Caedes: The intuition behind your argument is correct, however (by definition) the gravitational field on the inside of the hollow sphere due to the sphere is zero. The question is if a gravitational field of zero mean there is no gravity; I would tend to say yes because otherwise I would not know what no gravity means. Viv seem to distinguish between no acceleration and no total acceleration which is so silly I think it is beyond me to correct that misunderstanding.
Posts by bohm
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280the flood, mammoths, elphants, and food.
by Crazyguy inmy question is since it looks as though mammoths were alive after the flood and we know elephants are then how much food was needed to feed just these four animals for the time they were on the ark.
also was the ark, 500 feet long, big enough to hold the amount of food needed for just these 4 animals.. .
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280
the flood, mammoths, elphants, and food.
by Crazyguy inmy question is since it looks as though mammoths were alive after the flood and we know elephants are then how much food was needed to feed just these four animals for the time they were on the ark.
also was the ark, 500 feet long, big enough to hold the amount of food needed for just these 4 animals.. .
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bohm
Bohm: Can you eleborate then in what sense the radius of the second body enters into the derivation not covered by my description? Specifically, does the shell theorem in your oppinion not cover the case where a non-spherical body is inside a spherical shell?
Viv: I already did. I'm not re-typing it because you didn't grasp, read my post it or read a paper on it.
You quite plainly did not. That you insist you did, and are unable to substantiate your claims except insisting it is so is quite revealing.
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280
the flood, mammoths, elphants, and food.
by Crazyguy inmy question is since it looks as though mammoths were alive after the flood and we know elephants are then how much food was needed to feed just these four animals for the time they were on the ark.
also was the ark, 500 feet long, big enough to hold the amount of food needed for just these 4 animals.. .
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bohm
Bohm: Actually I would say there was no gravity inside the shell (or at the center of the earth), not just that it "cancelled" out, however clearly the answer depends on what we mean by there "being gravity"
Viv: If you disagree, please please please explain how mass can avoid warping space because it's inside of a shell. I await your math.
I notice you re-phrased what I wrote so as to create a strawman. Firstly, as is apparent in the context, I was treating the newtonian/relativistic example seperately. Secondly, you are talking about the effect of the mass *of an object inside the shell* whereas my statement was (and this is apparent if you read it) about the gravitational field *inside a hollow shell*. That you insert an object inside the hollow shell and discuss the gravitational effect *of that object* is the strawman
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280
the flood, mammoths, elphants, and food.
by Crazyguy inmy question is since it looks as though mammoths were alive after the flood and we know elephants are then how much food was needed to feed just these four animals for the time they were on the ark.
also was the ark, 500 feet long, big enough to hold the amount of food needed for just these 4 animals.. .
.
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bohm
Bohm: There is furthermore no "other" radius as you seem to suggest ("that's the radius you were missing, the second body") since the geometry of the other object does not matter insofar as the shell theorem is concerned, as long as it is either inside or outside the hollow sphere (if it is on the boundary the shell theorem still applies to the parts on either side of the boundary seperately).
Viv: Well, you were getting it. Read a paper on it rather than wikipedia.
So you disagree with this point? Can you eleborate then in what sense the radius of the second body enters into the derivation not covered by my description? Specifically, does the shell theorem in your oppinion not cover the case where a non-spherical body is inside a spherical shell?
Viv: Because it's not "no acceleration on an object inside the sphere", it's "total acceleration is equal to zero". Very different things.
Interesting. There is some basic confusion here on the meaning of acceleration. Try to give a counter example. How does the "total" acceleration of a body differ from it's acceleration?
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280
the flood, mammoths, elphants, and food.
by Crazyguy inmy question is since it looks as though mammoths were alive after the flood and we know elephants are then how much food was needed to feed just these four animals for the time they were on the ark.
also was the ark, 500 feet long, big enough to hold the amount of food needed for just these 4 animals.. .
.
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bohm
Caedes:
- Viv: So... how is there no gravity at the center if gravity is decelerating the object? See my previous post.
