Mass and energy from Earth's gravitational field

[John M]

Can someone please tell me how the energy field created by warped space (gravity) and centred at the Earth's core dissipates? Is it the pressure/compression of this force/energy that makes the core so volatile?

Whilst time slows at altitude, do we become lighter, as we are further away from the centre of the Earth and gravity weakens?

Also, if the Earth's gravity is supposed to be six times stronger than the moons, how does this correlate to mass? The moon maybe six times smaller than the Earth but this does not mean that it has six times less mass.

 

[Ibix]

Can someone please tell me how the energy field created by warped space (gravity) and centred at the Earth's core dissipates?

I don't know what this is supposed to mean. There is no "energy field created by warped space" in relativity. Perhaps you could ask your questiin in a different way?

Is it the pressure/compression of this force/energy that makes the core so volatile?

As far as I'm aware the core of the Earth is made of mostly iron and nickel. It's certainly not particularly volatile.

Whilst time slows at altitude

Clocks higher up run faster, not slower, than clocks lower down.

do we become lighter, as we are further away from the centre of the Earth and gravity weakens?

We do become lighter as we move away from a source of gravity like the Earth, assuming there is somewhere to stand to measure your weight. I'm not sure why you are relating this to gravitational time dilation - it is also a feature of Newtonian gravity, which does not have time dilation.

Also, if the Earth's gravity is supposed to be six times stronger than the moons, how does this correlate to mass? The moon maybe six times smaller than the Earth but this does not mean that it has six times less mass.

Newtonian physics will do for this - $F=GMm/r^2$, so the force of gravity at the surface of a spherical body depends on both its mass, $M$, and its radius, $r$.

Edit: and what do you mean by "six times smaller"? The Moon is about one quarter the diameter of the Earth, giving it about 7% the area and 2% the volume of the Earth. Its mass is about 1% that of Earth. I see no factor of six anywhere in that.

 

[John M]

Thank you for those answers. With regard to the volatility at the Earth's core, I was mistakenly referring to the outer core, which is molten. With regard to the 'energy' of warped space I am assuming that if you can warp anything, there must be something there to warp. I have called this energy. It could equally be called a force I suppose. The warping is drawn to the centre of the Earth and I wondered if it has any effect once it gets there?

 

[John M]

I don't know what this is supposed to mean. There is no "energy field created by warped space" in relativity. Perhaps you could ask your questiin in a different way?
As far as I'm aware the core of the Earth is made of mostly iron and nickel. It's certainly not particularly volatile.
Clocks higher up run faster, not slower, than clocks lower down.
We do become lighter as we move away from a source of gravity like the Earth, assuming there is somewhere to stand to measure your weight. I'm not sure why you are relating this to gravitational time dilation - it is also a feature of Newtonian gravity, which does not have time dilation.
Newtonian physics will do for this - $F=GMm/r^2$, so the force of gravity at the surface of a spherical body depends on both its mass, $M$, and its radius, $r$.

Edit: and what do you mean by "six times smaller"? The Moon is about one quarter the diameter of the Earth, giving it about 7% the area and 2% the volume of the Earth. Its mass is about 1% that of Earth. I see no factor of six anywhere in that.

We were taught at school that the moon was six times smaller than the earth. This was 50 years ago though.

 

[jbriggs444]

We were taught at school that the moon was six times smaller than the earth. This was 50 years ago though.

You were either taught incorrectly or are remembering incorrectly.

With regard to the 'energy' of warped space I am assuming that if you can warp anything, there must be something there to warp. I have called this energy. It could equally be called a force I suppose. The warping is drawn to the centre of the Earth and I wondered if it has any effect once it gets there?

This does not make any sense.

The "warpage" of space is a popular way to offer a visualization of the non-Euclidean geometry in general relativity. But it is only an analogy. It cannot be pushed very far. Space is not a physical substance that can be warped and that needs force or energy to be warped. The warpage is also not a physical substance that could be drawn to the center of the Earth.

 

[Ibix]

With regard to the 'energy' of warped space I am assuming that if you can warp anything, there must be something there to warp. I have called this energy. It could equally be called a force I suppose. The warping is drawn to the centre of the Earth and I wondered if it has any effect once it gets there?

Nothing is being warped, pop-sci descriptions notwithstanding. General relativity describes the rules of geometry near mass and energy, and the effects of these rules are what we call gravity. Since the particular rules predicted are similar to those on a curved surface embedded in a Euclidean space we describe spacetime as curved. But there's nothing to be distorted - spacetime is not actually a 4d curved sheet so far as we are aware.

What spacetime actually is and why it behaves as it does is not known (those questions may not even make sense). It most definitely is not an energy or a force. Nor is anything being "drawn" anywhere. The core of the Earth is hot partly from the kinetic energy of the infalling matter that condensed into the Earth and partly from radioactive decay, as far as I know. Gravity has nothing to do with it except in the mundane sense that it was gravity that caused all the matter making up the Earth to clump together in the first place.

 

[PeterDonis]

the Earth's gravity is supposed to be six times stronger than the moons

More precisely, the "acceleration due to gravity" at the Earth's surface is six times larger than the "acceleration due to gravity" at the Moon's surface.

The moon maybe six times smaller than the Earth but this does not mean that it has six times less mass.

Neither of these are true. The "acceleration due to gravity" at the surface of a body is $GM / r^2$. Look up the actual values for $G$ (Newton's gravitational constant) and the mass and radius of the Earth and Moon, and you will see the correct relationships and how they fit together to make the statement above true.

