that pete thread actually made me think (SHOCKING)

[[xeno]Julios]

No, because there are still gravitational forces. They are cancelling each other out (in relation to the earth and the object), but the forces in any given direction still exist.

Perhaps we are splitting haris here - you mentioned zero gravity, someone else said "No gravity" - a difference, IMHO. For example, you could calculate the gravitational force in any given direction...and it would have the same force in the opposite direction, netting you zero overall...
Do you get what I am trying to say?

zero gravity IS the same as no gravity.

[tnf]

Would the same apply to any system where all forces are balanced, so there is no net force in a given direction?
NVM - I suddenly see where I was misreading your point.

[tnf]

By the way, we are assuming the earth is a uniformly dense sphere here...correct? Because if it isn't, this whole thing is different.....

[tnf]

Well, just so that we can get a 100% definitive answer of how all this would be answered by a real-life physicist, I have emailed a friend of mine who is a physics professor at the local college. THat isn't because I doubted your answer julios, its just because I want closure...heheh....mainly insofar as how all the relevant definitions, terminology, etc., would be applied to this answer.

[[xeno]Julios]

By the way, we are assuming the earth is a uniformly dense sphere here...correct? Because if it isn't, this whole thing is different.....

aye.

[[xeno]Julios]

Well, just so that we can get a 100% definitive answer of how all this would be answered by a real-life physicist, I have emailed a friend of mine who is a physics professor at the local college. THat isn't because I doubted your answer julios, its just because I want closure...heheh....mainly insofar as how all the relevant definitions, terminology, etc., would be applied to this answer.

You should doubt my answer! Shows you're actually out there to understand rather than suck in the spoonfeed. Plus, as I said, my assertion is based on strong intuition rather than scholarship.

[tnf]

Well, I have this gut feeling your intuition is missing something...but I can't quite put my finger on what, exactly...and it has been so long since I've done more advanced kinematcis work. Had I been in the middle of my calc/physics class I think I would have been much more adept at answering this one.

[[xeno]Julios]

Imagine the following two situations:

Situation 1: There is a ball hanging in the middle of space, with a rope attached to each opposite end. Each rope is pulling with a force of 100 newtons. The net force on the ball is therefore 0 Newtons.

Situation 2: There is a ball hanging in the middle of space, equidistant between two planets on opposite ends. The net gravitaitional pull is zero.


Do you think they are similar, insofar as this discussion is concerned?

I contend that they are not, and i'll explain why after you respond.

[tnf]

You tell me why you think they are not. I can see how you could say they are in one way (simple vector additions) and how they are not in another.

But how do we fit relativity into #2 - that gravity is best viewed as objects bending spacetime (the bowling ball on the bed analogy.)

[tnf]

Why do I feel like I am in some socratic dialogue here....

[mjrpes]

Your needless use of complex terminoligy I find to be so utterly juvenile that this discussion ceases to be entertaining.

That's just the way the boy talks. You read enough academic journals and you'll being to think and speak in the language of acadamia quite well, too.

[[xeno]Julios]

You tell me why you think they are not. I can see how you could say they are in one way (simple vector additions) and how they are not in another.

But how do we fit relativity into #2 - that gravity is best viewed as objects bending spacetime (the bowling ball on the bed analogy.)

This is the reason they're different:

In the first scenario, the ropes are attached to only the ends of the ball. This means, that while the net force vector on the ball as a unitary entity is zero, there is stress on the insides of the ball. If you pull hard enough, the ball will split into two.

I don't think gravity works this way - a body inbetween two planets will not experience this stress of pulling. This is because the force of gravity acts upon every single particle in the ball at once.

Now I may be dead wrong about this, but this is my intuition.

[[xeno]Julios]

But how do we fit relativity into #2 - that gravity is best viewed as objects bending spacetime (the bowling ball on the bed analogy.)

I think you've now provided me with another way of arguing my point:

If you have two planets bending spacetime, then the spacetime inbetween them will be flat.

This flatness is the very nature of zero gravity.

Quite different from being pulled by two ropes.

[tnf]

You tell me why you think they are not. I can see how you could say they are in one way (simple vector additions) and how they are not in another.

But how do we fit relativity into #2 - that gravity is best viewed as objects bending spacetime (the bowling ball on the bed analogy.)

I don't think gravity works this way - a body inbetween two planets will not experience this stress of pulling. This is because the force of gravity acts upon every single particle in the ball at once.

Now I may be dead wrong about this, but this is my intuition.

Incorrect, if I understand you correctly. You are forgetting tidal forces. Lets say a guy approaches a black hole. The gravitational forces near his feet would be mh greater than those near his head...if he was going in feet first. There is much, much more to the hole 'what would happen as you approached a black hole' than this, but tidal forces are a key aspect.

" As he dropped farther and farther down these forces would increase indefinitely, and so would their difference. It is this latter which would be most operative in killing him, since it would stretch his body out to have indefinite length. However, at the same time his volume would constantly be reduced as he fell due to the general compression going on at the centre of the hole.

It is possible to calculate roughly how far away from the black star the astronaut would succumb to the mounting tidal forces and the bones and muscles of his body be elongated beyond breaking point along his length and be crushed beyond breaking point in all other directions. For a spaceman of avenge weight and with bones and muscles of normal strength he need only be one hundred kilometers away from a black hole of one solar mass in size before he was killed; he would still be a long way from its event horizon, which is only one and one-half kilometers. He could just get inside the event horizon of a black hole one thousand times heavier before he was killed by it, while for one a million times heavier he could get one hundred times closer to the singularity than the event horizon before he succumbed. For a black hole of the size of our galaxy he could get about a million times nearer the singularity than the critical radius before his end; in these last two cases the forces on him at the event horizon itself would be negligible."