- Caedes: The net effect would be that your acceleration due to gravity would be zero, not that there would be no gravity.
You are correct in your analysis of the well.
However with regards to there being no gravity however I would tend to disagree. I also think this is a point that has been confused on this thread and may also be the cause of some of the misunderstanding between me and Viviane.
Actually I would say there was no gravity inside the shell (or at the center of the earth), not just that it "cancelled" out, however clearly the answer depends on what we mean by there "being gravity"
In classical (Newtonian) physics, which is all I have discussed so far and seem relevant to the OP, there being gravity would to my mind mean the gravitational field was not zero -- however the gravitational field is zero inside a hollow shell (or in the center of the earth) per the shell theorem.
More interesting is perhaps to ask the question in the context of general relativity. The general formulation of the shell theorem in a relativistic setting is Birkhoffs theorem and according to it the space-time metric inside a hollow sphere is flat Minkowski, and a Minkowski metric is also that of empty space; this is not to say the space is globally flat as there would still be time-dilation effects comparing the inside of the sphere to the outside, also I am not touching upon the black-hole limit. These statements are consistent because the Minkowski metric on the inside and outside may differ, i.e. there is no continious *globally* flat Minkowski metric. It is a very strange and interesting situation actually.
when we intuitively insist on there being gravity (this is also what my intuition insists on BTW) this is merely because we "know" there must be gravity near a large object. However from a perspective of physics, we should first define what gravity (precense or absence) mean and then determine the answer. If we define gravity as being a vanishing gravitational field or Minkowski space-time metric then there is "no gravity"; mind in the context of GR this definition is far more questionable and an observer on the outside would disagree as there would be e.g. time dilation. Perhaps some GR geeks could weight in with their oppinion.
(updated).
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280
the flood, mammoths, elphants, and food.
by Crazyguy inmy question is since it looks as though mammoths were alive after the flood and we know elephants are then how much food was needed to feed just these four animals for the time they were on the ark.
also was the ark, 500 feet long, big enough to hold the amount of food needed for just these 4 animals.. .
.
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bohm
Howdy viviane!
- Bohm: i only expect you to tell me what you think i have done wrong. You hinted this had something to do with a radius and i asked the radius of what?
- Viv: You brought up shell theorem without understanding it. YOU brought the theorem up AND even included it in some rudimentary equations you wrote down. I can't read the theorem for you!
You are entitled to think I do not understand the shell theorem. Not only does it seem quite pointless for me to correct that misconception, you seem so invested in it I cannot see how I could do it in principle. Would a derivation serve? At any rate this is not my main point. I was referring to the following exchange:
- Bohm: so returning to the mineshaft, if we assume the earth is a body of uniform density the gravitational pull at a radius r will (per 1 of the shell theorem) scale as the mass (proportional to r^3) divided by square of distance (newtons low of gravitation) and so scale as r.
- Viv: So, even using classical mechanics, it's not, as you said, "no acceleration in a hollow sphere".
or
- Viv: BTW, for those about to say "B-b-b-but Shell Theorem!", it's got a LOT to do with the radius of the objet under questions. It's not as simple as reading Wikipedia.
- Bohm: the radius of which object? what part of wikipedia is wrong?
- Viv: Yes. "No gravity" isn't what the shell theorem says.
This went back and forth a bit. You have not tried to clarify the point about the radius:
Viv: The shell theorem shows that gravitational acceleration between two bodies can be calculated using the center of those bodies because, effectively, the TOTAL gravitational acceleration inside nets out to zero as can be shown using two perfectly spherical but hollow bodies and how, relative to the internal coordinates, gravitational acceleration is calculated relative to ANOTHER body either inside or external to the spherical hollow mass (that's the radius you were missing, the second body). That doesn't mean there IS NO GRAVITY or that it is not stronger inside the body in one corrdinate than in another place. It just means that it NETS to zero.
