# Which way is up?

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I have been reading a few rather dodgy threads pertaining to gravity. A question not related to those threads but induced by them occurs to me.

Firstly assume you have a hollow space and are not being crushed or burnt to a crisp at the centre of  the earth, the sun, or even a black hole

Assuming the above, would a gravitional force be felt. Would you feel any gravity at the dead centre of the earth, the sun, or a black hole? My reasoning being there is a equal amount of mass in all directions from the centre of any mass and gravity would pull equally in all directions producing weightlessness perhaps inside your hollow space.

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Posted (edited)

Google is good. Does the below also apply to a black hole, and how does this affect the pressure and heat at the centre of a planet.

The graph below shows how g varies with distance from the centre of a large spherical object (e.g. a planet or star) or uniform density.

As you can see, g varies with the inverse proportional to the distance, r, from the centre of the planet. However, this is only from the surface of that object i.e. 'R' is the radius of the planet. If you were to tunnel through the Earth towards the core the gravitational field strength would decrease linearly, until it reached zero when you were in the centre. Essentially you would hover in the centre of the Earth if you reached it and it was hollow. Conceptually, this is because all the mass will be pulling you equally in every direction, making the resultant force zero, meaning that you wouldn't accelerate in any direction.

The reason why this is so is given below:

Volume of a sphere (i.e. a planet):

Density, p (Greek letter 'rho'), of a uniform sphere:

Using both equations and rearranging to get m the subject of the forumla:

Use the equation for g and this equation for mass to get the following:

Finally:

And so, within the Earth's surface (i.e. r<R) the gravitational field strength, g, is directly proportional to the distance, r, from the centre of the planet.
42 minutes ago, interested said:

Does the below also apply to a black hole, and how does this affect the pressure and heat at the centre of a plane

As for the question, at the center of the Earth, the pull of gravity is equalized, and a person would feel weightless. However the pressure would be very high. Even though there is no pull of gravity, the pressure from higher layers of air would still be present. There is no anti gravity at the center which would push the air away. Pressure exists even in a weightless environment.

Having answered most of my own question by a spot of googling. Would the above also apply to a black hole ie does it also have no gravity at the centre and lots of pressure from the higher layers.

How does gravity affect the ticking of a clock as it moves from outer space down to the centre of a planet or black hole.?????????????

edit: Time dilation is not an affect of pressure. If Time slows down as gravity increases, what happens at the centre of the earth or black hole when there is no gravity only pressure does it speed up again????????????????

Edited by interested

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1 hour ago, interested said:

Would the above also apply to a black hole ie does it also have no gravity at the centre and lots of pressure from the higher layers.

The situation of a black hole is different because all the mass is (*) concentrated at the centre. So there would be no decrease in gravity as you approach the centre.

Quote

How does gravity affect the ticking of a clock as it moves from outer space down to the centre of a planet or black hole.?

Time dilation is due to gravitational potential, not gravitational force, so it would increase steadily as you approach the centre of the Earth.

A couple of other points...

The linear decrease of gravity inside the Earth is an idealisation assuming the density is the same everywhere. If you take the density of material into account, the gravity increases slightly first and then decreases.

Also, if there were a hollow in the centre then the gravity would drop to zero as soon as you enter the hollow. In fact, if the total mass of the Earth were concentrated in a thin shell (where the surface of the Earth is) then there would no gravity as soon as you get inside the shell. (But outside, it would make no difference.)

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43 minutes ago, Strange said:

Time dilation is due to gravitational potential, not gravitational force, so it would increase steadily as you approach the centre of the Earth.

Can you explain the above a bit, both Potential and Force can be viewed as a pressure gradient 1 Volt 1 Newton 1 G all potentials.

To have a gravitational potential one needs a gradient, at the centre of the earth assuming it is uniform(noted the earth is not uniform) there is a null point with no gradient at the centre ie no gravity, A null gravitational force/potential will also exist between the moon and earth, when the attraction forces of each are matched.

Why does this zero gravity point not affect time dilation, I read that the earths core is younger due to time dilation than the crust by about 2.5 days because of increased gravity as you approach the centre, but this is not true. Gravity reduces as you approach the centre of the earth, only the pressure will increase.

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Potential can be though of as the work needed to raise something and (ignoring the pressure and solidity of the material: imagine we are dealing with a tunnel going through the centre of the Earth) it would take work to let something from the centre towards the surface. Therefore the gravitational potential is greater as you approach the centre.

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37 minutes ago, Strange said:

Potential can be though of as the work needed to raise something and (ignoring the pressure and solidity of the material: imagine we are dealing with a tunnel going through the centre of the Earth) it would take work to let something from the centre towards the surface. Therefore the gravitational potential is greater as you approach the centre.