Plus, why would it act upon every single particle at once in the same manner? Atoms closer to the source of gravity would experience more gravitational force than those further away...if I am not mistaken. If the forces holding the ball together exceed the differences in forces of gravity 'pulling' them one
direction, the whole thing holds together...if not, it tears apart.

EDIT: Wait a minute, I see a misread again...you said acts on them all at once...you might not mean all at once with the same force...but I am not sure if that is what you meant or not.

[tnf]

But how do we fit relativity into #2 - that gravity is best viewed as objects bending spacetime (the bowling ball on the bed analogy.)

I think you've now provided me with another way of arguing my point:

If you have two planets bending spacetime, then the spacetime inbetween them will be flat.

This flatness is the very nature of zero gravity.

Quite different from being pulled by two ropes.

That gets interesting to think about from an infiniter number of angles by which we could take a plane and bisect each planet...how they would bend spacetime in every direction...

This is seriously cutting into my splinter cell time.

BTW - Jules did you ever pick up those CD's I recommended a long time ago - from barnes and noble - series of lectures by noted professors on plato, socrates, etc....?

[[xeno]Julios]

In the case of a black hole, you can think of a sloped dimple in spacetime that gets steeper in the direction of the hole. Now if your feet are at a steeper point along this slope, relative to your head, then there would be this stretching phenomenon.

In the case where there are two dimples that cancel each other out, you're left with flat region in the middle.

Or maybe it's not a flat region, but rather a flat point that's infinitessimaly small.

In which case, a ball could not fit entirely on that point.

Perhaps you're right afterall

[[xeno]Julios]

BTW - Jules did you ever pick up those CD's I recommended a long time ago - from barnes and noble - series of lectures by noted professors on plato, socrates, etc....?

hm remind me again? Is it the learning company?

I'm not a big fan of those oldschool philosophers - find it really hard to understand a lot of what they're saying. Haven't read much plato, and the little aritstotle i've read is so fuckin difficult to understand (not surprising considering they're translations of fragments of his lecture notes taken by students).

I know I should do the old philosophers some service, but i'm more interested in applied philosophy rather than "pure" philosophy.

[mjrpes]

tnf, maybe you can help me visualize the force of gravity between two objects at different distances between them. Here's a shitty visual aid I made:



The line at the bottom is the force of gravity that would be applied to an object (not drawn) as it made its way from a very far distance (infinity end), to the surface of a planet, and then passing through the planet to the centre. According to what you've been saying, force is highest at the surface of the planet, and then goes to zero at the centre. Would this change be linear, like I've drawn, or curved? My math/physics skills aren't good so I can't figure things out myself with Mr. Gravitational Equation.

EDIT: Just to be clear, I'm talking about change in acceleration (i.e., force applied), and not velocity.

[[xeno]Julios]

gravitational force attentuates as a function of the square of the distance. So it doesn't decrease at a steady rate. ( I think this holds for all forms of point source radiation in three dimensions - if it were a four dimensional sphere, then it would attenuate as a function of the cube of the distance I think).

[mjrpes]

Alright, but I don't know what you mean by a four dimensional sphere.

[tnf]

Just figure this - you are dividing by the distance squared. So, all other things equal, if you double the distance, you decrease the force of gravity by a factor of 4, if you quadruple the distance, you decrease the force by a factor of 16, etc....if you graphed it, you'd get an asymptotic graph, one that approached 0 force but never quite reached it.

[tnf]

Julios cannot avoid sprinkling big words, deep thoughts, and the basic jargon of philosophy into his answers. That is why I figured you'd be interested in classical philosophy.

I've noticed a big difference in the language I use to explain things since I started teaching high school science vs. doing research. I probably sound like a relatively undeducated, poorly versed dimwit when I try and explain ideas here.

[mjrpes]

Does this asymptotic graph hold as the object passes through the surface and heads to the centre?

[mjrpes]

Julios cannot avoid sprinkling big words, deep thoughts, and the basic jargon of philosophy into his answers. That is why I figured you'd be interested in classical philosophy.

Do you know what he meant by a forth dimensional sphere? Seems pretty non-philosophical related to me... maybe it's something Julios made up?

As for classical philosophy, Socrates wasn't a fan of big words and jargon either; his goal was to clarify meaning and he hated the obfuscation of the sophists (popular in his time). Plato his disciple feel more into that category, as his idea of 'forms' lead to abstractions, where you start to get jargon and deep thoughts. Aristotle seems to have taken this category to the extreme (from my futile attempts at understanding the man).

[[xeno]Julios]

I might not be able to explain this very well - i remember hearing about it in relation to Kant (might be something here: http://plato.stanford.edu/entries/kant-development/#5 )

Another way of putting it would be that energy emanating from a two dimensional circle would attenuate in a linear fashion. In a 3 dimensional sphere it attenuates as a square function, and in a four dimensional hypersphere it would attenuate as a cube function.

I threw that in to lend insight into the nature pf the relationship between geometry and physics.

Think about a two dimensional circle: There is a finite amount of energy issuing from its centre. At the centre point, the energy is 100 percent. As distance from centre increases, energy has to be distrubuted over the circumference of the circle. Circumference is 2 * pi * r, which is a linear function. Circumference is a one dimensional "entity".

In a three dimensional sphere, the energy has to be distributed over the surface of the sphere, and the equation for surface of a sphere is 4 * pi * r squared, which is a square function.

I'd imagine that the surface volume of a hypersphere might be 8 pi r cubed (or maybe 16 pi r cubed).