Just to make things easier...let's make this tunnel have Frictionless Walls...let's make the Earth a perfect equally distributed mass Sphere...and the tunnel going through it perfectly in line with it's axis...and forget about magnetic effect.

Split Infinity

 

So your answer is?

Tell me that and I will answer your questions.

Split Infinity

If everything is perfect and there is no friction, no magnetic drag, etc etc then the ball will oscillate from one end of the tube to the other. Not in a sine wave, because of the uneven mass distribution of the Earth (more mass near the centre), but something approximating a Sine Wave.

If there is friction, drag or some other dampening influence, then the amplitude of the ball's oscillation will keep reducing until the ball eventually comes to rest somewhere near to the Earth's centre, wherever the gravitational forces equal out in all directions. The ball will tend to sit to the side of the tube( if the tube is wider than the ball) as the "balance" position will be unstable.

Do I win a prize?

 

There seems to be a fair amount of language ( like "Expression of One Dimensionality" ) that do not mean very much in your question ( and why are there so many words with capital letters ) I am assuming that you do not know the answer to the question rather than trying to test us. In any case the answer, as usual, depends on what other assumptions you make. To make the problem simple most people use Newtonian mechanics, ignore the spin of the earth ( if not the object will hit the side of the tunnel ), ignore the orbital and other motions, assume spherical symmetry and uniform density and treat it as a 2 body problem ( ignore the rest of the universe ). Then the problem ( as I recall ) is just one of simple harmonic motion with the sum of gravitational and potential energy conserved. Even this assumes the earth is not moved by the mass falling thru it, this is not correct but can be fixed by using th concepts of cm frame and reduced mass. The two body problem of point masses interacting thru newtonian physics is generally considered completely solved. Not so the three body problem or 4, 5, ...... The fact that this is Celestial object does not seem to matter much to me what are you think of here.

 

If everything is perfect and there is no friction, no magnetic drag, etc etc then the ball will oscillate from one end of the tube to the other. Not in a sine wave, because of the uneven mass distribution of the Earth (more mass near the centre), but something approximating a Sine Wave.

If there is friction, drag or some other dampening influence, then the amplitude of the ball's oscillation will keep reducing until the ball eventually comes to rest somewhere near to the Earth's centre, wherever the gravitational forces equal out in all directions. The ball will tend to sit to the side of the tube( if the tube is wider than the ball) as the "balance" position will be unstable.

Do I win a prize?

As far as the second part of your answer...absolutely true. As far as the first part...very smart to mention the oscillation but unlike how a Pendulum where the arm is released at 90 degrees and if in a vaccuum using a frictionless swing mechanism...the arm will swing from 90 degrees up to 270 degreesand back and forth forever....Special Gravitic Effect at the center of Earth's Gravity Well will not allow this conservation.

I will explain and answer when answering the following post.

Split Infinity

 

There seems to be a fair amount of language ( like "Expression of One Dimensionality" ) that do not mean very much in your question ( and why are there so many words with capital letters ) I am assuming that you do not know the answer to the question rather than trying to test us. In any case the answer, as usual, depends on what other assumptions you make. To make the problem simple most people use Newtonian mechanics, ignore the spin of the earth ( if not the object will hit the side of the tunnel ), ignore the orbital and other motions, assume spherical symmetry and uniform density and treat it as a 2 body problem ( ignore the rest of the universe ). Then the problem ( as I recall ) is just one of simple harmonic motion with the sum of gravitational and potential energy conserved. Even this assumes the earth is not moved by the mass falling thru it, this is not correct but can be fixed by using th concepts of cm frame and reduced mass. The two body problem of point masses interacting thru newtonian physics is generally considered completely solved. Not so the three body problem or 4, 5, ...... The fact that this is Celestial object does not seem to matter much to me what are you think of here.

First thing you should know about me is I NEVER BLUFF. Thus I do not ask questions and pretend I know the answers if I don't. I will give a few examples to show all what I am refering to as far as the answer to this question.

Fist thing...although Gravity has been labeled the Weak Force...it is not a force at all but rather an EFFECT. A FORCE is defined as AN INTERACTION OF QUANTUM FIELDS. This is so in Magnetics or Electromagnetics, Kinetic Energy Transfer generated by Chemical Reaction, Matter with potential kinetic energy collision with other matter....etc...etc...etc.