But gravity reduces to zero at the centre of the earth, therefore to start it moving from the centre it has no mass only inertia. It will not have mass until it experiences gravity as it moves away from the centre of the earth. Maximum pressure will be experienced at the centre but no gravity until you move away. The gravitional effect as you approach the core is reduced. I am going to have to mull this one over, Im stuck in a loop.

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1 minute ago, interested said:

But gravity reduces to zero at the centre of the earth

Gravitational force reduce to zero. The gravitational potential (or space-time curvature, if you prefer) reaches a maximum there.

2 minutes ago, interested said:

it has no mass only inertia

It always has mass. Do you mean weight?

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13 minutes ago, interested said:

But gravity reduces to zero at the centre of the earth, therefore to start it moving from the centre it has no mass only inertia. It will not have mass until it experiences gravity as it moves away from the centre of the earth. Maximum pressure will be experienced at the centre but no gravity until you move away. The gravitional effect as you approach the core is reduced. I am going to have to mull this one over, Im stuck in a loop.

The fact that there is zero gravitational force at the center of the Earth does not mean that an object at the center of the Earth isn't at a lower gravitational potential than an object on the surface.  A difference in gravitational potential is tied to the energy needed to make the entire trip between two points and not what happens at the start or finish of the trip.   Using the standard reference which puts zero gravitational potential at an point an infinite distance from the gravity source, the gravitational potential from the surface of a sphere outward is found by  -GM/r,  where r is the distance from the center of the sphere.   As r gets smaller the potential goes more negative and thus becomes lower.

For a point inside a uniformly dense sphere, the potential is -GM [ (3R2-r2)/2R3] which reduces to -3GM/2R at the center.

-3gm/2R is more negative than -GM/r, so  the gravitational potential at the center is lower than at the surface.

Here's a graph for the gravitational potential for the Earth (assuming a uniform density) starting at the center and moving out to some distance above the surface. the green line marks off the radial distance of the Earth's surface.

The exact shape of the  curve on the left of the green line will be different  for the  real Earth due to the variance of density with depth, but will still be lower at the center than any other point.

Time dilation is related to the difference in gravitational potential and thus a clock at the center of the Earth, being at the lowest potential will run the slowest.

Going back to what I said about the potential difference applying to the entire trip, If you take a clock and move it from the center of the Earth to that point an infinite distance from the Earth, it will start at zero g and end at zero g,  but it will have raised its gravitational potential by a fair amount and will run faster at the far removed point than it did at the center of the Earth.

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1 hour ago, Janus said:

-3gm/2R is more negative than -GM/r, so  the gravitational potential at the center is lower than at the surface.

Oops. I got the sign of this the wrong way round in my head, which is why I said "maximum" rather than "minimum".

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3 hours ago, interested said:

To have a gravitational potential one needs a gradient, at the centre of the earth assuming it is uniform(noted the earth is not uniform) there is a null point with no gradient at the centre ie no gravity,

No, there will be a potential with a constant gravitational acceleration. Near the earth's surface, where we can approximate g as constant, the potential is gh, where h is the height above reference.

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30 minutes ago, swansont said:

No, there will be a potential with a constant gravitational acceleration. Near the earth's surface, where we can approximate g as constant, the potential is gh, where h is the height above reference.

Using the stretching of space analogy I can see the gravitational potential will be at a maximum in the centre of the earth,

Using the Quantum fluctuation/virtual graviton analogy would seem to imply that they are at a minimum in the centre of the earth, due to being mostly absorbed by the surrounding mass.

Also if there was a hollow sphere at the centre of the earth you would be weightless due to the gravitational forces all cancelling out, but the gravitational potential or stretching of space would be at a maximum and therefore time dilation would be at a maximum ie clocks run slower and what I read about the age of the centre being younger than the crust is in fact correct.

2 hours ago, Janus said:

Time dilation is related to the difference in gravitational potential and thus a clock at the center of the Earth, being at the lowest potential will run the slowest.

Got it thank you very much, gravitational potential more -ve at the centre ie lower.

Quick question what are the units on the left hand axis for gravitational potential, I can see the top axis must be metres. But looking at the equations I am not sure, normally I am used to seeing gravitational acceleration as m/s^2.   Gravitational potential seems to throw up a mixture of answers on google.

3 hours ago, Strange said:

It always has mass. Do you mean weight?

yes it will be weigtless at the centre of the earth.

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52 minutes ago, interested said:

Using the Quantum fluctuation/virtual graviton analogy would seem to imply that they are at a minimum in the centre of the earth, due to being mostly absorbed by the surrounding mass.

I think you are taking an over-simplistic approach to what "virtual particles" means.