There are some minor issues in this description I wont touch upon here. I do think i now understand the confusion regarding the second body. Firstly, notice that as best as i can tell what you wrote is in no way in contradiction to what I wrote. I claimed the acceleration of an object inside a hollow sphere was zero and you wrote: it's not, as you said, "no acceleration in a hollow sphere". I am still puzzled where you think the contradiction lie.
Now as regard to your point with the second radius. The shell theorem describes the vector field of force (the gravitational field) in any point inside or outside the hollow sphere due to the gravitational attraction of the hollow sphere. Can we agree upon this basic point?
Thus, the radius of this sphere matters insofar as it determines when an object is inside or outside the hollow sphere, however asides this trivial point the only thing that matters is the mass of the hollow sphere (see the wikipedia description or my description). There is furthermore no "other" radius as you seem to suggest ("that's the radius you were missing, the second body") since the geometry of the other object does not matter insofar as the shell theorem is concerned, as long as it is either inside or outside the hollow sphere (if it is on the boundary the shell theorem still applies to the parts on either side of the boundary seperately). This is simply because the force exerted at the other object is, independent of it's geometry, the integral of the vector field computed by the shell theorem over the density function of the object. Can we agree upon this point too?
Thus your characterization of the shell theorem as having to do with two *spherical* objects where the radius matters is an unecesary restriction of the version found at the wikipedia page (or as described by me) and that was what confused me.
- Viv: It's like sticking your hand in between a hungry lion and a steak and wondering why your hand is missing.
So you are comparing yourself to a hungry lion?
- Now that I've said all of that, a conversation I had with my son the other day seems salient. He's extremely intelligent and has recently been caught saying he knows things he doesn't.
I hope he was not "caught" in the same sence I was, that would be very frustrating for him, and that you did not act like a hungry lion to him.
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46
I am sooo screwed
by Yondaime inso last night i was talking to my sister about how i admired president obama's speech to the u.n that happened earlier that day.. i then compared the extremism of isis to how much of a fanatic my jw bil is.. at the end of the statement , my mom walked in to the kitchen.
she was standing in the living room and she heard everything i said.. she called the elders that night to tell them what i said so they can counsel me.. i'm going to meet with them after the meeting on sunday!.
what do i do?!!!!!.
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bohm
Of course you cannot remember what you said. what have they heard? That certainly cannot be correct.
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80
" Do not ask permission, just play the video--" service meeting instructions.
by prologos inthis statement startled me out of the pleasant mental absence during this week's "service" meeting.. pushing the org.
explanation: "the listener has time to interrupt, if they want--" .
together with an incredible boring "study" of an hand held device, or it's stored content, i will be a totally new crop of orgies at the halls,.
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bohm
"Robert had been a lifelong catholic, but one morning there was a knock on the door. 'There was two fellas in suits and that imediately impressed me', robert recalls. 'Then the older one showed an ipad in front of me with this video of two cartoon kids in a kind of factory. I know right then and there this was my religion and i havent looked backsince'. Despite loosing his wife and family robert has never regretted his decision: 'i sometimes think, if these guys had shown me a video by that asian guy who dance funny, i would have been a mooney!'"
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46
I am sooo screwed
by Yondaime inso last night i was talking to my sister about how i admired president obama's speech to the u.n that happened earlier that day.. i then compared the extremism of isis to how much of a fanatic my jw bil is.. at the end of the statement , my mom walked in to the kitchen.
she was standing in the living room and she heard everything i said.. she called the elders that night to tell them what i said so they can counsel me.. i'm going to meet with them after the meeting on sunday!.
what do i do?!!!!!.
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bohm
Rebel8 nailed it.
Play dumb and eat lots of garlic
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28
Waking up your spouse
by All for show ini am aware this has to be done quite carefully, but how?
while many may complain and see the hypocrisy within the kh's, maybe even with the gb, how does one bring up doctrine issues?
i surely can not tell my husband to "go look what jwfacts.com says".
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bohm
how 'in' do you think he is? How might he react to a question like: i sometimes wonder why they say we should never read others litterature but others should read ours. Have you ever thought about that?