With the exception of Gravitational Effect...everything else that will place matter into motion is a Force and an interaction of quantum fields. Gravity does not exist or is a result or created by Quantum Field Interaction.

Gravity is Space/Time Geometry and specifically...an Expression of One Dimensionality. Thus a Celestial Body which usually has a great amount of mass...will create a Gravity Well and thus a Warping of Space/Time. When I drop an Apple...there is no Force...no Quantum Fields...no particle or kinetic transfer placing the apple into motion. It is in motion because the Space/Time between it and Earth has been altered or warped.

When we look at Saturn which has 95 times the mass of Earth has only 91% of Earth's Gravitic Effect if you were able to be located on the surface of Saturn. Also such Gas Giants as well as Stars and Rocky Planets have much greater densities of matter and higher temps. at their core or center of gravity.

Thus within a Celestial Bodies Gravity Well...Gravitic Compression or the Highest level of Space/Time warpeture...or the Greatest Expression of One Dimensionality exists. Because of this...Specialised Gravitational Effects exist at these areas which due to their Space/Time Dimensionality will effect anything to a much greater degree that matter or energy at distance.

Thus the answer to this question is that the ball dropped will not exhibit action such as the never ending pendulum swing or continue to go to and from the tops of both tunnels...but rather be effected at the center of gravity by means of an all points of position one dimensional expression which will cause an entropic effect upon momentum.

Thus the ball will eventually stop at the center of gravity.

Another example to verify this is how a Gravity Well will create the needed Gravititc Compression and thus temps. to start Fusion. Such is the state of our Sun and all stars as once a Celestial Body obtains a Threshold state of quantitative matter it will create Fusion.

A Black Hole is the ultimate exaple of Specialized Gravitational Effect as well as Singularity or an actual One Dimensional State. Although a Black Hole is an actual state of One Dimensionality and not just an Expression of One Dimensionality...the two are connected in that both obtain Specialized Effects due to such created dimensionality.

Split Infinity

 

I find your explanations very unclear and very unconvincing.

Maybe you could take many steps back......

How about explaining the following, rather than just making a statement of how you think it works?

Thus the answer to this question is that the ball dropped will not exhibit action such as the never ending pendulum swing or continue to go to and from the tops of both tunnels...but rather be effected at the center of gravity by means of an all points of position one dimensional expression which will cause an entropic effect upon momentum.

I am guessing that maybe you are saying that gravity is much stronger at the Earth's centre, so Kinetic energy will be overpowered by the pull of gravity. This might make sense to me (but I have not studied the maths) and is maybe believable, but does not require any kind of singularity within the explanation. EDIT: Doh! . Now I am talking rubbish,, as Bill correctly points out with the following post.

 

I suspect just the opposite, you would have nulled gravity in the exact center of the earth, as the surrounding mass on all sides would cancel it out. As you get further from the center gravity (as we know it) would begin to assert itself, slowly.

 

I suspect just the opposite, you would have nulled gravity in the exact center of the earth, as the surrounding mass on all sides would cancel it out. As you get further from the center gravity (as we know it) would begin to assert itself, slowly.

Good point, I am not thinking clearly.

So can anyone work out what splitty is on about?

 

...Sounds like pseudo-science to me. Unfounded theories without any explication...

 

...Sounds like pseudo-science to me. Unfounded theories without any explication...

This is my strong belief too, but I think it is good manners to offer Splitty the opportunity to explain himself. I am confident that he will be unable to give any convincing theory or evidence to back up his ideas.

Over to you Splitty..... convince us...

 

First thing you should know about me is I NEVER BLUFF. Thus I do not ask questions and pretend I know the answers if I don't. I will give a few examples to show all what I am refering to as far as the answer to this question.

Fist thing...although Gravity has been labeled the Weak Force...it is not a force at all but rather an EFFECT. A FORCE is defined as AN INTERACTION OF QUANTUM FIELDS. This is so in Magnetics or Electromagnetics, Kinetic Energy Transfer generated by Chemical Reaction, Matter with potential kinetic energy collision with other matter....etc...etc...etc.