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Posted (edited)
1 hour ago, Strange said:

I think you are taking an over-simplistic approach to what "virtual particles" means.

You are possibly correct

But My view is that they are quantum fluctuations which appear and disappear at random out of the vacuum of space briefly violating the conservation of energy. The uncertainty principle of quantum mechanics allows violations of conservation of energy for short periods, any physical system with zero energy can spontaneously produce energetic particles.

Virtual particles also transmit forces and exist in various forms. The concept of virtual photons producing a magnetic field is a wave shape that moves in space around a magnet generated by electrons aligned inside the magnet or in coils of an electromagnet, the wave shape allows attraction and repulsion depending on polarity.

The concept of virtual graviton is possibly a little more open to interpretation, but think for gravity to be attributed to virtual gravitons they must be distributed throughout all of space like quantum fluctuations. Because nothing much gets out of a black hole I assume they are absorbed by mass not radiated by it. The absorption process must also cause the appearance of the stretching of space, so the volume of space full of virtual gravitons must flow towards the mass.

The graviton has never been detected but the casimir effect proves the existence of quantum fluctuations and the concept that the vacuum of space is not empty. Equating the virtual graviton with a quantum fluctuation I think is fair, but possibly strictly not correct. Quantum fluctuations have a restricted amount of space to appear in inside a solid mass, and if they do they will be quickly absorbed or as in the casimir effect restricted to wavelengths that fit in the gaps.

Are you possibly correct

Edited by interested

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3 hours ago, interested said:

Quick question what are the units on the left hand axis for gravitational potential, I can see the top axis must be metres. But looking at the equations I am not sure, normally I am used to seeing gravitational acceleration as m/s^2.   Gravitational potential seems to throw up a mixture of answers on google.

It is "specific energy" or energy per unit mass.  In this case it would be joules/kg

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1 hour ago, interested said:

The graviton has never been detected but the casimir effect proves the existence of quantum fluctuations and the concept that the vacuum of space is not empty. Equating the virtual graviton with a quantum fluctuation I think is fair, but possibly strictly not correct. Quantum fluctuations have a restricted amount of space to appear in inside a solid mass, and if they do they will be quickly absorbed or as in the casimir effect restricted to wavelengths that fit in the gaps.

Gravitons and quantum fluctuations are not the same thing. The Casimir force does not involve gravity; the solution to it is from electromagnetic boundary conditions. i.e. You are restricting photon modes.

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9 hours ago, Janus said:

It is "specific energy" or energy per unit mass.  In this case it would be joules/kg

Thanks for the clarification.

9 hours ago, swansont said:

Gravitons and quantum fluctuations are not the same thing. The Casimir force does not involve gravity; the solution to it is from electromagnetic boundary conditions. i.e. You are restricting photon modes.

Gravitons are theoretical but may exist they havent been detected yet. The Casimir effect I read was proof of the existence of quantum fluctuations and I read it works by restricting wavelengths of quantum fluctuations in the gap which I assume are photon modes.

The reason I mentioned the casimir effect is because it is proof of quantum fluctuations the virtual graviton is also a quantum fluctuation. In a perfect vacuum there are quantum fluctuations and appears to be no way of getting rid of them, but the casimir effect does restrict them, I reasoned that inside a mass quantum fluctuations are restricted, also which is reasonable to assume based on the casimir effect, a more dense piece of material will restrict them further. On mordreds thread what space is and on the thread I posted on, what is a vacuum, I think it is a chicken and egg scenario, for space to exist quantum fluctuations must exist.

The next is pure speculation but if space is a substance which I think is partly evidenced by space dragging and by string theory then if there is a gap in the substance of space/quantum fluctuations/virtual gravitons then more space will flow in to fill the gap creating the stretching of space effect.

The way in which the gravitational potential energy is at a maximum at the centre of a planet even though you would theoretically be weightless is intriguing and I wondered if the casimir effect was in any way involved.

I started a new speculative thread, due to moontanmans thread and being told I was hijacking again sorry  . The Casimir effect from this point of view is interesting in that I was wondering are there other ways in which this effect could be created over a large area via radio waves in the terrra hertz region which are possible to generate or by rapidly fluctuationg magnetic fields etc to warp space and create a warp drive type effect. If the casimir effect works between two plates then it will also work between atoms including at the centre of the earth.

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The term “virtual particles” is used in two different contexts. One is the temporary creation of particle pairs from the non-zero vacuum energy. The other is where (virtual) bosons are used to describe how various forces/interactions are quantised.

The existence of quantum fluctuations in empty space has no (direct) connection with the electromagnetic or gravitational force.

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54 minutes ago, interested said:

Gravitons are theoretical but may exist they havent been detected yet. The Casimir effect I read was proof of the existence of quantum fluctuations and I read it works by restricting wavelengths of quantum fluctuations in the gap which I assume are photon modes.