 

[PeterDonis]

Can someone please tell me how the energy field created by warped space (gravity) and centred at the Earth's core dissipates?

The spacetime curvature at the center of the Earth doesn't have to "dissipate". It's stable.

Is it the pressure/compression of this force/energy that makes the core so volatile?

No. Spacetime curvature is not a "force/energy".

 

[John M]

Nothing is being warped, pop-sci descriptions notwithstanding. General relativity describes the rules of geometry near mass and energy, and the effects of these rules are what we call gravity. Since the particular rules predicted are similar to those on a curved surface embedded in a Euclidean space we describe spacetime as curved. But there's nothing to be distorted - spacetime is not actually a 4d curved sheet so far as we are aware.

What spacetime actually is and why it behaves as it does is not known (those questions may not even make sense). It most definitely is not an energy or a force. Nor is anything being "drawn" anywhere. The core of the Earth is hot partly from the kinetic energy of the infalling matter that condensed into the Earth and partly from radioactive decay, as far as I know. Gravity has nothing to do with it except in the mundane sense that it was gravity that caused all the matter making up the Earth to clump together in the first place.

So, on the one hand we are led to believe that gravity is not a force in it's own right and is not attracting us to this planet and now on the other hand spacetime is not a force either and therefore is not pushing us on to this planet. Can you please explain just what is holding us here?

 

[PeterDonis]

gravity is not a force in it's own right

True.

and is not attracting us to this planet

False.

spacetime is not a force either

True.

and therefore is not pushing us on to this planet

False.

The geometry of spacetime tells you what trajectories are freely falling trajectories, i.e., what trajectories objects will follow if no force is acting on them. In the vicinity of the Earth, such free-falling trajectories converge towards the Earth's center. That's why rocks fall when you drop them. You can call this "gravity" or you can call it "spacetime curvature"; they're just different words for the same thing.

The force you feel when you stand on the Earth's surface is not "gravity"; it's the Earth's surface pushing up on you and preventing you from falling freely, the way you would if there were no force acting on you.

 

[Ibix]

I may have been slightly more general than I intended when I said nothing was drawn towards the centre of the Earth. A chunk of matter will follow a curve towards the Earth's centre, yes, unless prevented from doing so by (for example) the floor. But this happens because the rules of geometry around here are defined so that "straight on" always curves towards the Earth. It's not because something is yanking it that way (at least in GR).

In a sense, we fall towards the centre of the Earth because of Newton's first law of motion. It just turned out that "straight line" was a more complicated concept than he realized.

 

[Nugatory]

So, on the one hand we are led to believe that gravity is not a force in it's own right and is not attracting us to this planet and now on the other hand spacetime is not a force either and therefore is not pushing us on to this planet. Can you please explain just what is holding us here?

It's inertia. An object subject to no forces naturally moves in a straight line at a constant speed. Near the surface of the Earth spacetime is curved in such a way that the natural straight line paths (which must follow the curvature) of objects in free fall intersect the surface of the earth. Thus, the "force" that seems to be holding you onto against the surface of the planet is actually the surface of the planet pushing you off of your natural free fall trajectory.

If you search this forum you'll find a video by our own member @A.T. showing how curved spacetime (note that this curved spacetime not space!) produces the same effect as a force.

 

[John M]

Thank you all for your very comprehensive answers however no one has explained how/why space/time curves when near a mass. Also, surely an object that is subject to no forces remains stationary unless a force is applied. Isn't inertia just a state: i.e. it can be at rest or moving, as long as it doesn't change.

 

[Ibix]

Thank you all for your very comprehensive answers however no one has explained how/why space/time curves when near a mass.

Nobody ever has. Quantum gravity might help, but we haven't got that worked out yet. And it will probably leave you with another "but how..." question even if we do.

Also, surely an object that is subject to no forces remains stationary unless a force is applied.

No. It moves in a straight line (as Newton said). "Straight line" turns out not to actually be straight in general; Newton has no reason to consider non-Euclidean geometry. The word we use for the "natural" path of a body in spacetime is "geodesic".

 

[John M]

Bless you for sticking with me Ibix. The joy of Physics is that there are always questions. After all that have been asked by me, the conclusion is that whilst we know that space/time curvature has a tendency to make us fall towards the centre of the earth, we can't say why.

 

[jbriggs444]

Bless you for sticking with me Ibix. The joy of Physics is that there are always questions. After all that have been asked by me, the conclusion is that whilst we know that space/time curvature has a tendency to make us fall towards the centre of the earth, we can't say why.

It is always that way. If you've ever had a child ask "why" in an infinite loop, you will quickly reach the bottom of your ability to explain. At the bottom there will always be some unexplained "because that's the way it is".

Science is fairly good at "how" questions. It can tell us how gravity works and make predictions with exquisite precision. But it cannot tell "why" gravity works that way.

Feynman had something to say about "why". http://lesswrong.com/lw/99c/transcript_richard_feynman_on_why_questions/

 

[vanhees71]

I'd put it in a more positive way: At the bottom of a child's "why questions", as far as scientific matters are concerned, are the fundamental physical laws, as far as our present understanding reaches. These cannot be derived from even more simple laws, and their origin is entirely based on observation and experiments.

Trying to get "deeper" than that, leads to philosophical gibberish and esoterics, something I'd try to keep away from any child as long as I can ;-)).