With the exception of Gravitational Effect...everything else that will place matter into motion is a Force and an interaction of quantum fields. Gravity does not exist or is a result or created by Quantum Field Interaction.

Gravity is Space/Time Geometry and specifically...an Expression of One Dimensionality. Thus a Celestial Body which usually has a great amount of mass...will create a Gravity Well and thus a Warping of Space/Time. When I drop an Apple...there is no Force...no Quantum Fields...no particle or kinetic transfer placing the apple into motion. It is in motion because the Space/Time between it and Earth has been altered or warped.

When we look at Saturn which has 95 times the mass of Earth has only 91% of Earth's Gravitic Effect if you were able to be located on the surface of Saturn. Also such Gas Giants as well as Stars and Rocky Planets have much greater densities of matter and higher temps. at their core or center of gravity.

Thus within a Celestial Bodies Gravity Well...Gravitic Compression or the Highest level of Space/Time warpeture...or the Greatest Expression of One Dimensionality exists. Because of this...Specialised Gravitational Effects exist at these areas which due to their Space/Time Dimensionality will effect anything to a much greater degree that matter or energy at distance.

Thus the answer to this question is that the ball dropped will not exhibit action such as the never ending pendulum swing or continue to go to and from the tops of both tunnels...but rather be effected at the center of gravity by means of an all points of position one dimensional expression which will cause an entropic effect upon momentum.

Thus the ball will eventually stop at the center of gravity.

Another example to verify this is how a Gravity Well will create the needed Gravititc Compression and thus temps. to start Fusion. Such is the state of our Sun and all stars as once a Celestial Body obtains a Threshold state of quantitative matter it will create Fusion.

A Black Hole is the ultimate exaple of Specialized Gravitational Effect as well as Singularity or an actual One Dimensional State. Although a Black Hole is an actual state of One Dimensionality and not just an Expression of One Dimensionality...the two are connected in that both obtain Specialized Effects due to such created dimensionality.

Split Infinity

So much is off here, at least according to current physics ( no need to say Physics )

1) gravity is not the weak force, the weak force is, it and the strong force are nuclear forces, work pretty well in the standard model.

2) gravity is even weaker than the weak force.

3) gravity is not even a force in general relavity, it is a space time distortion and this is in a 4 dim space ( 3 of space 1 of time ).

4) not clear that celestial bodies are always massive, asteroids may be very low mass.

5) in GR objects take the shortest space time path ie a straight space time path, what it is depends on the metric, a key concept in GR, this may be what you mean.

6) there is no quantum theory of gravity that is widely accepted, there is a hope for it. GR is not quantum and works real well, it just does not play well with the other 3 forces ( which one have we not covered in this response )?

7) Saturn's mass is just a good as Earth's at "making gravity" there is no disparity. True for Newton and Einstein.

8) Gravitic Compression or the Highest level of Space/Time warpeture...or the Greatest Expression of One Dimensionality .... are all terms that have no technical meaning in physics.

9) Gravity is just the effect of mass at a distance.

10) Energy is mass ( and mass is energy ).

11) You answer about stopping at the center of the earth may be right, but you do not support it. With the assumptions I made it would not, if you use pretty much the same assumptions but general relativity, it would due to emission of gravitational waves, this is a very slow process, I suspect it would take longer than the age of the universe, someone would need to do the calculation.

12) A black hole is not One Dimensional State, like everything else they exist in 4 D space time. They do have that odd thing an event horizon. Keep in mind that many black holes have angular momentum "spin". A black hole is not ultimate, it is just singular. The universe probably has a better claim to be ultimate, and is largely governed by gravity.

Books on physics cover all of this

 

This is my strong belief too, but I think it is good manners to offer Splitty the opportunity to explain himself. I am confident that he will be unable to give any convincing theory or evidence to back up his ideas.

Over to you Splitty..... convince us...

Thank you for being polite.

Since there are so many here that are posting objections...I will try to streamline my answer and if I miss answering anyone...please make me aware of it.

The answer I have given to my own question is that the ball would eventually settle at the Earth's center of gravity.