The reason I mentioned the casimir effect is because it is proof of quantum fluctuations the virtual graviton is also a quantum fluctuation.

No, it is not. It is a virtual exchange particle, which is not the same thing. They have different representations in a Feynman diagram.

54 minutes ago, interested said:

I started a new speculative thread,

Which requires evidence, testability and/or a model. Not unsubstantiated conjecture.

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3 hours ago, swansont said:

No, it is not.

what is not ?

gravitons have not been detected, but may exist.

casimir effect is cited as proof of quantum fluctuations.

I think Strange has the answer as to what is and is not

4 hours ago, Strange said:

The term “virtual particles” is used in two different contexts. One is the temporary creation of particle pairs from the non-zero vacuum energy. The other is where (virtual) bosons are used to describe how various forces/interactions are quantised.

I will go away and have a read up on feynman diagrams.

3 hours ago, swansont said:

Which requires evidence, testability and/or a model. Not unsubstantiated conjecture

I asked a question is it possible to warp space, I have not developed a whole new theory of everything or even a model, but I guess that may be why there is no response.

4 hours ago, Strange said:

The existence of quantum fluctuations in empty space has no (direct) connection with the electromagnetic or gravitational force.

I read that there might be a connection between dark energy and gravity and quantum fluctuations in space, I just dont remember where at the moment, I will have a trawl and see what I can find. Perhaps I will post that as a new thread.

-------------------------------------------------------------------------------------

One final stupid question ref time dilation at the centre of the earth, if you had an empty sphere at the centre of the earth and the sphere had all the pressure sucked out of it, there would be no acceleration due to gravity, and no casmir effect between atoms restricting the appearance of virtual particles of any kind. Would the time dilation still be the same as it would in a space full of compressed matter.

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10 minutes ago, interested said:

if you had an empty sphere at the centre of the earth and the sphere had all the pressure sucked out of it, there would be no acceleration due to gravity, and no casmir effect between atoms restricting the appearance of virtual particles of any kind. Would the time dilation still be the same as it would in a space full of compressed matter.

I already answered this.

If the Earth were hollow, then there would no gravitational force as soon as you entered the hollow area. There would also be no further change in gravitational potential  and so the time dilation would the same everywhere within the hollow.

This (obviously) has nothing to do with virtual particles or the Casimir effect.

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54 minutes ago, interested said:

what is not ?

My answer should have given sufficient context for this, but it was "the virtual graviton is also a quantum fluctuation"

No, it is not.

54 minutes ago, interested said:

I asked a question

"The next is pure speculation but" is not a question.

54 minutes ago, interested said:

One final stupid question ref time dilation at the centre of the earth, if you had an empty sphere at the centre of the earth and the sphere had all the pressure sucked out of it, there would be no acceleration due to gravity, and no casmir effect between atoms restricting the appearance of virtual particles of any kind. Would the time dilation still be the same as it would in a space full of compressed matter.

Time dilation will depend on the gravitational potential, as has been explained several times.  If the gravitational potential is unchanged by your actions, the time dilation will be the same. If it differs, then the dilation will differ.

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Posted (edited)
4 hours ago, Strange said:

If the Earth were hollow, then there would no gravitational force as soon as you entered the hollow area. There would also be no further change in gravitational potential  and so the time dilation would the same everywhere within the hollow.

Thanks I forgot your earlier explanation, point driven home thanks

4 hours ago, swansont said:

virtual graviton

Is there any proof gravitons virtual or otherwise exist, have they ever been detected.

Mordred wrote the mantra all things are quantum fluctuations and or excitations, could he be right, or have I been mislead.

Edited by interested

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54 minutes ago, interested said:

Thanks I forgot your earlier explanation, point driven home thanks

Is there any proof gravitons virtual or otherwise exist, have they ever been detected.

Mordred wrote the mantra all things are quantum fluctuations and or excitations, could he be right, or have I been mislead.

Gravity, so far, is the outlier in a quantum description.

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1 hour ago, interested said:

Is there any proof gravitons virtual or otherwise exist, have they ever been detected.

No. There is not even a theory describing them fully. There are a few properties that they must have, if they exist (like being massless, spin 2, etc) because of the nature of gravity. But that's about it.

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2 hours ago, StringJunky said:

Gravity, so far, is the outlier in a quantum description.

Please expand

2 hours ago, Strange said:

No. There is not even a theory describing them fully. There are a few properties that they must have, if they exist (like being massless, spin 2, etc) because of the nature of gravity. But that's about it.

I know and it is complete conjecture, but why can the Casimir effect not be used to prove the existence of virtual gravitons.

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