (Big Bang), it would still be perfectly symmetrical - since nothing "outside" can destabilize the symmetry...
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It's all about geometry, one way or another.
Either the geometry and ways we use are correct even if 'plastic' and then you should be able to define a center even to a black hole. Or we don't really know how it is working and as Murchie wrote. "According to Micheo kaku, at the centre of spinning black holes is an eye, like the eye of a storm with the matter swirling around it, its a relatively new proposal."
Now, if that is correct then where did the geometry go?
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Rereading the citation, maybe he don't question a center, just propose a still area around it? :)
But I agree Frodeborli, there is nothing wrong in imaging a perfect symmetry, although, most everything we observe won't have it.