The reason for this...we are going to look at the specifics of Gravitational effect caused by a Planet...or any celestial body that is basically a sphere and not say...penut shaped like some asteroids which have two or more Gravity wells....the reason for this is at the center of gravity where lies the gravity well...Space/Time dimensionality is at it's greatest point of warpeture.

Reguardless of the size of a planet that is a spheriod...and reguardless of it's mass...the point of greatest Gravitational Effect will be at the center of the Gravity Well. The further the distance from this Gravity Well...the lessor the Space/Time Warpeture.

If this was not so then planets would not have their greatest density of matter at their center cores. Stars would just be a great collection of Gas and never obtain the need Gravitic Compression to cause Fusion.

This is also why that Saturn...even though it has 95.2 times the mass of Earth...still only has 91% of Earth's Gravitic Effect at it's equator. The distance from Saturns equatorial line to the ceter of it's Gravity Well is a radius of 9.5 Earth Diameters.

Due to the fact that the majority of Saturns mass exists at it's planetary core...and that the various gases that exist obove this to Saturns equator are much less dense than what the Earth's mass between it's core and equator...and the fact that Saturn's Gravity Well is at a distance of 9.5 Earth Diameters from it's equatorial line....Gravitic Effect is but 91% that of Earth at it's surface.

This reality is specific to the Space/Time warpeture as it exists from either planets Center point of Gravity and Gravity Well...away perpendicular to either planets Gravity well center line diameter through the planets.

Whether the distance between this center point of the Gravity well exists as Rock, Gas, Metal, Atmosphere or open Space...makes no difference as to the decrease of Warpeture of Space/Time as one get's farther away from the center point of the planet's Gravity Well.

Split Infinity

 

As far as my statements where I use the term...Gravity is an Expression of One Dimensionality...this is specific to how any amount of mass will warp the Space/Time and the matter itself that makes up this mass from a Center Point of it's Gravity Well.

All Universal Dimensional states are interconnective, associative and governed to an extent by each other.

Thus since Gravity is Space/Time dimensionality specific to One Dimensionality interconnectivity to all other dimensional states...the word EXPRESSION is used.

Split Infinity

 

I suspect just the opposite, you would have nulled gravity in the exact center of the earth, as the surrounding mass on all sides would cancel it out. As you get further from the center gravity (as we know it) would begin to assert itself, slowly.

Your statement...Nulled Gravity in the exact center of the Earth is incorrect and very much opposite of what is going on.

If your statement was true than Planets and Stars would not have their greatest material density at the Center point of their Gravity Wells.

Split Infinity

 

What you are describing is a model for space/time warping given solid objects. Each individual massive particle exerts a gravitational pull on all other particles.

If you were to, instead, split the earth in half and separate them by a significant distance, are you suggesting that they would have a gravitational pull where the center used to ? Based on your answers, your answer to this is yes. What if those two halves were brought very close together?

 

As far as Black Holes are concerned...many a Cosmologist and Physicist have tried...and failed miserably...at defining exactly what is going on. Stevie H. is an example of a person flip flopping on the math he developed as far as Black Holes...and this took a good amount of the short time he has left.

It is postulated that for every Black Hole that exists...there must be a White Hole existing and tied to the Black Hole...in another state of Reality.

A Black Hole occurs or exists either when a Red Giant has Fused the vast majority of it's Hydrogen into Helium and thus does not have enough outward Thermonuclear explosive force to prevent it's huge quantity of matter thus mass from collapsing.

Or Black Holes appear at the center of all Galaxies for the reason that at one time a vast amount of multiple stellar masses achieved a threshold state and collapsed into a state of Singularity.

Singularity is defined as a Universal One Dimensional State and at the point of the creation of a Black Hole...the Center Point of it's Gravity Well has broken through to another Universal State through the created Singularity.

We may see a Black Holes Accretion Disc but we cannot see or detect it's mass other than by observed Gravitational Effect.

Split Infinity

 

What you are describing is a model for space/time warping given solid objects. Each individual massive particle exerts a gravitational pull on all other particles.

If you were to, instead, split the earth in half and separate them by a significant distance, are you suggesting that they would have a gravitational pull where the center used to ? Based on your answers, your answer to this is yes. What if those two halves were brought very close together?

If you split Earth you would have TWO Center Points of existing Gravity Wells. And thus each half would restructure itself into as close to a sphere as possible and have at their Center of Gravity the greatest material density.

Split Infinity

 

If you split Earth you would have TWO Center Points of existing Gravity Wells. And thus each half would restructure itself into as close to a sphere as possible and have at their Center of Gravity the greatest material density.

Split Infinity

...and what if you were to continue halving the halves? Eventually you would come to the realization that mass exerts a gravitational pull on other particles. So each particle adds to the total gravitational effect a mass has on a given, external particle.

From this, we can ascertain that a hollowed out sphere with uniform density across its surface will exert a force on a particle in the middle, pulling it equally in all directions, canceling each infinitesimally small particle's effect.

 

...and what if you were to continue halving the halves? Eventually you would come to the realization that mass exerts a gravitational pull on other particles. So each particle adds to the total gravitational effect a mass has on a given, external particle.

From this, we can ascertain that a hollowed out sphere with uniform density across its surface will exert a force on a particle in the middle, pulling it equally in all directions, canceling each infinitesimally small particle's effect.

As far as continuing to split and resplit...each piece would have it's own Center of Gravity and Gravity Well.

Your second part of the question is asking me what would happen to a particle in the middle of a hollowed out sphere. If the sphere is hollowed out that would mean there is nothing at it's center.

But let's say there existed a Planet with a perfect sphere about the diameter of Earth and it was hollow and it's surface or crust was 200 miles thick and made out of Bucky Balls...a type of Carbon Molecule.

Let's say for kicks...we were able to teleport a solid ball of steel that was 1 mile in diameter to the very center of this hollowed sphere.

Fist of all it is IMPOSSIBLE for a Hollowed Out PLANET to exist this way and this size no matter how strong and interwoven the material...so let's use instead a Hollow Steel Ball Tennis Ball Sized...that we teleport a single carbon atom into it's center.

Since a structure like this at this size could maintain it's structure in Space...it would remain a hollow ball. It's Center Point of Gravity would be at every point of position existing at half the depth of the steel.

Since Gravitational Effect would be occuring from all points halfway through the depth of the steel...the carbon atom would be attracted to the specific gravity well that the Carbon Atoms Geometric Structure of it's nucleus allows for the shortest distance from that atoms nucleus Protons or Neutrons to the inside of the ball.

If the atoms nucleus was in perfect balance geometrically in all distances between all points of position to the center point of the thickness of steel...it would remain dead center of the hollowed ball.

Split Infinity

 

As far as continuing to split and resplit...each piece would have it's own Center of Gravity and Gravity Well.

Your second part of the question is asking me what would happen to a particle in the middle of a hollowed out sphere. If the sphere is hollowed out that would mean there is nothing at it's center.

But let's say there existed a Planet with a perfect sphere about the diameter of Earth and it was hollow and it's surface or crust was 200 miles thick and made out of Bucky Balls...a type of Carbon Molecule.

Let's say for kicks...we were able to teleport a solid ball of steel that was 1 mile in diameter to the very center of this hollowed sphere.

Fist of all it is IMPOSSIBLE for a Hollowed Out PLANET to exist this way and this size no matter how strong and interwoven the material...so let's use instead a Hollow Steel Ball Tennis Ball Sized...that we teleport a single carbon atom into it's center.

...but it's possible to make a tunnel through one!? This is theoretical, youcan't pick and choose what you want to theorize so as to prove a point without examining others.

Since a structure like this at this size could maintain it's structure in Space...it would remain a hollow ball. It's Center Point of Gravity would be at every point of position existing at half the depth of the steel.

It does not exist there, it exists everywhere,a force from each individual particle. The macroscopic model you are using no longer applies.

Since Gravitational Effect would be occuring from all points halfway through the depth of the steel...the carbon atom would be attracted to the specific gravity well that the Carbon Atoms Geometric Structure of it's nucleus allows for the shortest distance from that atoms nucleus Protons or Neutrons to the inside of the ball.

If the atoms nucleus was in perfect balance geometrically in all distances between all points of position to the center point of the thickness of steel...it would remain dead center of the hollowed ball.

Split Infinity

Now, assume the particle is displaced in a conservative system,what happens to the particle?